First stage of adding "Decimal" class to Squirrel\SquiLu using mpdecimal library http://www.bytereef.org/mpdecimal

ext/mpdecimal/basearith.c

@@ -0,0 +1,582 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include "constants.h"
+#include "memory.h"
+#include "typearith.h"
+#include "basearith.h"
+
+
+/*********************************************************************/
+/*                   Calculations in base MPD_RADIX                  */
+/*********************************************************************/
+
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *    w := sum of u (len m) and v (len n)
+ *    n > 0 and m >= n
+ * The calling function has to handle a possible final carry.
+ */
+mpd_uint_t
+_mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+	mpd_uint_t s;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	assert(n > 0 && m >= n);
+
+	/* add n members of u and v */
+	for (i = 0; i < n; i++) {
+		s = u[i] + (v[i] + carry);
+		carry = (s < u[i]) | (s >= MPD_RADIX);
+		w[i] = carry ? s-MPD_RADIX : s;
+	}
+	/* if there is a carry, propagate it */
+	for (; carry && i < m; i++) {
+		s = u[i] + carry;
+		carry = (s == MPD_RADIX);
+		w[i] = carry ? 0 : s;
+	}
+	/* copy the rest of u */
+	for (; i < m; i++) {
+		w[i] = u[i];
+	}
+
+	return carry;
+}
+
+/*
+ * Add the contents of u to w. Carries are propagated further. The caller
+ * has to make sure that w is big enough.
+ */
+void
+_mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
+{
+	mpd_uint_t s;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	if (n == 0) return;
+
+	/* add n members of u to w */
+	for (i = 0; i < n; i++) {
+		s = w[i] + (u[i] + carry);
+		carry = (s < w[i]) | (s >= MPD_RADIX);
+		w[i] = carry ? s-MPD_RADIX : s;
+	}
+	/* if there is a carry, propagate it */
+	for (; carry; i++) {
+		s = w[i] + carry;
+		carry = (s == MPD_RADIX);
+		w[i] = carry ? 0 : s;
+	}
+}
+
+/*
+ * Add v to w (len m). The calling function has to handle a possible
+ * final carry.
+ */
+mpd_uint_t
+_mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v)
+{
+	mpd_uint_t s;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	/* add v to u */
+	s = w[0] + v;
+	carry = (s < v) | (s >= MPD_RADIX);
+	w[0] = carry ? s-MPD_RADIX : s;
+
+	/* if there is a carry, propagate it */
+	for (i = 1; carry && i < m; i++) {
+		s = w[i] + carry;
+		carry = (s == MPD_RADIX);
+		w[i] = carry ? 0 : s;
+	}
+
+	return carry;
+}
+
+/* Increment u. The calling function has to handle a possible carry. */
+mpd_uint_t
+_mpd_baseincr(mpd_uint_t *u, mpd_size_t n)
+{
+	mpd_uint_t s;
+	mpd_uint_t carry = 1;
+	mpd_size_t i;
+
+	assert(n > 0);
+
+	/* if there is a carry, propagate it */
+	for (i = 0; carry && i < n; i++) {
+		s = u[i] + carry;
+		carry = (s == MPD_RADIX);
+		u[i] = carry ? 0 : s;
+	}
+
+	return carry;
+}
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *     w := difference of u (len m) and v (len n).
+ *     number in u >= number in v;
+ */
+void
+_mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+	mpd_uint_t d;
+	mpd_uint_t borrow = 0;
+	mpd_size_t i;
+
+	assert(m > 0 && n > 0);
+
+	/* subtract n members of v from u */
+	for (i = 0; i < n; i++) {
+		d = u[i] - (v[i] + borrow);
+		borrow = (u[i] < d);
+		w[i] = borrow ? d + MPD_RADIX : d;
+	}
+	/* if there is a borrow, propagate it */
+	for (; borrow && i < m; i++) {
+		d = u[i] - borrow;
+		borrow = (u[i] == 0);
+		w[i] = borrow ? MPD_RADIX-1 : d;
+	}
+	/* copy the rest of u */
+	for (; i < m; i++) {
+		w[i] = u[i];
+	}
+}
+
+/*
+ * Subtract the contents of u from w. w is larger than u. Borrows are
+ * propagated further, but eventually w can absorb the final borrow.
+ */
+void
+_mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n)
+{
+	mpd_uint_t d;
+	mpd_uint_t borrow = 0;
+	mpd_size_t i;
+
+	if (n == 0) return;
+
+	/* subtract n members of u from w */
+	for (i = 0; i < n; i++) {
+		d = w[i] - (u[i] + borrow);
+		borrow = (w[i] < d);
+		w[i] = borrow ? d + MPD_RADIX : d;
+	}
+	/* if there is a borrow, propagate it */
+	for (; borrow; i++) {
+		d = w[i] - borrow;
+		borrow = (w[i] == 0);
+		w[i] = borrow ? MPD_RADIX-1 : d;
+	}
+}
+
+/* w := product of u (len n) and v (single word) */
+void
+_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	assert(n > 0);
+
+	for (i=0; i < n; i++) {
+
+		_mpd_mul_words(&hi, &lo, u[i], v);
+		lo = carry + lo;
+		if (lo < carry) hi++;
+
+		_mpd_div_words_r(&carry, &w[i], hi, lo);
+	}
+	w[i] = carry;
+}
+
+/*
+ * Knuth, TAOCP, Volume 2, 4.3.1:
+ *     w := product of u (len m) and v (len n)
+ *     w must be initialized to zero
+ */
+void
+_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+             mpd_size_t m, mpd_size_t n)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t carry;
+	mpd_size_t i, j;
+
+	assert(m > 0 && n > 0);
+
+	for (j=0; j < n; j++) {
+		carry = 0;
+		for (i=0; i < m; i++) {
+
+			_mpd_mul_words(&hi, &lo, u[i], v[j]);
+			lo = w[i+j] + lo;
+			if (lo < w[i+j]) hi++;
+			lo = carry + lo;
+			if (lo < carry) hi++;
+
+			_mpd_div_words_r(&carry, &w[i+j], hi, lo);
+		}
+		w[j+m] = carry;
+	}
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
+ *     w := quotient of u (len n) divided by a single word v
+ */
+mpd_uint_t
+_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t rem = 0;
+	mpd_size_t i;
+
+	assert(n > 0);
+
+	for (i=n-1; i != MPD_SIZE_MAX; i--) {
+
+		_mpd_mul_words(&hi, &lo, rem, MPD_RADIX);
+		lo = u[i] + lo;
+		if (lo < u[i]) hi++;
+
+		_mpd_div_words(&w[i], &rem, hi, lo, v);
+	}
+
+	return rem;
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1:
+ *     q, r := quotient and remainder of uconst (len nplusm)
+ *             divided by vconst (len n)
+ *     nplusm > n
+ *
+ * If r is not NULL, r will contain the remainder. If r is NULL, the
+ * return value indicates if there is a remainder: 1 for true, 0 for
+ * false.  A return value of -1 indicates an error.
+ */
+int
+_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r,
+                const mpd_uint_t *uconst, const mpd_uint_t *vconst,
+                mpd_size_t nplusm, mpd_size_t n)
+{
+	mpd_uint_t ustatic[MPD_MINALLOC_MAX];
+	mpd_uint_t vstatic[MPD_MINALLOC_MAX];
+	mpd_uint_t *u = ustatic;
+	mpd_uint_t *v = vstatic;
+	mpd_uint_t d, qhat, rhat, w2[2];
+	mpd_uint_t hi, lo, x;
+	mpd_uint_t carry;
+	mpd_size_t i, j, m;
+	int retval = 0;
+
+	assert(n > 1 && nplusm >= n);
+	m = sub_size_t(nplusm, n);
+
+	/* D1: normalize */
+	d = MPD_RADIX / (vconst[n-1] + 1);
+
+	if (nplusm >= MPD_MINALLOC_MAX) {
+		if ((u = mpd_calloc(nplusm+1, sizeof *u)) == NULL) {
+			return -1;
+		}
+	}
+	if (n >= MPD_MINALLOC_MAX) {
+		if ((v = mpd_calloc(n+1, sizeof *v)) == NULL) {
+			mpd_free(u);
+			return -1;
+		}
+	}
+
+	_mpd_shortmul(u, uconst, nplusm, d);
+	_mpd_shortmul(v, vconst, n, d);
+
+	/* D2: loop */
+	rhat = 0;
+	for (j=m; j != MPD_SIZE_MAX; j--) {
+
+		/* D3: calculate qhat and rhat */
+		rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]);
+		qhat = w2[1] * MPD_RADIX + w2[0];
+
+		while (1) {
+			if (qhat < MPD_RADIX) {
+				_mpd_singlemul(w2, qhat, v[n-2]);
+				if (w2[1] <= rhat) {
+					if (w2[1] != rhat || w2[0] <= u[j+n-2]) {
+						break;
+					}
+				}
+			}
+			qhat -= 1;
+			rhat += v[n-1];
+			if (rhat < v[n-1] || rhat >= MPD_RADIX) {
+				break;
+			}
+		}
+		/* D4: multiply and subtract */
+		carry = 0;
+		for (i=0; i <= n; i++) {
+
+			_mpd_mul_words(&hi, &lo, qhat, v[i]);
+
+			lo = carry + lo;
+			if (lo < carry) hi++;
+
+			_mpd_div_words_r(&hi, &lo, hi, lo);
+
+			x = u[i+j] - lo;
+			carry = (u[i+j] < x);
+			u[i+j] = carry ? x+MPD_RADIX : x;
+			carry += hi;
+		}
+		q[j] = qhat;
+		/* D5: test remainder */
+		if (carry) {
+			q[j] -= 1;
+			/* D6: add back */
+			(void)_mpd_baseadd(u+j, u+j, v, n+1, n);
+		}
+	}
+
+	/* D8: unnormalize */
+	if (r != NULL) {
+		_mpd_shortdiv(r, u, n, d);
+		/* we are not interested in the return value here */
+		retval = 0;
+	}
+	else {
+		retval = !_mpd_isallzero(u, n);
+	}
+
+
+if (u != ustatic) mpd_free(u);
+if (v != vstatic) mpd_free(v);
+return retval;
+}
+
+/* Leftshift of src by shift digits; src may equal dest. */
+void
+_mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, mpd_size_t m,
+                mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+	/* spurious uninitialized warnings */
+	mpd_uint_t l=l, lprev=lprev, h=h;
+#else
+	mpd_uint_t l, lprev, h;
+#endif
+	mpd_uint_t q, r;
+	mpd_uint_t ph;
+
+	assert(m > 0 && n >= m);
+
+	_mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+	if (r != 0) {
+
+		ph = mpd_pow10[r];
+
+		--m; --n;
+		_mpd_divmod_pow10(&h, &lprev, src[m--], MPD_RDIGITS-r);
+		if (h != 0) {
+			dest[n--] = h;
+		}
+		for (; m != MPD_SIZE_MAX; m--,n--) {
+			_mpd_divmod_pow10(&h, &l, src[m], MPD_RDIGITS-r);
+			dest[n] = ph * lprev + h;
+			lprev = l;
+		}
+		dest[q] = ph * lprev;
+	}
+	else {
+		while (--m != MPD_SIZE_MAX) {
+			dest[m+q] = src[m];
+		}
+	}
+
+	mpd_uint_zero(dest, q);
+}
+
+/* Rightshift of src by shift digits; src may equal dest. */
+mpd_uint_t
+_mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
+                mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+	/* spurious uninitialized warnings */
+	mpd_uint_t l=l, h=h, hprev=hprev; /* low, high, previous high */
+#else
+	mpd_uint_t l, h, hprev; /* low, high, previous high */
+#endif
+	mpd_uint_t rnd, rest;   /* rounding digit, rest */
+	mpd_uint_t q, r;
+	mpd_size_t i, j;
+	mpd_uint_t ph;
+
+	assert(slen > 0);
+
+	_mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+	rnd = rest = 0;
+	if (r != 0) {
+
+		ph = mpd_pow10[MPD_RDIGITS-r];
+
+		_mpd_divmod_pow10(&hprev, &rest, src[q], r);
+		_mpd_divmod_pow10(&rnd, &rest, rest, r-1);
+
+		if (rest == 0 && q > 0) {
+			rest = !_mpd_isallzero(src, q);
+		}
+		h = hprev;
+		for (j=0,i=q+1; i<slen; i++,j++) {
+			_mpd_divmod_pow10(&h, &l, src[i], r);
+			dest[j] = ph * l + hprev;
+			hprev = h;
+		}
+		if (hprev != 0) {
+			dest[j] = hprev;
+		}
+	}
+	else {
+		if (q > 0) {
+			_mpd_divmod_pow10(&rnd, &rest, src[q-1], MPD_RDIGITS-1);
+			/* is there any non-zero digit below rnd? */
+			if (rest == 0) rest = !_mpd_isallzero(src, q-1);
+		}
+		for (j = 0; j < slen-q; j++) {
+			dest[j] = src[q+j];
+		}
+	}
+
+	/* 0-4  ==> rnd+rest < 0.5   */
+	/* 5    ==> rnd+rest == 0.5  */
+	/* 6-9  ==> rnd+rest > 0.5   */
+	return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
+}
+
+
+/*********************************************************************/
+/*                      Calculations in base b                       */
+/*********************************************************************/
+
+/*
+ * Add v to w (len m). The calling function has to handle a possible
+ * final carry.
+ */
+mpd_uint_t
+_mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, mpd_uint_t b)
+{
+	mpd_uint_t s;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	/* add v to u */
+	s = w[0] + v;
+	carry = (s < v) | (s >= b);
+	w[0] = carry ? s-b : s;
+
+	/* if there is a carry, propagate it */
+	for (i = 1; carry && i < m; i++) {
+		s = w[i] + carry;
+		carry = (s == b);
+		w[i] = carry ? 0 : s;
+	}
+
+	return carry;
+}
+
+/* w := product of u (len n) and v (single word) */
+void
+_mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                mpd_uint_t v, mpd_uint_t b)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t carry = 0;
+	mpd_size_t i;
+
+	assert(n > 0);
+
+	for (i=0; i < n; i++) {
+
+		_mpd_mul_words(&hi, &lo, u[i], v);
+		lo = carry + lo;
+		if (lo < carry) hi++;
+
+		_mpd_div_words(&carry, &w[i], hi, lo, b);
+	}
+	w[i] = carry;
+}
+
+/*
+ * Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
+ *     w := quotient of u (len n) divided by a single word v
+ */
+mpd_uint_t
+_mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                mpd_uint_t v, mpd_uint_t b)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t rem = 0;
+	mpd_size_t i;
+
+	assert(n > 0);
+
+	for (i=n-1; i != MPD_SIZE_MAX; i--) {
+
+		_mpd_mul_words(&hi, &lo, rem, b);
+		lo = u[i] + lo;
+		if (lo < u[i]) hi++;
+
+		_mpd_div_words(&w[i], &rem, hi, lo, v);
+	}
+
+	return rem;
+}
+
+
+

ext/mpdecimal/basearith.h

@@ -0,0 +1,180 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef BASEARITH_H
+#define BASEARITH_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "typearith.h"
+
+
+mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                        mpd_size_t m, mpd_size_t n);
+void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
+mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
+                           mpd_uint_t b);
+mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
+void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                  mpd_size_t m, mpd_size_t n);
+void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+                  mpd_size_t m, mpd_size_t n);
+void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                   mpd_uint_t v);
+void _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                     mpd_uint_t v, mpd_uint_t b);
+mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                         mpd_uint_t v);
+mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+                           mpd_uint_t v, mpd_uint_t b);
+int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
+                    const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
+void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
+                     mpd_size_t m, mpd_size_t shift);
+mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
+                           mpd_size_t shift);
+
+
+
+#ifdef CONFIG_64
+extern const mpd_uint_t mprime_rdx;
+
+/*
+ * Algorithm from: Division by Invariant Integers using Multiplication,
+ * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
+ * Conference on Programming Language Design and Implementation.
+ *
+ * http://gmplib.org/~tege/divcnst-pldi94.pdf
+ */
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+	mpd_uint_t n_adj, h, l, t;
+	mpd_uint_t n1_neg;
+
+	n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
+	n_adj = lo + (n1_neg & MPD_RADIX);
+
+	_mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
+	l = l + n_adj;
+	if (l < n_adj) h++;
+	t = h + hi; /* q1 */
+
+	t = MPD_UINT_MAX - t;
+
+	_mpd_mul_words(&h, &l, t, MPD_RADIX);
+	l = l + lo;
+	if (l < lo) h++;
+	h += hi;
+	h -= MPD_RADIX;
+
+	*q = (h - t);
+	*r = l + (MPD_RADIX & h);
+}
+#else
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+	_mpd_div_words(q, r, hi, lo, MPD_RADIX);
+}
+#endif
+
+
+/* Multiply two single base b words, store result in array w[2]. */
+static inline void
+_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
+{
+	mpd_uint_t hi, lo;
+
+	_mpd_mul_words(&hi, &lo, u, v);
+	_mpd_div_words_r(&w[1], &w[0], hi, lo);
+}
+
+/* Multiply u (len 2) and v (len 1 or 2). */
+static inline void
+_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
+{
+	mpd_uint_t hi, lo;
+
+	_mpd_mul_words(&hi, &lo, u[0], v[0]);
+	_mpd_div_words_r(&w[1], &w[0], hi, lo);
+
+	_mpd_mul_words(&hi, &lo, u[1], v[0]);
+	lo = w[1] + lo;
+	if (lo < w[1]) hi++;
+	_mpd_div_words_r(&w[2], &w[1], hi, lo);
+	if (m == 1) return;
+
+	_mpd_mul_words(&hi, &lo, u[0], v[1]);
+	lo = w[1] + lo;
+	if (lo < w[1]) hi++;
+	_mpd_div_words_r(&w[3], &w[1], hi, lo);
+
+	_mpd_mul_words(&hi, &lo, u[1], v[1]);
+	lo = w[2] + lo;
+	if (lo < w[2]) hi++;
+	lo = w[3] + lo;
+	if (lo < w[3]) hi++;
+	_mpd_div_words_r(&w[3], &w[2], hi, lo);
+}
+
+
+/*
+ * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
+ * is tested and the coefficient is regarded as "all zero".
+ */
+static inline int
+_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
+{
+	while (--len >= 0) {
+		if (data[len] != 0) return 0;
+	}
+	return 1;
+}
+
+/*
+ * Test if all words from data[len-1] to data[0] are MPD_RADIX-1 (all nines).
+ * Assumes that len > 0.
+ */
+static inline int
+_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
+{
+	while (--len >= 0) {
+		if (data[len] != MPD_RADIX-1) return 0;
+	}
+	return 1;
+}
+
+
+#endif /* BASEARITH_H */
+
+
+

ext/mpdecimal/bits.h

@@ -0,0 +1,196 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef BITS_H
+#define BITS_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+/* Check if n is a power of 2 */
+static inline int
+ispower2(mpd_size_t n)
+{
+	return n != 0 && (n & (n-1)) == 0;
+}
+
+#if defined(ANSI)
+/*
+ * Returns the most significant bit position of n from 0 to 32 (64).
+ * Caller has to make sure that n is not 0.
+ */
+static inline int
+mpd_bsr(mpd_size_t n)
+{
+	int pos = 0;
+	mpd_size_t tmp;
+
+#ifdef CONFIG_64
+	tmp = n >> 32;
+	if (tmp != 0) { n = tmp; pos += 32; }
+#endif
+	tmp = n >> 16;
+	if (tmp != 0) { n = tmp; pos += 16; }
+	tmp = n >> 8;
+	if (tmp != 0) { n = tmp; pos += 8; }
+	tmp = n >> 4;
+	if (tmp != 0) { n = tmp; pos += 4; }
+	tmp = n >> 2;
+	if (tmp != 0) { n = tmp; pos += 2; }
+	tmp = n >> 1;
+	if (tmp != 0) { n = tmp; pos += 1; }
+
+	return pos + (int)n - 1;
+}
+
+/*
+ * Returns the least significant bit position of n from 0 to 32 (64).
+ * Caller has to make sure that n is not 0.
+ */
+static inline int
+mpd_bsf(mpd_size_t n)
+{
+	int pos;
+
+#ifdef CONFIG_64
+	pos = 63;
+	if (n & 0x00000000FFFFFFFFULL) { pos -= 32; } else { n >>= 32; }
+	if (n & 0x000000000000FFFFULL) { pos -= 16; } else { n >>= 16; }
+	if (n & 0x00000000000000FFULL) { pos -=  8; } else { n >>=  8; }
+	if (n & 0x000000000000000FULL) { pos -=  4; } else { n >>=  4; }
+	if (n & 0x0000000000000003ULL) { pos -=  2; } else { n >>=  2; }
+	if (n & 0x0000000000000001ULL) { pos -=  1; }
+#else
+	pos = 31;
+	if (n & 0x000000000000FFFFUL) { pos -= 16; } else { n >>= 16; }
+	if (n & 0x00000000000000FFUL) { pos -=  8; } else { n >>=  8; }
+	if (n & 0x000000000000000FUL) { pos -=  4; } else { n >>=  4; }
+	if (n & 0x0000000000000003UL) { pos -=  2; } else { n >>=  2; }
+	if (n & 0x0000000000000001UL) { pos -=  1; }
+#endif
+	return pos;
+}
+/* END ANSI */
+
+#elif defined(ASM)
+/*
+ * Bit scan reverse.
+ * Caller has to make sure that a is not 0.
+ */
+static inline int
+mpd_bsr(mpd_size_t a)
+{
+	mpd_size_t retval;
+
+	__asm__ (
+#ifdef CONFIG_64
+		"bsrq %1, %0\n\t"
+#else
+		"bsr %1, %0\n\t"
+#endif
+		:"=r" (retval)
+		:"r" (a)
+		:"cc"
+	);
+
+	return (int)retval;
+}
+
+/*
+ * Bit scan forward.
+ * Caller has to make sure that a is not 0.
+ */
+static inline int
+mpd_bsf(mpd_size_t a)
+{
+	mpd_size_t retval;
+
+	__asm__ (
+#ifdef CONFIG_64
+		"bsfq %1, %0\n\t"
+#else
+		"bsf %1, %0\n\t"
+#endif
+		:"=r" (retval)
+		:"r" (a)
+		:"cc"
+	);
+
+	return (int)retval;
+}
+/* END ASM */
+
+#elif defined(MASM)
+#include <intrin.h>
+/*
+ * Bit scan reverse.
+ * Caller has to make sure that a is not 0.
+ */
+static inline int __cdecl
+mpd_bsr(mpd_size_t a)
+{
+	unsigned long retval;
+
+#ifdef CONFIG_64
+	_BitScanReverse64(&retval, a);
+#else
+	_BitScanReverse(&retval, a);
+#endif
+
+	return (int)retval;
+}
+
+/*
+ * Bit scan forward.
+ * Caller has to make sure that a is not 0.
+ */
+static inline int __cdecl
+mpd_bsf(mpd_size_t a)
+{
+	unsigned long retval;
+
+#ifdef CONFIG_64
+	_BitScanForward64(&retval, a);
+#else
+	_BitScanForward(&retval, a);
+#endif
+
+	return (int)retval;
+}
+/* END MASM (_MSC_VER) */
+#else
+  #error "missing preprocessor definitions"
+#endif /* BSR/BSF */
+
+
+#endif /* BITS_H */
+
+
+

ext/mpdecimal/constants.c

@@ -0,0 +1,132 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "constants.h"
+
+
+#if defined(CONFIG_64)
+
+  /* number-theory.c */
+  const mpd_uint_t mpd_moduli[3] = {
+    18446744069414584321ULL, 18446744056529682433ULL, 18446742974197923841ULL
+  };
+  const mpd_uint_t mpd_roots[3]  = {7ULL, 10ULL, 19ULL};
+
+  /* crt.c */
+  const mpd_uint_t INV_P1_MOD_P2   = 18446744055098026669ULL;
+  const mpd_uint_t INV_P1P2_MOD_P3 = 287064143708160ULL;
+  const mpd_uint_t LH_P1P2 = 18446744052234715137ULL;     /* (P1*P2) % 2^64 */
+  const mpd_uint_t UH_P1P2 = 18446744052234715141ULL;     /* (P1*P2) / 2^64 */
+
+  /* transpose.c */
+  const mpd_size_t mpd_bits[64] = {
+    1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,  2048, 4096, 8192, 16384,
+    32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
+    16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
+    2147483648ULL, 4294967296ULL, 8589934592ULL, 17179869184ULL, 34359738368ULL,
+    68719476736ULL, 137438953472ULL, 274877906944ULL, 549755813888ULL,
+    1099511627776ULL, 2199023255552ULL, 4398046511104, 8796093022208ULL,
+    17592186044416ULL, 35184372088832ULL, 70368744177664ULL, 140737488355328ULL,
+    281474976710656ULL, 562949953421312ULL, 1125899906842624ULL,
+    2251799813685248ULL, 4503599627370496ULL, 9007199254740992ULL,
+    18014398509481984ULL, 36028797018963968ULL, 72057594037927936ULL,
+    144115188075855872ULL, 288230376151711744ULL, 576460752303423488ULL,
+    1152921504606846976ULL, 2305843009213693952ULL, 4611686018427387904ULL,
+    9223372036854775808ULL
+  };
+
+  /* mpdecimal.c */
+  const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
+    1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
+    10000000000ULL,100000000000ULL,1000000000000ULL,10000000000000ULL,
+    100000000000000ULL,1000000000000000ULL,10000000000000000ULL,
+    100000000000000000ULL,1000000000000000000ULL,10000000000000000000ULL
+  };
+
+  /* magic number for constant division by MPD_RADIX */
+  const mpd_uint_t mprime_rdx = 15581492618384294730ULL;
+
+#elif defined(CONFIG_32)
+
+  /* number-theory.c */
+  const mpd_uint_t mpd_moduli[3]  = {2113929217UL, 2013265921UL, 1811939329UL};
+  const mpd_uint_t mpd_roots[3]   = {5UL, 31UL, 13UL};
+
+  /* PentiumPro modular multiplication: These constants have to be loaded as
+   * 80 bit long doubles, which are not supported by certain compilers. */
+  const uint32_t mpd_invmoduli[3][3] = {
+    {4293885170U, 2181570688U, 16352U},  /* ((long double) 1 / 2113929217UL) */
+    {1698898177U, 2290649223U, 16352U},  /* ((long double) 1 / 2013265921UL) */
+    {2716021846U, 2545165803U, 16352U}   /* ((long double) 1 / 1811939329UL) */
+  };
+
+  const float MPD_TWO63 = 9223372036854775808.0; /* 2^63 */
+
+  /* crt.c */
+  const mpd_uint_t INV_P1_MOD_P2   = 2013265901UL;
+  const mpd_uint_t INV_P1P2_MOD_P3 = 54UL;
+  const mpd_uint_t LH_P1P2 = 4127195137UL;  /* (P1*P2) % 2^32 */
+  const mpd_uint_t UH_P1P2 = 990904320UL;   /* (P1*P2) / 2^32 */
+
+  /* transpose.c */
+  const mpd_size_t mpd_bits[32] = {
+    1, 2, 4, 8, 16, 32, 64, 128, 256, 512,  1024,  2048, 4096, 8192, 16384,
+    32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608,
+    16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
+    2147483648UL
+  };
+
+  /* mpdecimal.c */
+  const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = {
+    1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000
+  };
+
+#else
+  #error "CONFIG_64 or CONFIG_32 must be defined."
+#endif
+
+const char *mpd_round_string[MPD_ROUND_GUARD] = {
+	"ROUND_UP",          /* round away from 0               */
+	"ROUND_DOWN",        /* round toward 0 (truncate)       */
+	"ROUND_CEILING",     /* round toward +infinity          */
+	"ROUND_FLOOR",       /* round toward -infinity          */
+	"ROUND_HALF_UP",     /* 0.5 is rounded up               */
+	"ROUND_HALF_DOWN",   /* 0.5 is rounded down             */
+	"ROUND_HALF_EVEN",   /* 0.5 is rounded to even          */
+	"ROUND_05UP",        /* round zero or five away from 0  */
+	"ROUND_TRUNC",       /* truncate, but set infinity      */
+};
+
+const char *mpd_clamp_string[MPD_CLAMP_GUARD] = {
+	"CLAMP_DEFAULT",
+	"CLAMP_IEEE_754"
+};
+
+

ext/mpdecimal/constants.h

@@ -0,0 +1,83 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CONSTANTS_H
+#define CONSTANTS_H
+
+
+#include "mpdecimal.h"
+
+
+/* choice of optimized functions */
+#if defined(CONFIG_64)
+/* x64 */
+  #define MULMOD(a, b) x64_mulmod(a, b, umod)
+  #define MULMOD2C(a0, a1, w) x64_mulmod2c(a0, a1, w, umod)
+  #define MULMOD2(a0, b0, a1, b1) x64_mulmod2(a0, b0, a1, b1, umod)
+  #define POWMOD(base, exp) x64_powmod(base, exp, umod)
+  #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
+#elif defined(PPRO)
+/* PentiumPro (or later) gcc inline asm */
+  #define MULMOD(a, b) ppro_mulmod(a, b, &dmod, dinvmod)
+  #define MULMOD2C(a0, a1, w) ppro_mulmod2c(a0, a1, w, &dmod, dinvmod)
+  #define MULMOD2(a0, b0, a1, b1) ppro_mulmod2(a0, b0, a1, b1, &dmod, dinvmod)
+  #define POWMOD(base, exp) ppro_powmod(base, exp, &dmod, dinvmod)
+  #define SETMODULUS(modnum) ppro_setmodulus(modnum, &umod, &dmod, dinvmod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) ppro_size3_ntt(x0, x1, x2, w3table, umod, &dmod, dinvmod)
+#else
+  /* ANSI C99 */
+  #define MULMOD(a, b) std_mulmod(a, b, umod)
+  #define MULMOD2C(a0, a1, w) std_mulmod2c(a0, a1, w, umod)
+  #define MULMOD2(a0, b0, a1, b1) std_mulmod2(a0, b0, a1, b1, umod)
+  #define POWMOD(base, exp) std_powmod(base, exp, umod)
+  #define SETMODULUS(modnum) std_setmodulus(modnum, &umod)
+  #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod)
+#endif
+
+/* PentiumPro (or later) gcc inline asm */
+extern const float MPD_TWO63;
+extern const uint32_t mpd_invmoduli[3][3];
+
+enum {P1, P2, P3};
+
+extern const mpd_uint_t mpd_moduli[];
+extern const mpd_uint_t mpd_roots[];
+extern const mpd_size_t mpd_bits[];
+extern const mpd_uint_t mpd_pow10[];
+
+extern const mpd_uint_t INV_P1_MOD_P2;
+extern const mpd_uint_t INV_P1P2_MOD_P3;
+extern const mpd_uint_t LH_P1P2;
+extern const mpd_uint_t UH_P1P2;
+
+
+#endif /* CONSTANTS_H */
+
+
+

ext/mpdecimal/context.c

@@ -0,0 +1,300 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <string.h>
+#include <signal.h>
+
+
+void
+mpd_dflt_traphandler(mpd_context_t *ctx UNUSED)
+{
+	raise(SIGFPE);
+}
+
+void (* mpd_traphandler)(mpd_context_t *) = mpd_dflt_traphandler;
+
+
+void
+mpd_setminalloc(mpd_ssize_t n)
+{
+	static int minalloc_is_set = 0;
+
+	if (minalloc_is_set) {
+		mpd_err_warn("mpd_setminalloc: ignoring request to set "
+		             "MPD_MINALLOC a second time\n");
+		return;
+	}
+	if (n < MPD_MINALLOC_MIN || n > MPD_MINALLOC_MAX) {
+		mpd_err_fatal("illegal value for MPD_MINALLOC"); /* GCOV_NOT_REACHED */
+	}
+	MPD_MINALLOC = n;
+	minalloc_is_set = 1;
+}
+
+void
+mpd_init(mpd_context_t *ctx, mpd_ssize_t prec)
+{
+	mpd_ssize_t ideal_minalloc;
+
+	mpd_defaultcontext(ctx);
+
+	if (!mpd_qsetprec(ctx, prec)) {
+		mpd_addstatus_raise(ctx, MPD_Invalid_context);
+		return;
+	}
+
+	ideal_minalloc = 2 * ((prec+MPD_RDIGITS-1) / MPD_RDIGITS);
+	if (ideal_minalloc < MPD_MINALLOC_MIN) ideal_minalloc = MPD_MINALLOC_MIN;
+	if (ideal_minalloc > MPD_MINALLOC_MAX) ideal_minalloc = MPD_MINALLOC_MAX;
+
+	mpd_setminalloc(ideal_minalloc);
+}
+
+void
+mpd_maxcontext(mpd_context_t *ctx)
+{
+	ctx->prec=MPD_MAX_PREC;
+	ctx->emax=MPD_MAX_EMAX;
+	ctx->emin=MPD_MIN_EMIN;
+	ctx->round=MPD_ROUND_HALF_EVEN;
+	ctx->traps=MPD_Traps;
+	ctx->status=0;
+	ctx->newtrap=0;
+	ctx->clamp=0;
+	ctx->allcr=1;
+}
+
+void
+mpd_maxcontext_plus(mpd_context_t *workctx, const mpd_context_t *ctx)
+{
+	workctx->prec = ctx->prec > MPD_MAX_PREC ? ctx->prec : MPD_MAX_PREC;
+	workctx->emax = ctx->emax > MPD_MAX_EMAX ? ctx->emax : MPD_MAX_EMAX;
+	workctx->emin = ctx->emin < MPD_MIN_EMIN ? ctx->emin : MPD_MIN_EMIN;
+	workctx->round=MPD_ROUND_HALF_EVEN;
+	workctx->traps=MPD_Traps;
+	workctx->status=0;
+	workctx->newtrap=0;
+	workctx->clamp=0;
+	workctx->allcr=1;
+}
+
+void
+mpd_defaultcontext(mpd_context_t *ctx)
+{
+	ctx->prec=2*MPD_RDIGITS;
+	ctx->emax=MPD_MAX_EMAX;
+	ctx->emin=MPD_MIN_EMIN;
+	ctx->round=MPD_ROUND_HALF_UP;
+	ctx->traps=MPD_Traps;
+	ctx->status=0;
+	ctx->newtrap=0;
+	ctx->clamp=0;
+	ctx->allcr=1;
+}
+
+void
+mpd_basiccontext(mpd_context_t *ctx)
+{
+	ctx->prec=9;
+	ctx->emax=MPD_MAX_EMAX;
+	ctx->emin=MPD_MIN_EMIN;
+	ctx->round=MPD_ROUND_HALF_UP;
+	ctx->traps=MPD_Traps|MPD_Clamped;
+	ctx->status=0;
+	ctx->newtrap=0;
+	ctx->clamp=0;
+	ctx->allcr=1;
+}
+
+int
+mpd_ieee_context(mpd_context_t *ctx, int bits)
+{
+	if (bits <= 0 || bits > MPD_IEEE_CONTEXT_MAX_BITS || bits % 32) {
+		return -1;
+	}
+
+	ctx->prec = 9 * (bits/32) - 2;
+	ctx->emax = 3 * ((mpd_ssize_t)1<<(bits/16+3));
+	ctx->emin = 1 - ctx->emax;
+	ctx->round=MPD_ROUND_HALF_EVEN;
+	ctx->traps=0;
+	ctx->status=0;
+	ctx->newtrap=0;
+	ctx->clamp=1;
+	ctx->allcr=1;
+
+	return 0;
+}
+
+mpd_ssize_t
+mpd_getprec(const mpd_context_t *ctx)
+{
+	return ctx->prec;
+}
+
+mpd_ssize_t
+mpd_getemax(const mpd_context_t *ctx)
+{
+	return ctx->emax;
+}
+
+mpd_ssize_t
+mpd_getemin(const mpd_context_t *ctx)
+{
+	return ctx->emin;
+}
+
+int
+mpd_getround(const mpd_context_t *ctx)
+{
+	return ctx->round;
+}
+
+uint32_t
+mpd_gettraps(const mpd_context_t *ctx)
+{
+	return ctx->traps;
+}
+
+uint32_t
+mpd_getstatus(const mpd_context_t *ctx)
+{
+	return ctx->status;
+}
+
+int
+mpd_getclamp(const mpd_context_t *ctx)
+{
+	return ctx->clamp;
+}
+
+int
+mpd_getcr(const mpd_context_t *ctx)
+{
+	return ctx->allcr;
+}
+
+
+int
+mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec)
+{
+	if (prec <= 0 || prec > MPD_MAX_PREC) {
+		return 0;
+	}
+	ctx->prec = prec;
+	return 1;
+}
+
+int
+mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax)
+{
+	if (emax < 0 || emax > MPD_MAX_EMAX) {
+		return 0;
+	}
+	ctx->emax = emax;
+	return 1;
+}
+
+int
+mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin)
+{
+	if (emin > 0 || emin < MPD_MIN_EMIN) {
+		return 0;
+	}
+	ctx->emin = emin;
+	return 1;
+}
+
+int
+mpd_qsetround(mpd_context_t *ctx, int round)
+{
+	int i;
+
+	for (i = 0; i < MPD_ROUND_GUARD; i++) {
+		if (i == round) {
+			ctx->round = round;
+			return 1;
+		}
+	}
+	return 0;
+}
+
+int
+mpd_qsettraps(mpd_context_t *ctx, uint32_t traps)
+{
+	if (traps > MPD_Max_status) {
+		return 0;
+	}
+	ctx->traps = traps;
+	return 1;
+}
+
+int
+mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags)
+{
+	if (flags > MPD_Max_status) {
+		return 0;
+	}
+	ctx->status = flags;
+	return 1;
+}
+
+int
+mpd_qsetclamp(mpd_context_t *ctx, int c)
+{
+	if (c != 0 && c != 1) {
+		return 0;
+	}
+	ctx->clamp = c;
+	return 1;
+}
+
+int
+mpd_qsetcr(mpd_context_t *ctx, int c)
+{
+	if (c != 0 && c != 1) {
+		return 0;
+	}
+	ctx->allcr = c;
+	return 1;
+}
+
+
+void
+mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags)
+{
+	ctx->status |= flags;
+	if (flags&ctx->traps) {
+		ctx->newtrap = (flags&ctx->traps);
+		mpd_traphandler(ctx);
+	}
+}
+
+

ext/mpdecimal/convolute.c

@@ -0,0 +1,170 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "bits.h"
+#include "constants.h"
+#include "fnt.h"
+#include "fourstep.h"
+#include "numbertheory.h"
+#include "sixstep.h"
+#include "umodarith.h"
+#include "convolute.h"
+
+
+/* Convolute the data in c1 and c2. Result is in c1. */
+int
+fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum)
+{
+	int (*fnt)(mpd_uint_t *, mpd_size_t, int);
+	int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t n_inv, umod;
+	mpd_size_t i;
+
+
+	SETMODULUS(modnum);
+	n_inv = POWMOD(n, (umod-2));
+
+	if (ispower2(n)) {
+		if (n > SIX_STEP_THRESHOLD) {
+			fnt = six_step_fnt;
+			inv_fnt = inv_six_step_fnt;
+		}
+		else {
+			fnt = std_fnt;
+			inv_fnt = std_inv_fnt;
+		}
+	}
+	else {
+		fnt = four_step_fnt;
+		inv_fnt = inv_four_step_fnt;
+	}
+
+	if (!fnt(c1, n, modnum)) {
+		return 0;
+	}
+	if (!fnt(c2, n, modnum)) {
+		return 0;
+	}
+	for (i = 0; i < n-1; i += 2) {
+		mpd_uint_t x0 = c1[i];
+		mpd_uint_t y0 = c2[i];
+		mpd_uint_t x1 = c1[i+1];
+		mpd_uint_t y1 = c2[i+1];
+		MULMOD2(&x0, y0, &x1, y1);
+		c1[i] = x0;
+		c1[i+1] = x1;
+	}
+
+	if (!inv_fnt(c1, n, modnum)) {
+		return 0;
+	}
+	for (i = 0; i < n-3; i += 4) {
+		mpd_uint_t x0 = c1[i];
+		mpd_uint_t x1 = c1[i+1];
+		mpd_uint_t x2 = c1[i+2];
+		mpd_uint_t x3 = c1[i+3];
+		MULMOD2C(&x0, &x1, n_inv);
+		MULMOD2C(&x2, &x3, n_inv);
+		c1[i] = x0;
+		c1[i+1] = x1;
+		c1[i+2] = x2;
+		c1[i+3] = x3;
+	}
+
+	return 1;
+}
+
+/* Autoconvolute the data in c1. Result is in c1. */
+int
+fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum)
+{
+	int (*fnt)(mpd_uint_t *, mpd_size_t, int);
+	int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int);
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t n_inv, umod;
+	mpd_size_t i;
+
+
+	SETMODULUS(modnum);
+	n_inv = POWMOD(n, (umod-2));
+
+	if (ispower2(n)) {
+		if (n > SIX_STEP_THRESHOLD) {
+			fnt = six_step_fnt;
+			inv_fnt = inv_six_step_fnt;
+		}
+		else {
+			fnt = std_fnt;
+			inv_fnt = std_inv_fnt;
+		}
+	}
+	else {
+		fnt = four_step_fnt;
+		inv_fnt = inv_four_step_fnt;
+	}
+
+	if (!fnt(c1, n, modnum)) {
+		return 0;
+	}
+	for (i = 0; i < n-1; i += 2) {
+		mpd_uint_t x0 = c1[i];
+		mpd_uint_t x1 = c1[i+1];
+		MULMOD2(&x0, x0, &x1, x1);
+		c1[i] = x0;
+		c1[i+1] = x1;
+	}
+
+	if (!inv_fnt(c1, n, modnum)) {
+		return 0;
+	}
+	for (i = 0; i < n-3; i += 4) {
+		mpd_uint_t x0 = c1[i];
+		mpd_uint_t x1 = c1[i+1];
+		mpd_uint_t x2 = c1[i+2];
+		mpd_uint_t x3 = c1[i+3];
+		MULMOD2C(&x0, &x1, n_inv);
+		MULMOD2C(&x2, &x3, n_inv);
+		c1[i] = x0;
+		c1[i+1] = x1;
+		c1[i+2] = x2;
+		c1[i+3] = x3;
+	}
+
+	return 1;
+}
+
+

ext/mpdecimal/convolute.h

@@ -0,0 +1,43 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CONVOLUTE_H
+#define CONVOLUTE_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+#define SIX_STEP_THRESHOLD 4096
+
+
+int fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum);
+int fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum);
+
+
+#endif

ext/mpdecimal/crt.c

@@ -0,0 +1,188 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <assert.h>
+#include "numbertheory.h"
+#include "umodarith.h"
+#include "crt.h"
+
+
+/*
+ * Functions for arithmetic on triple-word mpd_uint_t numbers.
+ */
+
+
+/* Multiply P1P2 by v, store result in w. */
+static inline void
+_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)
+{
+	mpd_uint_t hi1, hi2, lo;
+
+	_mpd_mul_words(&hi1, &lo, LH_P1P2, v);
+	w[0] = lo;
+
+	_mpd_mul_words(&hi2, &lo, UH_P1P2, v);
+	lo = hi1 + lo;
+	if (lo < hi1) hi2++;
+
+	w[1] = lo;
+	w[2] = hi2;
+}
+
+/* Add 3 words from v to w. The result is known to fit in w. */
+static inline void
+_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])
+{
+	mpd_uint_t carry;
+
+	w[0] = w[0] + v[0];
+	carry = (w[0] < v[0]);
+
+	w[1] = w[1] + v[1];
+	if (w[1] < v[1]) w[2]++;
+
+	w[1] = w[1] + carry;
+	if (w[1] < carry) w[2]++;
+
+	w[2] += v[2];
+}
+
+/* Divide 3 words in u by v, store result in w, return remainder. */
+static inline mpd_uint_t
+_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)
+{
+	mpd_uint_t r1 = u[2];
+	mpd_uint_t r2;
+
+	if (r1 < v) {
+		w[2] = 0;
+	}
+	else {
+		_mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */
+	}
+
+	_mpd_div_words(&w[1], &r2, r1, u[1], v);
+	_mpd_div_words(&w[0], &r1, r2, u[0], v);
+
+	return r1;
+}
+
+
+/*
+ * Chinese Remainder Theorem:
+ * Algorithm from Joerg Arndt, "Matters Computational",
+ * Chapter 37.4.1 [http://www.jjj.de/fxt/]
+ */
+
+/*
+ * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each
+ * triple of members of the arrays, find the unique z modulo p1*p2*p3.
+ *
+ * Overflow analysis for 32 bit:
+ *
+ * carry[3] can hold cmax = 2**96-1. Let c_i denote the carry at the
+ * beginning of the ith iteration. Let zmax be the maximum z.
+ *
+ * cmax = 2**96-1      = 79228162514264337593543950335
+ * zmax = (p1*p2*p3)-1 = 7711435583600944683209981953
+ *
+ * c_0 = 0
+ * c_1 = (c_0 + zmax) / 10**9 = 7711435583600944683
+ * c_2 = (c_1 + zmax) / 10**9 = 7711435591312380266
+ * c_3 = (c_2 + zmax) / 10**9 = 7711435591312380274
+ * c_4 = (c_3 + zmax) / 10**9 = 7711435591312380274
+ * (...)
+ *
+ * The carries do not increase, (c_i + zmax) cannot overflow.
+ *
+ *
+ * Overflow analysis for 64 bit:
+ *
+ * cmax = 2**192-1     = 6277101735386680763835789423207666416102355444464034512895
+ * zmax = (p1*p2*p3)-1 = 6277101353934753858413533876806988331203900781075588186113
+ *
+ * c_0 = 0
+ * c_1 = (c_0 + zmax) / 10**19 = 627710135393475385841353387680698833120
+ * c_2 = (c_1 + zmax) / 10**19 = 627710135393475385904124401220046371704
+ * c_3 = (c_2 + zmax) / 10**19 = 627710135393475385904124401220046371710
+ * c_4 = (c_3 + zmax) / 10**19 = 627710135393475385904124401220046371710
+ * (...)
+ *
+ * The carries do not increase. (c_i + zmax) cannot overflow.
+ */
+void
+crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)
+{
+	mpd_uint_t p1 = mpd_moduli[P1];
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t a1, a2, a3;
+	mpd_uint_t s;
+	mpd_uint_t z[3], t[3];
+	mpd_uint_t carry[3] = {0,0,0};
+	mpd_uint_t hi, lo;
+	mpd_size_t i;
+
+	for (i = 0; i < rsize; i++) {
+
+		a1 = x1[i];
+		a2 = x2[i];
+		a3 = x3[i];
+
+		SETMODULUS(P2);
+		s = ext_submod(a2, a1, umod);
+		s = MULMOD(s, INV_P1_MOD_P2);
+
+		_mpd_mul_words(&hi, &lo, s, p1);
+		lo = lo + a1;
+		if (lo < a1) hi++;
+
+		SETMODULUS(P3);
+		s = dw_submod(a3, hi, lo, umod);
+		s = MULMOD(s, INV_P1P2_MOD_P3);
+
+		z[0] = lo;
+		z[1] = hi;
+		z[2] = 0;
+
+		_crt_mulP1P2_3(t, s);
+		_crt_add3(z, t);
+		_crt_add3(carry, z);
+
+		x1[i] = _crt_div3(carry, carry, MPD_RADIX);
+	}
+
+	assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);
+}
+
+

ext/mpdecimal/crt.h

@@ -0,0 +1,40 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef CRT_H
+#define CRT_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+void crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t nmemb);
+
+
+#endif

ext/mpdecimal/difradix2.c

@@ -0,0 +1,163 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <assert.h>
+#include "bits.h"
+#include "numbertheory.h"
+#include "umodarith.h"
+#include "difradix2.h"
+
+
+/*
+ * Generate bit reversed words and carry out the permutation.
+ * Algorithm due to Brent Lehmann, see Joerg Arndt, "Matters Computational",
+ * Chapter 1.13.4. [http://www.jjj.de/fxt/]
+ */
+static inline void
+bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
+{
+	mpd_size_t x = 0;
+	mpd_size_t r = 0;
+	mpd_uint_t t;
+
+	do {
+		if (r > x) {
+			t = a[x];
+			a[x] = a[r];
+			a[r] = t;
+		}
+		x += 1;
+		r ^= (n - (n >> (mpd_bsf(x)+1)));
+	} while (x < n);
+}
+
+
+/* Fast Number Theoretic Transform, decimation in frequency. */
+void
+fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
+{
+	mpd_uint_t *wtable = tparams->wtable;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t u0, u1, v0, v1;
+	mpd_uint_t w, w0, w1, wstep;
+	mpd_size_t m ,mhalf;
+	mpd_size_t j, r;
+
+
+	assert(ispower2(n));
+	assert(n >= 4);
+
+	SETMODULUS(tparams->modnum);
+
+	mhalf = n / 2;
+	for (j = 0; j < mhalf; j += 2) {
+
+		w0 = wtable[j];
+		w1 = wtable[j+1];
+
+		u0 = a[j];
+		v0 = a[j+mhalf];
+
+		u1 = a[j+1];
+		v1 = a[j+1+mhalf];
+
+		a[j] = addmod(u0, v0, umod);
+		v0 = submod(u0, v0, umod);
+
+		a[j+1] = addmod(u1, v1, umod);
+		v1 = submod(u1, v1, umod);
+
+		MULMOD2(&v0, w0, &v1, w1);
+
+		a[j+mhalf] = v0;
+		a[j+1+mhalf] = v1;
+
+	}
+
+	wstep = 2;
+	for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
+
+		mhalf = m / 2;
+
+		/* j = 0 */
+		for (r = 0; r < n; r += 2*m) {
+
+			u0 = a[r];
+			v0 = a[r+mhalf];
+
+			u1 = a[m+r];
+			v1 = a[m+r+mhalf];
+
+			a[r] = addmod(u0, v0, umod);
+			v0 = submod(u0, v0, umod);
+
+			a[m+r] = addmod(u1, v1, umod);
+			v1 = submod(u1, v1, umod);
+
+			a[r+mhalf] = v0;
+			a[m+r+mhalf] = v1;
+		}
+
+		for (j = 1; j < mhalf; j++) {
+
+			w = wtable[j*wstep];
+
+			for (r = 0; r < n; r += 2*m) {
+
+				u0 = a[r+j];
+				v0 = a[r+j+mhalf];
+
+				u1 = a[m+r+j];
+				v1 = a[m+r+j+mhalf];
+
+				a[r+j] = addmod(u0, v0, umod);
+				v0 = submod(u0, v0, umod);
+
+				a[m+r+j] = addmod(u1, v1, umod);
+				v1 = submod(u1, v1, umod);
+
+				MULMOD2C(&v0, &v1, w);
+
+				a[r+j+mhalf] = v0;
+				a[m+r+j+mhalf] = v1;
+			}
+
+		}
+
+	}
+
+	bitreverse_permute(a, n);
+}
+
+

ext/mpdecimal/difradix2.h

@@ -0,0 +1,41 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef DIF_RADIX2_H
+#define DIF_RADIX2_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "numbertheory.h"
+
+
+void fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams);
+
+
+#endif

ext/mpdecimal/fnt.c

@@ -0,0 +1,78 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "difradix2.h"
+#include "numbertheory.h"
+#include "fnt.h"
+
+
+/* forward transform, sign = -1 */
+int
+std_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	struct fnt_params *tparams;
+
+	assert(ispower2(n));
+	assert(n >= 4);
+	assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+	if ((tparams = _mpd_init_fnt_params(n, -1, modnum)) == NULL) {
+		return 0;
+	}
+	fnt_dif2(a, n, tparams);
+
+	mpd_free(tparams);
+	return 1;
+}
+
+/* reverse transform, sign = 1 */
+int
+std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	struct fnt_params *tparams;
+
+	assert(ispower2(n));
+	assert(n >= 4);
+	assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+	if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) {
+		return 0;
+	}
+	fnt_dif2(a, n, tparams);
+
+	mpd_free(tparams);
+	return 1;
+}
+
+
+

ext/mpdecimal/fnt.h

@@ -0,0 +1,42 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef FNT_H
+#define FNT_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+int std_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
+int std_inv_fnt(mpd_uint_t a[], mpd_size_t n, int modnum);
+
+
+#endif
+

ext/mpdecimal/fourstep.c

@@ -0,0 +1,266 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <assert.h>
+#include "numbertheory.h"
+#include "sixstep.h"
+#include "transpose.h"
+#include "umodarith.h"
+#include "fourstep.h"
+
+
+/*
+ * A variant of the four-step algorithm from:
+ *
+ * David H. Bailey: FFTs in External or Hierarchical Memory, Journal of
+ * Supercomputing, vol. 4, no. 1 (March 1990), p. 23-35.
+ *
+ * URL: http://crd.lbl.gov/~dhbailey/dhbpapers/
+ */
+
+
+#ifndef PPRO
+static inline void
+std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
+              mpd_uint_t w3table[3], mpd_uint_t umod)
+{
+	mpd_uint_t r1, r2;
+	mpd_uint_t w;
+	mpd_uint_t s, tmp;
+
+
+	/* k = 0 -> w = 1 */
+	s = *x1;
+	s = addmod(s, *x2, umod);
+	s = addmod(s, *x3, umod);
+
+	r1 = s;
+
+	/* k = 1 */
+	s = *x1;
+
+	w = w3table[1];
+	tmp = MULMOD(*x2, w);
+	s = addmod(s, tmp, umod);
+
+	w = w3table[2];
+	tmp = MULMOD(*x3, w);
+	s = addmod(s, tmp, umod);
+
+	r2 = s;
+
+	/* k = 2 */
+	s = *x1;
+
+	w = w3table[2];
+	tmp = MULMOD(*x2, w);
+	s = addmod(s, tmp, umod);
+
+	w = w3table[1];
+	tmp = MULMOD(*x3, w);
+	s = addmod(s, tmp, umod);
+
+	*x3 = s;
+	*x2 = r2;
+	*x1 = r1;
+}
+#else /* PPRO */
+static inline void
+ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
+               mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
+{
+	mpd_uint_t r1, r2;
+	mpd_uint_t w;
+	mpd_uint_t s, tmp;
+
+
+	/* k = 0 -> w = 1 */
+	s = *x1;
+	s = addmod(s, *x2, umod);
+	s = addmod(s, *x3, umod);
+
+	r1 = s;
+
+	/* k = 1 */
+	s = *x1;
+
+	w = w3table[1];
+	tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
+	s = addmod(s, tmp, umod);
+
+	w = w3table[2];
+	tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
+	s = addmod(s, tmp, umod);
+
+	r2 = s;
+
+	/* k = 2 */
+	s = *x1;
+
+	w = w3table[2];
+	tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
+	s = addmod(s, tmp, umod);
+
+	w = w3table[1];
+	tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
+	s = addmod(s, tmp, umod);
+
+	*x3 = s;
+	*x2 = r2;
+	*x1 = r1;
+}
+#endif
+
+
+/* forward transform, sign = -1; transform length = 3 * 2^n */
+int
+four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	mpd_size_t R = 3; /* number of rows */
+	mpd_size_t C = n / 3; /* number of columns */
+	mpd_uint_t w3table[3];
+	mpd_uint_t kernel, w0, w1, wstep;
+	mpd_uint_t *s, *p0, *p1, *p2;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_size_t i, k;
+
+
+	assert(n >= 48);
+	assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+
+	SETMODULUS(modnum);
+	_mpd_init_w3table(w3table, -1, modnum);
+	/* size three ntt on the columns */
+	for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
+
+		SIZE3_NTT(p0, p1, p2, w3table);
+	}
+
+
+	kernel = _mpd_getkernel(n, -1, modnum);
+	for (i = 1; i < R; i++) {
+		w0 = 1;
+		w1 = POWMOD(kernel, i);
+		wstep = MULMOD(w1, w1);
+		for (k = 0; k < C-1; k += 2) {
+			mpd_uint_t x0 = a[i*C+k];
+			mpd_uint_t x1 = a[i*C+k+1];
+			MULMOD2(&x0, w0, &x1, w1);
+			MULMOD2C(&w0, &w1, wstep);
+			a[i*C+k] = x0;
+			a[i*C+k+1] = x1;
+		}
+	}
+
+	/* transform rows */
+	for (s = a; s < a+n; s += C) {
+		if (!six_step_fnt(s, C, modnum)) {
+			return 0;
+		}
+	}
+
+#if 0
+	/* An unordered transform is sufficient for convolution. */
+	if (ordered) {
+		transpose_3xpow2(a, R, C);
+	}
+#endif
+
+	return 1;
+}
+
+/* backward transform, sign = 1; transform length = 3 * 2^n */
+int
+inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	mpd_size_t R = 3; /* number of rows */
+	mpd_size_t C = n / 3; /* number of columns */
+	mpd_uint_t w3table[3];
+	mpd_uint_t kernel, w0, w1, wstep;
+	mpd_uint_t *s, *p0, *p1, *p2;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_size_t i, k;
+
+
+	assert(n >= 48);
+	assert(n <= 3*MPD_MAXTRANSFORM_2N);
+
+
+#if 0
+	/* An unordered transform is sufficient for convolution. */
+	if (ordered) {
+		transpose_3xpow2(a, C, R);
+	}
+#endif
+
+	/* transform rows */
+	for (s = a; s < a+n; s += C) {
+		if (!inv_six_step_fnt(s, C, modnum)) {
+			return 0;
+		}
+	}
+
+
+	SETMODULUS(modnum);
+	kernel = _mpd_getkernel(n, 1, modnum);
+	for (i = 1; i < R; i++) {
+		w0 = 1;
+		w1 = POWMOD(kernel, i);
+		wstep = MULMOD(w1, w1);
+		for (k = 0; k < C; k += 2) {
+			mpd_uint_t x0 = a[i*C+k];
+			mpd_uint_t x1 = a[i*C+k+1];
+			MULMOD2(&x0, w0, &x1, w1);
+			MULMOD2C(&w0, &w1, wstep);
+			a[i*C+k] = x0;
+			a[i*C+k+1] = x1;
+		}
+	}
+
+
+	_mpd_init_w3table(w3table, 1, modnum);
+	/* size three ntt on the columns */
+	for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
+
+		SIZE3_NTT(p0, p1, p2, w3table);
+	}
+
+	return 1;
+}
+
+

ext/mpdecimal/fourstep.h

@@ -0,0 +1,41 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef FOUR_STEP_H
+#define FOUR_STEP_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+int four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+int inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+
+
+#endif

ext/mpdecimal/io.c

@@ -0,0 +1,1397 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <limits.h>
+#include <assert.h>
+#include <errno.h>
+#include <locale.h>
+#include "bits.h"
+#include "constants.h"
+#include "memory.h"
+#include "typearith.h"
+#include "io.h"
+
+
+/*
+ * Work around the behavior of tolower() and strcasecmp() in certain
+ * locales. For example, in tr_TR.utf8:
+ *
+ * tolower((unsigned char)'I') == 'I'
+ *
+ * u is the exact uppercase version of l; n is strlen(l) or strlen(l)+1
+ */
+static inline int
+_mpd_strneq(const char *s, const char *l, const char *u, size_t n)
+{
+	while (--n != SIZE_MAX) {
+		if (*s != *l && *s != *u) {
+			return 0;
+		}
+		s++; u++; l++;
+	}
+
+	return 1;
+}
+
+static mpd_ssize_t
+strtoexp(const char *s)
+{
+	char *end;
+	mpd_ssize_t retval;
+
+	errno = 0;
+	retval = mpd_strtossize(s, &end, 10);
+	if (errno == 0 && !(*s != '\0' && *end == '\0'))
+		errno = EINVAL;
+
+	return retval;
+}
+
+/*
+ * Scan 'len' words. The most significant word contains 'r' digits,
+ * the remaining words are full words. Skip dpoint. The string 's' must
+ * consist of digits and an optional single decimal point at 'dpoint'.
+ */
+static void
+string_to_coeff(mpd_uint_t *data, const char *s, const char *dpoint, int r,
+                size_t len)
+{
+	int j;
+
+	if (r > 0) {
+		data[--len] = 0;
+		for (j = 0; j < r; j++, s++) {
+			if (s == dpoint) s++;
+			data[len] = 10 * data[len] + (*s - '0');
+		}
+	}
+
+	while (--len != SIZE_MAX) {
+		data[len] = 0;
+		for (j = 0; j < MPD_RDIGITS; j++, s++) {
+			if (s == dpoint) s++;
+			data[len] = 10 * data[len] + (*s - '0');
+		}
+	}
+}
+
+/*
+ * Scan for at most one decimal point and at most one indicator.
+ * Remove unneeded zeros before and after the decimal point.
+ * The first relevant digit will be the start of the coefficient.
+ * A decimal point may occur before an indicator.
+ * Plus or minus may occur directly after the indicator.
+ * The rest of the characters must be decimal digits.
+ *
+ * Return start of the coefficient or NULL or error. The end of
+ * the string is stored in 'end'.
+ */
+static const char *
+scan_dpoint_exp(const char *s, const char **dpoint, const char **exp,
+                const char **end)
+{
+	const char *coeff = NULL;
+
+	*dpoint = NULL;
+	*exp = NULL;
+	for (; *s != '\0'; s++) {
+		switch (*s) {
+		case '.':
+			if (*dpoint != NULL || *exp != NULL)
+				return NULL;
+			*dpoint = s;
+			break;
+		case 'E': case 'e':
+			if (*exp != NULL)
+				return NULL;
+			*exp = s;
+			if (*(s+1) == '+' || *(s+1) == '-')
+				s++;
+			break;
+		default:
+			if (!isdigit((uchar)*s))
+				return NULL;
+			if (coeff == NULL && *exp == NULL) {
+				if (*s == '0') {
+					if (!isdigit((uchar)*(s+1)))
+						if (!(*(s+1) == '.' &&
+						      isdigit((uchar)*(s+2))))
+							coeff = s;
+				}
+				else {
+					coeff = s;
+				}
+			}
+			break;
+
+		}
+	}
+
+	*end = s;
+	return coeff;
+}
+
+/* scan the payload of a NaN */
+static const char *
+scan_payload(const char *s, const char **end)
+{
+	const char *coeff;
+
+	while (*s == '0')
+		s++;
+	coeff = s;
+
+	while (isdigit((uchar)*s))
+		s++;
+	*end = s;
+
+	return (*s == '\0') ? coeff : NULL;
+}
+
+/* convert a character string to a decimal */
+void
+mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx,
+                uint32_t *status)
+{
+	mpd_ssize_t q, r, len;
+	const char *coeff, *end;
+	const char *dpoint = NULL, *exp = NULL;
+	size_t digits;
+	uint8_t sign = MPD_POS;
+
+	mpd_set_flags(dec, 0);
+	dec->len = 0;
+	dec->exp = 0;
+
+	/* [flags] */
+	if (*s == '+') {
+		s++;
+	}
+	else if (*s == '-') {
+		mpd_set_negative(dec);
+		sign = MPD_NEG;
+		s++;
+	}
+
+	if (_mpd_strneq(s, "nan", "NAN", 3)) { /* NaN */
+		s += 3;
+		mpd_setspecial(dec, sign, MPD_NAN);
+		if (*s == '\0')
+			return;
+		/* only digits for the diagnostic code */
+		if ((coeff = scan_payload(s, &end)) == NULL)
+			goto conversion_error;
+		/* payload consists entirely of zeros */
+		if (*coeff == '\0')
+			return;
+		digits = end - coeff;
+		/* prec >= 1, clamp is 0 or 1 */
+		if (digits > (size_t)(ctx->prec-ctx->clamp))
+			goto conversion_error;
+	} /* sNaN */
+	else if (_mpd_strneq(s, "snan", "SNAN", 4)) {
+		s += 4;
+		mpd_setspecial(dec, sign, MPD_SNAN);
+		if (*s == '\0')
+			return;
+		/* only digits for the diagnostic code */
+		if ((coeff = scan_payload(s, &end)) == NULL)
+			goto conversion_error;
+		/* payload consists entirely of zeros */
+		if (*coeff == '\0')
+			return;
+		digits = end - coeff;
+		if (digits > (size_t)(ctx->prec-ctx->clamp))
+			goto conversion_error;
+	}
+	else if (_mpd_strneq(s, "inf", "INF", 3)) {
+		s += 3;
+		if (*s == '\0' || _mpd_strneq(s, "inity", "INITY", 6)) {
+			/* numeric-value: infinity */
+			mpd_setspecial(dec, sign, MPD_INF);
+			return;
+		}
+		goto conversion_error;
+	}
+	else {
+		/* scan for start of coefficient, decimal point, indicator, end */
+		if ((coeff = scan_dpoint_exp(s, &dpoint, &exp, &end)) == NULL)
+			goto conversion_error;
+
+		/* numeric-value: [exponent-part] */
+		if (exp) {
+			/* exponent-part */
+			end = exp; exp++;
+			dec->exp = strtoexp(exp);
+			if (errno) {
+				if (!(errno == ERANGE &&
+				     (dec->exp == MPD_SSIZE_MAX ||
+				      dec->exp == MPD_SSIZE_MIN)))
+					goto conversion_error;
+			}
+		}
+
+	        digits = end - coeff;
+		if (dpoint) {
+			size_t fracdigits = end-dpoint-1;
+			if (dpoint > coeff) digits--;
+
+			if (fracdigits > MPD_MAX_PREC) {
+				goto conversion_error;
+			}
+			if (dec->exp < (MPD_SSIZE_MIN+1)+(mpd_ssize_t)fracdigits) {
+				dec->exp = MPD_SSIZE_MIN+1;
+			}
+			else {
+				dec->exp -= (mpd_ssize_t)fracdigits;
+			}
+		}
+		if (digits > MPD_MAX_PREC) {
+			goto conversion_error;
+		}
+		if (dec->exp > MPD_EXP_INF) {
+			dec->exp = MPD_EXP_INF;
+		}
+	}
+
+	_mpd_idiv_word(&q, &r, (mpd_ssize_t)digits, MPD_RDIGITS);
+
+	len = (r == 0) ? q : q+1;
+	if (len == 0) {
+		goto conversion_error; /* GCOV_NOT_REACHED */
+	}
+	if (!mpd_qresize(dec, len, status)) {
+		mpd_seterror(dec, MPD_Malloc_error, status);
+		return;
+	}
+	dec->len = len;
+
+	string_to_coeff(dec->data, coeff, dpoint, (int)r, len);
+
+	mpd_setdigits(dec);
+	mpd_qfinalize(dec, ctx, status);
+	return;
+
+conversion_error:
+	/* standard wants a positive NaN */
+	mpd_seterror(dec, MPD_Conversion_syntax, status);
+}
+
+/* print the exponent to a string */
+static inline char *
+exp_to_string(char *s, mpd_ssize_t x)
+{
+	mpd_ssize_t q, d;
+	char sign = '+';
+	int j;
+
+	if (x < 0) {
+		sign = '-';
+		x = -x;
+	}
+	*s++ = sign;
+
+	j = mpd_exp_digits(x) - 1;
+
+	for (; j != 0; --j) {
+		d = mpd_pow10[j];
+		q = x / d;
+		x -= d * q;
+		*s++ = '0' + (char)q;
+	}
+	*s++ = '0' + (char)x;
+
+	return s;
+}
+
+/* print coefficient to string, len(dec) > 0 */
+static inline char *
+coeff_to_string(char *s, const mpd_t *dec)
+{
+	mpd_uint_t x, q, d;
+	mpd_ssize_t i;
+	int j;
+
+	/* most significant word */
+	x = mpd_msword(dec);
+	j = mpd_word_digits(x) - 1;
+
+	for (; j != 0; --j) {
+		d = mpd_pow10[j];
+		q = x / d;
+		x -= d * q;
+		*s++ = '0' + (char)q;
+	}
+	*s++ = '0' + (char)x;
+
+	/* remaining full words */
+	for (i=dec->len-2; i >= 0; --i) {
+		x = dec->data[i];
+		for (j=MPD_RDIGITS-1; j != 0; --j) {
+			d = mpd_pow10[j];
+			q = x / d;
+			x -= d * q;
+			*s++ = '0' + (char)q;
+		}
+		*s++ = '0' + (char)x;
+	}
+
+	return s;
+}
+
+/* print coefficient to string, len(dec) > 0 */
+static inline char *
+coeff_to_string_dot(char *s, char *dot, const mpd_t *dec)
+{
+	mpd_uint_t x, q, d;
+	mpd_ssize_t i;
+	int j;
+
+	/* most significant word */
+	x = mpd_msword(dec);
+	j = mpd_word_digits(x) - 1;
+
+	for (; j >= 0; --j) {
+		if (s == dot)
+			*s++ = '.';
+		d = mpd_pow10[j];
+		q = x / d;
+		x -= d * q;
+		*s++ = '0' + (char)q;
+	}
+
+	/* remaining full words */
+	for (i=dec->len-2; i >= 0; --i) {
+		x = dec->data[i];
+		for (j=MPD_RDIGITS-1; j >= 0; --j) {
+			if (s == dot)
+				*s++ = '.';
+			d = mpd_pow10[j];
+			q = x / d;
+			x -= d * q;
+			*s++ = '0' + (char)q;
+		}
+	}
+
+	return s;
+}
+
+/* Format type */
+#define MPD_FMT_LOWER      0x00000000
+#define MPD_FMT_UPPER      0x00000001
+#define MPD_FMT_TOSCI      0x00000002
+#define MPD_FMT_TOENG      0x00000004
+#define MPD_FMT_EXP        0x00000008
+#define MPD_FMT_FIXED      0x00000010
+#define MPD_FMT_PERCENT    0x00000020
+#define MPD_FMT_SIGN_SPACE 0x00000040
+#define MPD_FMT_SIGN_PLUS  0x00000080
+
+/*
+ * Return the string representation of a decimal. Formatting is done according
+ * to 'flags'. A return value of NULL indicates MPD_Malloc_error.
+ *
+ * To allow formatting like [0e15, '.6e' -> 0.000000e-9], 'zeroexp' is used
+ * in combination with MPD_FMT_FIXED (see mpd_qformat for details).
+ */
+static char *
+_mpd_to_string(const mpd_t *dec, int flags, mpd_ssize_t zeroexp)
+{
+	char *decstring = NULL, *cp = NULL;
+	mpd_ssize_t ldigits, dplace;
+	mpd_ssize_t mem = 0, k;
+
+	if (mpd_isspecial(dec)) {
+
+		mem = sizeof "-Infinity";
+		if (mpd_isnan(dec) && dec->len > 0) {
+			/* diagnostic code */
+			mem += dec->digits;
+		}
+		cp = decstring = mpd_alloc(mem, sizeof *decstring);
+		if (cp == NULL) {
+			return NULL;
+		}
+
+		if (mpd_isnegative(dec)) {
+			*cp++ = '-';
+		}
+		else if (flags&MPD_FMT_SIGN_SPACE) {
+			*cp++ = ' ';
+		}
+		else if (flags&MPD_FMT_SIGN_PLUS) {
+			*cp++ = '+';
+		}
+
+		if (mpd_isnan(dec)) {
+			if (mpd_isqnan(dec)) {
+				strcpy(cp, "NaN");
+				cp += 3;
+			}
+			else {
+				strcpy(cp, "sNaN");
+				cp += 4;
+			}
+			if (dec->len > 0) { /* diagnostic code */
+				cp = coeff_to_string(cp, dec);
+			}
+		}
+		else if (mpd_isinfinite(dec)) {
+			strcpy(cp, "Infinity");
+			cp += 8;
+		}
+		else { /* debug */
+			abort(); /* GCOV_NOT_REACHED */
+		}
+	}
+	else {
+		assert(dec->len > 0);
+
+		/*
+		 * ldigits: Digits to the left of the decimal point, as if the
+		 *          number was written without exponent notation.
+		 *
+		 * dplace: Position of the decimal point relative to the first
+		 *         member of the coefficient.
+		 *
+		 * 0.00000_.____._____000000.
+		 *  ^      ^    ^           ^
+		 *  |      |    |           |
+		 *  |      |    |           `- dplace in the last position
+		 *  |      |    `- dplace in the middle of the coefficient
+		 *  |      ` dplace = 1 (after the first coefficient digit)
+		 *  `- dplace is negative
+		 */
+
+		ldigits = dec->digits + dec->exp;
+		dplace = 1; /* default for MPD_FMT_TOSCI, MPD_FMT_EXP */
+
+		if (flags&MPD_FMT_EXP) {
+			;
+		}
+		else if (flags&MPD_FMT_FIXED || (dec->exp <= 0 && ldigits > -6)) {
+			/* MPD_FMT_FIXED: always use fixed point notation.
+			 * MPD_FMT_TOSCI, MPD_FMT_TOENG: for a certain range,
+			 * override exponent notation. */
+			dplace = ldigits;
+		}
+		else if (flags&MPD_FMT_TOENG) {
+			if (mpd_iszero(dec)) {
+				/* If the exponent is divisible by three,
+				 * dplace = 1. Otherwise, move dplace one
+				 * or two places to the left. */
+				dplace = -1 + mod_mpd_ssize_t(dec->exp+2, 3);
+			}
+			else { /* ldigits-1 is the adjusted exponent, which
+				* should be divisible by three. If not, move
+				* dplace one or two places to the right. */
+				dplace += mod_mpd_ssize_t(ldigits-1, 3);
+			}
+		}
+
+		/*
+		 * Basic space requirements:
+		 *
+		 * [-][.][coeffdigits][E][-][expdigits+1][%]['\0']
+		 *
+		 * If the decimal point lies outside of the coefficient digits,
+		 * space is adjusted accordingly.
+		 */
+		if (dplace <= 0) {
+			mem = -dplace + dec->digits + 2;
+		}
+		else if (dplace >= dec->digits) {
+			mem = dplace;
+		}
+		else {
+			mem = dec->digits;
+		}
+		mem += (MPD_EXPDIGITS+1+6);
+
+		cp = decstring = mpd_alloc(mem, sizeof *decstring);
+		if (cp == NULL) {
+			return NULL;
+		}
+
+
+		if (mpd_isnegative(dec)) {
+			*cp++ = '-';
+		}
+		else if (flags&MPD_FMT_SIGN_SPACE) {
+			*cp++ = ' ';
+		}
+		else if (flags&MPD_FMT_SIGN_PLUS) {
+			*cp++ = '+';
+		}
+
+		if (dplace <= 0) {
+			/* space: -dplace+dec->digits+2 */
+			*cp++ = '0';
+			*cp++ = '.';
+			for (k = 0; k < -dplace; k++) {
+				*cp++ = '0';
+			}
+			cp = coeff_to_string(cp, dec);
+		}
+		else if (dplace >= dec->digits) {
+			/* space: dplace */
+			cp = coeff_to_string(cp, dec);
+			for (k = 0; k < dplace-dec->digits; k++) {
+				*cp++ = '0';
+			}
+		}
+		else {
+			/* space: dec->digits+1 */
+			cp = coeff_to_string_dot(cp, cp+dplace, dec);
+		}
+
+		/*
+		 * Conditions for printing an exponent:
+		 *
+		 *   MPD_FMT_TOSCI, MPD_FMT_TOENG: only if ldigits != dplace
+		 *   MPD_FMT_FIXED:                never (ldigits == dplace)
+		 *   MPD_FMT_EXP:                  always
+		 *   MPD_FMT_FIXED with zeroexp:   always
+		 */
+		if (ldigits != dplace || flags&MPD_FMT_EXP || zeroexp != MPD_SSIZE_MAX) {
+			/* space: expdigits+2 */
+			mpd_ssize_t x = (zeroexp != MPD_SSIZE_MAX) ? zeroexp : ldigits-dplace;
+			*cp++ = (flags&MPD_FMT_UPPER) ? 'E' : 'e';
+			cp = exp_to_string(cp, x);
+		}
+
+		if (flags&MPD_FMT_PERCENT) {
+			*cp++ = '%';
+		}
+	}
+
+	assert(cp < decstring+mem);
+	*cp = '\0';
+	return decstring;
+}
+
+char *
+mpd_to_sci(const mpd_t *dec, int fmt)
+{
+	int flags = MPD_FMT_TOSCI;
+
+	flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
+	return _mpd_to_string(dec, flags, MPD_SSIZE_MAX);
+}
+
+char *
+mpd_to_eng(const mpd_t *dec, int fmt)
+{
+	int flags = MPD_FMT_TOENG;
+
+	flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER;
+	return _mpd_to_string(dec, flags, MPD_SSIZE_MAX);
+}
+
+/* Copy a single UTF-8 char to dest. */
+static int
+_mpd_copy_utf8(char dest[5], const char *s)
+{
+	const uchar *cp = (const uchar *)s;
+	uchar lb, ub;
+	int count, i;
+
+
+	if (*cp == 0) {
+		/* empty string */
+		dest[0] = '\0';
+		return 0;
+	}
+	else if (*cp <= 0x7f) {
+		/* ascii */
+		dest[0] = *cp;
+		dest[1] = '\0';
+		return 1;
+	}
+	else if (0xc2 <= *cp && *cp <= 0xdf) {
+		lb = 0x80; ub = 0xbf;
+		count = 2;
+	}
+	else if (*cp == 0xe0) {
+		lb = 0xa0; ub = 0xbf;
+		count = 3;
+	}
+	else if (*cp <= 0xec) {
+		lb = 0x80; ub = 0xbf;
+		count = 3;
+	}
+	else if (*cp == 0xed) {
+		lb = 0x80; ub = 0x9f;
+		count = 3;
+	}
+	else if (*cp <= 0xef) {
+		lb = 0x80; ub = 0xbf;
+		count = 3;
+	}
+	else if (*cp == 0xf0) {
+		lb = 0x90; ub = 0xbf;
+		count = 4;
+	}
+	else if (*cp <= 0xf3) {
+		lb = 0x80; ub = 0xbf;
+		count = 4;
+	}
+	else if (*cp == 0xf4) {
+		lb = 0x80; ub = 0x8f;
+		count = 4;
+	}
+	else {
+		/* invalid */
+		goto error;
+	}
+
+	dest[0] = *cp++;
+	if (*cp < lb || ub < *cp) {
+		goto error;
+	}
+	dest[1] = *cp++;
+	for (i = 2; i < count; i++) {
+		if (*cp < 0x80 || 0xbf < *cp) {
+			goto error;
+		}
+		dest[i] = *cp++;
+	}
+	dest[i] = '\0';
+
+	return count;
+
+error:
+	dest[0] = '\0';
+	return -1;
+}
+
+int
+mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps)
+{
+	char *cp = (char *)fmt;
+	int have_align = 0, n;
+
+	/* defaults */
+	spec->min_width = 0;
+	spec->prec = -1;
+	spec->type = caps ? 'G' : 'g';
+	spec->align = '>';
+	spec->sign = '-';
+	spec->dot = "";
+	spec->sep = "";
+	spec->grouping = "";
+
+
+	/* presume that the first character is a UTF-8 fill character */
+	if ((n = _mpd_copy_utf8(spec->fill, cp)) < 0) {
+		return 0;
+	}
+
+	/* alignment directive, prefixed by a fill character */
+	if (*cp && (*(cp+n) == '<' || *(cp+n) == '>' ||
+	            *(cp+n) == '=' || *(cp+n) == '^')) {
+		cp += n;
+		spec->align = *cp++;
+		have_align = 1;
+	} /* alignment directive */
+	else {
+		/* default fill character */
+		spec->fill[0] = ' ';
+		spec->fill[1] = '\0';
+		if (*cp == '<' || *cp == '>' ||
+		    *cp == '=' || *cp == '^') {
+			spec->align = *cp++;
+			have_align = 1;
+		}
+	}
+
+	/* sign formatting */
+	if (*cp == '+' || *cp == '-' || *cp == ' ') {
+		spec->sign = *cp++;
+	}
+
+	/* zero padding */
+	if (*cp == '0') {
+		/* zero padding implies alignment, which should not be
+		 * specified twice. */
+		if (have_align) {
+			return 0;
+		}
+		spec->align = 'z';
+		spec->fill[0] = *cp++;
+		spec->fill[1] = '\0';
+	}
+
+	/* minimum width */
+	if (isdigit((uchar)*cp)) {
+		if (*cp == '0') {
+			return 0;
+		}
+		errno = 0;
+		spec->min_width = mpd_strtossize(cp, &cp, 10);
+		if (errno == ERANGE || errno == EINVAL) {
+			return 0;
+		}
+	}
+
+	/* thousands separator */
+	if (*cp == ',') {
+		spec->dot = ".";
+		spec->sep = ",";
+		spec->grouping = "\003\003";
+		cp++;
+	}
+
+	/* fraction digits or significant digits */
+	if (*cp == '.') {
+		cp++;
+		if (!isdigit((uchar)*cp)) {
+			return 0;
+		}
+		errno = 0;
+		spec->prec = mpd_strtossize(cp, &cp, 10);
+		if (errno == ERANGE || errno == EINVAL) {
+			return 0;
+		}
+	}
+
+	/* type */
+	if (*cp == 'E' || *cp == 'e' || *cp == 'F' || *cp == 'f' ||
+	    *cp == 'G' || *cp == 'g' || *cp == '%') {
+		spec->type = *cp++;
+	}
+	else if (*cp == 'N' || *cp == 'n') {
+		/* locale specific conversion */
+		struct lconv *lc;
+		spec->type = *cp++;
+		/* separator has already been specified */
+		if (*spec->sep) return 0;
+		spec->type = (spec->type == 'N') ? 'G' : 'g';
+		lc = localeconv();
+		spec->dot = lc->decimal_point;
+		spec->sep = lc->thousands_sep;
+		spec->grouping = lc->grouping;
+	}
+
+	/* check correctness */
+	if (*cp != '\0') {
+		return 0;
+	}
+
+	return 1;
+}
+
+/*
+ * The following functions assume that spec->min_width <= MPD_MAX_PREC, which
+ * is made sure in mpd_qformat_spec. Then, even with a spec that inserts a
+ * four-byte separator after each digit, nbytes in the following struct
+ * cannot overflow.
+ */
+
+/* Multibyte string */
+typedef struct {
+	mpd_ssize_t nbytes; /* length in bytes */
+	mpd_ssize_t nchars; /* length in chars */
+	mpd_ssize_t cur;    /* current write index */
+	char *data;
+} mpd_mbstr_t;
+
+static inline void
+_mpd_bcopy(char *dest, const char *src, mpd_ssize_t n)
+{
+	while (--n >= 0) {
+		dest[n] = src[n];
+	}
+}
+
+static inline void
+_mbstr_copy_char(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n)
+{
+	dest->nbytes += n;
+	dest->nchars += 1;
+	dest->cur -= n;
+
+	if (dest->data != NULL) {
+		_mpd_bcopy(dest->data+dest->cur, src, n);
+	}
+}
+
+static inline void
+_mbstr_copy_ascii(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n)
+{
+	dest->nbytes += n;
+	dest->nchars += n;
+	dest->cur -= n;
+
+	if (dest->data != NULL) {
+		_mpd_bcopy(dest->data+dest->cur, src, n);
+	}
+}
+
+static inline void
+_mbstr_copy_pad(mpd_mbstr_t *dest, mpd_ssize_t n)
+{
+	dest->nbytes += n;
+	dest->nchars += n;
+	dest->cur -= n;
+
+	if (dest->data != NULL) {
+		char*cp = dest->data + dest->cur;
+		while (--n >= 0) {
+			cp[n] = '0';
+		}
+	}
+}
+
+/*
+ * Copy the decimal to dest, adding separators according to
+ * spec->grouping. If leading zero padding is enabled and the
+ * result is smaller than spec->min_width, continue adding zeros
+ * and separators until min_width is reached.
+ */
+static void
+_mpd_add_sep_dot(mpd_mbstr_t *dest,
+                 const char *src, mpd_ssize_t n_src, /* integer part and length */
+                 const char *sign, const char *dot, const char *rest,
+                 mpd_spec_t *spec)
+{
+	mpd_ssize_t n_sep, n_sign, consume;
+	const char *g;
+	int pad = 0;
+
+	n_sign = sign ? 1 : 0;
+	n_sep = (mpd_ssize_t)strlen(spec->sep);
+	g = spec->grouping;
+	dest->cur = dest->nbytes;
+	dest->nbytes = dest->nchars = 0;
+
+	/* rest <= MPD_MAX_PREC */
+	_mbstr_copy_ascii(dest, rest, (mpd_ssize_t)strlen(rest));
+
+	if (dot) {
+		_mbstr_copy_char(dest, dot, (mpd_ssize_t)strlen(dot));
+	}
+
+	consume = *g;
+	while (1) {
+		if (*g == 0 || *g == CHAR_MAX || consume > n_src) {
+			consume = n_src;
+		}
+		n_src -= consume;
+		if (pad) {
+			_mbstr_copy_pad(dest, consume);
+		}
+		else {
+			_mbstr_copy_ascii(dest, src+n_src, consume);
+		}
+
+		if (n_src == 0) {
+			if (spec->align == 'z' &&
+			    dest->nchars + n_sign < spec->min_width) {
+				n_src = spec->min_width - (dest->nchars + n_sign);
+				consume = *g - consume;
+				pad = 1;
+				continue;
+			}
+			break;
+		}
+
+		if (n_sep > 0) {
+			if (pad && n_src > 1) n_src -= 1;
+			_mbstr_copy_char(dest, spec->sep, n_sep);
+		}
+
+		if (*g && *(g+1)) g++;
+		consume = *g;
+	}
+
+	if (sign) {
+		_mbstr_copy_ascii(dest, sign, 1);
+	}
+
+	if (dest->data) {
+		dest->data[dest->nbytes] = '\0';
+	}
+}
+
+/* Change decstring to locale-specific appearance. */
+static void
+_mpd_apply_lconv(mpd_mbstr_t *result, char *decstring, mpd_spec_t *spec,
+                 uint32_t *status)
+{
+	const char *sign = NULL, *intpart = NULL;
+	const char *dot = NULL, *rest = NULL;
+	const char *dp;
+	mpd_ssize_t n_int;
+
+	assert(result->data == NULL);
+
+	dp = decstring;
+	n_int = 0;
+
+	if (!isdigit((uchar)*dp)) {
+		sign = dp++;
+	}
+	if (isdigit((uchar)*dp)) {
+		intpart = dp++;
+		while (isdigit((uchar)*dp)) {
+			dp++;
+		}
+		n_int = (mpd_ssize_t)(dp-intpart);
+	}
+	if (*dp == '.') {
+		if (*spec->dot == '\0') {
+		        /* decimal point must be present */
+			*status |= MPD_Invalid_operation; /* GCOV_NOT_REACHED */
+			mpd_free(decstring); /* GCOV_NOT_REACHED */
+			return; /* GCOV_NOT_REACHED */
+		}
+		dp++; dot = spec->dot;
+	}
+	rest = dp;
+
+
+	if (!dot && !(intpart && *spec->sep && *spec->grouping)) {
+		result->data = decstring;
+		result->nbytes = result->nchars = (mpd_ssize_t)strlen(decstring);
+		return;
+	}
+
+	/* Get the size of the new decimal string after inserting dot and
+	 * separators. */
+	_mpd_add_sep_dot(result, intpart, n_int, sign, dot, rest, spec);
+
+	if ((result->data = mpd_alloc(result->nbytes+1, 1)) == NULL) {
+		*status |= MPD_Malloc_error;
+		mpd_free(decstring);
+		return;
+	}
+
+	/* Perform actual writes. */
+	_mpd_add_sep_dot(result, intpart, n_int, sign, dot, rest, spec);
+
+	mpd_free(decstring);
+}
+
+/* Add padding to the formatted string if necessary. */
+static void
+_mpd_add_pad(mpd_mbstr_t *result, mpd_spec_t *spec, uint32_t *status)
+{
+	if (result->nchars < spec->min_width) {
+		mpd_ssize_t add_chars, add_bytes;
+		size_t lpad = 0, rpad = 0;
+		size_t n_fill, len, i, j;
+		uint8_t err = 0;
+		char *cp;
+
+		n_fill = strlen(spec->fill);
+		add_chars = (spec->min_width - result->nchars);
+		/* max value: MPD_MAX_PREC * 4 */
+		add_bytes = add_chars * (mpd_ssize_t)n_fill;
+
+		cp = result->data = mpd_realloc(result->data,
+		                                result->nbytes+add_bytes+1,
+		                                sizeof *result->data, &err);
+		if (err) {
+			*status |= MPD_Malloc_error;
+			mpd_free(result->data);
+			result->data = NULL;
+			return;
+		}
+
+		if (spec->align == 'z') {
+			spec->align = '=';
+		}
+
+		if (spec->align == '<') {
+			rpad = add_chars;
+		}
+		else if (spec->align == '>' || spec->align == '=') {
+			lpad = add_chars;
+		}
+		else { /* align == '^' */
+			lpad = add_chars/2;
+			rpad = add_chars-lpad;
+		}
+
+		len = result->nbytes;
+		if (spec->align == '=' && (*cp == '-' || *cp == '+' ||
+		                           *cp == ' ')) {
+			/* leave sign in the leading position */
+			cp++; len--;
+		}
+
+		memmove(cp+n_fill*lpad, cp, len);
+		for (i = 0; i < lpad; i++) {
+			for (j = 0; j < n_fill; j++) {
+				cp[i*n_fill+j] = spec->fill[j];
+			}
+		}
+		cp += (n_fill*lpad + len);
+		for (i = 0; i < rpad; i++) {
+			for (j = 0; j < n_fill; j++) {
+				cp[i*n_fill+j] = spec->fill[j];
+			}
+		}
+
+		result->nbytes += add_bytes;
+		result->nchars += add_chars;
+		result->data[result->nbytes] = '\0';
+	}
+}
+
+/*
+ * Return the string representation of an mpd_t, formatted according to 'spec'.
+ * 'spec' is modified. The format specification is assumed to be valid. Memory
+ * errors are indicated as usual. This function is quiet.
+ */
+char *
+mpd_qformat_spec(const mpd_t *dec, mpd_spec_t *spec, const mpd_context_t *ctx,
+                 uint32_t *status)
+{
+	mpd_context_t workctx;
+	mpd_uint_t dt[MPD_MINALLOC_MAX];
+	mpd_t tmp = {MPD_STATIC|MPD_STATIC_DATA,0,0,0,MPD_MINALLOC_MAX,dt};
+	mpd_ssize_t prec, fracdigits, exp;
+	mpd_ssize_t zeroexp = MPD_SSIZE_MAX;
+	mpd_mbstr_t result;
+	char *decstring;
+	int flags = 0;
+
+
+	if (spec->min_width > MPD_MAX_PREC) {
+		*status |= MPD_Invalid_operation;
+		return NULL;
+	}
+
+	if (!mpd_qcopy(&tmp, dec, status)) {
+		return NULL;
+	}
+
+	if (spec->type == '%') {
+		tmp.exp += 2;
+		spec->type = 'f';
+		flags |= MPD_FMT_PERCENT;
+	}
+
+	if (isupper((uchar)spec->type)) {
+		spec->type = tolower((uchar)spec->type);
+		flags |= MPD_FMT_UPPER;
+	}
+	if (spec->sign == ' ') {
+		flags |= MPD_FMT_SIGN_SPACE;
+	}
+	else if (spec->sign == '+') {
+		flags |= MPD_FMT_SIGN_PLUS;
+	}
+
+	mpd_maxcontext_plus(&workctx, ctx);
+	workctx.round = ctx->round;
+	if (mpd_isspecial(&tmp)) {
+		/* no percent formatting */
+		flags |= MPD_FMT_TOSCI;
+		if (spec->align == 'z') {
+			spec->fill[0] = ' ';
+			spec->fill[1] = '\0';
+			spec->align = '>';
+		}
+	}
+	else if (spec->type == 'g') {
+		/* spec->prec: significant digits */
+		prec = (spec->prec < 0) ? dec->digits : spec->prec;
+		workctx.prec = (prec == 0) ? 1 : prec;
+		flags |= MPD_FMT_TOSCI;
+		mpd_qfinalize(&tmp, &workctx, &workctx.status);
+	}
+	else {
+		/* spec->prec: fraction digits */
+		if (spec->type == 'e') {
+			fracdigits = (spec->prec < 0) ? tmp.digits-1 : spec->prec;
+			if (mpd_iszero(&tmp)) {
+				zeroexp = tmp.exp+fracdigits;
+				exp = -fracdigits;
+				flags |= MPD_FMT_FIXED;
+			}
+			else {
+				exp = tmp.exp + tmp.digits-(fracdigits+1);
+				flags |= MPD_FMT_EXP;
+			}
+		}
+		else { /* 'f' */
+			fracdigits = spec->prec;
+			if (fracdigits < 0) {
+				fracdigits = (tmp.exp < 0) ? -tmp.exp : 0;
+			}
+			exp = -fracdigits;
+			fracdigits += (tmp.exp+tmp.digits);
+			fracdigits = (fracdigits < 0) ? 0 : fracdigits;
+			flags |= MPD_FMT_FIXED;
+		}
+		workctx.prec = fracdigits+1;
+		mpd_qrescale(&tmp, &tmp, exp, &workctx, &workctx.status);
+		if (tmp.digits > workctx.prec) {
+			mpd_qfinalize(&tmp, &workctx, &workctx.status);
+		}
+	}
+
+	if ((decstring = _mpd_to_string(&tmp, flags, zeroexp)) == NULL) {
+		*status |= MPD_Malloc_error;
+		mpd_del(&tmp);
+		return NULL;
+	}
+
+	result.data = decstring;
+	result.nbytes = result.nchars = 0;
+	if (!mpd_isspecial(&tmp) && *spec->dot != '\0') {
+		result.data = NULL;
+		_mpd_apply_lconv(&result, decstring, spec, status);
+		if (result.data == NULL) {
+			goto finish;
+		}
+	}
+
+	if (spec->min_width) {
+		if (result.nbytes == 0) {
+			result.nbytes = result.nchars =
+			        (mpd_ssize_t)strlen(result.data);
+		}
+		_mpd_add_pad(&result, spec, status);
+	}
+
+
+finish:
+	mpd_del(&tmp);
+	return result.data;
+}
+
+char *
+mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx,
+            uint32_t *status)
+{
+	mpd_spec_t spec;
+
+	if (!mpd_parse_fmt_str(&spec, fmt, 1)) {
+		*status |= MPD_Invalid_operation;
+		return NULL;
+	}
+
+	return mpd_qformat_spec(dec, &spec, ctx, status);
+}
+
+/*
+ * The specification has a *condition* called Invalid_operation and an
+ * IEEE *signal* called Invalid_operation. The former corresponds to
+ * MPD_Invalid_operation, the latter to MPD_IEEE_Invalid_operation.
+ * MPD_IEEE_Invalid_operation comprises the following conditions:
+ *
+ * [MPD_Conversion_syntax, MPD_Division_impossible, MPD_Division_undefined,
+ *  MPD_Fpu_error, MPD_Invalid_context, MPD_Invalid_operation,
+ *  MPD_Malloc_error]
+ *
+ * In the following functions, 'flag' denotes the condition, 'signal'
+ * denotes the IEEE signal.
+ */
+
+static const char *mpd_flag_string[MPD_NUM_FLAGS] = {
+	"Clamped",
+	"Conversion_syntax",
+	"Division_by_zero",
+	"Division_impossible",
+	"Division_undefined",
+	"Fpu_error",
+	"Inexact",
+	"Invalid_context",
+	"Invalid_operation",
+	"Malloc_error",
+	"Not_implemented",
+	"Overflow",
+	"Rounded",
+	"Subnormal",
+	"Underflow",
+};
+
+static const char *mpd_signal_string[MPD_NUM_FLAGS] = {
+	"Clamped",
+	"IEEE_Invalid_operation",
+	"Division_by_zero",
+	"IEEE_Invalid_operation",
+	"IEEE_Invalid_operation",
+	"IEEE_Invalid_operation",
+	"Inexact",
+	"IEEE_Invalid_operation",
+	"IEEE_Invalid_operation",
+	"IEEE_Invalid_operation",
+	"Not_implemented",
+	"Overflow",
+	"Rounded",
+	"Subnormal",
+	"Underflow",
+};
+
+/* print conditions to buffer, separated by spaces */
+int
+mpd_snprint_flags(char *dest, int nmemb, uint32_t flags)
+{
+	char *cp;
+	int n, j;
+
+	assert(nmemb >= MPD_MAX_FLAG_STRING);
+
+	*dest = '\0'; cp = dest;
+	for (j = 0; j < MPD_NUM_FLAGS; j++) {
+		if (flags & (1U<<j)) {
+			n = snprintf(cp, nmemb, "%s ", mpd_flag_string[j]);
+			if (n < 0 || n >= nmemb) return -1;
+			cp += n; nmemb -= n;
+		}
+	}
+
+	if (cp != dest) {
+		*(--cp) = '\0';
+	}
+
+	return (int)(cp-dest);
+}
+
+/* print conditions to buffer, in list form */
+int
+mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[])
+{
+	char *cp;
+	int n, j;
+
+	assert(nmemb >= MPD_MAX_FLAG_LIST);
+	if (flag_string == NULL) {
+		flag_string = mpd_flag_string;
+	}
+
+	*dest = '[';
+	*(dest+1) = '\0';
+	cp = dest+1;
+	--nmemb;
+
+	for (j = 0; j < MPD_NUM_FLAGS; j++) {
+		if (flags & (1U<<j)) {
+			n = snprintf(cp, nmemb, "%s, ", flag_string[j]);
+			if (n < 0 || n >= nmemb) return -1;
+			cp += n; nmemb -= n;
+		}
+	}
+
+	/* erase the last ", " */
+	if (cp != dest+1) {
+		cp -= 2;
+	}
+
+	*cp++ = ']';
+	*cp = '\0';
+
+	return (int)(cp-dest); /* strlen, without NUL terminator */
+}
+
+/* print signals to buffer, in list form */
+int
+mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[])
+{
+	char *cp;
+	int n, j;
+	int ieee_invalid_done = 0;
+
+	assert(nmemb >= MPD_MAX_SIGNAL_LIST);
+	if (signal_string == NULL) {
+		signal_string = mpd_signal_string;
+	}
+
+	*dest = '[';
+	*(dest+1) = '\0';
+	cp = dest+1;
+	--nmemb;
+
+	for (j = 0; j < MPD_NUM_FLAGS; j++) {
+		uint32_t f = flags & (1U<<j);
+		if (f) {
+			if (f&MPD_IEEE_Invalid_operation) {
+				if (ieee_invalid_done) {
+					continue;
+				}
+				ieee_invalid_done = 1;
+			}
+			n = snprintf(cp, nmemb, "%s, ", signal_string[j]);
+			if (n < 0 || n >= nmemb) return -1;
+			cp += n; nmemb -= n;
+		}
+	}
+
+	/* erase the last ", " */
+	if (cp != dest+1) {
+		cp -= 2;
+	}
+
+	*cp++ = ']';
+	*cp = '\0';
+
+	return (int)(cp-dest); /* strlen, without NUL terminator */
+}
+
+/* The following two functions are mainly intended for debugging. */
+void
+mpd_fprint(FILE *file, const mpd_t *dec)
+{
+	char *decstring;
+
+	decstring = mpd_to_sci(dec, 1);
+	if (decstring != NULL) {
+		fprintf(file, "%s\n", decstring);
+		mpd_free(decstring);
+	}
+	else {
+		fputs("mpd_fprint: output error\n", file); /* GCOV_NOT_REACHED */
+	}
+}
+
+void
+mpd_print(const mpd_t *dec)
+{
+	char *decstring;
+
+	decstring = mpd_to_sci(dec, 1);
+	if (decstring != NULL) {
+		printf("%s\n", decstring);
+		mpd_free(decstring);
+	}
+	else {
+		fputs("mpd_fprint: output error\n", stderr); /* GCOV_NOT_REACHED */
+	}
+}
+
+

ext/mpdecimal/io.h

@@ -0,0 +1,59 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef IO_H
+#define IO_H
+
+
+#include <errno.h>
+#include "mpdecimal.h"
+
+
+#if SIZE_MAX == MPD_SIZE_MAX
+  #define mpd_strtossize _mpd_strtossize
+#else
+static inline mpd_ssize_t
+mpd_strtossize(const char *s, char **end, int base)
+{
+	int64_t retval;
+
+	errno = 0;
+	retval = _mpd_strtossize(s, end, base);
+	if (errno == 0 && (retval > MPD_SSIZE_MAX || retval < MPD_SSIZE_MIN)) {
+		errno = ERANGE;
+	}
+	if (errno == ERANGE) {
+		return (retval < 0) ? MPD_SSIZE_MIN : MPD_SSIZE_MAX;
+	}
+
+	return (mpd_ssize_t)retval;
+}
+#endif
+
+
+#endif

ext/mpdecimal/memory.c

@@ -0,0 +1,239 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "typearith.h"
+#include "memory.h"
+
+
+mpd_ssize_t MPD_MINALLOC = MPD_MINALLOC_MIN;
+
+void *(* mpd_mallocfunc)(size_t size) = malloc;
+void *(* mpd_reallocfunc)(void *ptr, size_t size) = realloc;
+void *(* mpd_callocfunc)(size_t nmemb, size_t size) = calloc;
+void (* mpd_free)(void *ptr) = free;
+
+
+
+/* emulate calloc if it is not available */
+void *
+mpd_callocfunc_em(size_t nmemb, size_t size)
+{
+	void *ptr;
+	size_t req;
+
+#if MPD_SIZE_MAX < SIZE_MAX
+	if (nmemb > MPD_SIZE_MAX || size > MPD_SIZE_MAX) {
+		return NULL;
+	}
+#endif
+	req = mul_size_t((mpd_size_t)nmemb, (mpd_size_t)size);
+	if ((ptr = mpd_mallocfunc(req)) == NULL) {
+		return NULL;
+	}
+	/* used on uint32_t or uint64_t */
+	memset(ptr, 0, req);
+
+	return ptr;
+}
+
+
+/* malloc with overflow checking */
+void *
+mpd_alloc(mpd_size_t nmemb, mpd_size_t size)
+{
+	void *ptr;
+	mpd_size_t req;
+
+	req = mul_size_t(nmemb, size);
+	if ((ptr = mpd_mallocfunc(req)) == NULL) {
+		return NULL;
+	}
+
+	return ptr;
+}
+
+/* calloc with overflow checking */
+void *
+mpd_calloc(mpd_size_t nmemb, mpd_size_t size)
+{
+	void *ptr;
+
+	if ((ptr = mpd_callocfunc(nmemb, size)) == NULL) {
+		return NULL;
+	}
+
+	return ptr;
+}
+
+/* realloc with overflow checking */
+void *
+mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err)
+{
+	void *new;
+	mpd_size_t req;
+
+	req = mul_size_t(nmemb, size);
+	if ((new = mpd_reallocfunc(ptr, req)) == NULL) {
+		*err = 1;
+		return ptr;
+	}
+
+	return new;
+}
+
+/* struct hack malloc with overflow checking */
+void *
+mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size)
+{
+	void *ptr;
+	mpd_size_t req;
+
+	req = mul_size_t(nmemb, size);
+	req = add_size_t(req, struct_size);
+	if ((ptr = mpd_mallocfunc(req)) == NULL) {
+		return NULL;
+	}
+
+	return ptr;
+}
+
+
+/* Allocate a new decimal with data-size 'size'.
+ * In case of an error the return value is NULL.
+ */
+mpd_t *
+mpd_qnew_size(mpd_ssize_t size)
+{
+	mpd_t *result;
+
+	size = (size < MPD_MINALLOC) ? MPD_MINALLOC : size;
+
+	if ((result = mpd_alloc(1, sizeof *result)) == NULL) {
+		return NULL;
+	}
+	if ((result->data = mpd_alloc(size, sizeof *result->data)) == NULL) {
+		mpd_free(result);
+		return NULL;
+	}
+
+	result->flags = 0;
+	result->exp = 0;
+	result->digits = 0;
+	result->len = 0;
+	result->alloc = size;
+
+	return result;
+}
+
+/* Allocate a new decimal with data-size MPD_MINALLOC.
+ * In case of an error the return value is NULL.
+ */
+mpd_t *
+mpd_qnew(void)
+{
+	return mpd_qnew_size(MPD_MINALLOC);
+}
+
+/* Allocate new decimal. Caller can check for NULL or MPD_Malloc_error.
+ * Raises on error.
+ */
+mpd_t *
+mpd_new(mpd_context_t *ctx)
+{
+	mpd_t *result;
+
+	if ((result = mpd_qnew()) == NULL) {
+		mpd_addstatus_raise(ctx, MPD_Malloc_error);
+	}
+	return result;
+}
+
+int
+mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+	mpd_uint_t *p = result->data;
+
+	if ((result->data = mpd_alloc(size, sizeof *result->data)) == NULL) {
+		result->data = p;
+		mpd_set_qnan(result);
+		mpd_set_positive(result);
+		result->exp = result->digits = result->len = 0;
+		*status |= MPD_Malloc_error;
+		return 0;
+	}
+
+	memcpy(result->data, p, result->len * (sizeof *result->data));
+	result->alloc = size;
+	mpd_set_dynamic_data(result);
+	return 1;
+}
+
+int
+mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+	mpd_uint_t *p = result->data;
+
+	if ((result->data = mpd_calloc(size, sizeof *result->data)) == NULL) {
+		result->data = p;
+		mpd_set_qnan(result);
+		mpd_set_positive(result);
+		result->exp = result->digits = result->len = 0;
+		*status |= MPD_Malloc_error;
+		return 0;
+	}
+
+	result->alloc = size;
+	mpd_set_dynamic_data(result);
+
+	return 1;
+}
+
+int
+mpd_realloc_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+	uint8_t err = 0;
+
+	result->data = mpd_realloc(result->data, size, sizeof *result->data, &err);
+	if (!err) {
+		result->alloc = size;
+	}
+	else if (size > result->alloc) {
+		mpd_set_qnan(result);
+		mpd_set_positive(result);
+		result->exp = result->digits = result->len = 0;
+		*status |= MPD_Malloc_error;
+		return 0;
+	}
+
+	return 1;
+}
+
+

ext/mpdecimal/memory.h

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MEMORY_H
+#define MEMORY_H
+
+
+#include "mpdecimal.h"
+
+
+int mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+int mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+int mpd_realloc_dyn(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+
+
+#endif
+
+
+

ext/mpdecimal/mpdecimal.c

@@ -0,0 +1,7935 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <math.h>
+#include "basearith.h"
+#include "bits.h"
+#include "convolute.h"
+#include "crt.h"
+#include "errno.h"
+#include "memory.h"
+#include "typearith.h"
+#include "umodarith.h"
+#include "mptest.h"
+#include "mptypes.h"
+
+#ifdef PPRO
+  #if defined(_MSC_VER)
+    #include <float.h>
+    #pragma fenv_access(on)
+  #elif !defined(__OpenBSD__) && !defined(__NetBSD__)
+    /* C99 */
+    #include <fenv.h>
+    #pragma STDC FENV_ACCESS ON
+  #endif
+#endif
+
+#if defined(__x86_64__) && defined(__GLIBC__) && !defined(__INTEL_COMPILER)
+  #define USE_80BIT_LONG_DOUBLE
+#endif
+
+#if defined(_MSC_VER)
+  #define ALWAYS_INLINE __forceinline
+#elif defined(LEGACY_COMPILER)
+  #define ALWAYS_INLINE
+  #undef inline
+  #define inline
+#else
+  #ifdef TEST_COVERAGE
+    #define ALWAYS_INLINE
+  #else
+    #define ALWAYS_INLINE inline __attribute__ ((always_inline))
+  #endif
+#endif
+
+
+#define MPD_NEWTONDIV_CUTOFF 1024L
+
+#define MPD_NEW_STATIC(name, flags, exp, digits, len) \
+        mpd_uint_t name##_data[MPD_MINALLOC_MAX];                    \
+        mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \
+                      len, MPD_MINALLOC_MAX, name##_data}
+
+#define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \
+        mpd_uint_t name##_data[alloc] = {initval};                   \
+        mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits,  \
+                      len, alloc, name##_data}
+
+#define MPD_NEW_SHARED(name, a) \
+        mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \
+                      a->exp, a->digits, a->len, a->alloc, a->data}
+
+
+static mpd_uint_t data_one[1] = {1};
+static mpd_uint_t data_zero[1] = {0};
+static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one};
+static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1,
+                                data_one};
+static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero};
+
+static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx,
+                                  uint32_t *status);
+static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a,
+                       mpd_ssize_t exp);
+static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size);
+
+static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+                      const mpd_context_t *ctx, uint32_t *status);
+static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+                             const mpd_context_t *ctx, uint32_t *status);
+static void _mpd_qbarrett_divmod(mpd_t *q, mpd_t *r, const mpd_t *a,
+                                 const mpd_t *b, uint32_t *status);
+static inline void _mpd_qpow_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp,
+                uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status);
+
+mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n);
+
+
+/******************************************************************************/
+/*                  Performance critical inline functions                     */
+/******************************************************************************/
+
+#ifdef CONFIG_64
+/* Digits in a word, primarily useful for the most significant word. */
+ALWAYS_INLINE int
+mpd_word_digits(mpd_uint_t word)
+{
+	if (word < mpd_pow10[9]) {
+		if (word < mpd_pow10[4]) {
+			if (word < mpd_pow10[2]) {
+				return (word < mpd_pow10[1]) ? 1 : 2;
+			}
+			return (word < mpd_pow10[3]) ? 3 : 4;
+		}
+		if (word < mpd_pow10[6]) {
+			return (word < mpd_pow10[5]) ? 5 : 6;
+		}
+		if (word < mpd_pow10[8]) {
+			return (word < mpd_pow10[7]) ? 7 : 8;
+		}
+		return 9;
+	}
+	if (word < mpd_pow10[14]) {
+		if (word < mpd_pow10[11]) {
+			return (word < mpd_pow10[10]) ? 10 : 11;
+		}
+		if (word < mpd_pow10[13]) {
+			return (word < mpd_pow10[12]) ? 12 : 13;
+		}
+		return 14;
+	}
+	if (word < mpd_pow10[17]) {
+		if (word < mpd_pow10[16]) {
+			return (word < mpd_pow10[15]) ? 15 : 16;
+		}
+		return 17;
+	}
+
+	return (word < mpd_pow10[18]) ? 18 : 19;
+}
+#else
+ALWAYS_INLINE int
+mpd_word_digits(mpd_uint_t word)
+{
+	if (word < mpd_pow10[4]) {
+		if (word < mpd_pow10[2]) {
+			return (word < mpd_pow10[1]) ? 1 : 2;
+		}
+		return (word < mpd_pow10[3]) ? 3 : 4;
+	}
+	if (word < mpd_pow10[6]) {
+		return (word < mpd_pow10[5]) ? 5 : 6;
+	}
+	if (word < mpd_pow10[8]) {
+		return (word < mpd_pow10[7]) ? 7 : 8;
+	}
+
+	return (word < mpd_pow10[9]) ? 9 : 10;
+}
+#endif
+
+
+/* Adjusted exponent */
+ALWAYS_INLINE mpd_ssize_t
+mpd_adjexp(const mpd_t *dec)
+{
+	return (dec->exp + dec->digits) - 1;
+}
+
+/* Etiny */
+ALWAYS_INLINE mpd_ssize_t
+mpd_etiny(const mpd_context_t *ctx)
+{
+	return ctx->emin - (ctx->prec - 1);
+}
+
+/* Etop: used for folding down in IEEE clamping */
+ALWAYS_INLINE mpd_ssize_t
+mpd_etop(const mpd_context_t *ctx)
+{
+	return ctx->emax - (ctx->prec - 1);
+}
+
+/* Most significant word */
+ALWAYS_INLINE mpd_uint_t
+mpd_msword(const mpd_t *dec)
+{
+	assert(dec->len > 0);
+	return dec->data[dec->len-1];
+}
+
+/* Most significant digit of a word */
+inline mpd_uint_t
+mpd_msd(mpd_uint_t word)
+{
+	int n;
+
+	n = mpd_word_digits(word);
+	return word / mpd_pow10[n-1];
+}
+
+/* Least significant digit of a word */
+ALWAYS_INLINE mpd_uint_t
+mpd_lsd(mpd_uint_t word)
+{
+	return word % 10;
+}
+
+/* Coefficient size needed to store 'digits' */
+ALWAYS_INLINE mpd_ssize_t
+mpd_digits_to_size(mpd_ssize_t digits)
+{
+	mpd_ssize_t q, r;
+
+	_mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
+	return (r == 0) ? q : q+1;
+}
+
+/* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */
+inline int
+mpd_exp_digits(mpd_ssize_t exp)
+{
+	exp = (exp < 0) ? -exp : exp;
+	return mpd_word_digits(exp);
+}
+
+/* Canonical */
+ALWAYS_INLINE int
+mpd_iscanonical(const mpd_t *dec UNUSED)
+{
+	return 1;
+}
+
+/* Finite */
+ALWAYS_INLINE int
+mpd_isfinite(const mpd_t *dec)
+{
+	return !(dec->flags & MPD_SPECIAL);
+}
+
+/* Infinite */
+ALWAYS_INLINE int
+mpd_isinfinite(const mpd_t *dec)
+{
+	return dec->flags & MPD_INF;
+}
+
+/* NaN */
+ALWAYS_INLINE int
+mpd_isnan(const mpd_t *dec)
+{
+	return dec->flags & (MPD_NAN|MPD_SNAN);
+}
+
+/* Negative */
+ALWAYS_INLINE int
+mpd_isnegative(const mpd_t *dec)
+{
+	return dec->flags & MPD_NEG;
+}
+
+/* Positive */
+ALWAYS_INLINE int
+mpd_ispositive(const mpd_t *dec)
+{
+	return !(dec->flags & MPD_NEG);
+}
+
+/* qNaN */
+ALWAYS_INLINE int
+mpd_isqnan(const mpd_t *dec)
+{
+	return dec->flags & MPD_NAN;
+}
+
+/* Signed */
+ALWAYS_INLINE int
+mpd_issigned(const mpd_t *dec)
+{
+	return dec->flags & MPD_NEG;
+}
+
+/* sNaN */
+ALWAYS_INLINE int
+mpd_issnan(const mpd_t *dec)
+{
+	return dec->flags & MPD_SNAN;
+}
+
+/* Special */
+ALWAYS_INLINE int
+mpd_isspecial(const mpd_t *dec)
+{
+	return dec->flags & MPD_SPECIAL;
+}
+
+/* Zero */
+ALWAYS_INLINE int
+mpd_iszero(const mpd_t *dec)
+{
+	return !mpd_isspecial(dec) && mpd_msword(dec) == 0;
+}
+
+/* Test for zero when specials have been ruled out already */
+ALWAYS_INLINE int
+mpd_iszerocoeff(const mpd_t *dec)
+{
+	return mpd_msword(dec) == 0;
+}
+
+/* Normal */
+inline int
+mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx)
+{
+	if (mpd_isspecial(dec)) return 0;
+	if (mpd_iszerocoeff(dec)) return 0;
+
+	return mpd_adjexp(dec) >= ctx->emin;
+}
+
+/* Subnormal */
+inline int
+mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx)
+{
+	if (mpd_isspecial(dec)) return 0;
+	if (mpd_iszerocoeff(dec)) return 0;
+
+	return mpd_adjexp(dec) < ctx->emin;
+}
+
+/* Odd word */
+ALWAYS_INLINE int
+mpd_isoddword(mpd_uint_t word)
+{
+	return word & 1;
+}
+
+/* Odd coefficient */
+ALWAYS_INLINE int
+mpd_isoddcoeff(const mpd_t *dec)
+{
+	return mpd_isoddword(dec->data[0]);
+}
+
+/* 0 if dec is positive, 1 if dec is negative */
+ALWAYS_INLINE uint8_t
+mpd_sign(const mpd_t *dec)
+{
+	return dec->flags & MPD_NEG;
+}
+
+/* 1 if dec is positive, -1 if dec is negative */
+ALWAYS_INLINE int
+mpd_arith_sign(const mpd_t *dec)
+{
+	return 1 - 2 * mpd_isnegative(dec);
+}
+
+/* Radix */
+ALWAYS_INLINE long
+mpd_radix(void)
+{
+	return 10;
+}
+
+/* Dynamic decimal */
+ALWAYS_INLINE int
+mpd_isdynamic(mpd_t *dec)
+{
+	return !(dec->flags & MPD_STATIC);
+}
+
+/* Static decimal */
+ALWAYS_INLINE int
+mpd_isstatic(mpd_t *dec)
+{
+	return dec->flags & MPD_STATIC;
+}
+
+/* Data of decimal is dynamic */
+ALWAYS_INLINE int
+mpd_isdynamic_data(mpd_t *dec)
+{
+	return !(dec->flags & MPD_DATAFLAGS);
+}
+
+/* Data of decimal is static */
+ALWAYS_INLINE int
+mpd_isstatic_data(mpd_t *dec)
+{
+	return dec->flags & MPD_STATIC_DATA;
+}
+
+/* Data of decimal is shared */
+ALWAYS_INLINE int
+mpd_isshared_data(mpd_t *dec)
+{
+	return dec->flags & MPD_SHARED_DATA;
+}
+
+/* Data of decimal is const */
+ALWAYS_INLINE int
+mpd_isconst_data(mpd_t *dec)
+{
+	return dec->flags & MPD_CONST_DATA;
+}
+
+
+/******************************************************************************/
+/*                         Inline memory handling                             */
+/******************************************************************************/
+
+/* Fill destination with zeros */
+ALWAYS_INLINE void
+mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len)
+{
+	mpd_size_t i;
+
+	for (i = 0; i < len; i++) {
+		dest[i] = 0;
+	}
+}
+
+/* Free a decimal */
+ALWAYS_INLINE void
+mpd_del(mpd_t *dec)
+{
+	if (mpd_isdynamic_data(dec)) {
+		mpd_free(dec->data);
+	}
+	if (mpd_isdynamic(dec)) {
+		mpd_free(dec);
+	}
+}
+
+/*
+ * Update the memory size for the coefficient. Existing data up to size is
+ * left untouched.
+ *
+ * Error handling: When relloc fails, result->data will still be a valid pointer
+ * to the old memory area of size result->len. If the requested size is less than
+ * result->len, we can continue normally, so we treat the failure as a soft error.
+ * If the requested size is greater than the old area, MPD_Malloc_error is
+ * set and the result will be a NaN.
+ */
+ALWAYS_INLINE int
+mpd_qresize(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+	assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+	assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+	if (mpd_isstatic_data(result)) {
+		if (size > result->alloc) {
+			return mpd_switch_to_dyn(result, size, status);
+		}
+	}
+	else if (size != result->alloc && size >= MPD_MINALLOC) {
+		return mpd_realloc_dyn(result, size, status);
+	}
+
+	return 1;
+}
+
+/* Same as mpd_qresize, but the complete coefficient (including the old
+ * memory area!) is initialized to zero. */
+ALWAYS_INLINE int
+mpd_qresize_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+	assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+	assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+	if (mpd_isstatic_data(result)) {
+		if (size > result->alloc) {
+			return mpd_switch_to_dyn_zero(result, size, status);
+		}
+	}
+	else if (size != result->alloc && size >= MPD_MINALLOC) {
+		if (!mpd_realloc_dyn(result, size, status)) {
+			return 0;
+		}
+	}
+
+	mpd_uint_zero(result->data, size);
+
+	return 1;
+}
+
+/*
+ * Reduce memory size for the coefficient to MPD_MINALLOC. In theory,
+ * realloc may fail even when reducing the memory size. But in that case
+ * the old memory area is always big enough, so checking for MPD_Malloc_error
+ * is not imperative.
+ */
+ALWAYS_INLINE void
+mpd_minalloc(mpd_t *result)
+{
+	assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+	assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+	if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) {
+		uint8_t err = 0;
+		result->data = mpd_realloc(result->data, MPD_MINALLOC,
+		                           sizeof *result->data, &err);
+		if (!err) {
+			result->alloc = MPD_MINALLOC;
+		}
+	}
+}
+
+int
+mpd_resize(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qresize(result, size, &status)) {
+		mpd_addstatus_raise(ctx, status);
+		return 0;
+	}
+	return 1;
+}
+
+int
+mpd_resize_zero(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qresize_zero(result, size, &status)) {
+		mpd_addstatus_raise(ctx, status);
+		return 0;
+	}
+	return 1;
+}
+
+
+/******************************************************************************/
+/*                       Set attributes of a decimal                          */
+/******************************************************************************/
+
+/* Set digits. result->len is assumed to be correct. */
+inline void
+mpd_setdigits(mpd_t *result)
+{
+	mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result));
+	result->digits = wdigits + (result->len-1) * MPD_RDIGITS;
+}
+
+/* Set sign */
+ALWAYS_INLINE void
+mpd_set_sign(mpd_t *result, uint8_t sign)
+{
+	result->flags &= ~MPD_NEG;
+	result->flags |= sign;
+}
+
+/* Copy sign from another decimal */
+ALWAYS_INLINE void
+mpd_signcpy(mpd_t *result, mpd_t *a)
+{
+	uint8_t sign = a->flags&MPD_NEG;
+
+	result->flags &= ~MPD_NEG;
+	result->flags |= sign;
+}
+
+/* Set infinity */
+ALWAYS_INLINE void
+mpd_set_infinity(mpd_t *result)
+{
+	result->flags &= ~MPD_SPECIAL;
+	result->flags |= MPD_INF;
+}
+
+/* Set qNaN */
+ALWAYS_INLINE void
+mpd_set_qnan(mpd_t *result)
+{
+	result->flags &= ~MPD_SPECIAL;
+	result->flags |= MPD_NAN;
+}
+
+/* Set sNaN */
+ALWAYS_INLINE void
+mpd_set_snan(mpd_t *result)
+{
+	result->flags &= ~MPD_SPECIAL;
+	result->flags |= MPD_SNAN;
+}
+
+/* Set to negative */
+ALWAYS_INLINE void
+mpd_set_negative(mpd_t *result)
+{
+	result->flags |= MPD_NEG;
+}
+
+/* Set to positive */
+ALWAYS_INLINE void
+mpd_set_positive(mpd_t *result)
+{
+	result->flags &= ~MPD_NEG;
+}
+
+/* Set to dynamic */
+ALWAYS_INLINE void
+mpd_set_dynamic(mpd_t *result)
+{
+	result->flags &= ~MPD_STATIC;
+}
+
+/* Set to static */
+ALWAYS_INLINE void
+mpd_set_static(mpd_t *result)
+{
+	result->flags |= MPD_STATIC;
+}
+
+/* Set data to dynamic */
+ALWAYS_INLINE void
+mpd_set_dynamic_data(mpd_t *result)
+{
+	result->flags &= ~MPD_DATAFLAGS;
+}
+
+/* Set data to static */
+ALWAYS_INLINE void
+mpd_set_static_data(mpd_t *result)
+{
+	result->flags &= ~MPD_DATAFLAGS;
+	result->flags |= MPD_STATIC_DATA;
+}
+
+/* Set data to shared */
+ALWAYS_INLINE void
+mpd_set_shared_data(mpd_t *result)
+{
+	result->flags &= ~MPD_DATAFLAGS;
+	result->flags |= MPD_SHARED_DATA;
+}
+
+/* Set data to const */
+ALWAYS_INLINE void
+mpd_set_const_data(mpd_t *result)
+{
+	result->flags &= ~MPD_DATAFLAGS;
+	result->flags |= MPD_CONST_DATA;
+}
+
+/* Clear flags, preserving memory attributes. */
+ALWAYS_INLINE void
+mpd_clear_flags(mpd_t *result)
+{
+	result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+}
+
+/* Set flags, preserving memory attributes. */
+ALWAYS_INLINE void
+mpd_set_flags(mpd_t *result, uint8_t flags)
+{
+	result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+	result->flags |= flags;
+}
+
+/* Copy flags, preserving memory attributes of result. */
+ALWAYS_INLINE void
+mpd_copy_flags(mpd_t *result, const mpd_t *a)
+{
+	uint8_t aflags = a->flags;
+	result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+	result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS));
+}
+
+/* Make a work context */
+static inline void
+mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx)
+{
+	workctx->prec = ctx->prec;
+	workctx->emax = ctx->emax;
+	workctx->emin = ctx->emin;
+	workctx->round = ctx->round;
+	workctx->traps = 0;
+	workctx->status= 0;
+	workctx->newtrap= 0;
+	workctx->clamp = ctx->clamp;
+	workctx->allcr = ctx->allcr;
+}
+
+
+/******************************************************************************/
+/*                  Getting and setting parts of decimals                     */
+/******************************************************************************/
+
+/* Flip the sign of a decimal */
+static inline void
+_mpd_negate(mpd_t *dec)
+{
+	dec->flags ^= MPD_NEG;
+}
+
+/* Set coefficient to zero */
+void
+mpd_zerocoeff(mpd_t *result)
+{
+	mpd_minalloc(result);
+	result->digits = 1;
+	result->len = 1;
+	result->data[0] = 0;
+}
+
+/* Set the coefficient to all nines. */
+void
+mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_ssize_t len, r;
+
+	_mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
+	len = (r == 0) ? len : len+1;
+
+	if (!mpd_qresize(result, len, status)) {
+		return;
+	}
+
+	result->len = len;
+	result->digits = ctx->prec;
+
+	--len;
+	if (r > 0) {
+		result->data[len--] = mpd_pow10[r]-1;
+	}
+	for (; len >= 0; --len) {
+		result->data[len] = MPD_RADIX-1;
+	}
+}
+
+/*
+ * Cut off the most significant digits so that the rest fits in ctx->prec.
+ * Cannot fail.
+ */
+static void
+_mpd_cap(mpd_t *result, const mpd_context_t *ctx)
+{
+	uint32_t dummy;
+	mpd_ssize_t len, r;
+
+	if (result->len > 0 && result->digits > ctx->prec) {
+		_mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
+		len = (r == 0) ? len : len+1;
+
+		if (r != 0) {
+			result->data[len-1] %= mpd_pow10[r];
+		}
+
+		len = _mpd_real_size(result->data, len);
+		/* resize to fewer words cannot fail */
+		mpd_qresize(result, len, &dummy);
+		result->len = len;
+		mpd_setdigits(result);
+	}
+	if (mpd_iszero(result)) {
+		_settriple(result, mpd_sign(result), 0, result->exp);
+	}
+}
+
+/*
+ * Cut off the most significant digits of a NaN payload so that the rest
+ * fits in ctx->prec - ctx->clamp. Cannot fail.
+ */
+static void
+_mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx)
+{
+	uint32_t dummy;
+	mpd_ssize_t prec;
+	mpd_ssize_t len, r;
+
+	prec = ctx->prec - ctx->clamp;
+	if (result->len > 0 && result->digits > prec) {
+		if (prec == 0) {
+			mpd_minalloc(result);
+			result->len = result->digits = 0;
+		}
+		else {
+			_mpd_idiv_word(&len, &r, prec, MPD_RDIGITS);
+			len = (r == 0) ? len : len+1;
+
+			if (r != 0) {
+				 result->data[len-1] %= mpd_pow10[r];
+			}
+
+			len = _mpd_real_size(result->data, len);
+			/* resize to fewer words cannot fail */
+			mpd_qresize(result, len, &dummy);
+			result->len = len;
+			mpd_setdigits(result);
+			if (mpd_iszerocoeff(result)) {
+				/* NaN0 is not a valid representation */
+				result->len = result->digits = 0;
+			}
+		}
+	}
+}
+
+/*
+ * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS.
+ * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit
+ * machines.
+ *
+ * The result of the operation will be in lo. If the operation is impossible,
+ * hi will be nonzero. This is used to indicate an error.
+ */
+static inline void
+_mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec,
+                  unsigned int n)
+{
+	mpd_uint_t r, tmp;
+
+	assert(0 < n && n <= MPD_RDIGITS+1);
+
+	_mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS);
+	r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */
+
+	*hi = 0;
+	*lo = dec->data[dec->len-1];
+	if (n <= r) {
+		*lo /= mpd_pow10[r-n];
+	}
+	else if (dec->len > 1) {
+		/* at this point 1 <= r < n <= MPD_RDIGITS+1 */
+		_mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]);
+		tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)];
+		*lo = *lo + tmp;
+		if (*lo < tmp) (*hi)++;
+	}
+}
+
+
+/******************************************************************************/
+/*                   Gathering information about a decimal                    */
+/******************************************************************************/
+
+/* The real size of the coefficient without leading zero words. */
+static inline mpd_ssize_t
+_mpd_real_size(mpd_uint_t *data, mpd_ssize_t size)
+{
+	while (size > 1 && data[size-1] == 0) {
+		size--;
+	}
+
+	return size;
+}
+
+/* Return number of trailing zeros. No errors are possible. */
+mpd_ssize_t
+mpd_trail_zeros(const mpd_t *dec)
+{
+	mpd_uint_t word;
+	mpd_ssize_t i, tz = 0;
+
+	for (i=0; i < dec->len; ++i) {
+		if (dec->data[i] != 0) {
+			word = dec->data[i];
+			tz = i * MPD_RDIGITS;
+			while (word % 10 == 0) {
+				word /= 10;
+				tz++;
+			}
+			break;
+		}
+	}
+
+	return tz;
+}
+
+/* Integer: Undefined for specials */
+static int
+_mpd_isint(const mpd_t *dec)
+{
+	mpd_ssize_t tz;
+
+	if (mpd_iszerocoeff(dec)) {
+		return 1;
+	}
+
+	tz = mpd_trail_zeros(dec);
+	return (dec->exp + tz >= 0);
+}
+
+/* Integer */
+int
+mpd_isinteger(const mpd_t *dec)
+{
+	if (mpd_isspecial(dec)) {
+		return 0;
+	}
+	return _mpd_isint(dec);
+}
+
+/* Word is a power of 10 */
+static int
+mpd_word_ispow10(mpd_uint_t word)
+{
+	int n;
+
+	n = mpd_word_digits(word);
+	if (word == mpd_pow10[n-1]) {
+		return 1;
+	}
+
+	return 0;
+}
+
+/* Coefficient is a power of 10 */
+static int
+mpd_coeff_ispow10(const mpd_t *dec)
+{
+	if (mpd_word_ispow10(mpd_msword(dec))) {
+		if (_mpd_isallzero(dec->data, dec->len-1)) {
+			return 1;
+		}
+	}
+
+	return 0;
+}
+
+/* All digits of a word are nines */
+static int
+mpd_word_isallnine(mpd_uint_t word)
+{
+	int n;
+
+	n = mpd_word_digits(word);
+	if (word == mpd_pow10[n]-1) {
+		return 1;
+	}
+
+	return 0;
+}
+
+/* All digits of the coefficient are nines */
+static int
+mpd_coeff_isallnine(const mpd_t *dec)
+{
+	if (mpd_word_isallnine(mpd_msword(dec))) {
+		if (_mpd_isallnine(dec->data, dec->len-1)) {
+			return 1;
+		}
+	}
+
+	return 0;
+}
+
+/* Odd decimal: Undefined for non-integers! */
+int
+mpd_isodd(const mpd_t *dec)
+{
+	mpd_uint_t q, r;
+	assert(mpd_isinteger(dec));
+	if (mpd_iszerocoeff(dec)) return 0;
+	if (dec->exp < 0) {
+		_mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS);
+		q = dec->data[q] / mpd_pow10[r];
+		return mpd_isoddword(q);
+	}
+	return dec->exp == 0 && mpd_isoddword(dec->data[0]);
+}
+
+/* Even: Undefined for non-integers! */
+int
+mpd_iseven(const mpd_t *dec)
+{
+	return !mpd_isodd(dec);
+}
+
+/******************************************************************************/
+/*                      Getting and setting decimals                          */
+/******************************************************************************/
+
+/* Internal function: Set a static decimal from a triple, no error checking. */
+static void
+_ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
+{
+	mpd_set_flags(result, sign);
+	result->exp = exp;
+	_mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
+	result->len = (result->data[1] == 0) ? 1 : 2;
+	mpd_setdigits(result);
+}
+
+/* Internal function: Set a decimal from a triple, no error checking. */
+static void
+_settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
+{
+	mpd_minalloc(result);
+	mpd_set_flags(result, sign);
+	result->exp = exp;
+	_mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
+	result->len = (result->data[1] == 0) ? 1 : 2;
+	mpd_setdigits(result);
+}
+
+/* Set a special number from a triple */
+void
+mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type)
+{
+	mpd_minalloc(result);
+	result->flags &= ~(MPD_NEG|MPD_SPECIAL);
+	result->flags |= (sign|type);
+	result->exp = result->digits = result->len = 0;
+}
+
+/* Set result of NaN with an error status */
+void
+mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status)
+{
+	mpd_minalloc(result);
+	mpd_set_qnan(result);
+	mpd_set_positive(result);
+	result->exp = result->digits = result->len = 0;
+	*status |= flags;
+}
+
+/* quietly set a static decimal from an mpd_ssize_t */
+void
+mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
+                uint32_t *status)
+{
+	mpd_uint_t u;
+	uint8_t sign = MPD_POS;
+
+	if (a < 0) {
+		if (a == MPD_SSIZE_MIN) {
+			u = (mpd_uint_t)MPD_SSIZE_MAX +
+			    (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX));
+		}
+		else {
+			u = -a;
+		}
+		sign = MPD_NEG;
+	}
+	else {
+		u = a;
+	}
+	_ssettriple(result, sign, u, 0);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a static decimal from an mpd_uint_t */
+void
+mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
+               uint32_t *status)
+{
+	_ssettriple(result, MPD_POS, a, 0);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a static decimal from an int32_t */
+void
+mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a static decimal from a uint32_t */
+void
+mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	mpd_qsset_uint(result, a, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* quietly set a static decimal from an int64_t */
+void
+mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a static decimal from a uint64_t */
+void
+mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	mpd_qsset_uint(result, a, ctx, status);
+}
+#endif
+
+/* quietly set a decimal from an mpd_ssize_t */
+void
+mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
+               uint32_t *status)
+{
+	mpd_minalloc(result);
+	mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a decimal from an mpd_uint_t */
+void
+mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	_settriple(result, MPD_POS, a, 0);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a decimal from an int32_t */
+void
+mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
+             uint32_t *status)
+{
+	mpd_qset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a decimal from a uint32_t */
+void
+mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
+             uint32_t *status)
+{
+	mpd_qset_uint(result, a, ctx, status);
+}
+
+#if defined(CONFIG_32) && !defined(LEGACY_COMPILER)
+/* set a decimal from a uint64_t */
+static void
+_c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status)
+{
+	mpd_uint_t w[3];
+	uint64_t q;
+	int i, len;
+
+	len = 0;
+	do {
+		q = u / MPD_RADIX;
+		w[len] = (mpd_uint_t)(u - q * MPD_RADIX);
+		u = q; len++;
+	} while (u != 0);
+
+	if (!mpd_qresize(result, len, status)) {
+		return;
+	}
+	for (i = 0; i < len; i++) {
+		result->data[i] = w[i];
+	}
+
+	mpd_set_sign(result, sign);
+	result->exp = 0;
+	result->len = len;
+	mpd_setdigits(result);
+}
+
+static void
+_c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	_c32setu64(result, a, MPD_POS, status);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* set a decimal from an int64_t */
+static void
+_c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	uint64_t u;
+	uint8_t sign = MPD_POS;
+
+	if (a < 0) {
+		if (a == INT64_MIN) {
+			u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX));
+		}
+		else {
+			u = -a;
+		}
+		sign = MPD_NEG;
+	}
+	else {
+		u = a;
+	}
+	_c32setu64(result, u, sign, status);
+	mpd_qfinalize(result, ctx, status);
+}
+#endif /* CONFIG_32 && !LEGACY_COMPILER */
+
+#ifndef LEGACY_COMPILER
+/* quietly set a decimal from an int64_t */
+void
+mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+             uint32_t *status)
+{
+#ifdef CONFIG_64
+	mpd_qset_ssize(result, a, ctx, status);
+#else
+	_c32_qset_i64(result, a, ctx, status);
+#endif
+}
+
+/* quietly set a decimal from a uint64_t */
+void
+mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+             uint32_t *status)
+{
+#ifdef CONFIG_64
+	mpd_qset_uint(result, a, ctx, status);
+#else
+	_c32_qset_u64(result, a, ctx, status);
+#endif
+}
+#endif /* !LEGACY_COMPILER */
+
+
+/*
+ * Quietly get an mpd_uint_t from a decimal. Assumes
+ * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for
+ * 32 and 64 bit machines.
+ *
+ * If the operation is impossible, MPD_Invalid_operation is set.
+ */
+static mpd_uint_t
+_mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status)
+{
+	mpd_t tmp;
+	mpd_uint_t tmp_data[2];
+	mpd_uint_t lo, hi;
+
+	if (mpd_isspecial(a)) {
+		*status |= MPD_Invalid_operation;
+		return MPD_UINT_MAX;
+	}
+	if (mpd_iszero(a)) {
+		return 0;
+	}
+	if (use_sign && mpd_isnegative(a)) {
+		*status |= MPD_Invalid_operation;
+		return MPD_UINT_MAX;
+	}
+
+	if (a->digits+a->exp > MPD_RDIGITS+1) {
+		*status |= MPD_Invalid_operation;
+		return MPD_UINT_MAX;
+	}
+
+	if (a->exp < 0) {
+		if (!_mpd_isint(a)) {
+			*status |= MPD_Invalid_operation;
+			return MPD_UINT_MAX;
+		}
+		/* At this point a->digits+a->exp <= MPD_RDIGITS+1,
+		 * so the shift fits. */
+		tmp.data = tmp_data;
+		tmp.flags = MPD_STATIC|MPD_CONST_DATA;
+		mpd_qsshiftr(&tmp, a, -a->exp);
+		tmp.exp = 0;
+		a = &tmp;
+	}
+
+	_mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1);
+	if (hi) {
+		*status |= MPD_Invalid_operation;
+		return MPD_UINT_MAX;
+	}
+
+	if (a->exp > 0) {
+		_mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]);
+		if (hi) {
+			*status |= MPD_Invalid_operation;
+			return MPD_UINT_MAX;
+		}
+	}
+
+	return lo;
+}
+
+/*
+ * Sets Invalid_operation for:
+ *   - specials
+ *   - negative numbers (except negative zero)
+ *   - non-integers
+ *   - overflow
+ */
+mpd_uint_t
+mpd_qget_uint(const mpd_t *a, uint32_t *status)
+{
+	return _mpd_qget_uint(1, a, status);
+}
+
+/* Same as above, but gets the absolute value, i.e. the sign is ignored. */
+mpd_uint_t
+mpd_qabs_uint(const mpd_t *a, uint32_t *status)
+{
+	return _mpd_qget_uint(0, a, status);
+}
+
+/* quietly get an mpd_ssize_t from a decimal */
+mpd_ssize_t
+mpd_qget_ssize(const mpd_t *a, uint32_t *status)
+{
+	mpd_uint_t u;
+	int isneg;
+
+	u = mpd_qabs_uint(a, status);
+	if (*status&MPD_Invalid_operation) {
+		return MPD_SSIZE_MAX;
+	}
+
+	isneg = mpd_isnegative(a);
+	if (u <= MPD_SSIZE_MAX) {
+		return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u;
+	}
+	else if (isneg && u-1 == MPD_SSIZE_MAX) {
+		return MPD_SSIZE_MIN;
+	}
+
+	*status |= MPD_Invalid_operation;
+	return MPD_SSIZE_MAX;
+}
+
+#ifdef CONFIG_64
+/* quietly get a uint64_t from a decimal */
+uint64_t
+mpd_qget_u64(const mpd_t *a, uint32_t *status)
+{
+	return mpd_qget_uint(a, status);
+}
+
+/* quietly get an int64_t from a decimal */
+int64_t
+mpd_qget_i64(const mpd_t *a, uint32_t *status)
+{
+	return mpd_qget_ssize(a, status);
+}
+#else
+/* quietly get a uint32_t from a decimal */
+uint32_t
+mpd_qget_u32(const mpd_t *a, uint32_t *status)
+{
+	return mpd_qget_uint(a, status);
+}
+
+/* quietly get an int32_t from a decimal */
+int32_t
+mpd_qget_i32(const mpd_t *a, uint32_t *status)
+{
+	return mpd_qget_ssize(a, status);
+}
+#endif
+
+
+/******************************************************************************/
+/*         Filtering input of functions, finalizing output of functions       */
+/******************************************************************************/
+
+/*
+ * Check if the operand is NaN, copy to result and return 1 if this is
+ * the case. Copying can fail since NaNs are allowed to have a payload that
+ * does not fit in MPD_MINALLOC.
+ */
+int
+mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+               uint32_t *status)
+{
+	if (mpd_isnan(a)) {
+		*status |= mpd_issnan(a) ? MPD_Invalid_operation : 0;
+		mpd_qcopy(result, a, status);
+		mpd_set_qnan(result);
+		_mpd_fix_nan(result, ctx);
+		return 1;
+	}
+	return 0;
+}
+
+/*
+ * Check if either operand is NaN, copy to result and return 1 if this
+ * is the case. Copying can fail since NaNs are allowed to have a payload
+ * that does not fit in MPD_MINALLOC.
+ */
+int
+mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b,
+                const mpd_context_t *ctx, uint32_t *status)
+{
+	if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) {
+		const mpd_t *choice = b;
+		if (mpd_issnan(a)) {
+			choice = a;
+			*status |= MPD_Invalid_operation;
+		}
+		else if (mpd_issnan(b)) {
+			*status |= MPD_Invalid_operation;
+		}
+		else if (mpd_isqnan(a)) {
+			choice = a;
+		}
+		mpd_qcopy(result, choice, status);
+		mpd_set_qnan(result);
+		_mpd_fix_nan(result, ctx);
+		return 1;
+	}
+	return 0;
+}
+
+/*
+ * Check if one of the operands is NaN, copy to result and return 1 if this
+ * is the case. Copying can fail since NaNs are allowed to have a payload
+ * that does not fit in MPD_MINALLOC.
+ */
+static int
+mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
+                 const mpd_context_t *ctx, uint32_t *status)
+{
+	if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) {
+		const mpd_t *choice = c;
+		if (mpd_issnan(a)) {
+			choice = a;
+			*status |= MPD_Invalid_operation;
+		}
+		else if (mpd_issnan(b)) {
+			choice = b;
+			*status |= MPD_Invalid_operation;
+		}
+		else if (mpd_issnan(c)) {
+			*status |= MPD_Invalid_operation;
+		}
+		else if (mpd_isqnan(a)) {
+			choice = a;
+		}
+		else if (mpd_isqnan(b)) {
+			choice = b;
+		}
+		mpd_qcopy(result, choice, status);
+		mpd_set_qnan(result);
+		_mpd_fix_nan(result, ctx);
+		return 1;
+	}
+	return 0;
+}
+
+/* Check if rounding digit 'rnd' leads to an increment. */
+static inline int
+_mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx)
+{
+	int ld;
+
+	switch (ctx->round) {
+	case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC:
+		return 0;
+	case MPD_ROUND_HALF_UP:
+		return (rnd >= 5);
+	case MPD_ROUND_HALF_EVEN:
+		return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec));
+	case MPD_ROUND_CEILING:
+		return !(rnd == 0 || mpd_isnegative(dec));
+	case MPD_ROUND_FLOOR:
+		return !(rnd == 0 || mpd_ispositive(dec));
+	case MPD_ROUND_HALF_DOWN:
+		return (rnd > 5);
+	case MPD_ROUND_UP:
+		return !(rnd == 0);
+	case MPD_ROUND_05UP:
+		ld = (int)mpd_lsd(dec->data[0]);
+		return (!(rnd == 0) && (ld == 0 || ld == 5));
+	default:
+		/* Without a valid context, further results will be undefined. */
+		return 0; /* GCOV_NOT_REACHED */
+	}
+}
+
+/*
+ * Apply rounding to a decimal that has been right-shifted into a full
+ * precision decimal. If an increment leads to an overflow of the precision,
+ * adjust the coefficient and the exponent and check the new exponent for
+ * overflow.
+ */
+static inline void
+_mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+                 uint32_t *status)
+{
+	if (_mpd_rnd_incr(dec, rnd, ctx)) {
+		/* We have a number with exactly ctx->prec digits. The increment
+		 * can only lead to an overflow if the decimal is all nines. In
+		 * that case, the result is a power of ten with prec+1 digits.
+		 *
+		 * If the precision is a multiple of MPD_RDIGITS, this situation is
+		 * detected by _mpd_baseincr returning a carry.
+		 * If the precision is not a multiple of MPD_RDIGITS, we have to
+		 * check if the result has one digit too many.
+		 */
+		mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+		if (carry) {
+			dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1];
+			dec->exp += 1;
+			_mpd_check_exp(dec, ctx, status);
+			return;
+		}
+		mpd_setdigits(dec);
+		if (dec->digits > ctx->prec) {
+			mpd_qshiftr_inplace(dec, 1);
+			dec->exp += 1;
+			dec->digits = ctx->prec;
+			_mpd_check_exp(dec, ctx, status);
+		}
+	}
+}
+
+/*
+ * Apply rounding to a decimal. Allow overflow of the precision.
+ */
+static inline void
+_mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+                        uint32_t *status)
+{
+	if (_mpd_rnd_incr(dec, rnd, ctx)) {
+		mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+		if (carry) {
+			if (!mpd_qresize(dec, dec->len+1, status)) {
+				return;
+			}
+			dec->data[dec->len] = 1;
+			dec->len += 1;
+		}
+		mpd_setdigits(dec);
+	}
+}
+
+/*
+ * Apply rounding to a decimal that has been right-shifted into a decimal
+ * with full precision or less. Return failure if an increment would
+ * overflow the precision.
+ */
+static inline int
+_mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+                     uint32_t *status)
+{
+	if (_mpd_rnd_incr(dec, rnd, ctx)) {
+		mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+		if (carry) {
+			if (!mpd_qresize(dec, dec->len+1, status)) {
+				return 0;
+			}
+			dec->data[dec->len] = 1;
+			dec->len += 1;
+		}
+		mpd_setdigits(dec);
+		if (dec->digits > ctx->prec) {
+			mpd_seterror(dec, MPD_Invalid_operation, status);
+			return 0;
+		}
+	}
+	return 1;
+}
+
+/* Check a normal number for overflow, underflow, clamping. If the operand
+   is modified, it will be zero, special or (sub)normal with a coefficient
+   that fits into the current context precision. */
+static inline void
+_mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_ssize_t adjexp, etiny, shift;
+	int rnd;
+
+	adjexp = mpd_adjexp(dec);
+	if (adjexp > ctx->emax) {
+
+		if (mpd_iszerocoeff(dec)) {
+			dec->exp = ctx->emax;
+			if (ctx->clamp) {
+				dec->exp -= (ctx->prec-1);
+			}
+			mpd_zerocoeff(dec);
+			*status |= MPD_Clamped;
+			return;
+		}
+
+		switch (ctx->round) {
+		case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN:
+		case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP:
+		case MPD_ROUND_TRUNC:
+			mpd_setspecial(dec, mpd_sign(dec), MPD_INF);
+			break;
+		case MPD_ROUND_DOWN: case MPD_ROUND_05UP:
+			mpd_qmaxcoeff(dec, ctx, status);
+			dec->exp = ctx->emax - ctx->prec + 1;
+			break;
+		case MPD_ROUND_CEILING:
+			if (mpd_isnegative(dec)) {
+				mpd_qmaxcoeff(dec, ctx, status);
+				dec->exp = ctx->emax - ctx->prec + 1;
+			}
+			else {
+				mpd_setspecial(dec, MPD_POS, MPD_INF);
+			}
+			break;
+		case MPD_ROUND_FLOOR:
+			if (mpd_ispositive(dec)) {
+				mpd_qmaxcoeff(dec, ctx, status);
+				dec->exp = ctx->emax - ctx->prec + 1;
+			}
+			else {
+				mpd_setspecial(dec, MPD_NEG, MPD_INF);
+			}
+			break;
+		default: /* debug */
+			abort(); /* GCOV_NOT_REACHED */
+		}
+
+		*status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+
+	} /* fold down */
+	else if (ctx->clamp && dec->exp > mpd_etop(ctx)) {
+		/* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1:
+		 *   (1) shift = exp -emax+prec-1 > 0
+		 *   (2) digits+shift = exp+digits-1 - emax + prec <= prec */
+		shift = dec->exp - mpd_etop(ctx);
+		if (!mpd_qshiftl(dec, dec, shift, status)) {
+			return;
+		}
+		dec->exp -= shift;
+		*status |= MPD_Clamped;
+		if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) {
+			/* Underflow is impossible, since exp < etiny=emin-prec+1
+			 * and exp > etop=emax-prec+1 would imply emax < emin. */
+			*status |= MPD_Subnormal;
+		}
+	}
+	else if (adjexp < ctx->emin) {
+
+		etiny = mpd_etiny(ctx);
+
+		if (mpd_iszerocoeff(dec)) {
+			if (dec->exp < etiny) {
+				dec->exp = etiny;
+				mpd_zerocoeff(dec);
+				*status |= MPD_Clamped;
+			}
+			return;
+		}
+
+		*status |= MPD_Subnormal;
+		if (dec->exp < etiny) {
+			/* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1:
+			 *   (1) shift = emin-prec+1 - exp > 0
+			 *   (2) digits-shift = exp+digits-1 - emin + prec < prec */
+			shift = etiny - dec->exp;
+			rnd = (int)mpd_qshiftr_inplace(dec, shift);
+			dec->exp = etiny;
+			/* We always have a spare digit in case of an increment. */
+			_mpd_apply_round_excess(dec, rnd, ctx, status);
+			*status |= MPD_Rounded;
+			if (rnd) {
+				*status |= (MPD_Inexact|MPD_Underflow);
+				if (mpd_iszerocoeff(dec)) {
+					mpd_zerocoeff(dec);
+					*status |= MPD_Clamped;
+				}
+			}
+		}
+		/* Case exp >= etiny=emin-prec+1:
+		 *   (1) adjexp=exp+digits-1 < emin
+		 *   (2) digits < emin-exp+1 <= prec */
+	}
+}
+
+/* Transcendental functions do not always set Underflow reliably,
+ * since they only use as much precision as is necessary for correct
+ * rounding. If a result like 1.0000000000e-101 is finalized, there
+ * is no rounding digit that would trigger Underflow. But we can
+ * assume Inexact, so a short check suffices. */
+static inline void
+mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+	if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) &&
+	    dec->exp < mpd_etiny(ctx)) {
+		*status |= MPD_Underflow;
+	}
+}
+
+/* Check if a normal number must be rounded after the exponent has been checked. */
+static inline void
+_mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_uint_t rnd;
+	mpd_ssize_t shift;
+
+	/* must handle specials: _mpd_check_exp() can produce infinities or NaNs */
+	if (mpd_isspecial(dec)) {
+		return;
+	}
+
+	if (dec->digits > ctx->prec) {
+		shift = dec->digits - ctx->prec;
+		rnd = mpd_qshiftr_inplace(dec, shift);
+		dec->exp += shift;
+		_mpd_apply_round(dec, rnd, ctx, status);
+		*status |= MPD_Rounded;
+		if (rnd) {
+			*status |= MPD_Inexact;
+		}
+	}
+}
+
+/* Finalize all operations. */
+void
+mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
+{
+	if (mpd_isspecial(result)) {
+		if (mpd_isnan(result)) {
+			_mpd_fix_nan(result, ctx);
+		}
+		return;
+	}
+
+	_mpd_check_exp(result, ctx, status);
+	_mpd_check_round(result, ctx, status);
+}
+
+
+/******************************************************************************/
+/*                                 Copying                                    */
+/******************************************************************************/
+
+/* Internal function: Copy a decimal, share data with src: USE WITH CARE! */
+static inline void
+_mpd_copy_shared(mpd_t *dest, const mpd_t *src)
+{
+	dest->flags = src->flags;
+	dest->exp = src->exp;
+	dest->digits = src->digits;
+	dest->len = src->len;
+	dest->alloc = src->alloc;
+	dest->data = src->data;
+
+	mpd_set_shared_data(dest);
+}
+
+/*
+ * Copy a decimal. In case of an error, status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+	if (result == a) return 1;
+
+	if (!mpd_qresize(result, a->len, status)) {
+		return 0;
+	}
+
+	mpd_copy_flags(result, a);
+	result->exp = a->exp;
+	result->digits = a->digits;
+	result->len = a->len;
+	memcpy(result->data, a->data, a->len * (sizeof *result->data));
+
+	return 1;
+}
+
+/*
+ * Copy to a decimal with a static buffer. The caller has to make sure that
+ * the buffer is big enough. Cannot fail.
+ */
+static void
+mpd_qcopy_static(mpd_t *result, const mpd_t *a)
+{
+	if (result == a) return;
+
+	memcpy(result->data, a->data, a->len * (sizeof *result->data));
+
+	mpd_copy_flags(result, a);
+	result->exp = a->exp;
+	result->digits = a->digits;
+	result->len = a->len;
+}
+
+/*
+ * Return a newly allocated copy of the operand. In case of an error,
+ * status is set to MPD_Malloc_error and the return value is NULL.
+ */
+mpd_t *
+mpd_qncopy(const mpd_t *a)
+{
+	mpd_t *result;
+
+	if ((result = mpd_qnew_size(a->len)) == NULL) {
+		return NULL;
+	}
+	memcpy(result->data, a->data, a->len * (sizeof *result->data));
+	mpd_copy_flags(result, a);
+	result->exp = a->exp;
+	result->digits = a->digits;
+	result->len = a->len;
+
+	return result;
+}
+
+/*
+ * Copy a decimal and set the sign to positive. In case of an error, the
+ * status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+	if (!mpd_qcopy(result, a, status)) {
+		return 0;
+	}
+	mpd_set_positive(result);
+	return 1;
+}
+
+/*
+ * Copy a decimal and negate the sign. In case of an error, the
+ * status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+	if (!mpd_qcopy(result, a, status)) {
+		return 0;
+	}
+	_mpd_negate(result);
+	return 1;
+}
+
+/*
+ * Copy a decimal, setting the sign of the first operand to the sign of the
+ * second operand. In case of an error, the status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+	uint8_t sign_b = mpd_sign(b); /* result may equal b! */
+
+	if (!mpd_qcopy(result, a, status)) {
+		return 0;
+	}
+	mpd_set_sign(result, sign_b);
+	return 1;
+}
+
+
+/******************************************************************************/
+/*                                Comparisons                                 */
+/******************************************************************************/
+
+/*
+ * For all functions that compare two operands and return an int the usual
+ * convention applies to the return value:
+ *
+ * -1 if op1 < op2
+ *  0 if op1 == op2
+ *  1 if op1 > op2
+ *
+ *  INT_MAX for error
+ */
+
+
+/* Convenience macro. If a and b are not equal, return from the calling
+ * function with the correct comparison value. */
+#define CMP_EQUAL_OR_RETURN(a, b)  \
+        if (a != b) {              \
+                if (a < b) {       \
+                        return -1; \
+                }                  \
+                return 1;          \
+        }
+
+/*
+ * Compare the data of big and small. This function does the equivalent
+ * of first shifting small to the left and then comparing the data of
+ * big and small, except that no allocation for the left shift is needed.
+ */
+static int
+_mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m,
+             mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+	/* spurious uninitialized warnings */
+	mpd_uint_t l=l, lprev=lprev, h=h;
+#else
+	mpd_uint_t l, lprev, h;
+#endif
+	mpd_uint_t q, r;
+	mpd_uint_t ph, x;
+
+	assert(m > 0 && n >= m && shift > 0);
+
+	_mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+	if (r != 0) {
+
+		ph = mpd_pow10[r];
+
+		--m; --n;
+		_mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r);
+		if (h != 0) {
+			CMP_EQUAL_OR_RETURN(big[n], h)
+			--n;
+		}
+		for (; m != MPD_SIZE_MAX; m--,n--) {
+			_mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r);
+			x = ph * lprev + h;
+			CMP_EQUAL_OR_RETURN(big[n], x)
+			lprev = l;
+		}
+		x = ph * lprev;
+		CMP_EQUAL_OR_RETURN(big[q], x)
+	}
+	else {
+		while (--m != MPD_SIZE_MAX) {
+			CMP_EQUAL_OR_RETURN(big[m+q], small[m])
+		}
+	}
+
+	return !_mpd_isallzero(big, q);
+}
+
+/* Compare two decimals with the same adjusted exponent. */
+static int
+_mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b)
+{
+	mpd_ssize_t shift, i;
+
+	if (a->exp != b->exp) {
+		/* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so
+		 * a->exp - b->exp = b->digits - a->digits. */
+		shift = a->exp - b->exp;
+		if (shift > 0) {
+			return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift);
+		}
+		else {
+			return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift);
+		}
+	}
+
+	/*
+	 * At this point adjexp(a) == adjexp(b) and a->exp == b->exp,
+	 * so a->digits == b->digits, therefore a->len == b->len.
+	 */
+	for (i = a->len-1; i >= 0; --i) {
+		CMP_EQUAL_OR_RETURN(a->data[i], b->data[i])
+	}
+
+	return 0;
+}
+
+/* Compare two numerical values. */
+static int
+_mpd_cmp(const mpd_t *a, const mpd_t *b)
+{
+	mpd_ssize_t adjexp_a, adjexp_b;
+
+	/* equal pointers */
+	if (a == b) {
+		return 0;
+	}
+
+	/* infinities */
+	if (mpd_isinfinite(a)) {
+		if (mpd_isinfinite(b)) {
+			return mpd_isnegative(b) - mpd_isnegative(a);
+		}
+		return mpd_arith_sign(a);
+	}
+	if (mpd_isinfinite(b)) {
+		return -mpd_arith_sign(b);
+	}
+
+	/* zeros */
+	if (mpd_iszerocoeff(a)) {
+		if (mpd_iszerocoeff(b)) {
+			return 0;
+		}
+		return -mpd_arith_sign(b);
+	}
+	if (mpd_iszerocoeff(b)) {
+		return mpd_arith_sign(a);
+	}
+
+	/* different signs */
+	if (mpd_sign(a) != mpd_sign(b)) {
+		return mpd_sign(b) - mpd_sign(a);
+	}
+
+	/* different adjusted exponents */
+	adjexp_a = mpd_adjexp(a);
+	adjexp_b = mpd_adjexp(b);
+	if (adjexp_a != adjexp_b) {
+		if (adjexp_a < adjexp_b) {
+			return -1 * mpd_arith_sign(a);
+		}
+		return mpd_arith_sign(a);
+	}
+
+	/* same adjusted exponents */
+	return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a);
+}
+
+/* Compare the absolutes of two numerical values. */
+static int
+_mpd_cmp_abs(const mpd_t *a, const mpd_t *b)
+{
+	mpd_ssize_t adjexp_a, adjexp_b;
+
+	/* equal pointers */
+	if (a == b) {
+		return 0;
+	}
+
+	/* infinities */
+	if (mpd_isinfinite(a)) {
+		if (mpd_isinfinite(b)) {
+			return 0;
+		}
+		return 1;
+	}
+	if (mpd_isinfinite(b)) {
+		return -1;
+	}
+
+	/* zeros */
+	if (mpd_iszerocoeff(a)) {
+		if (mpd_iszerocoeff(b)) {
+			return 0;
+		}
+		return -1;
+	}
+	if (mpd_iszerocoeff(b)) {
+		return 1;
+	}
+
+	/* different adjusted exponents */
+	adjexp_a = mpd_adjexp(a);
+	adjexp_b = mpd_adjexp(b);
+	if (adjexp_a != adjexp_b) {
+		if (adjexp_a < adjexp_b) {
+			return -1;
+		}
+		return 1;
+	}
+
+	/* same adjusted exponents */
+	return _mpd_cmp_same_adjexp(a, b);
+}
+
+/* Compare two values and return an integer result. */
+int
+mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_isnan(a) || mpd_isnan(b)) {
+			*status |= MPD_Invalid_operation;
+			return INT_MAX;
+		}
+	}
+
+	return _mpd_cmp(a, b);
+}
+
+/*
+ * Compare a and b, convert the the usual integer result to a decimal and
+ * store it in 'result'. For convenience, the integer result of the comparison
+ * is returned. Comparisons involving NaNs return NaN/INT_MAX.
+ */
+int
+mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return INT_MAX;
+		}
+	}
+
+	c = _mpd_cmp(a, b);
+	_settriple(result, (c < 0), (c != 0), 0);
+	return c;
+}
+
+/* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */
+int
+mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b,
+                    const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			*status |= MPD_Invalid_operation;
+			return INT_MAX;
+		}
+	}
+
+	c = _mpd_cmp(a, b);
+	_settriple(result, (c < 0), (c != 0), 0);
+	return c;
+}
+
+/* Compare the operands using a total order. */
+int
+mpd_cmp_total(const mpd_t *a, const mpd_t *b)
+{
+	mpd_t aa, bb;
+	int nan_a, nan_b;
+	int c;
+
+	if (mpd_sign(a) != mpd_sign(b)) {
+		return mpd_sign(b) - mpd_sign(a);
+	}
+
+
+	if (mpd_isnan(a)) {
+		c = 1;
+		if (mpd_isnan(b)) {
+			nan_a = (mpd_isqnan(a)) ? 1 : 0;
+			nan_b = (mpd_isqnan(b)) ? 1 : 0;
+			if (nan_b == nan_a) {
+				if (a->len > 0 && b->len > 0) {
+					_mpd_copy_shared(&aa, a);
+					_mpd_copy_shared(&bb, b);
+					aa.exp = bb.exp = 0;
+					/* compare payload */
+					c = _mpd_cmp_abs(&aa, &bb);
+				}
+				else {
+					c = (a->len > 0) - (b->len > 0);
+				}
+			}
+			else {
+				c = nan_a - nan_b;
+			}
+		}
+	}
+	else if (mpd_isnan(b)) {
+		c = -1;
+	}
+	else {
+		c = _mpd_cmp_abs(a, b);
+		if (c == 0 && a->exp != b->exp) {
+			c = (a->exp < b->exp) ? -1 : 1;
+		}
+	}
+
+	return c * mpd_arith_sign(a);
+}
+
+/*
+ * Compare a and b according to a total order, convert the usual integer result
+ * to a decimal and store it in 'result'. For convenience, the integer result
+ * of the comparison is returned.
+ */
+int
+mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b)
+{
+	int c;
+
+	c = mpd_cmp_total(a, b);
+	_settriple(result, (c < 0), (c != 0), 0);
+	return c;
+}
+
+/* Compare the magnitude of the operands using a total order. */
+int
+mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b)
+{
+	mpd_t aa, bb;
+
+	_mpd_copy_shared(&aa, a);
+	_mpd_copy_shared(&bb, b);
+
+	mpd_set_positive(&aa);
+	mpd_set_positive(&bb);
+
+	return mpd_cmp_total(&aa, &bb);
+}
+
+/*
+ * Compare the magnitude of a and b according to a total order, convert the
+ * the usual integer result to a decimal and store it in 'result'.
+ * For convenience, the integer result of the comparison is returned.
+ */
+int
+mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b)
+{
+	int c;
+
+	c = mpd_cmp_total_mag(a, b);
+	_settriple(result, (c < 0), (c != 0), 0);
+	return c;
+}
+
+/* Determine an ordering for operands that are numerically equal. */
+static inline int
+_mpd_cmp_numequal(const mpd_t *a, const mpd_t *b)
+{
+	int sign_a, sign_b;
+	int c;
+
+	sign_a = mpd_sign(a);
+	sign_b = mpd_sign(b);
+	if (sign_a != sign_b) {
+		c = sign_b - sign_a;
+	}
+	else {
+		c = (a->exp < b->exp) ? -1 : 1;
+		c *= mpd_arith_sign(a);
+	}
+
+	return c;
+}
+
+
+/******************************************************************************/
+/*                         Shifting the coefficient                           */
+/******************************************************************************/
+
+/*
+ * Shift the coefficient of the operand to the left, no check for specials.
+ * Both operands may be the same pointer. If the result length has to be
+ * increased, mpd_qresize() might fail with MPD_Malloc_error.
+ */
+int
+mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
+{
+	mpd_ssize_t size;
+
+	assert(n >= 0);
+
+	if (mpd_iszerocoeff(a) || n == 0) {
+		return mpd_qcopy(result, a, status);
+	}
+
+	size = mpd_digits_to_size(a->digits+n);
+	if (!mpd_qresize(result, size, status)) {
+		return 0; /* result is NaN */
+	}
+
+	_mpd_baseshiftl(result->data, a->data, size, a->len, n);
+
+	mpd_copy_flags(result, a);
+	result->len = size;
+	result->exp = a->exp;
+	result->digits = a->digits+n;
+
+	return 1;
+}
+
+/* Determine the rounding indicator if all digits of the coefficient are shifted
+ * out of the picture. */
+static mpd_uint_t
+_mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd)
+{
+	mpd_uint_t rnd = 0, rest = 0, word;
+
+	word = data[len-1];
+	/* special treatment for the most significant digit if shift == digits */
+	if (use_msd) {
+		_mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1);
+		if (len > 1 && rest == 0) {
+			 rest = !_mpd_isallzero(data, len-1);
+		}
+	}
+	else {
+		rest = !_mpd_isallzero(data, len);
+	}
+
+	return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
+}
+
+/*
+ * Same as mpd_qshiftr(), but 'result' is a static array. It is the
+ * caller's responsibility to make sure that the array is big enough.
+ * The function cannot fail.
+ */
+mpd_uint_t
+mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n)
+{
+	mpd_uint_t rnd;
+	mpd_ssize_t size;
+
+	assert(n >= 0);
+
+	if (mpd_iszerocoeff(a) || n == 0) {
+		mpd_qcopy_static(result, a);
+		return 0;
+	}
+
+	if (n >= a->digits) {
+		rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
+		mpd_zerocoeff(result);
+		result->digits = 1;
+		size = 1;
+	}
+	else {
+		result->digits = a->digits-n;
+		size = mpd_digits_to_size(result->digits);
+		rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+	}
+
+	mpd_copy_flags(result, a);
+	result->exp = a->exp;
+	result->len = size;
+
+	return rnd;
+}
+
+/*
+ * Inplace shift of the coefficient to the right, no check for specials.
+ * Returns the rounding indicator for mpd_rnd_incr().
+ * The function cannot fail.
+ */
+mpd_uint_t
+mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n)
+{
+	uint32_t dummy;
+	mpd_uint_t rnd;
+	mpd_ssize_t size;
+
+	assert(n >= 0);
+
+	if (mpd_iszerocoeff(result) || n == 0) {
+		return 0;
+	}
+
+	if (n >= result->digits) {
+		rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits));
+		mpd_zerocoeff(result);
+		result->digits = 1;
+		size = 1;
+	}
+	else {
+		rnd = _mpd_baseshiftr(result->data, result->data, result->len, n);
+		result->digits -= n;
+		size = mpd_digits_to_size(result->digits);
+		/* reducing the size cannot fail */
+		mpd_qresize(result, size, &dummy);
+	}
+
+	result->len = size;
+
+	return rnd;
+}
+
+/*
+ * Shift the coefficient of the operand to the right, no check for specials.
+ * Both operands may be the same pointer. Returns the rounding indicator to
+ * be used by mpd_rnd_incr(). If the result length has to be increased,
+ * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those
+ * cases, MPD_UINT_MAX is returned.
+ */
+mpd_uint_t
+mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
+{
+	mpd_uint_t rnd;
+	mpd_ssize_t size;
+
+	assert(n >= 0);
+
+	if (mpd_iszerocoeff(a) || n == 0) {
+		if (!mpd_qcopy(result, a, status)) {
+			return MPD_UINT_MAX;
+		}
+		return 0;
+	}
+
+	if (n >= a->digits) {
+		rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
+		mpd_zerocoeff(result);
+		result->digits = 1;
+		size = 1;
+	}
+	else {
+		result->digits = a->digits-n;
+		size = mpd_digits_to_size(result->digits);
+		if (result == a) {
+			rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+			/* reducing the size cannot fail */
+			mpd_qresize(result, size, status);
+		}
+		else {
+			if (!mpd_qresize(result, size, status)) {
+				return MPD_UINT_MAX;
+			}
+			rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+		}
+	}
+
+	mpd_copy_flags(result, a);
+	result->exp = a->exp;
+	result->len = size;
+
+	return rnd;
+}
+
+
+/******************************************************************************/
+/*                         Miscellaneous operations                           */
+/******************************************************************************/
+
+/* Logical And */
+void
+mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	const mpd_t *big = a, *small = b;
+	mpd_uint_t x, y, z, xbit, ybit;
+	int k, mswdigits;
+	mpd_ssize_t i;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b) ||
+	    mpd_isnegative(a) || mpd_isnegative(b) ||
+	    a->exp != 0 || b->exp != 0) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (b->digits > a->digits) {
+		big = b;
+		small = a;
+	}
+	if (!mpd_qresize(result, big->len, status)) {
+		return;
+	}
+
+
+	/* full words */
+	for (i = 0; i < small->len-1; i++) {
+		x = small->data[i];
+		y = big->data[i];
+		z = 0;
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			xbit = x % 10;
+			x /= 10;
+			ybit = y % 10;
+			y /= 10;
+			if (xbit > 1 || ybit > 1) {
+				goto invalid_operation;
+			}
+			z += (xbit&ybit) ? mpd_pow10[k] : 0;
+		}
+		result->data[i] = z;
+	}
+	/* most significant word of small */
+	x = small->data[i];
+	y = big->data[i];
+	z = 0;
+	mswdigits = mpd_word_digits(x);
+	for (k = 0; k < mswdigits; k++) {
+		xbit = x % 10;
+		x /= 10;
+		ybit = y % 10;
+		y /= 10;
+		if (xbit > 1 || ybit > 1) {
+			goto invalid_operation;
+		}
+		z += (xbit&ybit) ? mpd_pow10[k] : 0;
+	}
+	result->data[i++] = z;
+
+	/* scan the rest of y for digit > 1 */
+	for (; k < MPD_RDIGITS; k++) {
+		ybit = y % 10;
+		y /= 10;
+		if (ybit > 1) {
+			goto invalid_operation;
+		}
+	}
+	/* scan the rest of big for digit > 1 */
+	for (; i < big->len; i++) {
+		y = big->data[i];
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			ybit = y % 10;
+			y /= 10;
+			if (ybit > 1) {
+				goto invalid_operation;
+			}
+		}
+	}
+
+	mpd_clear_flags(result);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, small->len);
+	mpd_qresize(result, result->len, status);
+	mpd_setdigits(result);
+	_mpd_cap(result, ctx);
+	return;
+
+invalid_operation:
+	mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/* Class of an operand. Returns a pointer to the constant name. */
+const char *
+mpd_class(const mpd_t *a, const mpd_context_t *ctx)
+{
+	if (mpd_isnan(a)) {
+		if (mpd_isqnan(a))
+			return "NaN";
+		else
+			return "sNaN";
+	}
+	else if (mpd_ispositive(a)) {
+		if (mpd_isinfinite(a))
+			return "+Infinity";
+		else if (mpd_iszero(a))
+			return "+Zero";
+		else if (mpd_isnormal(a, ctx))
+			return "+Normal";
+		else
+			return "+Subnormal";
+	}
+	else {
+		if (mpd_isinfinite(a))
+			return "-Infinity";
+		else if (mpd_iszero(a))
+			return "-Zero";
+		else if (mpd_isnormal(a, ctx))
+			return "-Normal";
+		else
+			return "-Subnormal";
+	}
+}
+
+/* Logical Xor */
+void
+mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+            uint32_t *status)
+{
+	mpd_uint_t x, z, xbit;
+	mpd_ssize_t i, digits, len;
+	mpd_ssize_t q, r;
+	int k;
+
+	if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	digits = (a->digits < ctx->prec) ? ctx->prec : a->digits;
+	_mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
+	len = (r == 0) ? q : q+1;
+	if (!mpd_qresize(result, len, status)) {
+		return;
+	}
+
+	for (i = 0; i < len; i++) {
+		x = (i < a->len) ?  a->data[i] : 0;
+		z = 0;
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			xbit = x % 10;
+			x /= 10;
+			if (xbit > 1) {
+				goto invalid_operation;
+			}
+			z += !xbit ? mpd_pow10[k] : 0;
+		}
+		result->data[i] = z;
+	}
+
+	mpd_clear_flags(result);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, len);
+	mpd_qresize(result, result->len, status);
+	mpd_setdigits(result);
+	_mpd_cap(result, ctx);
+	return;
+
+invalid_operation:
+	mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/* Exponent of the magnitude of the most significant digit of the operand. */
+void
+mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+          uint32_t *status)
+{
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		mpd_setspecial(result, MPD_POS, MPD_INF);
+	}
+	else if (mpd_iszerocoeff(a)) {
+		mpd_setspecial(result, MPD_NEG, MPD_INF);
+		*status |= MPD_Division_by_zero;
+	}
+	else {
+		mpd_qset_ssize(result, mpd_adjexp(a), ctx, status);
+	}
+}
+
+/* Logical Or */
+void
+mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b,
+        const mpd_context_t *ctx, uint32_t *status)
+{
+	const mpd_t *big = a, *small = b;
+	mpd_uint_t x, y, z, xbit, ybit;
+	int k, mswdigits;
+	mpd_ssize_t i;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b) ||
+	    mpd_isnegative(a) || mpd_isnegative(b) ||
+	    a->exp != 0 || b->exp != 0) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (b->digits > a->digits) {
+		big = b;
+		small = a;
+	}
+	if (!mpd_qresize(result, big->len, status)) {
+		return;
+	}
+
+
+	/* full words */
+	for (i = 0; i < small->len-1; i++) {
+		x = small->data[i];
+		y = big->data[i];
+		z = 0;
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			xbit = x % 10;
+			x /= 10;
+			ybit = y % 10;
+			y /= 10;
+			if (xbit > 1 || ybit > 1) {
+				goto invalid_operation;
+			}
+			z += (xbit|ybit) ? mpd_pow10[k] : 0;
+		}
+		result->data[i] = z;
+	}
+	/* most significant word of small */
+	x = small->data[i];
+	y = big->data[i];
+	z = 0;
+	mswdigits = mpd_word_digits(x);
+	for (k = 0; k < mswdigits; k++) {
+		xbit = x % 10;
+		x /= 10;
+		ybit = y % 10;
+		y /= 10;
+		if (xbit > 1 || ybit > 1) {
+			goto invalid_operation;
+		}
+		z += (xbit|ybit) ? mpd_pow10[k] : 0;
+	}
+
+	/* scan and copy the rest of y for digit > 1 */
+	for (; k < MPD_RDIGITS; k++) {
+		ybit = y % 10;
+		y /= 10;
+		if (ybit > 1) {
+			goto invalid_operation;
+		}
+		z += ybit*mpd_pow10[k];
+	}
+	result->data[i++] = z;
+	/* scan and copy the rest of big for digit > 1 */
+	for (; i < big->len; i++) {
+		y = big->data[i];
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			ybit = y % 10;
+			y /= 10;
+			if (ybit > 1) {
+				goto invalid_operation;
+			}
+		}
+		result->data[i] = big->data[i];
+	}
+
+	mpd_clear_flags(result);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, big->len);
+	mpd_qresize(result, result->len, status);
+	mpd_setdigits(result);
+	_mpd_cap(result, ctx);
+	return;
+
+invalid_operation:
+	mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/*
+ * Rotate the coefficient of a by b->data digits. b must be an integer with
+ * exponent 0.
+ */
+void
+mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b,
+            const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	MPD_NEW_STATIC(tmp,0,0,0,0);
+	MPD_NEW_STATIC(big,0,0,0,0);
+	MPD_NEW_STATIC(small,0,0,0,0);
+	mpd_ssize_t n, lshift, rshift;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+	}
+	if (b->exp != 0 || mpd_isinfinite(b)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	n = mpd_qget_ssize(b, &workstatus);
+	if (workstatus&MPD_Invalid_operation) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (n > ctx->prec || n < -ctx->prec) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_isinfinite(a)) {
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+	if (n >= 0) {
+		lshift = n;
+		rshift = ctx->prec-n;
+	}
+	else {
+		lshift = ctx->prec+n;
+		rshift = -n;
+	}
+
+	if (a->digits > ctx->prec) {
+		if (!mpd_qcopy(&tmp, a, status)) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			goto finish;
+		}
+		_mpd_cap(&tmp, ctx);
+		a = &tmp;
+	}
+
+	if (!mpd_qshiftl(&big, a, lshift, status)) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		goto finish;
+	}
+	_mpd_cap(&big, ctx);
+
+	if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		goto finish;
+	}
+	_mpd_qadd(result, &big, &small, ctx, status);
+
+
+finish:
+	mpd_del(&tmp);
+	mpd_del(&big);
+	mpd_del(&small);
+}
+
+/*
+ * b must be an integer with exponent 0 and in the range +-2*(emax + prec).
+ * XXX: In my opinion +-(2*emax + prec) would be more sensible.
+ * The result is a with the value of b added to its exponent.
+ */
+void
+mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b,
+            const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_uint_t n, maxjump;
+#ifndef LEGACY_COMPILER
+	int64_t exp;
+#else
+	mpd_uint_t x;
+	int x_sign, n_sign;
+	mpd_ssize_t exp;
+#endif
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+	}
+	if (b->exp != 0 || mpd_isinfinite(b)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	n = mpd_qabs_uint(b, &workstatus);
+	/* the spec demands this */
+	maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec);
+
+	if (n > maxjump || workstatus&MPD_Invalid_operation) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_isinfinite(a)) {
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+#ifndef LEGACY_COMPILER
+	exp = a->exp + (int64_t)n * mpd_arith_sign(b);
+	exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp;
+	exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp;
+#else
+	x = (a->exp < 0) ? -a->exp : a->exp;
+	x_sign = (a->exp < 0) ? 1 : 0;
+	n_sign = mpd_isnegative(b) ? 1 : 0;
+
+	if (x_sign == n_sign) {
+		x = x + n;
+		if (x < n) x = MPD_UINT_MAX;
+	}
+	else {
+		x_sign = (x >= n) ? x_sign : n_sign;
+		x = (x >= n) ? x - n : n - x;
+	}
+	if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF;
+	if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP;
+	exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x;
+#endif
+
+	mpd_qcopy(result, a, status);
+	result->exp = (mpd_ssize_t)exp;
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Shift the coefficient by n digits, positive n is a left shift. In the case
+ * of a left shift, the result is decapitated to fit the context precision. If
+ * you don't want that, use mpd_shiftl().
+ */
+void
+mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx,
+            uint32_t *status)
+{
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+	if (n >= 0 && n <= ctx->prec) {
+		mpd_qshiftl(result, a, n, status);
+		_mpd_cap(result, ctx);
+	}
+	else if (n < 0 && n >= -ctx->prec) {
+		if (!mpd_qcopy(result, a, status)) {
+			return;
+		}
+		_mpd_cap(result, ctx);
+		mpd_qshiftr_inplace(result, -n);
+	}
+	else {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+	}
+}
+
+/*
+ * Same as mpd_shiftn(), but the shift is specified by the decimal b, which
+ * must be an integer with a zero exponent. Infinities remain infinities.
+ */
+void
+mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
+           uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_ssize_t n;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+	}
+	if (b->exp != 0 || mpd_isinfinite(b)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	n = mpd_qget_ssize(b, &workstatus);
+	if (workstatus&MPD_Invalid_operation) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (n > ctx->prec || n < -ctx->prec) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_isinfinite(a)) {
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+	if (n >= 0) {
+		mpd_qshiftl(result, a, n, status);
+		_mpd_cap(result, ctx);
+	}
+	else {
+		if (!mpd_qcopy(result, a, status)) {
+			return;
+		}
+		_mpd_cap(result, ctx);
+		mpd_qshiftr_inplace(result, -n);
+	}
+}
+
+/* Logical Xor */
+void
+mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b,
+        const mpd_context_t *ctx, uint32_t *status)
+{
+	const mpd_t *big = a, *small = b;
+	mpd_uint_t x, y, z, xbit, ybit;
+	int k, mswdigits;
+	mpd_ssize_t i;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b) ||
+	    mpd_isnegative(a) || mpd_isnegative(b) ||
+	    a->exp != 0 || b->exp != 0) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (b->digits > a->digits) {
+		big = b;
+		small = a;
+	}
+	if (!mpd_qresize(result, big->len, status)) {
+		return;
+	}
+
+
+	/* full words */
+	for (i = 0; i < small->len-1; i++) {
+		x = small->data[i];
+		y = big->data[i];
+		z = 0;
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			xbit = x % 10;
+			x /= 10;
+			ybit = y % 10;
+			y /= 10;
+			if (xbit > 1 || ybit > 1) {
+				goto invalid_operation;
+			}
+			z += (xbit^ybit) ? mpd_pow10[k] : 0;
+		}
+		result->data[i] = z;
+	}
+	/* most significant word of small */
+	x = small->data[i];
+	y = big->data[i];
+	z = 0;
+	mswdigits = mpd_word_digits(x);
+	for (k = 0; k < mswdigits; k++) {
+		xbit = x % 10;
+		x /= 10;
+		ybit = y % 10;
+		y /= 10;
+		if (xbit > 1 || ybit > 1) {
+			goto invalid_operation;
+		}
+		z += (xbit^ybit) ? mpd_pow10[k] : 0;
+	}
+
+	/* scan and copy the rest of y for digit > 1 */
+	for (; k < MPD_RDIGITS; k++) {
+		ybit = y % 10;
+		y /= 10;
+		if (ybit > 1) {
+			goto invalid_operation;
+		}
+		z += ybit*mpd_pow10[k];
+	}
+	result->data[i++] = z;
+	/* scan and copy the rest of big for digit > 1 */
+	for (; i < big->len; i++) {
+		y = big->data[i];
+		for (k = 0; k < MPD_RDIGITS; k++) {
+			ybit = y % 10;
+			y /= 10;
+			if (ybit > 1) {
+				goto invalid_operation;
+			}
+		}
+		result->data[i] = big->data[i];
+	}
+
+	mpd_clear_flags(result);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, big->len);
+	mpd_qresize(result, result->len, status);
+	mpd_setdigits(result);
+	_mpd_cap(result, ctx);
+	return;
+
+invalid_operation:
+	mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+
+/******************************************************************************/
+/*                         Arithmetic operations                              */
+/******************************************************************************/
+
+/*
+ * The absolute value of a. If a is negative, the result is the same
+ * as the result of the minus operation. Otherwise, the result is the
+ * result of the plus operation.
+ */
+void
+mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+         uint32_t *status)
+{
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+	}
+
+	if (mpd_isnegative(a)) {
+		mpd_qminus(result, a, ctx, status);
+	}
+	else {
+		mpd_qplus(result, a, ctx, status);
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+static inline void
+_mpd_ptrswap(mpd_t **a, mpd_t **b)
+{
+	mpd_t *t = *a;
+	*a = *b;
+	*b = t;
+}
+
+/* Add or subtract infinities. */
+static void
+_mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
+                 uint32_t *status)
+{
+	if (mpd_isinfinite(a)) {
+		if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+		}
+		else {
+			mpd_setspecial(result, mpd_sign(a), MPD_INF);
+		}
+		return;
+	}
+	assert(mpd_isinfinite(b));
+	mpd_setspecial(result, sign_b, MPD_INF);
+}
+
+/* Add or subtract non-special numbers. */
+static void
+_mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_t *big, *small;
+	MPD_NEW_STATIC(big_aligned,0,0,0,0);
+	MPD_NEW_CONST(tiny,0,0,0,1,1,1);
+	mpd_uint_t carry;
+	mpd_ssize_t newsize, shift;
+	mpd_ssize_t exp, i;
+	int swap = 0;
+
+
+	/* compare exponents */
+	big = (mpd_t *)a; small = (mpd_t *)b;
+	if (big->exp != small->exp) {
+		if (small->exp > big->exp) {
+			_mpd_ptrswap(&big, &small);
+			swap++;
+		}
+		if (!mpd_iszerocoeff(big)) {
+			/* Test for adjexp(small) + big->digits < adjexp(big), if big-digits > prec
+			 * Test for adjexp(small) + prec + 1    < adjexp(big), if big-digits <= prec
+			 * If true, the magnitudes of the numbers are so far apart that one can as
+			 * well add or subtract 1*10**big->exp. */
+			exp = big->exp - 1;
+			exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1;
+			if (mpd_adjexp(small) < exp) {
+				mpd_copy_flags(&tiny, small);
+				tiny.exp = exp;
+				tiny.digits = 1;
+				tiny.len = 1;
+				tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1;
+				small = &tiny;
+			}
+			/* this cannot wrap: the difference is positive and <= maxprec+1 */
+			shift = big->exp - small->exp;
+			if (!mpd_qshiftl(&big_aligned, big, shift, status)) {
+				mpd_seterror(result, MPD_Malloc_error, status);
+				goto finish;
+			}
+			big = &big_aligned;
+		}
+	}
+	result->exp = small->exp;
+
+
+	/* compare length of coefficients */
+	if (big->len < small->len) {
+		_mpd_ptrswap(&big, &small);
+		swap++;
+	}
+
+	newsize = big->len;
+	if (!mpd_qresize(result, newsize, status)) {
+		goto finish;
+	}
+
+	if (mpd_sign(a) == sign_b) {
+
+		carry = _mpd_baseadd(result->data, big->data, small->data,
+		                     big->len, small->len);
+
+		if (carry) {
+			newsize = big->len + 1;
+			if (!mpd_qresize(result, newsize, status)) {
+				goto finish;
+			}
+			result->data[newsize-1] = carry;
+		}
+
+		result->len = newsize;
+		mpd_set_flags(result, sign_b);
+	}
+	else {
+		if (big->len == small->len) {
+			for (i=big->len-1; i >= 0; --i) {
+				if (big->data[i] != small->data[i]) {
+					if (big->data[i] < small->data[i]) {
+						_mpd_ptrswap(&big, &small);
+						swap++;
+					}
+					break;
+				}
+			}
+		}
+
+		_mpd_basesub(result->data, big->data, small->data,
+		             big->len, small->len);
+		newsize = _mpd_real_size(result->data, big->len);
+		/* resize to smaller cannot fail */
+		(void)mpd_qresize(result, newsize, status);
+
+		result->len = newsize;
+		sign_b = (swap & 1) ? sign_b : mpd_sign(a);
+		mpd_set_flags(result, sign_b);
+
+		if (mpd_iszerocoeff(result)) {
+			mpd_set_positive(result);
+			if (ctx->round == MPD_ROUND_FLOOR) {
+				mpd_set_negative(result);
+			}
+		}
+	}
+
+	mpd_setdigits(result);
+
+finish:
+	mpd_del(&big_aligned);
+}
+
+/* Add a and b. No specials, no finalizing. */
+static void
+_mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+          const mpd_context_t *ctx, uint32_t *status)
+{
+	_mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
+}
+
+/* Subtract b from a. No specials, no finalizing. */
+static void
+_mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	 _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
+}
+
+/* Add a and b. */
+void
+mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+		_mpd_qaddsub_inf(result, a, b, mpd_sign(b), status);
+		return;
+	}
+
+	_mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* Subtract b from a. */
+void
+mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+		_mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status);
+		return;
+	}
+
+	_mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* Add decimal and mpd_ssize_t. */
+void
+mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_ssize(&bb, b, &maxcontext, status);
+	mpd_qadd(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Add decimal and mpd_uint_t. */
+void
+mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_uint(&bb, b, &maxcontext, status);
+	mpd_qadd(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Subtract mpd_ssize_t from decimal. */
+void
+mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_ssize(&bb, b, &maxcontext, status);
+	mpd_qsub(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Subtract mpd_uint_t from decimal. */
+void
+mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_uint(&bb, b, &maxcontext, status);
+	mpd_qsub(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Add decimal and int32_t. */
+void
+mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qadd_ssize(result, a, b, ctx, status);
+}
+
+/* Add decimal and uint32_t. */
+void
+mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qadd_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Add decimal and int64_t. */
+void
+mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qadd_ssize(result, a, b, ctx, status);
+}
+
+/* Add decimal and uint64_t. */
+void
+mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qadd_uint(result, a, b, ctx, status);
+}
+#endif
+
+/* Subtract int32_t from decimal. */
+void
+mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qsub_ssize(result, a, b, ctx, status);
+}
+
+/* Subtract uint32_t from decimal. */
+void
+mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qsub_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Subtract int64_t from decimal. */
+void
+mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qsub_ssize(result, a, b, ctx, status);
+}
+
+/* Subtract uint64_t from decimal. */
+void
+mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qsub_uint(result, a, b, ctx, status);
+}
+#endif
+
+
+/* Divide infinities. */
+static void
+_mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	if (mpd_isinfinite(a)) {
+		if (mpd_isinfinite(b)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+		return;
+	}
+	assert(mpd_isinfinite(b));
+	_settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx));
+	*status |= MPD_Clamped;
+}
+
+enum {NO_IDEAL_EXP, SET_IDEAL_EXP};
+/* Divide a by b. */
+static void
+_mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b,
+          const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(aligned,0,0,0,0);
+	mpd_uint_t ld;
+	mpd_ssize_t shift, exp, tz;
+	mpd_ssize_t newsize;
+	mpd_ssize_t ideal_exp;
+	mpd_uint_t rem;
+	uint8_t sign_a = mpd_sign(a);
+	uint8_t sign_b = mpd_sign(b);
+
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			return;
+		}
+		_mpd_qdiv_inf(q, a, b, ctx, status);
+		return;
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(q, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_setspecial(q, sign_a^sign_b, MPD_INF);
+			*status |= MPD_Division_by_zero;
+		}
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		exp = a->exp - b->exp;
+		_settriple(q, sign_a^sign_b, 0, exp);
+		mpd_qfinalize(q, ctx, status);
+		return;
+	}
+
+	shift = (b->digits - a->digits) + ctx->prec + 1;
+	ideal_exp = a->exp - b->exp;
+	exp = ideal_exp - shift;
+	if (shift > 0) {
+		if (!mpd_qshiftl(&aligned, a, shift, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+		a = &aligned;
+	}
+	else if (shift < 0) {
+		shift = -shift;
+		if (!mpd_qshiftl(&aligned, b, shift, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+		b = &aligned;
+	}
+
+
+	newsize = a->len - b->len + 1;
+	if ((q != b && q != a) || (q == b && newsize > b->len)) {
+		if (!mpd_qresize(q, newsize, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+	}
+
+
+	if (b->len == 1) {
+		rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
+	}
+	else if (a->len < 2*MPD_NEWTONDIV_CUTOFF &&
+	         b->len < MPD_NEWTONDIV_CUTOFF) {
+		int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data,
+		                          a->len, b->len);
+		if (ret < 0) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+		rem = ret;
+	}
+	else {
+		MPD_NEW_STATIC(r,0,0,0,0);
+		_mpd_qbarrett_divmod(q, &r, a, b, status);
+		if (mpd_isspecial(q) || mpd_isspecial(&r)) {
+			mpd_del(&r);
+			goto finish;
+		}
+		rem = !mpd_iszerocoeff(&r);
+		mpd_del(&r);
+		newsize = q->len;
+	}
+
+	newsize = _mpd_real_size(q->data, newsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(q, newsize, status);
+	q->len = newsize;
+	mpd_setdigits(q);
+
+	shift = ideal_exp - exp;
+	if (rem) {
+		ld = mpd_lsd(q->data[0]);
+		if (ld == 0 || ld == 5) {
+			q->data[0] += 1;
+		}
+	}
+	else if (action == SET_IDEAL_EXP && shift > 0) {
+		tz = mpd_trail_zeros(q);
+		shift = (tz > shift) ? shift : tz;
+		mpd_qshiftr_inplace(q, shift);
+		exp += shift;
+	}
+
+	mpd_set_flags(q, sign_a^sign_b);
+	q->exp = exp;
+
+
+finish:
+	mpd_del(&aligned);
+	mpd_qfinalize(q, ctx, status);
+}
+
+/* Divide a by b. */
+void
+mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	_mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, status);
+}
+
+/* Internal function. */
+static void
+_mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+	     const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(aligned,0,0,0,0);
+	mpd_ssize_t qsize, rsize;
+	mpd_ssize_t ideal_exp, expdiff, shift;
+	uint8_t sign_a = mpd_sign(a);
+	uint8_t sign_ab = mpd_sign(a)^mpd_sign(b);
+
+
+	ideal_exp = (a->exp > b->exp) ?  b->exp : a->exp;
+	if (mpd_iszerocoeff(a)) {
+		if (!mpd_qcopy(r, a, status)) {
+			goto nanresult; /* GCOV_NOT_REACHED */
+		}
+		r->exp = ideal_exp;
+		_settriple(q, sign_ab, 0, 0);
+		return;
+	}
+
+	expdiff = mpd_adjexp(a) - mpd_adjexp(b);
+	if (expdiff < 0) {
+		if (a->exp > b->exp) {
+			/* positive and less than b->digits - a->digits */
+			shift = a->exp - b->exp;
+			if (!mpd_qshiftl(r, a, shift, status)) {
+				goto nanresult;
+			}
+			r->exp = ideal_exp;
+		}
+		else {
+			if (!mpd_qcopy(r, a, status)) {
+				goto nanresult;
+			}
+		}
+		_settriple(q, sign_ab, 0, 0);
+		return;
+	}
+	if (expdiff > ctx->prec) {
+		*status |= MPD_Division_impossible;
+		goto nanresult;
+	}
+
+
+	/*
+	 * At this point we have:
+	 *   (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec
+	 *   (2) a->exp - b->exp >= b->digits - a->digits
+	 *   (3) a->exp - b->exp <= prec + b->digits - a->digits
+	 */
+	if (a->exp != b->exp) {
+		shift = a->exp - b->exp;
+		if (shift > 0) {
+			/* by (3), after the shift a->digits <= prec + b->digits */
+			if (!mpd_qshiftl(&aligned, a, shift, status)) {
+				goto nanresult;
+			}
+			a = &aligned;
+		}
+		else  {
+			shift = -shift;
+			/* by (2), after the shift b->digits <= a->digits */
+			if (!mpd_qshiftl(&aligned, b, shift, status)) {
+				goto nanresult;
+			}
+			b = &aligned;
+		}
+	}
+
+
+	qsize = a->len - b->len + 1;
+	if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) {
+		if (!mpd_qresize(q, qsize, status)) {
+			goto nanresult;
+		}
+	}
+
+	rsize = b->len;
+	if (!(r == a && rsize < a->len)) {
+		if (!mpd_qresize(r, rsize, status)) {
+			goto nanresult;
+		}
+	}
+
+	if (b->len == 1) {
+		if (a->len == 1) {
+			_mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]);
+		}
+		else {
+			r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
+		}
+	}
+	else if (a->len < 2*MPD_NEWTONDIV_CUTOFF &&
+	         b->len < MPD_NEWTONDIV_CUTOFF) {
+		int ret;
+		ret = _mpd_basedivmod(q->data, r->data, a->data, b->data,
+		                      a->len, b->len);
+		if (ret == -1) {
+			*status |= MPD_Malloc_error;
+			goto nanresult;
+		}
+	}
+	else {
+		_mpd_qbarrett_divmod(q, r, a, b, status);
+		if (mpd_isspecial(q) || mpd_isspecial(r)) {
+			goto nanresult;
+		}
+		if (mpd_isinfinite(q) || q->digits > ctx->prec) {
+			*status |= MPD_Division_impossible;
+			goto nanresult;
+		}
+		qsize = q->len;
+		rsize = r->len;
+	}
+
+	qsize = _mpd_real_size(q->data, qsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(q, qsize, status);
+	q->len = qsize;
+	mpd_setdigits(q);
+	mpd_set_flags(q, sign_ab);
+	q->exp = 0;
+	if (q->digits > ctx->prec) {
+		*status |= MPD_Division_impossible;
+		goto nanresult;
+	}
+
+	rsize = _mpd_real_size(r->data, rsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(r, rsize, status);
+	r->len = rsize;
+	mpd_setdigits(r);
+	mpd_set_flags(r, sign_a);
+	r->exp = ideal_exp;
+
+out:
+	mpd_del(&aligned);
+	return;
+
+nanresult:
+	mpd_setspecial(q, MPD_POS, MPD_NAN);
+	mpd_setspecial(r, MPD_POS, MPD_NAN);
+	goto out;
+}
+
+/* Integer division with remainder. */
+void
+mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+            const mpd_context_t *ctx, uint32_t *status)
+{
+	uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			mpd_qcopy(r, q, status);
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			if (mpd_isinfinite(b)) {
+				mpd_setspecial(q, MPD_POS, MPD_NAN);
+			}
+			else {
+				mpd_setspecial(q, sign, MPD_INF);
+			}
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= MPD_Invalid_operation;
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			if (!mpd_qcopy(r, a, status)) {
+				mpd_seterror(q, MPD_Malloc_error, status);
+				return;
+			}
+			mpd_qfinalize(r, ctx, status);
+			_settriple(q, sign, 0, 0);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_setspecial(q, MPD_POS, MPD_NAN);
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= MPD_Division_undefined;
+		}
+		else {
+			mpd_setspecial(q, sign, MPD_INF);
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= (MPD_Division_by_zero|MPD_Invalid_operation);
+		}
+		return;
+	}
+
+	_mpd_qdivmod(q, r, a, b, ctx, status);
+	mpd_qfinalize(q, ctx, status);
+	mpd_qfinalize(r, ctx, status);
+}
+
+void
+mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b,
+            const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(r,0,0,0,0);
+	uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
+			mpd_seterror(q, MPD_Invalid_operation, status);
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			mpd_setspecial(q, sign, MPD_INF);
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			_settriple(q, sign, 0, 0);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(q, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_setspecial(q, sign, MPD_INF);
+			*status |= MPD_Division_by_zero;
+		}
+		return;
+	}
+
+
+	_mpd_qdivmod(q, &r, a, b, ctx, status);
+	mpd_del(&r);
+	mpd_qfinalize(q, ctx, status);
+}
+
+/* Divide decimal by mpd_ssize_t. */
+void
+mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_ssize(&bb, b, &maxcontext, status);
+	mpd_qdiv(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Divide decimal by mpd_uint_t. */
+void
+mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_uint(&bb, b, &maxcontext, status);
+	mpd_qdiv(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Divide decimal by int32_t. */
+void
+mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qdiv_ssize(result, a, b, ctx, status);
+}
+
+/* Divide decimal by uint32_t. */
+void
+mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qdiv_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Divide decimal by int64_t. */
+void
+mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qdiv_ssize(result, a, b, ctx, status);
+}
+
+/* Divide decimal by uint64_t. */
+void
+mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qdiv_uint(result, a, b, ctx, status);
+}
+#endif
+
+#if defined(_MSC_VER)
+  /* conversion from 'double' to 'mpd_ssize_t', possible loss of data */
+  #pragma warning(disable:4244)
+#endif
+/*
+ * Get the number of iterations for the Horner scheme in _mpd_qexp().
+ */
+static inline mpd_ssize_t
+_mpd_get_exp_iterations(const mpd_t *a, mpd_ssize_t prec)
+{
+	mpd_uint_t dummy;
+	mpd_uint_t msdigits;
+	double f;
+
+	/* 9 is MPD_RDIGITS for 32 bit platforms */
+	_mpd_get_msdigits(&dummy, &msdigits, a, 9);
+	f = ((double)msdigits + 1) / mpd_pow10[mpd_word_digits(msdigits)];
+
+#ifdef CONFIG_64
+  #ifdef USE_80BIT_LONG_DOUBLE
+	return ceill((1.435*(long double)prec - 1.182)
+	             / log10l((long double)prec/f));
+  #else
+	/* prec > floor((1ULL<<53) / 1.435) */
+	if (prec > 6276793905742851LL) {
+		return MPD_SSIZE_MAX;
+	}
+	return ceil((1.435*(double)prec - 1.182) / log10((double)prec/f));
+  #endif
+#else /* CONFIG_32 */
+	return ceil((1.435*(double)prec - 1.182) / log10((double)prec/f));
+	#if defined(_MSC_VER)
+	  #pragma warning(default:4244)
+	#endif
+#endif
+}
+
+/*
+ * Internal function, specials have been dealt with.
+ *
+ * The algorithm is from Hull&Abrham, Variable Precision Exponential Function,
+ * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986.
+ *
+ * Main differences:
+ *
+ *  - The number of iterations for the Horner scheme is calculated using the
+ *    C log10() function.
+ *
+ *  - The analysis for early abortion has been adapted for the mpd_t
+ *    ranges.
+ */
+static void
+_mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+          uint32_t *status)
+{
+	mpd_context_t workctx;
+	MPD_NEW_STATIC(tmp,0,0,0,0);
+	MPD_NEW_STATIC(sum,0,0,0,0);
+	MPD_NEW_CONST(word,0,0,0,1,1,1);
+	mpd_ssize_t j, n, t;
+
+	assert(!mpd_isspecial(a));
+
+	/*
+	 * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where r < 1 and t >= 0.
+	 *
+	 * If t > 0, we have:
+	 *
+	 *   (1) 0.1 <= r < 1, so e^r >= e^0.1. Overflow in the final power operation
+	 *       will occur when (e^0.1)^(10^t) > 10^(emax+1). If we consider MAX_EMAX,
+	 *       this will happen for t > 10 (32 bit) or (t > 19) (64 bit).
+	 *
+	 *   (2) -1 < r <= -0.1, so e^r > e^-1. Underflow in the final power operation
+	 *       will occur when (e^-1)^(10^t) < 10^(etiny-1). If we consider MIN_ETINY,
+	 *       this will also happen for t > 10 (32 bit) or (t > 19) (64 bit).
+	 */
+#if defined(CONFIG_64)
+	#define MPD_EXP_MAX_T 19
+#elif defined(CONFIG_32)
+	#define MPD_EXP_MAX_T 10
+#endif
+	t = a->digits + a->exp;
+	t = (t > 0) ? t : 0;
+	if (t > MPD_EXP_MAX_T) {
+		if (mpd_ispositive(a)) {
+			mpd_setspecial(result, MPD_POS, MPD_INF);
+			*status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+		}
+		else {
+			_settriple(result, MPD_POS, 0, mpd_etiny(ctx));
+			*status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal|
+			            MPD_Underflow|MPD_Clamped);
+		}
+		return;
+	}
+
+	mpd_maxcontext(&workctx);
+	workctx.prec = ctx->prec + t + 2;
+	workctx.prec = (workctx.prec < 9) ? 9 : workctx.prec;
+	workctx.round = MPD_ROUND_HALF_EVEN;
+
+	if ((n = _mpd_get_exp_iterations(a, workctx.prec)) == MPD_SSIZE_MAX) {
+		mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */
+		goto finish; /* GCOV_UNLIKELY */
+	}
+
+	if (!mpd_qcopy(result, a, status)) {
+		goto finish;
+	}
+	result->exp -= t;
+
+	_settriple(&sum, MPD_POS, 1, 0);
+
+	for (j = n-1; j >= 1; j--) {
+		word.data[0] = j;
+		mpd_setdigits(&word);
+		mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status);
+		mpd_qmul(&sum, &sum, &tmp, &workctx, &workctx.status);
+		mpd_qadd(&sum, &sum, &one, &workctx, &workctx.status);
+	}
+
+#ifdef CONFIG_64
+	_mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
+#else
+	if (t <= MPD_MAX_POW10) {
+		_mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
+	}
+	else {
+		t -= MPD_MAX_POW10;
+		_mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS,
+		               &workctx, status);
+		_mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status);
+	}
+#endif
+
+
+finish:
+	mpd_del(&tmp);
+	mpd_del(&sum);
+	*status |= (workctx.status&MPD_Errors);
+	*status |= (MPD_Inexact|MPD_Rounded);
+}
+
+/* exp(a) */
+void
+mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+         uint32_t *status)
+{
+	mpd_context_t workctx;
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isnegative(a)) {
+			_settriple(result, MPD_POS, 0, 0);
+		}
+		else {
+			mpd_setspecial(result, MPD_POS, MPD_INF);
+		}
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		_settriple(result, MPD_POS, 1, 0);
+		return;
+	}
+
+	workctx = *ctx;
+	workctx.round = MPD_ROUND_HALF_EVEN;
+
+	if (ctx->allcr) {
+		MPD_NEW_STATIC(t1, 0,0,0,0);
+		MPD_NEW_STATIC(t2, 0,0,0,0);
+		MPD_NEW_STATIC(ulp, 0,0,0,0);
+		MPD_NEW_STATIC(aa, 0,0,0,0);
+		mpd_ssize_t prec;
+
+		if (result == a) {
+			if (!mpd_qcopy(&aa, a, status)) {
+				mpd_seterror(result, MPD_Malloc_error, status);
+				return;
+			}
+			a = &aa;
+		}
+
+		workctx.clamp = 0;
+		prec = ctx->prec + 3;
+		while (1) {
+			workctx.prec = prec;
+			_mpd_qexp(result, a, &workctx, status);
+			_ssettriple(&ulp, MPD_POS, 1,
+			            result->exp + result->digits-workctx.prec-1);
+
+			workctx.prec = ctx->prec;
+			mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+			mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+			if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+			    mpd_qcmp(&t1, &t2, status) == 0) {
+				workctx.clamp = ctx->clamp;
+				mpd_check_underflow(result, &workctx, status);
+				mpd_qfinalize(result, &workctx, status);
+				break;
+			}
+			prec += MPD_RDIGITS;
+		}
+		mpd_del(&t1);
+		mpd_del(&t2);
+		mpd_del(&ulp);
+		mpd_del(&aa);
+	}
+	else {
+		_mpd_qexp(result, a, &workctx, status);
+		mpd_check_underflow(result, &workctx, status);
+		mpd_qfinalize(result, &workctx, status);
+	}
+}
+
+/* Fused multiply-add: (a * b) + c, with a single final rounding. */
+void
+mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_t *cc = (mpd_t *)c;
+
+	if (result == c) {
+		if ((cc = mpd_qncopy(c)) == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			return;
+		}
+	}
+
+	_mpd_qmul(result, a, b, ctx, &workstatus);
+	if (!(workstatus&MPD_Invalid_operation)) {
+		mpd_qadd(result, result, cc, ctx, &workstatus);
+	}
+
+	if (cc != c) mpd_del(cc);
+	*status |= workstatus;
+}
+
+static inline int
+ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec,
+                 mpd_ssize_t initprec)
+{
+	mpd_ssize_t k;
+	int i;
+
+	assert(maxprec >= 2 && initprec >= 2);
+	if (maxprec <= initprec) return -1;
+
+	i = 0; k = maxprec;
+	do {
+		k = (k+2) / 2;
+		klist[i++] = k;
+	} while (k > initprec);
+
+	return i-1;
+}
+
+/* Two word initial approximations for ln(10) */
+#ifdef CONFIG_64
+#if MPD_RDIGITS != 19
+  #error "mpdecimal.c: MPD_RDIGITS must be 19."
+#endif
+static mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {
+  179914546843642076, 2302585092994045684
+};
+static mpd_uint_t mpd_ln10_init[2] = {
+  179914546843642076, 2302585092994045684
+};
+#else
+#if MPD_RDIGITS != 9
+  #error "mpdecimal.c: MPD_RDIGITS must be 9."
+#endif
+static mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {299404568, 230258509};
+static mpd_uint_t mpd_ln10_init[2] = {299404568, 230258509};
+#endif
+/* mpd_ln10 is cached in order to speed up computations */
+mpd_t mpd_ln10 = {MPD_STATIC|MPD_STATIC_DATA, -(2*MPD_RDIGITS-1),
+                  2*MPD_RDIGITS, 2, MPD_MINALLOC_MAX, mpd_ln10_data};
+
+static void
+mpd_reset_ln10(void)
+{
+	if (mpd_isdynamic_data(&mpd_ln10)) {
+		mpd_free(mpd_ln10.data);
+	}
+	mpd_ln10.data = mpd_ln10_data;
+	mpd_ln10_data[0] = mpd_ln10_init[0];
+	mpd_ln10_data[1] = mpd_ln10_init[1];
+	mpd_ln10.flags = MPD_STATIC|MPD_STATIC_DATA;
+	mpd_ln10.exp = -(2*MPD_RDIGITS-1);
+	mpd_ln10.digits = 2*MPD_RDIGITS;
+	mpd_ln10.len = 2;
+	mpd_ln10.alloc = MPD_MINALLOC_MAX;
+}
+
+/*
+ * Initializes or updates mpd_ln10. If mpd_ln10 is cached and has exactly the
+ * requested precision, the function returns. If the cached precision is greater
+ * than the requested precision, mpd_ln10 is shifted to the requested precision.
+ *
+ * The function can fail with MPD_Malloc_error.
+ */
+void
+mpd_update_ln10(mpd_ssize_t maxprec, uint32_t *status)
+{
+	mpd_context_t varcontext, maxcontext;
+	MPD_NEW_STATIC(tmp, 0,0,0,0);
+	MPD_NEW_CONST(static10, 0,0,2,1,1,10);
+	mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+	int i;
+
+	if (mpd_isspecial(&mpd_ln10)) {
+		mpd_reset_ln10();
+	}
+
+	if (mpd_ln10.digits > maxprec) {
+		/* shift to smaller cannot fail */
+		mpd_qshiftr_inplace(&mpd_ln10, mpd_ln10.digits-maxprec);
+		mpd_ln10.exp = -(mpd_ln10.digits-1);
+		return;
+	}
+	else if (mpd_ln10.digits == maxprec) {
+		return;
+	}
+
+	mpd_maxcontext(&maxcontext);
+	mpd_maxcontext(&varcontext);
+	varcontext.round = MPD_ROUND_TRUNC;
+
+	i = ln_schedule_prec(klist, maxprec+2, mpd_ln10.digits);
+	for (; i >= 0; i--) {
+		varcontext.prec = 2*klist[i]+3;
+		mpd_ln10.flags ^= MPD_NEG;
+		_mpd_qexp(&tmp, &mpd_ln10, &varcontext, status);
+		mpd_ln10.flags ^= MPD_NEG;
+		mpd_qmul(&tmp, &static10, &tmp, &varcontext, status);
+		mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
+		mpd_qadd(&mpd_ln10, &mpd_ln10, &tmp, &maxcontext, status);
+		if (mpd_isspecial(&mpd_ln10)) {
+			break;
+		}
+	}
+
+	mpd_del(&tmp);
+	varcontext.prec = maxprec;
+	varcontext.round = MPD_ROUND_HALF_EVEN;
+	mpd_qfinalize(&mpd_ln10, &varcontext, status);
+}
+
+/* Initial approximations for the ln() iteration */
+static const uint16_t lnapprox[900] = {
+  /* index 0 - 400: log((i+100)/100) * 1000 */
+  0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157,
+  166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278,
+  285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385,
+  392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482,
+  489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571,
+  577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652,
+  658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728,
+  732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798,
+  802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863,
+  867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924,
+  928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982,
+  986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030,
+  1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075,
+  1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118,
+  1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160,
+  1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200,
+  1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238,
+  1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275,
+  1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311,
+  1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345,
+  1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379,
+  1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411,
+  1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442,
+  1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472,
+  1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502,
+  1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530,
+  1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558,
+  1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585,
+  1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609,
+  /* index 401 - 899: -log((i+100)/1000) * 1000 */
+  691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664,
+  662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635,
+  633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607,
+  605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580,
+  578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553,
+  552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528,
+  526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502,
+  501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478,
+  476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454,
+  453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431,
+  429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408,
+  406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386,
+  384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364,
+  362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342,
+  341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322,
+  320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301,
+  300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281,
+  280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261,
+  260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242,
+  241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223,
+  222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205,
+  203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186,
+  185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168,
+  167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151,
+  150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134,
+  132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116,
+  115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100,
+  99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79,
+  78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59,
+  58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39,
+  38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19,
+  18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
+};
+
+/* Internal ln() function that does not check for specials, zero or one. */
+static void
+_mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+         uint32_t *status)
+{
+	mpd_context_t varcontext, maxcontext;
+	mpd_t *z = (mpd_t *) result;
+	MPD_NEW_STATIC(v,0,0,0,0);
+	MPD_NEW_STATIC(vtmp,0,0,0,0);
+	MPD_NEW_STATIC(tmp,0,0,0,0);
+	mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+	mpd_ssize_t maxprec, shift, t;
+	mpd_ssize_t a_digits, a_exp;
+	mpd_uint_t dummy, x;
+	int i;
+
+	assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a));
+
+	/*
+	 * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10),
+	 * where 0.5 < v <= 5.
+	 */
+	if (!mpd_qcopy(&v, a, status)) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		goto finish;
+	}
+
+	/* Initial approximation: we have at least one non-zero digit */
+	_mpd_get_msdigits(&dummy, &x, &v, 3);
+	if (x < 10) x *= 10;
+	if (x < 100) x *= 10;
+	x -= 100;
+
+	/* a may equal z */
+	a_digits = a->digits;
+	a_exp = a->exp;
+
+	mpd_minalloc(z);
+	mpd_clear_flags(z);
+	z->data[0] = lnapprox[x];
+	z->len = 1;
+	z->exp = -3;
+	mpd_setdigits(z);
+
+	if (x <= 400) {
+		v.exp = -(a_digits - 1);
+		t = a_exp + a_digits - 1;
+	}
+	else {
+		v.exp = -a_digits;
+		t = a_exp + a_digits;
+		mpd_set_negative(z);
+	}
+
+	mpd_maxcontext(&maxcontext);
+	mpd_maxcontext(&varcontext);
+	varcontext.round = MPD_ROUND_TRUNC;
+
+	maxprec = ctx->prec + 2;
+	if (x <= 10 || x >= 805) {
+		/* v is close to 1: Estimate the magnitude of the logarithm.
+		 * If v = 1 or ln(v) will underflow, skip the loop. Otherwise,
+		 * adjust the precision upwards in order to obtain a sufficient
+		 * number of significant digits.
+		 *
+		 *   1) x/(1+x) < ln(1+x) < x, for x > -1, x != 0
+		 *
+		 *   2) (v-1)/v < ln(v) < v-1
+		 */
+		mpd_t *lower = &tmp;
+		mpd_t *upper = &vtmp;
+		int cmp = _mpd_cmp(&v, &one);
+
+		varcontext.round = MPD_ROUND_CEILING;
+		varcontext.prec = maxprec;
+		mpd_qsub(upper, &v, &one, &varcontext, &varcontext.status);
+		varcontext.round = MPD_ROUND_FLOOR;
+		mpd_qdiv(lower, upper, &v, &varcontext, &varcontext.status);
+		varcontext.round = MPD_ROUND_TRUNC;
+
+		if (cmp < 0) {
+			_mpd_ptrswap(&upper, &lower);
+		}
+		if (mpd_adjexp(upper) < mpd_etiny(ctx)) {
+			_settriple(z, (cmp<0), 1, mpd_etiny(ctx)-1);
+			goto postloop;
+		}
+		if (mpd_adjexp(lower) < 0) {
+			maxprec = maxprec - mpd_adjexp(lower);
+		}
+	}
+
+	i = ln_schedule_prec(klist, maxprec, 2);
+	for (; i >= 0; i--) {
+		varcontext.prec = 2*klist[i]+3;
+		z->flags ^= MPD_NEG;
+		_mpd_qexp(&tmp, z, &varcontext, status);
+		z->flags ^= MPD_NEG;
+
+		if (v.digits > varcontext.prec) {
+			shift = v.digits - varcontext.prec;
+			mpd_qshiftr(&vtmp, &v, shift, status);
+			vtmp.exp += shift;
+			mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status);
+		}
+		else {
+			mpd_qmul(&tmp, &v, &tmp, &varcontext, status);
+		}
+
+		mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
+		mpd_qadd(z, z, &tmp, &maxcontext, status);
+		if (mpd_isspecial(z)) {
+			break;
+		}
+	}
+
+postloop:
+	mpd_update_ln10(maxprec+2, status);
+	mpd_qmul_ssize(&tmp, &mpd_ln10, t, &maxcontext, status);
+	varcontext.prec = maxprec+2;
+	mpd_qadd(result, &tmp, z, &varcontext, status);
+
+
+finish:
+	mpd_del(&v);
+	mpd_del(&vtmp);
+	mpd_del(&tmp);
+}
+
+/* ln(a) */
+void
+mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+        uint32_t *status)
+{
+	mpd_context_t workctx;
+	mpd_ssize_t adjexp, t;
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isnegative(a)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		mpd_setspecial(result, MPD_POS, MPD_INF);
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		mpd_setspecial(result, MPD_NEG, MPD_INF);
+		return;
+	}
+	if (mpd_isnegative(a)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (_mpd_cmp(a, &one) == 0) {
+		_settriple(result, MPD_POS, 0, 0);
+		return;
+	}
+	/* Check if the result will overflow.
+	 *
+	 * 1) adjexp(a) + 1 > log10(a) >= adjexp(a)
+	 *
+	 * 2) |log10(a)| >= adjexp(a), if adjexp(a) >= 0
+	 *    |log10(a)| > -adjexp(a)-1, if adjexp(a) < 0
+	 *
+	 * 3) |log(a)| > 2*|log10(a)|
+	 */
+	adjexp = mpd_adjexp(a);
+	t = (adjexp < 0) ? -adjexp-1 : adjexp;
+	t *= 2;
+	if (mpd_exp_digits(t)-1 > ctx->emax) {
+		*status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+		mpd_setspecial(result, (adjexp<0), MPD_INF);
+		return;
+	}
+
+	workctx = *ctx;
+	workctx.round = MPD_ROUND_HALF_EVEN;
+
+	if (ctx->allcr) {
+		MPD_NEW_STATIC(t1, 0,0,0,0);
+		MPD_NEW_STATIC(t2, 0,0,0,0);
+		MPD_NEW_STATIC(ulp, 0,0,0,0);
+		MPD_NEW_STATIC(aa, 0,0,0,0);
+		mpd_ssize_t prec;
+
+		if (result == a) {
+			if (!mpd_qcopy(&aa, a, status)) {
+				mpd_seterror(result, MPD_Malloc_error, status);
+				return;
+			}
+			a = &aa;
+		}
+
+		workctx.clamp = 0;
+		prec = ctx->prec + 3;
+		while (1) {
+			workctx.prec = prec;
+			_mpd_qln(result, a, &workctx, status);
+			_ssettriple(&ulp, MPD_POS, 1,
+			            result->exp + result->digits-workctx.prec-1);
+
+			workctx.prec = ctx->prec;
+			mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+			mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+			if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+			    mpd_qcmp(&t1, &t2, status) == 0) {
+				workctx.clamp = ctx->clamp;
+				mpd_check_underflow(result, &workctx, status);
+				mpd_qfinalize(result, &workctx, status);
+				break;
+			}
+			prec += MPD_RDIGITS;
+		}
+		mpd_del(&t1);
+		mpd_del(&t2);
+		mpd_del(&ulp);
+		mpd_del(&aa);
+	}
+	else {
+		_mpd_qln(result, a, &workctx, status);
+		mpd_check_underflow(result, &workctx, status);
+		mpd_qfinalize(result, &workctx, status);
+	}
+}
+
+/* Internal log10() function that does not check for specials, zero, ... */
+static void
+_mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+            uint32_t *status)
+{
+	mpd_context_t workctx;
+
+	mpd_maxcontext(&workctx);
+	workctx.prec = ctx->prec + 3;
+	_mpd_qln(result, a, &workctx, status);
+	mpd_update_ln10(workctx.prec, status);
+
+	workctx = *ctx;
+	workctx.round = MPD_ROUND_HALF_EVEN;
+	_mpd_qdiv(NO_IDEAL_EXP, result, result, &mpd_ln10, &workctx, status);
+}
+
+/* log10(a) */
+void
+mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+           uint32_t *status)
+{
+	mpd_context_t workctx;
+	mpd_ssize_t adjexp, t;
+
+	workctx = *ctx;
+	workctx.round = MPD_ROUND_HALF_EVEN;
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isnegative(a)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		mpd_setspecial(result, MPD_POS, MPD_INF);
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		mpd_setspecial(result, MPD_NEG, MPD_INF);
+		return;
+	}
+	if (mpd_isnegative(a)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_coeff_ispow10(a)) {
+		uint8_t sign = 0;
+		adjexp = mpd_adjexp(a);
+		if (adjexp < 0) {
+			sign = 1;
+			adjexp = -adjexp;
+		}
+		_settriple(result, sign, adjexp, 0);
+		mpd_qfinalize(result, &workctx, status);
+		return;
+	}
+	/* Check if the result will overflow.
+	 *
+	 * 1) adjexp(a) + 1 > log10(a) >= adjexp(a)
+	 *
+	 * 2) |log10(a)| >= adjexp(a), if adjexp(a) >= 0
+	 *    |log10(a)| > -adjexp(a)-1, if adjexp(a) < 0
+	 */
+	adjexp = mpd_adjexp(a);
+	t = (adjexp < 0) ? -adjexp-1 : adjexp;
+	if (mpd_exp_digits(t)-1 > ctx->emax) {
+		*status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+		mpd_setspecial(result, (adjexp<0), MPD_INF);
+		return;
+	}
+
+	if (ctx->allcr) {
+		MPD_NEW_STATIC(t1, 0,0,0,0);
+		MPD_NEW_STATIC(t2, 0,0,0,0);
+		MPD_NEW_STATIC(ulp, 0,0,0,0);
+		MPD_NEW_STATIC(aa, 0,0,0,0);
+		mpd_ssize_t prec;
+
+		if (result == a) {
+			if (!mpd_qcopy(&aa, a, status)) {
+				mpd_seterror(result, MPD_Malloc_error, status);
+				return;
+			}
+			a = &aa;
+		}
+
+		workctx.clamp = 0;
+		prec = ctx->prec + 3;
+		while (1) {
+			workctx.prec = prec;
+			_mpd_qlog10(result, a, &workctx, status);
+			_ssettriple(&ulp, MPD_POS, 1,
+			            result->exp + result->digits-workctx.prec-1);
+
+			workctx.prec = ctx->prec;
+			mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+			mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+			if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+			    mpd_qcmp(&t1, &t2, status) == 0) {
+				workctx.clamp = ctx->clamp;
+				mpd_check_underflow(result, &workctx, status);
+				mpd_qfinalize(result, &workctx, status);
+				break;
+			}
+			prec += MPD_RDIGITS;
+		}
+		mpd_del(&t1);
+		mpd_del(&t2);
+		mpd_del(&ulp);
+		mpd_del(&aa);
+	}
+	else {
+		_mpd_qlog10(result, a, &workctx, status);
+		mpd_check_underflow(result, &workctx, status);
+	}
+}
+
+/*
+ * Maximum of the two operands. Attention: If one operand is a quiet NaN and the
+ * other is numeric, the numeric operand is returned. This may not be what one
+ * expects.
+ */
+void
+mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isqnan(a) && !mpd_isnan(b)) {
+		mpd_qcopy(result, b, status);
+	}
+	else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+		mpd_qcopy(result, a, status);
+	}
+	else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+		return;
+	}
+	else {
+		c = _mpd_cmp(a, b);
+		if (c == 0) {
+			c = _mpd_cmp_numequal(a, b);
+		}
+
+		if (c < 0) {
+			mpd_qcopy(result, b, status);
+		}
+		else {
+			mpd_qcopy(result, a, status);
+		}
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Maximum magnitude: Same as mpd_max(), but compares the operands with their
+ * sign ignored.
+ */
+void
+mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isqnan(a) && !mpd_isnan(b)) {
+		mpd_qcopy(result, b, status);
+	}
+	else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+		mpd_qcopy(result, a, status);
+	}
+	else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+		return;
+	}
+	else {
+		c = _mpd_cmp_abs(a, b);
+		if (c == 0) {
+			c = _mpd_cmp_numequal(a, b);
+		}
+
+		if (c < 0) {
+			mpd_qcopy(result, b, status);
+		}
+		else {
+			mpd_qcopy(result, a, status);
+		}
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Minimum of the two operands. Attention: If one operand is a quiet NaN and the
+ * other is numeric, the numeric operand is returned. This may not be what one
+ * expects.
+ */
+void
+mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isqnan(a) && !mpd_isnan(b)) {
+		mpd_qcopy(result, b, status);
+	}
+	else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+		mpd_qcopy(result, a, status);
+	}
+	else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+		return;
+	}
+	else {
+		c = _mpd_cmp(a, b);
+		if (c == 0) {
+			c = _mpd_cmp_numequal(a, b);
+		}
+
+		if (c < 0) {
+			mpd_qcopy(result, a, status);
+		}
+		else {
+			mpd_qcopy(result, b, status);
+		}
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Minimum magnitude: Same as mpd_min(), but compares the operands with their
+ * sign ignored.
+ */
+void
+mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isqnan(a) && !mpd_isnan(b)) {
+		mpd_qcopy(result, b, status);
+	}
+	else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+		mpd_qcopy(result, a, status);
+	}
+	else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+		return;
+	}
+	else {
+		c = _mpd_cmp_abs(a, b);
+		if (c == 0) {
+			c = _mpd_cmp_numequal(a, b);
+		}
+
+		if (c < 0) {
+			mpd_qcopy(result, a, status);
+		}
+		else {
+			mpd_qcopy(result, b, status);
+		}
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* Minimum space needed for the result array in _karatsuba_rec(). */
+static inline mpd_size_t
+_kmul_resultsize(mpd_size_t la, mpd_size_t lb)
+{
+	mpd_size_t n, m;
+
+	n = add_size_t(la, lb);
+	n = add_size_t(n, 1);
+
+	m = (la+1)/2 + 1;
+	m = mul_size_t(m, 3);
+
+	return (m > n) ? m : n;
+}
+
+/* Work space needed in _karatsuba_rec(). lim >= 4 */
+static inline mpd_size_t
+_kmul_worksize(mpd_size_t n, mpd_size_t lim)
+{
+	mpd_size_t m;
+
+	if (n <= lim) {
+		return 0;
+	}
+
+	m = (n+1)/2 + 1;
+
+	return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim));
+}
+
+
+#define MPD_KARATSUBA_BASECASE 16  /* must be >= 4 */
+
+/*
+ * Add the product of a and b to c.
+ * c must be _kmul_resultsize(la, lb) in size.
+ * w is used as a work array and must be _kmul_worksize(a, lim) in size.
+ * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication
+ * Algorithm. In "Design and implementation of symbolic computation systems",
+ * Springer, 1993, ISBN 354057235X, 9783540572350.
+ */
+static void
+_karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
+               mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
+{
+	mpd_size_t m, lt;
+
+	assert (la >= lb && lb > 0);
+
+	if (la <= MPD_KARATSUBA_BASECASE) {
+		_mpd_basemul(c, a, b, la, lb);
+		return;
+	}
+
+	m = (la+1)/2;  // ceil(la/2)
+
+	/* lb <= m < la */
+	if (lb <= m) {
+
+		/* lb can now be larger than la-m */
+		if (lb > la-m) {
+			lt = lb + lb + 1;       // space needed for result array
+			mpd_uint_zero(w, lt);   // clear result array
+			_karatsuba_rec(w, b, a+m, w+lt, lb, la-m); // b*ah
+		}
+		else {
+			lt = (la-m) + (la-m) + 1;  // space needed for result array
+			mpd_uint_zero(w, lt);      // clear result array
+			_karatsuba_rec(w, a+m, b, w+lt, la-m, lb); // ah*b
+		}
+		_mpd_baseaddto(c+m, w, (la-m)+lb);      // add ah*b*B**m
+
+		lt = m + m + 1;         // space needed for the result array
+		mpd_uint_zero(w, lt);   // clear result array
+		_karatsuba_rec(w, a, b, w+lt, m, lb);  // al*b
+		_mpd_baseaddto(c, w, m+lb);    // add al*b
+
+		return;
+	}
+
+	/* la >= lb > m */
+	memcpy(w, a, m * sizeof *w);
+	w[m] = 0;
+	_mpd_baseaddto(w, a+m, la-m);
+
+	memcpy(w+(m+1), b, m * sizeof *w);
+	w[m+1+m] = 0;
+	_mpd_baseaddto(w+(m+1), b+m, lb-m);
+
+	_karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1);
+
+	lt = (la-m) + (la-m) + 1;
+	mpd_uint_zero(w, lt);
+
+	_karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m);
+
+	_mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
+	_mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
+
+	lt = m + m + 1;
+	mpd_uint_zero(w, lt);
+
+	_karatsuba_rec(w, a, b, w+lt, m, m);
+	_mpd_baseaddto(c, w, m+m);
+	_mpd_basesubfrom(c+m, w, m+m);
+
+	return;
+}
+
+/*
+ * Multiply u and v, using Karatsuba multiplication. Returns a pointer
+ * to the result or NULL in case of failure (malloc error).
+ * Conditions: ulen >= vlen, ulen >= 4
+ */
+mpd_uint_t *
+_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v,
+          mpd_size_t ulen, mpd_size_t vlen,
+          mpd_size_t *rsize)
+{
+	mpd_uint_t *result = NULL, *w = NULL;
+	mpd_size_t m;
+
+	assert(ulen >= 4);
+	assert(ulen >= vlen);
+
+	*rsize = _kmul_resultsize(ulen, vlen);
+	if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
+		return NULL;
+	}
+
+	m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE);
+	if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
+		mpd_free(result);
+		return NULL;
+	}
+
+	_karatsuba_rec(result, u, v, w, ulen, vlen);
+
+
+	if (w) mpd_free(w);
+	return result;
+}
+
+
+/* Determine the minimum length for the number theoretic transform. */
+static inline mpd_size_t
+_mpd_get_transform_len(mpd_size_t rsize)
+{
+	mpd_size_t log2rsize;
+	mpd_size_t x, step;
+
+	assert(rsize >= 4);
+	log2rsize = mpd_bsr(rsize);
+
+	if (rsize <= 1024) {
+		x = ONE_UM<<log2rsize;
+		return (rsize == x) ? x : x<<1;
+	}
+	else if (rsize <= MPD_MAXTRANSFORM_2N) {
+		x = ONE_UM<<log2rsize;
+		if (rsize == x) return x;
+		step = x>>1;
+		x += step;
+		return (rsize <= x) ? x : x + step;
+	}
+	else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) {
+		return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2;
+	}
+	else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
+		return 3*MPD_MAXTRANSFORM_2N;
+	}
+	else {
+		return MPD_SIZE_MAX;
+	}
+}
+
+#ifdef PPRO
+#ifndef _MSC_VER
+static inline unsigned short
+_mpd_get_control87(void)
+{
+	unsigned short cw;
+
+	__asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
+	return cw;
+}
+
+static inline void
+_mpd_set_control87(unsigned short cw)
+{
+	__asm__ __volatile__ ("fldcw %0" : : "m" (cw));
+}
+#endif
+
+unsigned int
+mpd_set_fenv(void)
+{
+	unsigned int cw;
+#ifdef _MSC_VER
+	cw = _control87(0, 0);
+	_control87((_RC_CHOP|_PC_64), (_MCW_RC|_MCW_PC));
+#else
+	cw = _mpd_get_control87();
+	_mpd_set_control87(cw|0x780);
+#endif
+	return cw;
+}
+
+void
+mpd_restore_fenv(unsigned int cw)
+{
+#ifdef _MSC_VER
+	_control87(cw, (_MCW_RC|_MCW_PC));
+#else
+	_mpd_set_control87((unsigned short)cw);
+#endif
+}
+#endif /* PPRO */
+
+/*
+ * Multiply u and v, using the fast number theoretic transform. Returns
+ * a pointer to the result or NULL in case of failure (malloc error).
+ */
+mpd_uint_t *
+_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v,
+            mpd_size_t ulen, mpd_size_t vlen,
+            mpd_size_t *rsize)
+{
+	mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL;
+	mpd_size_t n;
+
+#ifdef PPRO
+	unsigned int cw;
+	cw = mpd_set_fenv();
+#endif
+
+	*rsize = add_size_t(ulen, vlen);
+	if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) {
+		goto malloc_error;
+	}
+
+	if ((c1 = mpd_calloc(sizeof *c1, n)) == NULL) {
+		goto malloc_error;
+	}
+	if ((c2 = mpd_calloc(sizeof *c2, n)) == NULL) {
+		goto malloc_error;
+	}
+	if ((c3 = mpd_calloc(sizeof *c3, n)) == NULL) {
+		goto malloc_error;
+	}
+
+	memcpy(c1, u, ulen * (sizeof *c1));
+	memcpy(c2, u, ulen * (sizeof *c2));
+	memcpy(c3, u, ulen * (sizeof *c3));
+
+	if (u == v) {
+		if (!fnt_autoconvolute(c1, n, P1) ||
+		    !fnt_autoconvolute(c2, n, P2) ||
+		    !fnt_autoconvolute(c3, n, P3)) {
+			goto malloc_error;
+		}
+	}
+	else {
+		if ((vtmp = mpd_calloc(sizeof *vtmp, n)) == NULL) {
+			goto malloc_error;
+		}
+
+		memcpy(vtmp, v, vlen * (sizeof *vtmp));
+		if (!fnt_convolute(c1, vtmp, n, P1)) {
+			mpd_free(vtmp);
+			goto malloc_error;
+		}
+
+		memcpy(vtmp, v, vlen * (sizeof *vtmp));
+		mpd_uint_zero(vtmp+vlen, n-vlen);
+		if (!fnt_convolute(c2, vtmp, n, P2)) {
+			mpd_free(vtmp);
+			goto malloc_error;
+		}
+
+		memcpy(vtmp, v, vlen * (sizeof *vtmp));
+		mpd_uint_zero(vtmp+vlen, n-vlen);
+		if (!fnt_convolute(c3, vtmp, n, P3)) {
+			mpd_free(vtmp);
+			goto malloc_error;
+		}
+
+		mpd_free(vtmp);
+	}
+
+	crt3(c1, c2, c3, *rsize);
+
+out:
+#ifdef PPRO
+	mpd_restore_fenv(cw);
+#endif
+	if (c2) mpd_free(c2);
+	if (c3) mpd_free(c3);
+	return c1;
+
+malloc_error:
+	if (c1) mpd_free(c1);
+	c1 = NULL;
+	goto out;
+}
+
+
+/*
+ * Karatsuba multiplication with FNT/basemul as the base case.
+ */
+static int
+_karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
+                   mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
+{
+	mpd_size_t m, lt;
+
+	assert (la >= lb && lb > 0);
+
+	if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) {
+
+		if (lb <= 192) {
+			_mpd_basemul(c, b, a, lb, la);
+		}
+		else {
+			mpd_uint_t *result;
+			mpd_size_t dummy;
+
+			if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) {
+				return 0;
+			}
+			memcpy(c, result, (la+lb) * (sizeof *result));
+			mpd_free(result);
+		}
+		return 1;
+	}
+
+	m = (la+1)/2;  // ceil(la/2)
+
+	/* lb <= m < la */
+	if (lb <= m) {
+
+		/* lb can now be larger than la-m */
+		if (lb > la-m) {
+			lt = lb + lb + 1;       // space needed for result array
+			mpd_uint_zero(w, lt);   // clear result array
+			if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { // b*ah
+				return 0; /* GCOV_UNLIKELY */
+			}
+		}
+		else {
+			lt = (la-m) + (la-m) + 1;  // space needed for result array
+			mpd_uint_zero(w, lt);      // clear result array
+			if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { // ah*b
+				return 0; /* GCOV_UNLIKELY */
+			}
+		}
+		_mpd_baseaddto(c+m, w, (la-m)+lb); // add ah*b*B**m
+
+		lt = m + m + 1;         // space needed for the result array
+		mpd_uint_zero(w, lt);   // clear result array
+		if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) {  // al*b
+			return 0; /* GCOV_UNLIKELY */
+		}
+		_mpd_baseaddto(c, w, m+lb);       // add al*b
+
+		return 1;
+	}
+
+	/* la >= lb > m */
+	memcpy(w, a, m * sizeof *w);
+	w[m] = 0;
+	_mpd_baseaddto(w, a+m, la-m);
+
+	memcpy(w+(m+1), b, m * sizeof *w);
+	w[m+1+m] = 0;
+	_mpd_baseaddto(w+(m+1), b+m, lb-m);
+
+	if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) {
+		return 0; /* GCOV_UNLIKELY */
+	}
+
+	lt = (la-m) + (la-m) + 1;
+	mpd_uint_zero(w, lt);
+
+	if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) {
+		return 0; /* GCOV_UNLIKELY */
+	}
+
+	_mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
+	_mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
+
+	lt = m + m + 1;
+	mpd_uint_zero(w, lt);
+
+	if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) {
+		return 0; /* GCOV_UNLIKELY */
+	}
+	_mpd_baseaddto(c, w, m+m);
+	_mpd_basesubfrom(c+m, w, m+m);
+
+	return 1;
+}
+
+/*
+ * Multiply u and v, using Karatsuba multiplication with the FNT as the
+ * base case. Returns a pointer to the result or NULL in case of failure
+ * (malloc error). Conditions: ulen >= vlen, ulen >= 4.
+ */
+mpd_uint_t *
+_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v,
+              mpd_size_t ulen, mpd_size_t vlen,
+              mpd_size_t *rsize)
+{
+	mpd_uint_t *result = NULL, *w = NULL;
+	mpd_size_t m;
+
+	assert(ulen >= 4);
+	assert(ulen >= vlen);
+
+	*rsize = _kmul_resultsize(ulen, vlen);
+	if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
+		return NULL;
+	}
+
+	m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2));
+	if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
+		mpd_free(result); /* GCOV_UNLIKELY */
+		return NULL; /* GCOV_UNLIKELY */
+	}
+
+	if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) {
+		mpd_free(result);
+		result = NULL;
+	}
+
+
+	if (w) mpd_free(w);
+	return result;
+}
+
+
+/* Deal with the special cases of multiplying infinities. */
+static void
+_mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+	if (mpd_isinfinite(a)) {
+		if (mpd_iszero(b)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+		}
+		else {
+			mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+		}
+		return;
+	}
+	assert(mpd_isinfinite(b));
+	if (mpd_iszero(a)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+	}
+	else {
+		mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+	}
+}
+
+/*
+ * Internal function: Multiply a and b. _mpd_qmul deals with specials but
+ * does NOT finalize the result. This is for use in mpd_fma().
+ */
+static inline void
+_mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+          const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_t *big = (mpd_t *)a, *small = (mpd_t *)b;
+	mpd_uint_t *rdata = NULL;
+	mpd_uint_t rbuf[MPD_MINALLOC_MAX];
+	mpd_size_t rsize, i;
+
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+		_mpd_qmul_inf(result, a, b, status);
+		return;
+	}
+
+	if (small->len > big->len) {
+		_mpd_ptrswap(&big, &small);
+	}
+
+	rsize = big->len + small->len;
+
+	if (big->len == 1) {
+		_mpd_singlemul(result->data, big->data[0], small->data[0]);
+		goto finish;
+	}
+	if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) {
+		if (big->len == 2) {
+			_mpd_mul_2_le2(rbuf, big->data, small->data, small->len);
+		}
+		else {
+			mpd_uint_zero(rbuf, rsize);
+			if (small->len == 1) {
+				_mpd_shortmul(rbuf, big->data, big->len, small->data[0]);
+			}
+			else {
+				_mpd_basemul(rbuf, small->data, big->data, small->len, big->len);
+			}
+		}
+		if (!mpd_qresize(result, rsize, status)) {
+			return;
+		}
+		for(i = 0; i < rsize; i++) {
+			result->data[i] = rbuf[i];
+		}
+		goto finish;
+	}
+
+
+	if (small->len == 1) {
+		if ((rdata = mpd_calloc(rsize, sizeof *rdata)) == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			return;
+		}
+		_mpd_shortmul(rdata, big->data, big->len, small->data[0]);
+	}
+	else if (rsize <= 1024) {
+		rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize);
+		if (rdata == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			return;
+		}
+	}
+	else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
+		rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize);
+		if (rdata == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			return;
+		}
+	}
+	else {
+		rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize);
+		if (rdata == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status); /* GCOV_UNLIKELY */
+			return; /* GCOV_UNLIKELY */
+		}
+	}
+
+	if (mpd_isdynamic_data(result)) {
+		mpd_free(result->data);
+	}
+	result->data = rdata;
+	result->alloc = rsize;
+	mpd_set_dynamic_data(result);
+
+
+finish:
+	mpd_set_flags(result, mpd_sign(a)^mpd_sign(b));
+	result->exp = big->exp + small->exp;
+	result->len = _mpd_real_size(result->data, rsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(result, result->len, status);
+	mpd_setdigits(result);
+}
+
+/* Multiply a and b. */
+void
+mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	_mpd_qmul(result, a, b, ctx, status);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* Multiply decimal and mpd_ssize_t. */
+void
+mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_ssize(&bb, b, &maxcontext, status);
+	mpd_qmul(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+/* Multiply decimal and mpd_uint_t. */
+void
+mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(bb,0,0,0,0);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_qsset_uint(&bb, b, &maxcontext, status);
+	mpd_qmul(result, a, &bb, ctx, status);
+	mpd_del(&bb);
+}
+
+void
+mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qmul_ssize(result, a, b, ctx, status);
+}
+
+void
+mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qmul_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qmul_ssize(result, a, b, ctx, status);
+}
+
+void
+mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_qmul_uint(result, a, b, ctx, status);
+}
+#endif
+
+/* Like the minus operator. */
+void
+mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+           uint32_t *status)
+{
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+	}
+
+	if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
+		mpd_qcopy_abs(result, a, status);
+	}
+	else {
+		mpd_qcopy_negate(result, a, status);
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* Like the plus operator. */
+void
+mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+          uint32_t *status)
+{
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+	}
+
+	if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
+		mpd_qcopy_abs(result, a, status);
+	}
+	else {
+		mpd_qcopy(result, a, status);
+	}
+
+	mpd_qfinalize(result, ctx, status);
+}
+
+/* The largest representable number that is smaller than the operand. */
+void
+mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+                uint32_t *status)
+{
+	mpd_context_t workctx; /* function context */
+	MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			if (mpd_isnegative(a)) {
+				mpd_qcopy(result, a, status);
+				return;
+			}
+			else {
+				mpd_clear_flags(result);
+				mpd_qmaxcoeff(result, ctx, status);
+				if (mpd_isnan(result)) {
+					return;
+				}
+				result->exp = ctx->emax - ctx->prec + 1;
+				return;
+			}
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+
+	mpd_workcontext(&workctx, ctx);
+	workctx.round = MPD_ROUND_FLOOR;
+
+	if (!mpd_qcopy(result, a, status)) {
+		return;
+	}
+
+	mpd_qfinalize(result, &workctx, &workctx.status);
+	if (workctx.status&(MPD_Inexact|MPD_Errors)) {
+		*status |= (workctx.status&MPD_Errors);
+		return;
+	}
+
+	workctx.status = 0;
+	mpd_qsub(result, a, &tiny, &workctx, &workctx.status);
+	*status |= (workctx.status&MPD_Errors);
+}
+
+/* The smallest representable number that is larger than the operand. */
+void
+mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+               uint32_t *status)
+{
+	mpd_context_t workctx;
+	MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			if (mpd_ispositive(a)) {
+				mpd_qcopy(result, a, status);
+			}
+			else {
+				mpd_clear_flags(result);
+				mpd_qmaxcoeff(result, ctx, status);
+				if (mpd_isnan(result)) {
+					return;
+				}
+				mpd_set_flags(result, MPD_NEG);
+				result->exp = mpd_etop(ctx);
+			}
+			return;
+		}
+	}
+
+	mpd_workcontext(&workctx, ctx);
+	workctx.round = MPD_ROUND_CEILING;
+
+	if (!mpd_qcopy(result, a, status)) {
+		return;
+	}
+
+	mpd_qfinalize(result, &workctx, &workctx.status);
+	if (workctx.status & (MPD_Inexact|MPD_Errors)) {
+		*status |= (workctx.status&MPD_Errors);
+		return;
+	}
+
+	workctx.status = 0;
+	mpd_qadd(result, a, &tiny, &workctx, &workctx.status);
+	*status |= (workctx.status&MPD_Errors);
+}
+
+/*
+ * The number closest to the first operand that is in the direction towards
+ * the second operand.
+ */
+void
+mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b,
+                 const mpd_context_t *ctx, uint32_t *status)
+{
+	int c;
+
+	if (mpd_isnan(a) || mpd_isnan(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status))
+			return;
+	}
+
+	c = _mpd_cmp(a, b);
+	if (c == 0) {
+		mpd_qcopy_sign(result, a, b, status);
+		return;
+	}
+
+	if (c < 0) {
+		mpd_qnext_plus(result, a, ctx, status);
+	}
+	else {
+		mpd_qnext_minus(result, a, ctx, status);
+	}
+
+	if (mpd_isinfinite(result)) {
+		*status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact);
+	}
+	else if (mpd_adjexp(result) < ctx->emin) {
+		*status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact);
+		if (mpd_iszero(result)) {
+			*status |= MPD_Clamped;
+		}
+	}
+}
+
+/*
+ * Internal function: Integer power with mpd_uint_t exponent, base is modified!
+ * Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpow_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp, uint8_t resultsign,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_uint_t n;
+
+	if (exp == 0) {
+		_settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */
+		return; /* GCOV_NOT_REACHED */
+	}
+
+	if (!mpd_qcopy(result, base, status)) {
+		return;
+	}
+
+	n = mpd_bits[mpd_bsr(exp)];
+	while (n >>= 1) {
+		mpd_qmul(result, result, result, ctx, &workstatus);
+		if (exp & n) {
+			mpd_qmul(result, result, base, ctx, &workstatus);
+		}
+		if (workstatus & (MPD_Overflow|MPD_Clamped)) {
+			break;
+		}
+	}
+
+	*status |= workstatus;
+	mpd_set_sign(result, resultsign);
+}
+
+/*
+ * Internal function: Integer power with mpd_t exponent, tbase and texp
+ * are modified!! Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_context_t maxctx;
+	MPD_NEW_CONST(two,0,0,1,1,1,2);
+
+
+	mpd_maxcontext(&maxctx);
+
+	/* resize to smaller cannot fail */
+	mpd_qcopy(result, &one, status);
+
+	while (!mpd_iszero(texp)) {
+		if (mpd_isodd(texp)) {
+			mpd_qmul(result, result, tbase, ctx, &workstatus);
+			*status |= workstatus;
+			if (workstatus & (MPD_Overflow|MPD_Clamped)) {
+				break;
+			}
+		}
+		mpd_qmul(tbase, tbase, tbase, ctx, &workstatus);
+		mpd_qdivint(texp, texp, &two, &maxctx, &workstatus);
+		if (mpd_isnan(tbase) || mpd_isnan(texp)) {
+			mpd_seterror(result, workstatus&MPD_Errors, status);
+			return;
+		}
+	}
+	mpd_set_sign(result, resultsign);
+}
+
+/*
+ * The power function for integer exponents.
+ */
+static void
+_mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+              uint8_t resultsign,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t workctx;
+	MPD_NEW_STATIC(tbase,0,0,0,0);
+	MPD_NEW_STATIC(texp,0,0,0,0);
+	mpd_ssize_t n;
+
+
+	mpd_workcontext(&workctx, ctx);
+	workctx.prec += (exp->digits + exp->exp + 2);
+	workctx.round = MPD_ROUND_HALF_EVEN;
+	workctx.clamp = 0;
+	if (mpd_isnegative(exp)) {
+		mpd_qdiv(&tbase, &one, base, &workctx, status);
+		if (*status&MPD_Errors) {
+			mpd_setspecial(result, MPD_POS, MPD_NAN);
+			goto finish;
+		}
+	}
+	else {
+		if (!mpd_qcopy(&tbase, base, status)) {
+			mpd_setspecial(result, MPD_POS, MPD_NAN);
+			goto finish;
+		}
+	}
+
+	n = mpd_qabs_uint(exp, &workctx.status);
+	if (workctx.status&MPD_Invalid_operation) {
+		if (!mpd_qcopy(&texp, exp, status)) {
+			mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */
+			goto finish; /* GCOV_UNLIKELY */
+		}
+		_mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status);
+	}
+	else {
+		_mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status);
+	}
+
+	if (mpd_isinfinite(result)) {
+		/* for ROUND_DOWN, ROUND_FLOOR, etc. */
+		_settriple(result, resultsign, 1, MPD_EXP_INF);
+	}
+
+finish:
+	mpd_del(&tbase);
+	mpd_del(&texp);
+	mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * This is an internal function that does not check for NaNs.
+ */
+static int
+_qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign,
+                    const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_ssize_t shift;
+	int cmp;
+
+	if ((cmp = _mpd_cmp(base, &one)) == 0) {
+		shift = ctx->prec-1;
+		mpd_qshiftl(result, &one, shift, status);
+		result->exp = -shift;
+		mpd_set_flags(result, resultsign);
+		*status |= (MPD_Inexact|MPD_Rounded);
+	}
+
+	return cmp;
+}
+
+/*
+ * If base equals one, calculate the correct power of one result.
+ * Otherwise, result is undefined. Return the value of the comparison
+ * against 1.
+ *
+ * This is an internal function that does not check for specials.
+ */
+static int
+_qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+                uint8_t resultsign,
+                const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_ssize_t shift;
+	int cmp;
+
+	if ((cmp = _mpd_cmp_abs(base, &one)) == 0) {
+		if (_mpd_isint(exp)) {
+			if (mpd_isnegative(exp)) {
+				_settriple(result, resultsign, 1, 0);
+				return 0;
+			}
+			/* 1.000**3 = 1.000000000 */
+			mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus);
+			if (workstatus&MPD_Errors) {
+				*status |= (workstatus&MPD_Errors);
+				return 0;
+			}
+			/* digits-1 after exponentiation */
+			shift = mpd_qget_ssize(result, &workstatus);
+			/* shift is MPD_SSIZE_MAX if result is too large */
+			if (shift > ctx->prec-1) {
+				shift = ctx->prec-1;
+				*status |= MPD_Rounded;
+			}
+		}
+		else if (mpd_ispositive(base)) {
+			shift = ctx->prec-1;
+			*status |= (MPD_Inexact|MPD_Rounded);
+		}
+		else {
+			return -2; /* GCOV_NOT_REACHED */
+		}
+		if (!mpd_qshiftl(result, &one, shift, status)) {
+			return 0;
+		}
+		result->exp = -shift;
+		mpd_set_flags(result, resultsign);
+	}
+
+	return cmp;
+}
+
+/*
+ * Detect certain over/underflow of x**y.
+ * ACL2 proof: pow_bounds.lisp.
+ *
+ *   Symbols:
+ *
+ *     e: EXP_INF or EXP_CLAMP
+ *     x: base
+ *     y: exponent
+ *
+ *     omega(e) = log10(abs(e))
+ *     zeta(x)  = log10(abs(log10(x)))
+ *     theta(y) = log10(abs(y))
+ *
+ *   Upper and lower bounds:
+ *
+ *     ub_omega(e) = ceil(log10(abs(e)))
+ *     lb_theta(y) = floor(log10(abs(y)))
+ *
+ *                  | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10
+ *     lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1
+ *                  | floor(log10(abs((x-1)/100))) if 1 < x < 10
+ *
+ *   ub_omega(e) and lb_theta(y) are obviously upper and lower bounds
+ *   for omega(e) and theta(y).
+ *
+ *   lb_zeta is a lower bound for zeta(x):
+ *
+ *     x < 1/10 or x >= 10:
+ *
+ *       abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10
+ *       is strictly increasing, the end result is a lower bound.
+ *
+ *     1/10 <= x < 1:
+ *
+ *       We use: log10(x) <= (x-1)/log(10)
+ *               abs(log10(x)) >= abs(x-1)/log(10)
+ *               abs(log10(x)) >= abs(x-1)/10
+ *
+ *     1 < x < 10:
+ *
+ *       We use: (x-1)/(x*log(10)) < log10(x)
+ *               abs((x-1)/100) < abs(log10(x))
+ *
+ *       XXX: abs((x-1)/10) would work, need ACL2 proof.
+ *
+ *
+ *   Let (0 < x < 1 and y < 0) or (x > 1 and y > 0).                  (H1)
+ *   Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y)                 (H2)
+ *
+ *   Then:
+ *       log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)).   (1)
+ *                   exp_inf < log10(x) * y                            (2)
+ *               10**exp_inf < x**y                                    (3)
+ *
+ *   Let (0 < x < 1 and y > 0) or (x > 1 and y < 0).                  (H3)
+ *   Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y)               (H4)
+ *
+ *   Then:
+ *     log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)).   (4)
+ *              log10(x) * y < exp_clamp                               (5)
+ *                      x**y < 10**exp_clamp                           (6)
+ *
+ */
+static mpd_ssize_t
+_lower_bound_zeta(const mpd_t *x, uint32_t *status)
+{
+	mpd_context_t maxctx;
+	MPD_NEW_STATIC(scratch,0,0,0,0);
+	mpd_ssize_t t, u;
+
+	t = mpd_adjexp(x);
+	if (t > 0) {
+                /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */
+		return mpd_exp_digits(t) - 1;
+	}
+	else if (t < -1) {
+		/* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */
+		return mpd_exp_digits(t+1) - 1;
+	}
+	else {
+		mpd_maxcontext(&maxctx);
+		mpd_qsub(&scratch, x, &one, &maxctx, status);
+		if (mpd_isspecial(&scratch)) {
+			mpd_del(&scratch);
+			return MPD_SSIZE_MAX;
+		}
+		u = mpd_adjexp(&scratch);
+		mpd_del(&scratch);
+
+		/* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10))
+		 * t == 0,  1 < x < 10    -> floor(log10(abs(x-1)/100)) */
+		return (t == 0) ? u-2 : u-1;
+	}
+}
+
+/*
+ * Detect cases of certain overflow/underflow in the power function.
+ * Assumptions: x != 1, y != 0. The proof above is for positive x.
+ * If x is negative and y is an odd integer, x**y == -(abs(x)**y),
+ * so the analysis does not change.
+ */
+static int
+_qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y,
+                   uint8_t resultsign,
+                   const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_SHARED(abs_x, x);
+	mpd_ssize_t ub_omega, lb_zeta, lb_theta;
+	uint8_t sign;
+
+	mpd_set_positive(&abs_x);
+
+	lb_theta = mpd_adjexp(y);
+	lb_zeta = _lower_bound_zeta(&abs_x, status);
+	if (lb_zeta == MPD_SSIZE_MAX) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		return 1;
+	}
+
+	sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y);
+	if (sign == 0) {
+		/* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */
+		ub_omega = mpd_exp_digits(ctx->emax);
+		if (ub_omega < lb_zeta + lb_theta) {
+			_settriple(result, resultsign, 1, MPD_EXP_INF);
+			mpd_qfinalize(result, ctx, status);
+			return 1;
+		}
+	}
+	else {
+                /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */
+		ub_omega = mpd_exp_digits(mpd_etiny(ctx));
+		if (ub_omega < lb_zeta + lb_theta) {
+			_settriple(result, resultsign, 1, mpd_etiny(ctx)-1);
+			mpd_qfinalize(result, ctx, status);
+			return 1;
+		}
+	}
+
+	return 0;
+}
+
+/*
+ * TODO: Implement algorithm for computing exact powers from decimal.py.
+ * In order to prevent infinite loops, this has to be called before
+ * using Ziv's strategy for correct rounding.
+ */
+/*
+static int
+_mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+                const mpd_context_t *ctx, uint32_t *status)
+{
+	return 0;
+}
+*/
+
+/* The power function for real exponents */
+static void
+_mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+               const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t workctx;
+	MPD_NEW_STATIC(texp,0,0,0,0);
+
+	if (!mpd_qcopy(&texp, exp, status)) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		return;
+	}
+
+	mpd_maxcontext(&workctx);
+	workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec;
+	workctx.prec += (4 + MPD_EXPDIGITS);
+	workctx.round = MPD_ROUND_HALF_EVEN;
+	workctx.allcr = ctx->allcr;
+
+	mpd_qln(result, base, &workctx, &workctx.status);
+	mpd_qmul(result, result, &texp, &workctx, &workctx.status);
+	mpd_qexp(result, result, &workctx, status);
+
+	mpd_del(&texp);
+	*status |= (workctx.status&MPD_Errors);
+	*status |= (MPD_Inexact|MPD_Rounded);
+}
+
+/* The power function: base**exp */
+void
+mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+         const mpd_context_t *ctx, uint32_t *status)
+{
+	uint8_t resultsign = 0;
+	int intexp = 0;
+	int cmp;
+
+	if (mpd_isspecial(base) || mpd_isspecial(exp)) {
+		if (mpd_qcheck_nans(result, base, exp, ctx, status)) {
+			return;
+		}
+	}
+	if (mpd_isinteger(exp)) {
+		intexp = 1;
+		resultsign = mpd_isnegative(base) && mpd_isodd(exp);
+	}
+
+	if (mpd_iszero(base)) {
+		if (mpd_iszero(exp)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+		}
+		else if (mpd_isnegative(exp)) {
+			mpd_setspecial(result, resultsign, MPD_INF);
+		}
+		else {
+			_settriple(result, resultsign, 0, 0);
+		}
+		return;
+	}
+	if (mpd_isnegative(base)) {
+		if (!intexp || mpd_isinfinite(exp)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+	}
+	if (mpd_isinfinite(exp)) {
+		/* power of one */
+		cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status);
+		if (cmp == 0) {
+			return;
+		}
+		else {
+			cmp *= mpd_arith_sign(exp);
+			if (cmp < 0) {
+				_settriple(result, resultsign, 0, 0);
+			}
+			else {
+				mpd_setspecial(result, resultsign, MPD_INF);
+			}
+		}
+		return;
+	}
+	if (mpd_isinfinite(base)) {
+		if (mpd_iszero(exp)) {
+			_settriple(result, resultsign, 1, 0);
+		}
+		else if (mpd_isnegative(exp)) {
+			_settriple(result, resultsign, 0, 0);
+		}
+		else {
+			mpd_setspecial(result, resultsign, MPD_INF);
+		}
+		return;
+	}
+	if (mpd_iszero(exp)) {
+		_settriple(result, resultsign, 1, 0);
+		return;
+	}
+	if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) {
+		return;
+	}
+	if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) {
+		return;
+	}
+
+	if (intexp) {
+		_mpd_qpow_int(result, base, exp, resultsign, ctx, status);
+	}
+	else {
+		_mpd_qpow_real(result, base, exp, ctx, status);
+		if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) {
+			mpd_ssize_t shift = ctx->prec-1;
+			mpd_qshiftl(result, &one, shift, status);
+			result->exp = -shift;
+		}
+		if (mpd_isinfinite(result)) {
+			/* for ROUND_DOWN, ROUND_FLOOR, etc. */
+			_settriple(result, MPD_POS, 1, MPD_EXP_INF);
+		}
+		mpd_qfinalize(result, ctx, status);
+	}
+}
+
+/*
+ * Internal function: Integer powmod with mpd_uint_t exponent, base is modified!
+ * Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp,
+                  mpd_t *mod, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+
+	mpd_maxcontext(&maxcontext);
+
+	/* resize to smaller cannot fail */
+	mpd_qcopy(result, &one, status);
+
+	while (exp > 0) {
+		if (exp & 1) {
+			mpd_qmul(result, result, base, &maxcontext, status);
+			mpd_qrem(result, result, mod, &maxcontext, status);
+		}
+		mpd_qmul(base, base, base, &maxcontext, status);
+		mpd_qrem(base, base, mod, &maxcontext, status);
+		exp >>= 1;
+	}
+}
+
+/* The powmod function: (base**exp) % mod */
+void
+mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+            const mpd_t *mod,
+            const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxcontext;
+	MPD_NEW_STATIC(tbase,0,0,0,0);
+	MPD_NEW_STATIC(texp,0,0,0,0);
+	MPD_NEW_STATIC(tmod,0,0,0,0);
+	MPD_NEW_STATIC(tmp,0,0,0,0);
+	MPD_NEW_CONST(two,0,0,1,1,1,2);
+	mpd_ssize_t tbase_exp, texp_exp;
+	mpd_ssize_t i;
+	mpd_t t;
+	mpd_uint_t r;
+	uint8_t sign;
+
+
+	if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) {
+		if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) {
+			return;
+		}
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+
+	if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_iszerocoeff(mod)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	sign = (mpd_isnegative(base)) && (mpd_isodd(exp));
+	if (mpd_iszerocoeff(exp)) {
+		if (mpd_iszerocoeff(base)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1;
+		_settriple(result, sign, r, 0);
+		return;
+	}
+	if (mpd_isnegative(exp)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (mpd_iszerocoeff(base)) {
+		_settriple(result, sign, 0, 0);
+		return;
+	}
+	if (mod->digits+mod->exp > ctx->prec) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (!mpd_qcopy(&tmod, mod, status)) {
+		goto mpd_errors;
+	}
+	mpd_set_positive(&tmod);
+
+	mpd_maxcontext(&maxcontext);
+
+	mpd_qround_to_int(&tbase, base, &maxcontext, status);
+	mpd_qround_to_int(&texp, exp, &maxcontext, status);
+	mpd_qround_to_int(&tmod, &tmod, &maxcontext, status);
+
+	tbase_exp = tbase.exp;
+	tbase.exp = 0;
+	texp_exp = texp.exp;
+	texp.exp = 0;
+
+	/* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */
+	mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+	_settriple(result, MPD_POS, 1, tbase_exp);
+	mpd_qrem(result, result, &tmod, &maxcontext, status);
+	mpd_qmul(&tbase, &tbase, result, &maxcontext, status);
+	mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+	if (mpd_isspecial(&tbase) ||
+	    mpd_isspecial(&texp) ||
+	    mpd_isspecial(&tmod)) {
+		goto mpd_errors;
+	}
+
+	for (i = 0; i < texp_exp; i++) {
+		_mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status);
+		t = tmp;
+		tmp = tbase;
+		tbase = t;
+	}
+	if (mpd_isspecial(&tbase)) {
+		goto mpd_errors; /* GCOV_UNLIKELY */
+	}
+
+	/* resize to smaller cannot fail */
+	mpd_qcopy(result, &one, status);
+	while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) {
+		if (mpd_isodd(&texp)) {
+			mpd_qmul(result, result, &tbase, &maxcontext, status);
+			mpd_qrem(result, result, &tmod, &maxcontext, status);
+		}
+		mpd_qmul(&tbase, &tbase, &tbase, &maxcontext, status);
+		mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+		mpd_qdivint(&texp, &texp, &two, &maxcontext, status);
+	}
+	if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) ||
+            mpd_isspecial(&tmod) || mpd_isspecial(result)) {
+		/* MPD_Malloc_error */
+		goto mpd_errors;
+	}
+	else {
+		mpd_set_sign(result, sign);
+	}
+
+out:
+	mpd_del(&tbase);
+	mpd_del(&texp);
+	mpd_del(&tmod);
+	mpd_del(&tmp);
+	mpd_qfinalize(result, ctx, status);
+	return;
+
+mpd_errors:
+	mpd_setspecial(result, MPD_POS, MPD_NAN);
+	goto out;
+}
+
+void
+mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_ssize_t b_exp = b->exp;
+	mpd_ssize_t expdiff, shift;
+	mpd_uint_t rnd;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
+			mpd_qcopy(result, a, status);
+			return;
+		}
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (mpd_iszero(a)) {
+		_settriple(result, mpd_sign(a), 0, b->exp);
+		mpd_qfinalize(result, ctx, status);
+		return;
+	}
+
+
+	expdiff = a->exp - b->exp;
+	if (a->digits + expdiff > ctx->prec) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (expdiff >= 0) {
+		shift = expdiff;
+		if (!mpd_qshiftl(result, a, shift, status)) {
+			return;
+		}
+		result->exp = b_exp;
+	}
+	else {
+		/* At this point expdiff < 0 and a->digits+expdiff <= prec,
+		 * so the shift before an increment will fit in prec. */
+		shift = -expdiff;
+		rnd = mpd_qshiftr(result, a, shift, status);
+		if (rnd == MPD_UINT_MAX) {
+			return;
+		}
+		result->exp = b_exp;
+		if (!_mpd_apply_round_fit(result, rnd, ctx, status)) {
+			return;
+		}
+		workstatus |= MPD_Rounded;
+		if (rnd) {
+			workstatus |= MPD_Inexact;
+		}
+	}
+
+	if (mpd_adjexp(result) > ctx->emax ||
+	    mpd_adjexp(result) < mpd_etiny(ctx)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	*status |= workstatus;
+	mpd_qfinalize(result, ctx, status);
+}
+
+void
+mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+            uint32_t *status)
+{
+	mpd_ssize_t shift, maxexp, maxshift;
+	uint8_t sign_a = mpd_sign(a);
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+	if (!mpd_qcopy(result, a, status)) {
+		return;
+	}
+	mpd_qfinalize(result, ctx, status);
+	if (mpd_isspecial(result)) {
+		return;
+	}
+	if (mpd_iszero(result)) {
+		_settriple(result, sign_a, 0, 0);
+		return;
+	}
+
+	shift = mpd_trail_zeros(result);
+	maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax;
+	/* After the finalizing above result->exp <= maxexp. */
+	maxshift = maxexp - result->exp;
+	shift = (shift > maxshift) ? maxshift : shift;
+
+	mpd_qshiftr_inplace(result, shift);
+	result->exp += shift;
+}
+
+void
+mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
+         uint32_t *status)
+{
+	MPD_NEW_STATIC(q,0,0,0,0);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(r, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			mpd_seterror(r, MPD_Invalid_operation, status);
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			mpd_qcopy(r, a, status);
+			mpd_qfinalize(r, ctx, status);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(r, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_seterror(r, MPD_Invalid_operation, status);
+		}
+		return;
+	}
+
+	_mpd_qdivmod(&q, r, a, b, ctx, status);
+	mpd_del(&q);
+	mpd_qfinalize(r, ctx, status);
+}
+
+void
+mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t workctx;
+	MPD_NEW_STATIC(btmp,0,0,0,0);
+	MPD_NEW_STATIC(q,0,0,0,0);
+	mpd_ssize_t expdiff, floordigits;
+	int cmp, isodd, allnine;
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(r, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			mpd_seterror(r, MPD_Invalid_operation, status);
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			mpd_qcopy(r, a, status);
+			mpd_qfinalize(r, ctx, status);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(r,  MPD_Division_undefined, status);
+		}
+		else {
+			mpd_seterror(r,  MPD_Invalid_operation, status);
+		}
+		return;
+	}
+
+	if (r == b) {
+		if (!mpd_qcopy(&btmp, b, status)) {
+			mpd_seterror(r, MPD_Malloc_error, status);
+			return;
+		}
+		b = &btmp;
+	}
+
+	workctx = *ctx;
+	workctx.prec = a->digits;
+	workctx.prec = (workctx.prec > ctx->prec) ? workctx.prec : ctx->prec;
+
+	_mpd_qdivmod(&q, r, a, b, &workctx, status);
+	if (mpd_isnan(&q) || mpd_isnan(r) || q.digits > ctx->prec) {
+		mpd_seterror(r, MPD_Division_impossible, status);
+		goto finish;
+	}
+	if (mpd_iszerocoeff(r)) {
+		goto finish;
+	}
+
+	/* Deal with cases like rmnx078:
+	 * remaindernear 999999999.5 1 -> NaN Division_impossible */
+	expdiff = mpd_adjexp(b) - mpd_adjexp(r);
+	if (-1 <= expdiff && expdiff <= 1) {
+
+		mpd_qtrunc(&q, &q, &workctx, &workctx.status);
+		allnine = mpd_coeff_isallnine(&q);
+		floordigits = q.digits;
+		isodd = mpd_isodd(&q);
+
+		mpd_maxcontext(&workctx);
+		if (mpd_sign(a) == mpd_sign(b)) {
+			_mpd_qsub(&q, r, b, &workctx, &workctx.status);
+			if (workctx.status&MPD_Errors) {
+				mpd_seterror(r, workctx.status&MPD_Errors, status);
+				goto finish;
+			}
+		}
+		else {
+			_mpd_qadd(&q, r, b, &workctx, &workctx.status);
+			if (workctx.status&MPD_Errors) {
+				mpd_seterror(r, workctx.status&MPD_Errors, status);
+				goto finish;
+			}
+		}
+
+		cmp = mpd_cmp_total_mag(&q, r);
+		if (cmp < 0 || (cmp == 0 && isodd)) {
+			if (allnine && floordigits == ctx->prec) {
+				mpd_seterror(r, MPD_Division_impossible, status);
+				goto finish;
+			}
+			mpd_qcopy(r, &q, status);
+			*status &= ~MPD_Rounded;
+		}
+	}
+
+
+finish:
+	mpd_del(&btmp);
+	mpd_del(&q);
+	mpd_qfinalize(r, ctx, status);
+}
+
+/*
+ * Rescale a number so that it has exponent 'exp'. Does not regard
+ * context precision, emax, emin, but uses the rounding mode.
+ * Special numbers are quietly copied.
+ */
+void
+mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
+             const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_ssize_t expdiff, shift;
+	mpd_uint_t rnd;
+
+	if (mpd_isspecial(a)) {
+		mpd_qcopy(result, a, status);
+		return;
+	}
+
+	if (exp > MPD_MAX_EMAX || exp < MPD_MIN_ETINY) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (mpd_iszero(a)) {
+		_settriple(result, mpd_sign(a), 0, exp);
+		return;
+	}
+
+	expdiff = a->exp - exp;
+	if (expdiff >= 0) {
+		shift = expdiff;
+		if (!mpd_qshiftl(result, a, shift, status)) {
+			return;
+		}
+		result->exp = exp;
+	}
+	else {
+		shift = -expdiff;
+		rnd = mpd_qshiftr(result, a, shift, status);
+		if (rnd == MPD_UINT_MAX) {
+			return;
+		}
+		result->exp = exp;
+		_mpd_apply_round_excess(result, rnd, ctx, status);
+		*status |= MPD_Rounded;
+		if (rnd) {
+			*status |= MPD_Inexact;
+		}
+	}
+
+	if (mpd_issubnormal(result, ctx)) {
+		*status |= MPD_Subnormal;
+	}
+}
+
+/* Round to an integer according to 'action' and ctx->round. */
+enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC, TO_INT_FLOOR, TO_INT_CEIL};
+static void
+_mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a,
+                        const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_uint_t rnd;
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		mpd_qcopy(result, a, status);
+		return;
+	}
+	if (a->exp >= 0) {
+		mpd_qcopy(result, a, status);
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		_settriple(result, mpd_sign(a), 0, 0);
+		return;
+	}
+
+	rnd = mpd_qshiftr(result, a, -a->exp, status);
+	if (rnd == MPD_UINT_MAX) {
+		return;
+	}
+	result->exp = 0;
+
+	if (action == TO_INT_EXACT || action == TO_INT_SILENT) {
+		_mpd_apply_round_excess(result, rnd, ctx, status);
+		if (action == TO_INT_EXACT) {
+			*status |= MPD_Rounded;
+			if (rnd) {
+				*status |= MPD_Inexact;
+			}
+		}
+	}
+	else if (action == TO_INT_FLOOR) {
+		if (rnd && mpd_isnegative(result)) {
+			_mpd_qsub(result, result, &one, ctx, status);
+		}
+	}
+	else if (action == TO_INT_CEIL) {
+		if (rnd && mpd_ispositive(result)) {
+			_mpd_qadd(result, result, &one, ctx, status);
+		}
+	}
+}
+
+void
+mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+                   uint32_t *status)
+{
+	(void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status);
+}
+
+void
+mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+                  uint32_t *status)
+{
+	(void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status);
+}
+
+void
+mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	(void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status);
+}
+
+void
+mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+           uint32_t *status)
+{
+	(void)_mpd_qround_to_integral(TO_INT_FLOOR, result, a, ctx, status);
+}
+
+void
+mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+          uint32_t *status)
+{
+	(void)_mpd_qround_to_integral(TO_INT_CEIL, result, a, ctx, status);
+}
+
+int
+mpd_same_quantum(const mpd_t *a, const mpd_t *b)
+{
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		return ((mpd_isnan(a) && mpd_isnan(b)) ||
+			(mpd_isinfinite(a) && mpd_isinfinite(b)));
+	}
+
+	return a->exp == b->exp;
+}
+
+/* Schedule the increase in precision for the Newton iteration. */
+static inline int
+recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
+                    mpd_ssize_t maxprec, mpd_ssize_t initprec)
+{
+	mpd_ssize_t k;
+	int i;
+
+	assert(maxprec > 0 && initprec > 0);
+	if (maxprec <= initprec) return -1;
+
+	i = 0; k = maxprec;
+	do {
+		k = (k+1) / 2;
+		klist[i++] = k;
+	} while (k > initprec);
+
+	return i-1;
+}
+
+/*
+ * Initial approximation for the reciprocal. Result has MPD_RDIGITS-2
+ * significant digits.
+ */
+static void
+_mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status)
+{
+	mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]}; /* 10**(2*MPD_RDIGITS-2) */
+	mpd_uint_t dummy, word;
+	int n;
+
+	_mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS);
+	n = mpd_word_digits(word);
+	word *= mpd_pow10[MPD_RDIGITS-n];
+
+	mpd_qresize(z, 2, status);
+	(void)_mpd_shortdiv(z->data, p10data, 2, word);
+
+	mpd_clear_flags(z);
+	z->exp = -(v->exp + v->digits) - (MPD_RDIGITS-2);
+	z->len = (z->data[1] == 0) ? 1 : 2;
+	mpd_setdigits(z);
+}
+
+/* Reciprocal, calculated with Newton's Method */
+static void
+_mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+                 uint32_t *status)
+{
+	mpd_context_t varcontext, maxcontext;
+	mpd_t *z = result;         /* current approximation */
+	mpd_t *v;                  /* a, normalized to a number between 0.1 and 1 */
+	MPD_NEW_SHARED(vtmp, a);   /* by default v will share data with a */
+	MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
+	MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
+	MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */
+	mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+	mpd_ssize_t adj, maxprec, initprec;
+	uint8_t sign = mpd_sign(a);
+	int i;
+
+	v = &vtmp;
+	if (result == a) {
+		if ((v = mpd_qncopy(a)) == NULL) { /* GCOV_NOT_REACHED */
+			mpd_seterror(result, MPD_Malloc_error, status); /* GCOV_NOT_REACHED */
+			goto finish; /* GCOV_NOT_REACHED */
+		}
+	}
+
+	mpd_clear_flags(v);
+	adj = v->digits + v->exp;
+	v->exp = -v->digits;
+
+	/* initial approximation */
+	_mpd_qreciprocal_approx(z, v, status);
+
+	mpd_maxcontext(&varcontext);
+	mpd_maxcontext(&maxcontext);
+	varcontext.round = MPD_ROUND_TRUNC;
+	maxcontext.round = MPD_ROUND_TRUNC;
+
+	maxprec = (v->digits > ctx->prec) ? v->digits : ctx->prec;
+	maxprec += 2;
+	initprec = MPD_RDIGITS-3;
+
+	i = recpr_schedule_prec(klist, maxprec, initprec);
+	for (; i >= 0; i--) {
+		mpd_qmul(&s, z, z, &maxcontext, status);
+		varcontext.prec = 2*klist[i] + 5;
+		if (v->digits > varcontext.prec) {
+			mpd_qshiftr(&t, v, v->digits-varcontext.prec, status);
+			t.exp = -varcontext.prec;
+			mpd_qmul(&t, &t, &s, &varcontext, status);
+		}
+		else {
+			mpd_qmul(&t, v, &s, &varcontext, status);
+		}
+		mpd_qmul(&s, z, &two, &maxcontext, status);
+		mpd_qsub(z, &s, &t, &maxcontext, status);
+	}
+
+	if (!mpd_isspecial(z)) {
+		z->exp -= adj;
+		mpd_set_flags(z, sign);
+	}
+
+finish:
+	mpd_del(&s);
+	mpd_del(&t);
+	if (v != &vtmp) mpd_del(v);
+	mpd_qfinalize(z, ctx, status);
+}
+
+/*
+ * Integer division with remainder of the coefficients: coeff(a) / coeff(b).
+ * This function is for large numbers where it is faster to divide by
+ * multiplying the dividend by the reciprocal of the divisor.
+ * The inexact result is fixed by a small loop, which should not take
+ * more than 2 iterations.
+ */
+static void
+_mpd_qbarrett_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+                     uint32_t *status)
+{
+	mpd_context_t workctx;
+	mpd_t *qq = q, *rr = r;
+	mpd_t aa, bb;
+	int k;
+
+	mpd_maxcontext(&workctx);
+	_mpd_copy_shared(&aa, a);
+	_mpd_copy_shared(&bb, b);
+
+	mpd_set_positive(&aa);
+	mpd_set_positive(&bb);
+	aa.exp = 0;
+	bb.exp = 0;
+
+	if (q == a || q == b) {
+		if ((qq = mpd_qnew()) == NULL) {
+			*status |= MPD_Malloc_error;
+			goto nanresult;
+		}
+	}
+	if (r == a || r == b) {
+		if ((rr = mpd_qnew()) == NULL) {
+			*status |= MPD_Malloc_error;
+			goto nanresult;
+		}
+	}
+
+	/* maximum length of q + 3 digits */
+	workctx.prec = aa.digits - bb.digits + 1 + 3;
+	/* we get the reciprocal with precision maxlen(q) + 3 */
+	_mpd_qreciprocal(rr, &bb, &workctx, &workctx.status);
+
+	mpd_qmul(qq, &aa, rr, &workctx, &workctx.status);
+	mpd_qtrunc(qq, qq, &workctx, &workctx.status);
+
+	workctx.prec = aa.digits + 3;
+	/* get the remainder */
+	mpd_qmul(rr, &bb, qq, &workctx, &workctx.status);
+	mpd_qsub(rr, &aa, rr, &workctx, &workctx.status);
+
+	/* Fix the result. Algorithm from: Karl Hasselstrom, Fast Division of Large Integers */
+	for (k = 0;; k++) {
+		if (mpd_isspecial(rr)) {
+			*status |= (workctx.status&MPD_Errors);
+			goto nanresult;
+		}
+		if (k > 2) {
+			mpd_err_warn("_mpd_barrett_divmod: k > 2 in correcting loop"); /* GCOV_NOT_REACHED */
+			abort(); /* GCOV_NOT_REACHED */
+		}
+		else if (_mpd_cmp(&zero, rr) == 1) {
+			mpd_qadd(rr, rr, &bb, &workctx, &workctx.status);
+			mpd_qadd(qq, qq, &minus_one, &workctx, &workctx.status);
+		}
+		else if (_mpd_cmp(rr, &bb) == -1) {
+			break;
+		}
+		else {
+			mpd_qsub(rr, rr, &bb, &workctx, &workctx.status);
+			mpd_qadd(qq, qq, &one, &workctx, &workctx.status);
+		}
+	}
+
+	if (qq != q) {
+		if (!mpd_qcopy(q, qq, status)) {
+			goto nanresult; /* GCOV_UNLIKELY */
+		}
+		mpd_del(qq);
+	}
+	if (rr != r) {
+		if (!mpd_qcopy(r, rr, status)) {
+			goto nanresult; /* GCOV_UNLIKELY */
+		}
+		mpd_del(rr);
+	}
+
+	*status |= (workctx.status&MPD_Errors);
+	return;
+
+
+nanresult:
+	if (qq && qq != q) mpd_del(qq);
+	if (rr && rr != r) mpd_del(rr);
+	mpd_setspecial(q, MPD_POS, MPD_NAN);
+	mpd_setspecial(r, MPD_POS, MPD_NAN);
+}
+
+static inline int
+invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
+                      mpd_ssize_t maxprec, mpd_ssize_t initprec)
+{
+	mpd_ssize_t k;
+	int i;
+
+	assert(maxprec >= 3 && initprec >= 3);
+	if (maxprec <= initprec) return -1;
+
+	i = 0; k = maxprec;
+	do {
+		k = (k+3) / 2;
+		klist[i++] = k;
+	} while (k > initprec);
+
+	return i-1;
+}
+
+/*
+ * Initial approximation for the inverse square root.
+ *
+ *   Input:
+ *     v := 7 or 8 decimal digits with an implicit exponent of 10**-6,
+ *          representing a number 1 <= x < 100.
+ *
+ *   Output:
+ *     An approximation to 1/sqrt(v)
+ */
+static inline void
+_invroot_init_approx(mpd_t *z, mpd_uint_t v)
+{
+	mpd_uint_t lo = 1000;
+	mpd_uint_t hi = 10000;
+	mpd_uint_t a, sq;
+
+	assert(v >= lo*lo && v < (hi+1)*(hi+1));
+
+	for(;;) {
+		a = (lo + hi) / 2;
+		sq = a * a;
+		if (v >= sq) {
+			if (v < sq + 2*a + 1) {
+				break;
+			}
+			lo = a + 1;
+		}
+		else {
+			hi = a - 1;
+		}
+	}
+
+	/* At this point a/1000 is an approximation to sqrt(v). */
+	mpd_minalloc(z);
+	mpd_clear_flags(z);
+	z->data[0] = 1000000000UL / a;
+	z->len = 1;
+	z->exp = -6;
+	mpd_setdigits(z);
+}
+
+static void
+_mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+              uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_context_t varcontext, maxcontext;
+	mpd_t *z = result;         /* current approximation */
+	mpd_t *v;                  /* a, normalized to a number between 1 and 100 */
+	MPD_NEW_SHARED(vtmp, a);   /* by default v will share data with a */
+	MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
+	MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
+	MPD_NEW_CONST(one_half,0,-1,1,1,1,5);
+	MPD_NEW_CONST(three,0,0,1,1,1,3);
+	mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+	mpd_ssize_t ideal_exp, shift;
+	mpd_ssize_t adj, tz;
+	mpd_ssize_t maxprec, fracdigits;
+	mpd_uint_t x, dummy;
+	int i, n;
+
+
+	ideal_exp = -(a->exp - (a->exp & 1)) / 2;
+
+	v = &vtmp;
+	if (result == a) {
+		if ((v = mpd_qncopy(a)) == NULL) {
+			mpd_seterror(result, MPD_Malloc_error, status);
+			return;
+		}
+	}
+
+	/* normalize a to 1 <= v < 100 */
+	if ((v->digits+v->exp) & 1) {
+		fracdigits = v->digits - 1;
+		v->exp = -fracdigits;
+		n = (v->digits > 7) ? 7 : (int)v->digits;
+		_mpd_get_msdigits(&dummy, &x, v, n);
+		if (n < 7) {
+			x *= mpd_pow10[7-n];
+		}
+	}
+	else {
+		fracdigits = v->digits - 2;
+		v->exp = -fracdigits;
+		n = (v->digits > 8) ? 8 : (int)v->digits;
+		_mpd_get_msdigits(&dummy, &x, v, n);
+		if (n < 8) {
+			x *= mpd_pow10[8-n];
+		}
+	}
+	adj = (a->exp-v->exp) / 2;
+
+	/* initial approximation */
+	_invroot_init_approx(z, x);
+
+	mpd_maxcontext(&maxcontext);
+	mpd_maxcontext(&varcontext);
+	varcontext.round = MPD_ROUND_TRUNC;
+	maxprec = ctx->prec + 2;
+
+	i = invroot_schedule_prec(klist, maxprec, 3);
+	for (; i >= 0; i--) {
+		varcontext.prec = 2*klist[i]+2;
+		mpd_qmul(&s, z, z, &maxcontext, &workstatus);
+		if (v->digits > varcontext.prec) {
+			shift = v->digits - varcontext.prec;
+			mpd_qshiftr(&t, v, shift, &workstatus);
+			t.exp += shift;
+			mpd_qmul(&t, &t, &s, &varcontext, &workstatus);
+		}
+		else {
+			mpd_qmul(&t, v, &s, &varcontext, &workstatus);
+		}
+		mpd_qsub(&t, &three, &t, &maxcontext, &workstatus);
+		mpd_qmul(z, z, &t, &varcontext, &workstatus);
+		mpd_qmul(z, z, &one_half, &maxcontext, &workstatus);
+	}
+
+	z->exp -= adj;
+
+	tz = mpd_trail_zeros(result);
+	shift = ideal_exp - result->exp;
+	shift = (tz > shift) ? shift : tz;
+	if (shift > 0) {
+		mpd_qshiftr_inplace(result, shift);
+		result->exp += shift;
+	}
+
+
+	mpd_del(&s);
+	mpd_del(&t);
+	if (v != &vtmp) mpd_del(v);
+	*status |= (workstatus&MPD_Errors);
+	varcontext = *ctx;
+	varcontext.round = MPD_ROUND_HALF_EVEN;
+	mpd_qfinalize(result, &varcontext, status);
+}
+
+void
+mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+             uint32_t *status)
+{
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isnegative(a)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		/* positive infinity */
+		_settriple(result, MPD_POS, 0, mpd_etiny(ctx));
+		*status |= MPD_Clamped;
+		return;
+	}
+	if (mpd_iszero(a)) {
+		mpd_setspecial(result, mpd_sign(a), MPD_INF);
+		*status |= MPD_Division_by_zero;
+		return;
+	}
+	if (mpd_isnegative(a)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	_mpd_qinvroot(result, a, ctx, status);
+}
+
+/*
+ * Ensure correct rounding. Algorithm after Hull & Abrham, "Properly Rounded
+ * Variable Precision Square Root", ACM Transactions on Mathematical Software,
+ * Vol. 11, No. 3.
+ */
+static void
+_mpd_fix_sqrt(mpd_t *result, const mpd_t *a, mpd_t *tmp,
+              const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_context_t maxctx;
+	MPD_NEW_CONST(u,0,0,1,1,1,5);
+
+	mpd_maxcontext(&maxctx);
+	u.exp = u.digits - ctx->prec + result->exp - 1;
+
+	_mpd_qsub(tmp, result, &u, &maxctx, status);
+	if (*status&MPD_Errors)	goto nanresult;
+
+	_mpd_qmul(tmp, tmp, tmp, &maxctx, status);
+	if (*status&MPD_Errors)	goto nanresult;
+
+	if (_mpd_cmp(tmp, a) == 1) {
+		u.exp += 1;
+		u.data[0] = 1;
+		_mpd_qsub(result, result, &u, &maxctx, status);
+	}
+	else {
+		_mpd_qadd(tmp, result, &u, &maxctx, status);
+		if (*status&MPD_Errors)	goto nanresult;
+
+		_mpd_qmul(tmp, tmp, tmp, &maxctx, status);
+		if (*status&MPD_Errors)	goto nanresult;
+
+		if (_mpd_cmp(tmp, a) == -1) {
+			u.exp += 1;
+			u.data[0] = 1;
+			_mpd_qadd(result, result, &u, &maxctx, status);
+		}
+	}
+
+	return;
+
+nanresult:
+	mpd_setspecial(result, MPD_POS, MPD_NAN);
+}
+
+void
+mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+          uint32_t *status)
+{
+	uint32_t workstatus = 0;
+	mpd_context_t varcontext;
+	mpd_t *z = result;         /* current approximation */
+	MPD_NEW_STATIC(v,0,0,0,0); /* a, normalized to a number between 1 and 10 */
+	MPD_NEW_STATIC(vtmp,0,0,0,0);
+	MPD_NEW_STATIC(tmp,0,0,0,0);
+	mpd_ssize_t ideal_exp, shift;
+	mpd_ssize_t target_prec, fracdigits;
+	mpd_ssize_t a_exp, a_digits;
+	mpd_ssize_t adj, tz;
+	mpd_uint_t dummy, t;
+	int exact = 0;
+
+
+	varcontext = *ctx;
+	varcontext.round = MPD_ROUND_HALF_EVEN;
+	ideal_exp = (a->exp - (a->exp & 1)) / 2;
+
+	if (mpd_isspecial(a)) {
+		if (mpd_qcheck_nan(result, a, ctx, status)) {
+			return;
+		}
+		if (mpd_isnegative(a)) {
+			mpd_seterror(result, MPD_Invalid_operation, status);
+			return;
+		}
+		mpd_setspecial(result, MPD_POS, MPD_INF);
+		return;
+	}
+	if (mpd_iszero(a)) {
+		_settriple(result, mpd_sign(a), 0, ideal_exp);
+		mpd_qfinalize(result, ctx, status);
+		return;
+	}
+	if (mpd_isnegative(a)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+
+	if (!mpd_qcopy(&v, a, status)) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		goto finish;
+	}
+
+	a_exp = a->exp;
+	a_digits = a->digits;
+
+	/* normalize a to 1 <= v < 100 */
+	if ((v.digits+v.exp) & 1) {
+		fracdigits = v.digits - 1;
+		v.exp = -fracdigits;
+		_mpd_get_msdigits(&dummy, &t, &v, 3);
+		t = t < 100 ? t*10 : t;
+		t = t < 100 ? t*10 : t;
+	}
+	else {
+		fracdigits = v.digits - 2;
+		v.exp = -fracdigits;
+		_mpd_get_msdigits(&dummy, &t, &v, 4);
+		t = t < 1000 ? t*10 : t;
+		t = t < 1000 ? t*10 : t;
+		t = t < 1000 ? t*10 : t;
+	}
+	adj = (a_exp-v.exp) / 2;
+
+
+	/* use excess digits */
+	target_prec = (a_digits > ctx->prec) ? a_digits : ctx->prec;
+	target_prec += 2;
+	varcontext.prec = target_prec + 3;
+
+	/* invroot is much faster for large numbers */
+	_mpd_qinvroot(&tmp, &v, &varcontext, &workstatus);
+
+	varcontext.prec = target_prec;
+	_mpd_qdiv(NO_IDEAL_EXP, z, &one, &tmp, &varcontext, &workstatus);
+
+
+	tz = mpd_trail_zeros(result);
+	if ((result->digits-tz)*2-1 <= v.digits) {
+		_mpd_qmul(&tmp, result, result, &varcontext, &workstatus);
+		if (workstatus&MPD_Errors) {
+			mpd_seterror(result, workstatus&MPD_Errors, status);
+			goto finish;
+		}
+		exact = (_mpd_cmp(&tmp, &v) == 0);
+	}
+	*status |= (workstatus&MPD_Errors);
+
+	if (!exact && !mpd_isspecial(result) && !mpd_iszero(result)) {
+		_mpd_fix_sqrt(result, &v, &tmp, &varcontext, status);
+		if (mpd_isspecial(result)) goto finish;
+		*status |= (MPD_Rounded|MPD_Inexact);
+	}
+
+	result->exp += adj;
+	if (exact) {
+		shift = ideal_exp - result->exp;
+		shift = (tz > shift) ? shift : tz;
+		if (shift > 0) {
+			mpd_qshiftr_inplace(result, shift);
+			result->exp += shift;
+		}
+	}
+
+
+finish:
+	mpd_del(&v);
+	mpd_del(&vtmp);
+	mpd_del(&tmp);
+	varcontext.prec = ctx->prec;
+	mpd_qfinalize(result, &varcontext, status);
+}
+
+
+/******************************************************************************/
+/*                              Base conversions                              */
+/******************************************************************************/
+
+/*
+ * Returns the space needed to represent an integer mpd_t in base 'base'.
+ * The result is undefined for non-integers.
+ *
+ * Max space needed:
+ *
+ *   base^n >= 10^(digits+exp)
+ *   n >= log10(10^(digits+exp))/log10(base) = (digits+exp) / log10(base)
+ */
+size_t
+mpd_sizeinbase(mpd_t *a, uint32_t base)
+{
+	size_t x;
+
+	assert(mpd_isinteger(a));
+	if (mpd_iszero(a)) {
+		return 1;
+	}
+
+	x = a->digits+a->exp;
+
+#ifdef CONFIG_64
+  #ifdef USE_80BIT_LONG_DOUBLE
+	return (long double)x / log10(base) + 3;
+  #else
+	/* x > floor(((1ULL<<53)-3) * log10(2)) */
+	if (x > 2711437152599294ULL) {
+		return SIZE_MAX;
+	}
+	return (double)x / log10(base) + 3;
+  #endif
+#else /* CONFIG_32 */
+{
+	double y =  x / log10(base) + 3;
+	return (y > SIZE_MAX) ? SIZE_MAX : (size_t)y;
+}
+#endif
+}
+
+/*
+ * Returns the space needed to import a base 'base' integer of length 'srclen'.
+ */
+static inline mpd_ssize_t
+_mpd_importsize(size_t srclen, uint32_t base)
+{
+#if SIZE_MAX == UINT64_MAX
+  #ifdef USE_80BIT_LONG_DOUBLE
+	long double x = (long double)srclen * (log10(base)/MPD_RDIGITS) + 3;
+  #else
+	double x;
+	if (srclen > (1ULL<<53)) {
+		return MPD_SSIZE_MAX;
+	}
+	x = (double)srclen * (log10(base)/MPD_RDIGITS) + 3;
+  #endif
+#else
+	double x = srclen * (log10(base)/MPD_RDIGITS) + 3;
+#endif
+	return (x > MPD_MAXIMPORT) ? MPD_SSIZE_MAX : (mpd_ssize_t)x;
+}
+
+
+static inline size_t
+_to_base_u16(uint16_t *w, size_t wlen, mpd_uint_t wbase,
+             mpd_uint_t *u, mpd_ssize_t ulen)
+{
+	size_t n = 0;
+
+	assert(wlen > 0 && ulen > 0);
+
+	do {
+		w[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase);
+		/* ulen will be at least 1. u[ulen-1] can only be zero if ulen == 1 */
+		ulen = _mpd_real_size(u, ulen);
+
+	} while (u[ulen-1] != 0 && n < wlen);
+
+	/* proper termination condition */
+	assert(u[ulen-1] == 0);
+
+	return n;
+}
+
+static inline void
+_from_base_u16(mpd_uint_t *w, mpd_ssize_t wlen,
+               const mpd_uint_t *u, size_t ulen, uint32_t ubase)
+{
+	mpd_ssize_t m = 1;
+	mpd_uint_t carry;
+
+	assert(wlen > 0 && ulen > 0);
+
+	w[0] = u[--ulen];
+	while (--ulen != SIZE_MAX && m < wlen) {
+		_mpd_shortmul(w, w, m, ubase);
+		m = _mpd_real_size(w, m+1);
+		carry = _mpd_shortadd(w, m, u[ulen]);
+		if (carry) w[m++] = carry;
+	}
+
+	/* proper termination condition */
+	assert(ulen == SIZE_MAX);
+}
+
+/* target base wbase <= source base ubase */
+static inline size_t
+_baseconv_to_smaller(uint32_t *w, size_t wlen, mpd_uint_t wbase,
+                     mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase)
+{
+	size_t n = 0;
+
+	assert(wlen > 0 && ulen > 0);
+
+	do {
+		w[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase);
+		/* ulen will be at least 1. u[ulen-1] can only be zero if ulen == 1 */
+		ulen = _mpd_real_size(u, ulen);
+
+	} while (u[ulen-1] != 0 && n < wlen);
+
+	/* proper termination condition */
+	assert(u[ulen-1] == 0);
+
+	return n;
+}
+
+/* target base wbase >= source base ubase */
+static inline void
+_baseconv_to_larger(mpd_uint_t *w, mpd_ssize_t wlen, mpd_uint_t wbase,
+                    const mpd_uint_t *u, size_t ulen, mpd_uint_t ubase)
+{
+	mpd_ssize_t m = 1;
+	mpd_uint_t carry;
+
+	assert(wlen > 0 && ulen > 0);
+
+	w[0] = u[--ulen];
+	while (--ulen != SIZE_MAX && m < wlen) {
+		_mpd_shortmul_b(w, w, m, ubase, wbase);
+		m = _mpd_real_size(w, m+1);
+		carry = _mpd_shortadd_b(w, m, u[ulen], wbase);
+		if (carry) w[m++] = carry;
+	}
+
+	/* proper termination condition */
+	assert(ulen == SIZE_MAX);
+}
+
+
+/*
+ * Converts an integer mpd_t to a multiprecision integer with
+ * base <= UINT16_MAX+1. The least significant word of the result
+ * is rdata[0].
+ */
+size_t
+mpd_qexport_u16(uint16_t *rdata, size_t rlen, uint32_t rbase,
+                const mpd_t *src, uint32_t *status)
+{
+	mpd_t *tsrc;
+	size_t n;
+
+	assert(rbase <= (1U<<16));
+	assert(rlen <= SIZE_MAX/(sizeof *rdata));
+
+	if (mpd_isspecial(src) || !_mpd_isint(src)) {
+		*status |= MPD_Invalid_operation;
+		return SIZE_MAX;
+	}
+
+	memset(rdata, 0, rlen * (sizeof *rdata));
+
+	if (mpd_iszero(src)) {
+		return 1;
+	}
+
+	if ((tsrc = mpd_qnew()) == NULL) {
+		*status |= MPD_Malloc_error;
+		return SIZE_MAX;
+	}
+
+	if (src->exp >= 0) {
+		if (!mpd_qshiftl(tsrc, src, src->exp, status)) {
+			mpd_del(tsrc);
+			return SIZE_MAX;
+		}
+	}
+	else {
+		if (mpd_qshiftr(tsrc, src, -src->exp, status) == MPD_UINT_MAX) {
+			mpd_del(tsrc);
+			return SIZE_MAX;
+		}
+	}
+
+	n = _to_base_u16(rdata, rlen, rbase, tsrc->data, tsrc->len);
+
+	mpd_del(tsrc);
+	return n;
+}
+
+/*
+ * Converts an integer mpd_t to a multiprecision integer with
+ * base <= UINT32_MAX. The least significant word of the result
+ * is rdata[0].
+ */
+size_t
+mpd_qexport_u32(uint32_t *rdata, size_t rlen, uint32_t rbase,
+                const mpd_t *src, uint32_t *status)
+{
+	mpd_t *tsrc;
+	size_t n;
+
+	if (mpd_isspecial(src) || !_mpd_isint(src)) {
+		*status |= MPD_Invalid_operation;
+		return SIZE_MAX;
+	}
+#if MPD_SIZE_MAX < SIZE_MAX
+	if (rlen > MPD_SSIZE_MAX) {
+		*status |= MPD_Invalid_operation;
+		return SIZE_MAX;
+	}
+#endif
+
+	assert(rlen <= SIZE_MAX/(sizeof *rdata));
+	memset(rdata, 0, rlen * (sizeof *rdata));
+
+	if (mpd_iszero(src)) {
+		return 1;
+	}
+
+	if ((tsrc = mpd_qnew()) == NULL) {
+		*status |= MPD_Malloc_error;
+		return SIZE_MAX;
+	}
+
+	if (src->exp >= 0) {
+		if (!mpd_qshiftl(tsrc, src, src->exp, status)) {
+			mpd_del(tsrc);
+			return SIZE_MAX;
+		}
+	}
+	else {
+		if (mpd_qshiftr(tsrc, src, -src->exp, status) == MPD_UINT_MAX) {
+			mpd_del(tsrc);
+			return SIZE_MAX;
+		}
+	}
+
+#ifdef CONFIG_64
+	n = _baseconv_to_smaller(rdata, rlen, rbase,
+	                         tsrc->data, tsrc->len, MPD_RADIX);
+#else
+	if (rbase <= MPD_RADIX) {
+		n = _baseconv_to_smaller(rdata, rlen, rbase,
+		                         tsrc->data, tsrc->len, MPD_RADIX);
+	}
+	else {
+		_baseconv_to_larger(rdata, (mpd_ssize_t)rlen, rbase,
+		                    tsrc->data, tsrc->len, MPD_RADIX);
+		n = _mpd_real_size(rdata, (mpd_ssize_t)rlen);
+	}
+#endif
+
+	mpd_del(tsrc);
+	return n;
+}
+
+
+/*
+ * Converts a multiprecision integer with base <= UINT16_MAX+1 to an mpd_t.
+ * The least significant word of the source is srcdata[0].
+ */
+void
+mpd_qimport_u16(mpd_t *result,
+                const uint16_t *srcdata, size_t srclen,
+                uint8_t srcsign, uint32_t srcbase,
+                const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_uint_t *usrc; /* uint16_t src copied to an mpd_uint_t array */
+	mpd_ssize_t rlen; /* length of the result */
+	size_t n = 0;
+
+	assert(srclen > 0);
+	assert(srcbase <= (1U<<16));
+
+	if ((rlen = _mpd_importsize(srclen, srcbase)) == MPD_SSIZE_MAX) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (srclen > MPD_SIZE_MAX/(sizeof *usrc)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if ((usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc)) == NULL) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		return;
+	}
+	for (n = 0; n < srclen; n++) {
+		usrc[n] = srcdata[n];
+	}
+
+	/* result->data is initialized to zero */
+	if (!mpd_qresize_zero(result, rlen, status)) {
+		goto finish;
+	}
+
+	_from_base_u16(result->data, rlen, usrc, srclen, srcbase);
+
+	mpd_set_flags(result, srcsign);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, rlen);
+	mpd_setdigits(result);
+
+	mpd_qresize(result, result->len, status);
+	mpd_qfinalize(result, ctx, status);
+
+
+finish:
+	mpd_free(usrc);
+}
+
+/*
+ * Converts a multiprecision integer with base <= UINT32_MAX to an mpd_t.
+ * The least significant word of the source is srcdata[0].
+ */
+void
+mpd_qimport_u32(mpd_t *result,
+                const uint32_t *srcdata, size_t srclen,
+                uint8_t srcsign, uint32_t srcbase,
+                const mpd_context_t *ctx, uint32_t *status)
+{
+	mpd_uint_t *usrc; /* uint32_t src copied to an mpd_uint_t array */
+	mpd_ssize_t rlen; /* length of the result */
+	size_t n = 0;
+
+	assert(srclen > 0);
+
+	if ((rlen = _mpd_importsize(srclen, srcbase)) == MPD_SSIZE_MAX) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if (srclen > MPD_SIZE_MAX/(sizeof *usrc)) {
+		mpd_seterror(result, MPD_Invalid_operation, status);
+		return;
+	}
+	if ((usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc)) == NULL) {
+		mpd_seterror(result, MPD_Malloc_error, status);
+		return;
+	}
+	for (n = 0; n < srclen; n++) {
+		usrc[n] = srcdata[n];
+	}
+
+	/* result->data is initialized to zero */
+	if (!mpd_qresize_zero(result, rlen, status)) {
+		goto finish;
+	}
+
+#ifdef CONFIG_64
+	_baseconv_to_larger(result->data, rlen, MPD_RADIX,
+	                    usrc, srclen, srcbase);
+#else
+	if (srcbase <= MPD_RADIX) {
+		_baseconv_to_larger(result->data, rlen, MPD_RADIX,
+		                    usrc, srclen, srcbase);
+	}
+	else {
+		_baseconv_to_smaller(result->data, rlen, MPD_RADIX,
+		                     usrc, (mpd_ssize_t)srclen, srcbase);
+	}
+#endif
+
+	mpd_set_flags(result, srcsign);
+	result->exp = 0;
+	result->len = _mpd_real_size(result->data, rlen);
+	mpd_setdigits(result);
+
+	mpd_qresize(result, result->len, status);
+	mpd_qfinalize(result, ctx, status);
+
+
+finish:
+	mpd_free(usrc);
+}
+
+
+/*********************************************************************/
+/*                   Testcases for Newton Division                   */
+/*********************************************************************/
+
+static void
+_mpd_qtest_newtondiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b,
+                     const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(aligned,0,0,0,0);
+	mpd_uint_t ld;
+	mpd_ssize_t shift, exp, tz;
+	mpd_ssize_t newsize;
+	mpd_ssize_t ideal_exp;
+	mpd_uint_t rem;
+	uint8_t sign_a = mpd_sign(a);
+	uint8_t sign_b = mpd_sign(b);
+
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			return;
+		}
+		_mpd_qdiv_inf(q, a, b, ctx, status);
+		return;
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(q, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_setspecial(q, sign_a^sign_b, MPD_INF);
+			*status |= MPD_Division_by_zero;
+		}
+		return;
+	}
+	if (mpd_iszerocoeff(a)) {
+		exp = a->exp - b->exp;
+		_settriple(q, sign_a^sign_b, 0, exp);
+		mpd_qfinalize(q, ctx, status);
+		return;
+	}
+
+	shift = (b->digits - a->digits) + ctx->prec + 1;
+	ideal_exp = a->exp - b->exp;
+	exp = ideal_exp - shift;
+	if (shift > 0) {
+		if (!mpd_qshiftl(&aligned, a, shift, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+		a = &aligned;
+	}
+	else if (shift < 0) {
+		shift = -shift;
+		if (!mpd_qshiftl(&aligned, b, shift, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+		b = &aligned;
+	}
+
+
+	newsize = a->len - b->len + 1;
+	if ((q != b && q != a) || (q == b && newsize > b->len)) {
+		if (!mpd_qresize(q, newsize, status)) {
+			mpd_seterror(q, MPD_Malloc_error, status);
+			goto finish;
+		}
+	}
+
+
+	{
+		MPD_NEW_STATIC(r,0,0,0,0);
+		_mpd_qbarrett_divmod(q, &r, a, b, status);
+		if (mpd_isspecial(q) || mpd_isspecial(&r)) {
+			mpd_del(&r);
+			goto finish;
+		}
+		rem = !mpd_iszerocoeff(&r);
+		mpd_del(&r);
+		newsize = q->len;
+	}
+
+	newsize = _mpd_real_size(q->data, newsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(q, newsize, status);
+	q->len = newsize;
+	mpd_setdigits(q);
+
+	shift = ideal_exp - exp;
+	if (rem) {
+		ld = mpd_lsd(q->data[0]);
+		if (ld == 0 || ld == 5) {
+			q->data[0] += 1;
+		}
+	}
+	else if (action == SET_IDEAL_EXP && shift > 0) {
+		tz = mpd_trail_zeros(q);
+		shift = (tz > shift) ? shift : tz;
+		mpd_qshiftr_inplace(q, shift);
+		exp += shift;
+	}
+
+	mpd_set_flags(q, sign_a^sign_b);
+	q->exp = exp;
+
+
+finish:
+	mpd_del(&aligned);
+	mpd_qfinalize(q, ctx, status);
+}
+
+static void
+mpd_qtest_newtondiv(mpd_t *q, const mpd_t *a, const mpd_t *b,
+                    const mpd_context_t *ctx, uint32_t *status)
+{
+	_mpd_qtest_newtondiv(SET_IDEAL_EXP, q, a, b, ctx, status);
+}
+
+static void
+_mpd_qtest_barrett_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+                          const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(aligned,0,0,0,0);
+	mpd_ssize_t qsize, rsize;
+	mpd_ssize_t ideal_exp, expdiff, shift;
+	uint8_t sign_a = mpd_sign(a);
+	uint8_t sign_ab = mpd_sign(a)^mpd_sign(b);
+
+
+	ideal_exp = (a->exp > b->exp) ?  b->exp : a->exp;
+	if (mpd_iszerocoeff(a)) {
+		if (!mpd_qcopy(r, a, status)) {
+			goto nanresult; /* GCOV_NOT_REACHED */
+		}
+		r->exp = ideal_exp;
+		_settriple(q, sign_ab, 0, 0);
+		return;
+	}
+
+	expdiff = mpd_adjexp(a) - mpd_adjexp(b);
+	if (expdiff < 0) {
+		if (a->exp > b->exp) {
+			/* positive and less than b->digits - a->digits */
+			shift = a->exp - b->exp;
+			if (!mpd_qshiftl(r, a, shift, status)) {
+				goto nanresult;
+			}
+			r->exp = ideal_exp;
+		}
+		else {
+			if (!mpd_qcopy(r, a, status)) {
+				goto nanresult;
+			}
+		}
+		_settriple(q, sign_ab, 0, 0);
+		return;
+	}
+	if (expdiff > ctx->prec) {
+		*status |= MPD_Division_impossible;
+		goto nanresult;
+	}
+
+
+	/*
+	 * At this point we have:
+	 *   (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec
+	 *   (2) a->exp - b->exp >= b->digits - a->digits
+	 *   (3) a->exp - b->exp <= prec + b->digits - a->digits
+	 */
+	if (a->exp != b->exp) {
+		shift = a->exp - b->exp;
+		if (shift > 0) {
+			/* by (3), after the shift a->digits <= prec + b->digits */
+			if (!mpd_qshiftl(&aligned, a, shift, status)) {
+				goto nanresult;
+			}
+			a = &aligned;
+		}
+		else  {
+			shift = -shift;
+			/* by (2), after the shift b->digits <= a->digits */
+			if (!mpd_qshiftl(&aligned, b, shift, status)) {
+				goto nanresult;
+			}
+			b = &aligned;
+		}
+	}
+
+
+	qsize = a->len - b->len + 1;
+	if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) {
+		if (!mpd_qresize(q, qsize, status)) {
+			goto nanresult;
+		}
+	}
+
+	rsize = b->len;
+	if (!(r == a && rsize < a->len)) {
+		if (!mpd_qresize(r, rsize, status)) {
+			goto nanresult;
+		}
+	}
+
+	_mpd_qbarrett_divmod(q, r, a, b, status);
+	if (mpd_isspecial(q) || mpd_isspecial(r)) {
+		goto nanresult;
+	}
+	if (mpd_isinfinite(q) || q->digits > ctx->prec) {
+		*status |= MPD_Division_impossible;
+		goto nanresult;
+	}
+	qsize = q->len;
+	rsize = r->len;
+
+	qsize = _mpd_real_size(q->data, qsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(q, qsize, status);
+	q->len = qsize;
+	mpd_setdigits(q);
+	mpd_set_flags(q, sign_ab);
+	q->exp = 0;
+	if (q->digits > ctx->prec) {
+		*status |= MPD_Division_impossible; /* GCOV_NOT_REACHED */
+		goto nanresult; /* GCOV_NOT_REACHED */
+	}
+
+	rsize = _mpd_real_size(r->data, rsize);
+	/* resize to smaller cannot fail */
+	mpd_qresize(r, rsize, status);
+	r->len = rsize;
+	mpd_setdigits(r);
+	mpd_set_flags(r, sign_a);
+	r->exp = ideal_exp;
+
+out:
+	mpd_del(&aligned);
+	return;
+
+nanresult:
+	mpd_setspecial(q, MPD_POS, MPD_NAN);
+	mpd_setspecial(r, MPD_POS, MPD_NAN);
+	goto out;
+}
+
+static void
+mpd_qtest_newtondivint(mpd_t *q, const mpd_t *a, const mpd_t *b,
+                       const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(r,0,0,0,0);
+	uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
+			mpd_seterror(q, MPD_Invalid_operation, status);
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			mpd_setspecial(q, sign, MPD_INF);
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			_settriple(q, sign, 0, 0);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(q, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_setspecial(q, sign, MPD_INF);
+			*status |= MPD_Division_by_zero;
+		}
+		return;
+	}
+
+	_mpd_qtest_barrett_divmod(q, &r, a, b, ctx, status);
+	mpd_del(&r);
+	mpd_qfinalize(q, ctx, status);
+}
+
+static void
+mpd_qtest_newtonrem(mpd_t *r, const mpd_t *a, const mpd_t *b,
+                    const mpd_context_t *ctx, uint32_t *status)
+{
+	MPD_NEW_STATIC(q,0,0,0,0);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(r, a, b, ctx, status)) {
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			mpd_seterror(r, MPD_Invalid_operation, status);
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			mpd_qcopy(r, a, status);
+			mpd_qfinalize(r, ctx, status);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_seterror(r, MPD_Division_undefined, status);
+		}
+		else {
+			mpd_seterror(r, MPD_Invalid_operation, status);
+		}
+		return;
+	}
+
+	_mpd_qtest_barrett_divmod(&q, r, a, b, ctx, status);
+	mpd_del(&q);
+	mpd_qfinalize(r, ctx, status);
+}
+
+static void
+mpd_qtest_newtondivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+                       const mpd_context_t *ctx, uint32_t *status)
+{
+	uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+	if (mpd_isspecial(a) || mpd_isspecial(b)) {
+		if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+			mpd_qcopy(r, q, status);
+			return;
+		}
+		if (mpd_isinfinite(a)) {
+			if (mpd_isinfinite(b)) {
+				mpd_setspecial(q, MPD_POS, MPD_NAN);
+			}
+			else {
+				mpd_setspecial(q, sign, MPD_INF);
+			}
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= MPD_Invalid_operation;
+			return;
+		}
+		if (mpd_isinfinite(b)) {
+			if (!mpd_qcopy(r, a, status)) {
+				mpd_seterror(q, MPD_Malloc_error, status);
+				return;
+			}
+			mpd_qfinalize(r, ctx, status);
+			_settriple(q, sign, 0, 0);
+			return;
+		}
+		/* debug */
+		abort(); /* GCOV_NOT_REACHED */
+	}
+	if (mpd_iszerocoeff(b)) {
+		if (mpd_iszerocoeff(a)) {
+			mpd_setspecial(q, MPD_POS, MPD_NAN);
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= MPD_Division_undefined;
+		}
+		else {
+			mpd_setspecial(q, sign, MPD_INF);
+			mpd_setspecial(r, MPD_POS, MPD_NAN);
+			*status |= (MPD_Division_by_zero|MPD_Invalid_operation);
+		}
+		return;
+	}
+
+	_mpd_qtest_barrett_divmod(q, r, a, b, ctx, status);
+	mpd_qfinalize(q, ctx, status);
+	mpd_qfinalize(r, ctx, status);
+}
+
+void
+mpd_test_newtondiv(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qtest_newtondiv(q, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_test_newtondivint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qtest_newtondivint(q, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_test_newtonrem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qtest_newtonrem(r, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_test_newtondivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qtest_newtondivmod(q, r, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+

ext/mpdecimal/mpdecimal.cbp

@@ -0,0 +1,107 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
+<CodeBlocks_project_file>
+	<FileVersion major="1" minor="6" />
+	<Project>
+		<Option title="mpdecimal" />
+		<Option pch_mode="2" />
+		<Option compiler="gcc" />
+		<Build>
+			<Target title="Debug">
+				<Option output="libmpdecimal" prefix_auto="1" extension_auto="1" />
+				<Option working_dir="" />
+				<Option object_output="obj/Debug/" />
+				<Option type="2" />
+				<Option compiler="gcc" />
+				<Option createDefFile="1" />
+				<Compiler>
+					<Add option="-Wall" />
+					<Add option="-g" />
+				</Compiler>
+			</Target>
+			<Target title="Release">
+				<Option output="libmpdecimal" prefix_auto="1" extension_auto="1" />
+				<Option working_dir="" />
+				<Option object_output="/home/mingo/dev/mpdecimal-2.3//.objs" />
+				<Option type="2" />
+				<Option compiler="gcc" />
+				<Option createDefFile="1" />
+				<Compiler>
+					<Add option="-Wall" />
+					<Add option="-O2" />
+				</Compiler>
+				<Linker>
+					<Add option="-s" />
+				</Linker>
+			</Target>
+		</Build>
+		<Compiler>
+			<Add option="-DCONFIG_32=1" />
+			<Add option="-DPPRO=1" />
+			<Add option="-DASM=1" />
+		</Compiler>
+		<Unit filename="basearith.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="basearith.h" />
+		<Unit filename="constants.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="constants.h" />
+		<Unit filename="context.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="convolute.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="convolute.h" />
+		<Unit filename="crt.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="crt.h" />
+		<Unit filename="difradix2.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="difradix2.h" />
+		<Unit filename="fnt.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="fnt.h" />
+		<Unit filename="fourstep.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="fourstep.h" />
+		<Unit filename="io.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="io.h" />
+		<Unit filename="memory.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="memory.h" />
+		<Unit filename="mpdecimal.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="mpdecimal.h" />
+		<Unit filename="mpsignal.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="numbertheory.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="numbertheory.h" />
+		<Unit filename="sixstep.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="sixstep.h" />
+		<Unit filename="transpose.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="transpose.h" />
+		<Extensions>
+			<envvars />
+			<code_completion />
+			<lib_finder disable_auto="1" />
+			<debugger />
+		</Extensions>
+	</Project>
+</CodeBlocks_project_file>

ext/mpdecimal/mpdecimal.h

@@ -0,0 +1,751 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MPDECIMAL_H
+#define MPDECIMAL_H
+
+
+#ifdef __cplusplus
+extern "C" {
+#define __STDC_LIMIT_MACROS
+#endif
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <assert.h>
+#include <stdint.h>
+
+
+#if !defined(__GNUC_STDC_INLINE__)
+  #define __GNUC_STDC_INLINE__
+#endif
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
+  #define UNUSED __attribute__((unused))
+#else
+  #define UNUSED
+#endif
+
+
+/******************************************************************************/
+/*                              Configuration                                 */
+/******************************************************************************/
+
+/* ABI: 32-bit */
+#ifdef CONFIG_64
+  #error "cannot use CONFIG_64 with 32-bit header."
+#endif
+
+#ifndef CONFIG_32
+  #define CONFIG_32
+#endif
+
+
+/* BEGIN CONFIG_64 */
+#if defined(CONFIG_64)
+/* types for modular and base arithmetic */
+#define MPD_UINT_MAX UINT64_MAX
+#define MPD_BITS_PER_UINT 64
+typedef uint64_t mpd_uint_t;  /* unsigned mod type */
+
+#define MPD_SIZE_MAX SIZE_MAX
+typedef size_t mpd_size_t; /* unsigned size type */
+
+/* type for exp, digits, len, prec */
+#define MPD_SSIZE_MAX INT64_MAX
+#define MPD_SSIZE_MIN INT64_MIN
+typedef int64_t mpd_ssize_t;
+#define _mpd_strtossize strtoll
+
+/* decimal arithmetic */
+#define MPD_RADIX 10000000000000000000ULL  /* 10**19 */
+#define MPD_RDIGITS 19
+#define MPD_MAX_POW10 19
+#define MPD_EXPDIGITS 19  /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
+
+#define MPD_MAXTRANSFORM_2N 4294967296ULL      /* 2**32 */
+#define MPD_MAX_PREC 999999999999999999LL
+#define MPD_MAX_PREC_LOG2 64
+#define MPD_ELIMIT  1000000000000000000LL
+#define MPD_MAX_EMAX   999999999999999999LL    /* ELIMIT-1 */
+#define MPD_MIN_EMIN  (-999999999999999999LL)  /* -EMAX */
+#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
+#define MPD_EXP_INF 2000000000000000001LL
+#define MPD_EXP_CLAMP (-4000000000000000001LL)
+#define MPD_MAXIMPORT 105263157894736842L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
+/* END CONFIG_64 */
+
+
+/* BEGIN CONFIG_32 */
+#elif defined(CONFIG_32)
+/* types for modular and base arithmetic */
+#define MPD_UINT_MAX UINT32_MAX
+#define MPD_BITS_PER_UINT 32
+typedef uint32_t mpd_uint_t;  /* unsigned mod type */
+
+#ifndef LEGACY_COMPILER
+#define MPD_UUINT_MAX UINT64_MAX
+typedef uint64_t mpd_uuint_t; /* double width unsigned mod type */
+#endif
+
+#define MPD_SIZE_MAX SIZE_MAX
+typedef size_t mpd_size_t; /* unsigned size type */
+
+/* type for dec->len, dec->exp, ctx->prec */
+#define MPD_SSIZE_MAX INT32_MAX
+#define MPD_SSIZE_MIN INT32_MIN
+typedef int32_t mpd_ssize_t;
+#define _mpd_strtossize strtol
+
+/* decimal arithmetic */
+#define MPD_RADIX 1000000000UL  /* 10**9 */
+#define MPD_RDIGITS 9
+#define MPD_MAX_POW10 9
+#define MPD_EXPDIGITS 10 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */
+
+#define MPD_MAXTRANSFORM_2N 33554432UL /* 2**25 */
+#define MPD_MAX_PREC 425000000L
+#define MPD_MAX_PREC_LOG2 32
+#define MPD_ELIMIT 425000001L
+#define MPD_MAX_EMAX 425000000L        /* ELIMIT-1 */
+#define MPD_MIN_EMIN (-425000000L)     /* -EMAX */
+#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1))
+#define MPD_EXP_INF 1000000001L      /* allows for emax=999999999 in the tests */
+#define MPD_EXP_CLAMP (-2000000001L) /* allows for emin=-999999999 in the tests */
+#define MPD_MAXIMPORT 94444445L      /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */
+/* END CONFIG_32 */
+
+#else
+  #error "define CONFIG_64 or CONFIG_32"
+#endif
+/* END CONFIG */
+
+
+#if MPD_SIZE_MAX != MPD_UINT_MAX
+  #error "unsupported platform: need mpd_size_t == mpd_uint_t"
+#endif
+
+
+/******************************************************************************/
+/*                                Context                                     */
+/******************************************************************************/
+
+enum {
+	MPD_ROUND_UP,          /* round away from 0               */
+	MPD_ROUND_DOWN,        /* round toward 0 (truncate)       */
+	MPD_ROUND_CEILING,     /* round toward +infinity          */
+	MPD_ROUND_FLOOR,       /* round toward -infinity          */
+	MPD_ROUND_HALF_UP,     /* 0.5 is rounded up               */
+	MPD_ROUND_HALF_DOWN,   /* 0.5 is rounded down             */
+	MPD_ROUND_HALF_EVEN,   /* 0.5 is rounded to even          */
+	MPD_ROUND_05UP,        /* round zero or five away from 0  */
+	MPD_ROUND_TRUNC,       /* truncate, but set infinity      */
+	MPD_ROUND_GUARD
+};
+
+enum { MPD_CLAMP_DEFAULT, MPD_CLAMP_IEEE_754, MPD_CLAMP_GUARD };
+
+extern const char *mpd_round_string[MPD_ROUND_GUARD];
+extern const char *mpd_clamp_string[MPD_CLAMP_GUARD];
+
+
+typedef struct {
+	mpd_ssize_t prec;   /* precision */
+	mpd_ssize_t emax;   /* max positive exp */
+	mpd_ssize_t emin;   /* min negative exp */
+	uint32_t traps;     /* status events that should be trapped */
+	uint32_t status;    /* status flags */
+	uint32_t newtrap;   /* set by mpd_addstatus_raise() */
+	int      round;     /* rounding mode */
+	int      clamp;     /* clamp mode */
+	int      allcr;     /* all functions correctly rounded */
+} mpd_context_t;
+
+
+/* Status flags */
+#define MPD_Clamped             0x00000001U
+#define MPD_Conversion_syntax   0x00000002U
+#define MPD_Division_by_zero    0x00000004U
+#define MPD_Division_impossible 0x00000008U
+#define MPD_Division_undefined  0x00000010U
+#define MPD_Fpu_error           0x00000020U
+#define MPD_Inexact             0x00000040U
+#define MPD_Invalid_context     0x00000080U
+#define MPD_Invalid_operation   0x00000100U
+#define MPD_Malloc_error        0x00000200U
+#define MPD_Not_implemented     0x00000400U
+#define MPD_Overflow            0x00000800U
+#define MPD_Rounded             0x00001000U
+#define MPD_Subnormal           0x00002000U
+#define MPD_Underflow           0x00004000U
+#define MPD_Max_status         (0x00008000U-1U)
+
+/* Conditions that result in an IEEE 754 exception */
+#define MPD_IEEE_Invalid_operation (MPD_Conversion_syntax |   \
+                                    MPD_Division_impossible | \
+                                    MPD_Division_undefined |  \
+                                    MPD_Fpu_error |           \
+                                    MPD_Invalid_context |     \
+                                    MPD_Invalid_operation |   \
+                                    MPD_Malloc_error)         \
+
+/* Errors that require the result of an operation to be set to NaN */
+#define MPD_Errors (MPD_IEEE_Invalid_operation | \
+                    MPD_Division_by_zero)
+
+/* Default traps */
+#define MPD_Traps (MPD_IEEE_Invalid_operation | \
+                   MPD_Division_by_zero |       \
+                   MPD_Overflow |               \
+                   MPD_Underflow)
+
+/* Official name */
+#define MPD_Insufficient_storage MPD_Malloc_error
+
+/* IEEE 754 interchange format contexts */
+#define MPD_IEEE_CONTEXT_MAX_BITS 512 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */
+#define MPD_DECIMAL32 32
+#define MPD_DECIMAL64 64
+#define MPD_DECIMAL128 128
+
+
+#define MPD_MINALLOC_MIN 2
+#define MPD_MINALLOC_MAX 64
+extern mpd_ssize_t MPD_MINALLOC;
+extern void (* mpd_traphandler)(mpd_context_t *);
+void mpd_dflt_traphandler(mpd_context_t *);
+
+void mpd_setminalloc(mpd_ssize_t n);
+void mpd_init(mpd_context_t *ctx, mpd_ssize_t prec);
+
+void mpd_maxcontext(mpd_context_t *ctx);
+void mpd_maxcontext_plus(mpd_context_t *workctx, const mpd_context_t *ctx);
+void mpd_defaultcontext(mpd_context_t *ctx);
+void mpd_basiccontext(mpd_context_t *ctx);
+int mpd_ieee_context(mpd_context_t *ctx, int bits);
+
+mpd_ssize_t mpd_getprec(const mpd_context_t *ctx);
+mpd_ssize_t mpd_getemax(const mpd_context_t *ctx);
+mpd_ssize_t mpd_getemin(const mpd_context_t *ctx);
+int mpd_getround(const mpd_context_t *ctx);
+uint32_t mpd_gettraps(const mpd_context_t *ctx);
+uint32_t mpd_getstatus(const mpd_context_t *ctx);
+int mpd_getclamp(const mpd_context_t *ctx);
+int mpd_getcr(const mpd_context_t *ctx);
+
+int mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec);
+int mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax);
+int mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin);
+int mpd_qsetround(mpd_context_t *ctx, int newround);
+int mpd_qsettraps(mpd_context_t *ctx, uint32_t flags);
+int mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags);
+int mpd_qsetclamp(mpd_context_t *ctx, int c);
+int mpd_qsetcr(mpd_context_t *ctx, int c);
+void mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags);
+
+
+/******************************************************************************/
+/*                           Decimal Arithmetic                               */
+/******************************************************************************/
+
+/* mpd_t flags */
+#define MPD_POS                 ((uint8_t)0)
+#define MPD_NEG                 ((uint8_t)1)
+#define MPD_INF                 ((uint8_t)2)
+#define MPD_NAN                 ((uint8_t)4)
+#define MPD_SNAN                ((uint8_t)8)
+#define MPD_SPECIAL (MPD_INF|MPD_NAN|MPD_SNAN)
+#define MPD_STATIC              ((uint8_t)16)
+#define MPD_STATIC_DATA         ((uint8_t)32)
+#define MPD_SHARED_DATA         ((uint8_t)64)
+#define MPD_CONST_DATA          ((uint8_t)128)
+#define MPD_DATAFLAGS (MPD_STATIC_DATA|MPD_SHARED_DATA|MPD_CONST_DATA)
+
+/* mpd_t */
+typedef struct {
+	uint8_t flags;
+	mpd_ssize_t exp;
+	mpd_ssize_t digits;
+	mpd_ssize_t len;
+	mpd_ssize_t alloc;
+	mpd_uint_t *data;
+} mpd_t;
+
+
+typedef unsigned char uchar;
+extern mpd_t mpd_ln10;
+
+
+/******************************************************************************/
+/*                       Quiet, thread-safe functions                         */
+/******************************************************************************/
+
+/* format specification */
+typedef struct {
+	mpd_ssize_t min_width; /* minimum field width */
+	mpd_ssize_t prec;      /* fraction digits or significant digits */
+	char type;             /* conversion specifier */
+	char align;            /* alignment */
+	char sign;             /* sign printing/alignment */
+	char fill[5];          /* fill character */
+	const char *dot;       /* decimal point */
+	const char *sep;       /* thousands separator */
+	const char *grouping;  /* grouping of digits */
+} mpd_spec_t;
+
+/* output to a string */
+char *mpd_to_sci(const mpd_t *dec, int fmt);
+char *mpd_to_eng(const mpd_t *dec, int fmt);
+int mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps);
+char * mpd_qformat_spec(const mpd_t *dec, mpd_spec_t *spec, const mpd_context_t *ctx, uint32_t *status);
+char *mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, uint32_t *status);
+
+#define MPD_NUM_FLAGS 15
+#define MPD_MAX_FLAG_STRING 208
+#define MPD_MAX_FLAG_LIST (MPD_MAX_FLAG_STRING+18)
+#define MPD_MAX_SIGNAL_LIST 121
+int mpd_snprint_flags(char *dest, int nmemb, uint32_t flags);
+int mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]);
+int mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]);
+
+/* output to a file */
+void mpd_fprint(FILE *file, const mpd_t *dec);
+void mpd_print(const mpd_t *dec);
+
+/* assignment from a string */
+void mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, uint32_t *status);
+
+/* set to NaN with error flags */
+void mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status);
+/* set a special with sign and type */
+void mpd_setspecial(mpd_t *dec, uint8_t sign, uint8_t type);
+/* set coefficient to zero or all nines */
+void mpd_zerocoeff(mpd_t *result);
+void mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
+
+/* quietly assign a C integer type to an mpd_t */
+void mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
+#ifndef LEGACY_COMPILER
+void mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
+#endif
+
+/* quietly assign a C integer type to an mpd_t with a static coefficient */
+void mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status);
+
+/* quietly get a C integer type from an mpd_t */
+mpd_ssize_t mpd_qget_ssize(const mpd_t *dec, uint32_t *status);
+mpd_uint_t mpd_qget_uint(const mpd_t *dec, uint32_t *status);
+mpd_uint_t mpd_qabs_uint(const mpd_t *dec, uint32_t *status);
+
+
+/* quiet functions */
+int mpd_qcheck_nan(mpd_t *nanresult, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qcheck_nans(mpd_t *nanresult, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status);
+
+const char * mpd_class(const mpd_t *a, const mpd_context_t *ctx);
+
+int mpd_qcopy(mpd_t *result, const mpd_t *a,  uint32_t *status);
+mpd_t *mpd_qncopy(const mpd_t *a);
+int mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status);
+int mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status);
+int mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status);
+
+void mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_same_quantum(const mpd_t *a, const mpd_t *b);
+
+void mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
+mpd_uint_t mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status);
+mpd_uint_t mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n);
+void mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, uint32_t *status);
+
+int mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status);
+int mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+int mpd_cmp_total(const mpd_t *a, const mpd_t *b);
+int mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b);
+int mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b);
+int mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b);
+
+void mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+
+void mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_update_ln10(mpd_ssize_t prec, uint32_t *status);
+void mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status);
+
+
+size_t mpd_sizeinbase(mpd_t *a, uint32_t base);
+void mpd_qimport_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen,
+                     uint8_t srcsign, uint32_t srcbase,
+                     const mpd_context_t *ctx, uint32_t *status);
+void mpd_qimport_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen,
+                     uint8_t srcsign, uint32_t srcbase,
+                     const mpd_context_t *ctx, uint32_t *status);
+size_t mpd_qexport_u16(uint16_t *rdata, size_t rlen, uint32_t base,
+                       const mpd_t *src, uint32_t *status);
+size_t mpd_qexport_u32(uint32_t *rdata, size_t rlen, uint32_t base,
+                       const mpd_t *src, uint32_t *status);
+
+
+/******************************************************************************/
+/*                           Signalling functions                             */
+/******************************************************************************/
+
+char * mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx);
+void mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
+void mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx);
+size_t mpd_export_u16(uint16_t *rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
+size_t mpd_export_u32(uint32_t *rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx);
+void mpd_finalize(mpd_t *result, mpd_context_t *ctx);
+int mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+int mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx);
+void mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx);
+void mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
+void mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
+void mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
+void mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
+void mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx);
+void mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx);
+void mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx);
+void mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx);
+#ifndef LEGACY_COMPILER
+void mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
+void mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
+#endif
+mpd_ssize_t mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx);
+mpd_uint_t mpd_get_uint(const mpd_t *a, mpd_context_t *ctx);
+mpd_uint_t mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx);
+void mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+mpd_uint_t mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+void mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx);
+void mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+int mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+int mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+int mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, mpd_context_t *ctx);
+void mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx);
+void mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx);
+void mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx);
+void mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx);
+void mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx);
+void mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, mpd_context_t *ctx);
+void mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx);
+void mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+void mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+void mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx);
+
+
+/******************************************************************************/
+/*                          Configuration specific                            */
+/******************************************************************************/
+
+#ifdef CONFIG_64
+void mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status);
+int64_t mpd_qget_i64(const mpd_t *dec, uint32_t *status);
+uint64_t mpd_qget_u64(const mpd_t *dec, uint32_t *status);
+
+void mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status);
+void mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status);
+
+void mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx);
+void mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx);
+int64_t mpd_get_i64(const mpd_t *a, mpd_context_t *ctx);
+uint64_t mpd_get_u64(const mpd_t *a, mpd_context_t *ctx);
+
+void mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+void mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx);
+void mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx);
+#else
+int32_t mpd_qget_i32(const mpd_t *dec, uint32_t *status);
+uint32_t mpd_qget_u32(const mpd_t *dec, uint32_t *status);
+int32_t mpd_get_i32(const mpd_t *a, mpd_context_t *ctx);
+uint32_t mpd_get_u32(const mpd_t *a, mpd_context_t *ctx);
+#endif
+
+
+/******************************************************************************/
+/*                       Get attributes of a decimal                          */
+/******************************************************************************/
+
+mpd_ssize_t mpd_adjexp(const mpd_t *dec);
+mpd_ssize_t mpd_etiny(const mpd_context_t *ctx);
+mpd_ssize_t mpd_etop(const mpd_context_t *ctx);
+mpd_uint_t mpd_msword(const mpd_t *dec);
+int mpd_word_digits(mpd_uint_t word);
+/* most significant digit of a word */
+mpd_uint_t mpd_msd(mpd_uint_t word);
+/* least significant digit of a word */
+mpd_uint_t mpd_lsd(mpd_uint_t word);
+/* coefficient size needed to store 'digits' */
+mpd_ssize_t mpd_digits_to_size(mpd_ssize_t digits);
+/* number of digits in the exponent, undefined for MPD_SSIZE_MIN */
+int mpd_exp_digits(mpd_ssize_t exp);
+int mpd_iscanonical(const mpd_t *dec UNUSED);
+int mpd_isfinite(const mpd_t *dec);
+int mpd_isinfinite(const mpd_t *dec);
+int mpd_isinteger(const mpd_t *dec);
+int mpd_isnan(const mpd_t *dec);
+int mpd_isnegative(const mpd_t *dec);
+int mpd_ispositive(const mpd_t *dec);
+int mpd_isqnan(const mpd_t *dec);
+int mpd_issigned(const mpd_t *dec);
+int mpd_issnan(const mpd_t *dec);
+int mpd_isspecial(const mpd_t *dec);
+int mpd_iszero(const mpd_t *dec);
+/* undefined for special numbers */
+int mpd_iszerocoeff(const mpd_t *dec);
+int mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx);
+int mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx);
+/* odd word */
+int mpd_isoddword(mpd_uint_t word);
+/* odd coefficient */
+int mpd_isoddcoeff(const mpd_t *dec);
+/* odd decimal, only defined for integers */
+int mpd_isodd(const mpd_t *dec);
+/* even decimal, only defined for integers */
+int mpd_iseven(const mpd_t *dec);
+/* 0 if dec is positive, 1 if dec is negative */
+uint8_t mpd_sign(const mpd_t *dec);
+/* 1 if dec is positive, -1 if dec is negative */
+int mpd_arith_sign(const mpd_t *dec);
+long mpd_radix(void);
+int mpd_isdynamic(mpd_t *dec);
+int mpd_isstatic(mpd_t *dec);
+int mpd_isdynamic_data(mpd_t *dec);
+int mpd_isstatic_data(mpd_t *dec);
+int mpd_isshared_data(mpd_t *dec);
+int mpd_isconst_data(mpd_t *dec);
+mpd_ssize_t mpd_trail_zeros(const mpd_t *dec);
+
+
+/******************************************************************************/
+/*                       Set attributes of a decimal                          */
+/******************************************************************************/
+
+/* set number of decimal digits in the coefficient */
+void mpd_setdigits(mpd_t *result);
+void mpd_set_sign(mpd_t *result, uint8_t sign);
+/* copy sign from another decimal */
+void mpd_signcpy(mpd_t *result, mpd_t *a);
+void mpd_set_infinity(mpd_t *result);
+void mpd_set_qnan(mpd_t *result);
+void mpd_set_snan(mpd_t *result);
+void mpd_set_negative(mpd_t *result);
+void mpd_set_positive(mpd_t *result);
+void mpd_set_dynamic(mpd_t *result);
+void mpd_set_static(mpd_t *result);
+void mpd_set_dynamic_data(mpd_t *result);
+void mpd_set_static_data(mpd_t *result);
+void mpd_set_shared_data(mpd_t *result);
+void mpd_set_const_data(mpd_t *result);
+void mpd_clear_flags(mpd_t *result);
+void mpd_set_flags(mpd_t *result, uint8_t flags);
+void mpd_copy_flags(mpd_t *result, const mpd_t *a);
+
+
+/******************************************************************************/
+/*                              Error Macros                                  */
+/******************************************************************************/
+
+#define mpd_err_fatal(...) \
+        do {fprintf(stderr, "%s:%d: error: ", __FILE__, __LINE__); \
+            fprintf(stderr, __VA_ARGS__);  fputc('\n', stderr); \
+            exit(1); \
+        } while (0)
+#define mpd_err_warn(...) \
+        do {fprintf(stderr, "%s:%d: warning: ", __FILE__, __LINE__); \
+            fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \
+        } while (0)
+
+
+/******************************************************************************/
+/*                            Memory handling                                 */
+/******************************************************************************/
+
+extern void *(* mpd_mallocfunc)(size_t size);
+extern void *(* mpd_callocfunc)(size_t nmemb, size_t size);
+extern void *(* mpd_reallocfunc)(void *ptr, size_t size);
+extern void (* mpd_free)(void *ptr);
+
+void *mpd_callocfunc_em(size_t nmemb, size_t size);
+
+void *mpd_alloc(mpd_size_t nmemb, mpd_size_t size);
+void *mpd_calloc(mpd_size_t nmemb, mpd_size_t size);
+void *mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err);
+void *mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size);
+
+mpd_t *mpd_qnew(void);
+mpd_t *mpd_new(mpd_context_t *ctx);
+mpd_t *mpd_qnew_size(mpd_ssize_t size);
+void mpd_del(mpd_t *dec);
+
+void mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len);
+int mpd_qresize(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+int mpd_qresize_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status);
+void mpd_minalloc(mpd_t *result);
+
+int mpd_resize(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx);
+int mpd_resize_zero(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx);
+
+
+#ifdef __cplusplus
+} /* END extern "C" */
+#endif
+
+
+#endif /* MPDECIMAL_H */
+
+
+

ext/mpdecimal/mpsignal.c

@@ -0,0 +1,964 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+
+
+char *
+mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx)
+{
+	char *ret;
+	uint32_t status = 0;
+	ret = mpd_qformat(dec, fmt, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+
+void
+mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen,
+               uint8_t srcsign, uint32_t base, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qimport_u16(result, srcdata, srclen, srcsign, base, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen,
+               uint8_t srcsign, uint32_t base, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qimport_u32(result, srcdata, srclen, srcsign, base, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+size_t
+mpd_export_u16(uint16_t *rdata, size_t rlen, uint32_t base, const mpd_t *src,
+               mpd_context_t *ctx)
+{
+	size_t n;
+	uint32_t status = 0;
+	n = mpd_qexport_u16(rdata, rlen, base, src, &status);
+	mpd_addstatus_raise(ctx, status);
+	return n;
+}
+
+size_t
+mpd_export_u32(uint32_t *rdata, size_t rlen, uint32_t base, const mpd_t *src,
+               mpd_context_t *ctx)
+{
+	size_t n;
+	uint32_t status = 0;
+	n = mpd_qexport_u32(rdata, rlen, base, src, &status);
+	mpd_addstatus_raise(ctx, status);
+	return n;
+}
+
+void
+mpd_finalize(mpd_t *result, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qfinalize(result, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+int
+mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (mpd_qcheck_nan(result, a, ctx, &status)) {
+		mpd_addstatus_raise(ctx, status);
+		return 1;
+	}
+	return 0;
+}
+
+int
+mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (mpd_qcheck_nans(result, a, b, ctx, &status)) {
+		mpd_addstatus_raise(ctx, status);
+		return 1;
+	}
+	return 0;
+}
+
+void
+mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_string(result, s, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmaxcoeff(result, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+/* set static mpd from signed integer */
+void
+mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_ssize(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_i32(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_i64(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+/* set static mpd from unsigned integer */
+void
+mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_uint(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_u32(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsset_u64(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+/* set mpd from signed integer */
+void
+mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_ssize(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_i32(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifndef LEGACY_COMPILER
+void
+mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_i64(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+/* set mpd from unsigned integer */
+void
+mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_uint(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_u32(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifndef LEGACY_COMPILER
+void
+mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qset_u64(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+/* convert mpd to signed integer */
+mpd_ssize_t
+mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_ssize_t ret;
+
+	ret = mpd_qget_ssize(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+
+#ifdef CONFIG_32
+int32_t
+mpd_get_i32(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	int32_t ret;
+
+	ret = mpd_qget_i32(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+#else
+int64_t
+mpd_get_i64(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	int64_t ret;
+
+	ret = mpd_qget_i64(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+#endif
+
+mpd_uint_t
+mpd_get_uint(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_uint_t ret;
+
+	ret = mpd_qget_uint(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+
+mpd_uint_t
+mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_uint_t ret;
+
+	ret = mpd_qabs_uint(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+
+#ifdef CONFIG_32
+uint32_t
+mpd_get_u32(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	uint32_t ret;
+
+	ret = mpd_qget_u32(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+#else
+uint64_t
+mpd_get_u64(const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	uint64_t ret;
+
+	ret = mpd_qget_u64(a, &status);
+	mpd_addstatus_raise(ctx, status);
+	return ret;
+}
+#endif
+
+void
+mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qand(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qcopy(result, a, &status)) {
+		mpd_addstatus_raise(ctx, status);
+	}
+}
+
+void
+mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	mpd_copy(result, a, ctx);
+}
+
+void
+mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qcopy_abs(result, a, &status)) {
+		mpd_addstatus_raise(ctx, status);
+	}
+}
+
+void
+mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qcopy_negate(result, a, &status)) {
+		mpd_addstatus_raise(ctx, status);
+	}
+}
+
+void
+mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	if (!mpd_qcopy_sign(result, a, b, &status)) {
+		mpd_addstatus_raise(ctx, status);
+	}
+}
+
+void
+mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qinvert(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qlogb(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qor(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qrotate(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qscaleb(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qshiftl(result, a, n, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+mpd_uint_t
+mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_uint_t rnd;
+
+	rnd = mpd_qshiftr(result, a, n, &status);
+	mpd_addstatus_raise(ctx, status);
+	return rnd;
+}
+
+void
+mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qshiftn(result, a, n, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qshift(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qxor(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qabs(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+int
+mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	int c;
+	c = mpd_qcmp(a, b, &status);
+	mpd_addstatus_raise(ctx, status);
+	return c;
+}
+
+int
+mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	int c;
+	c = mpd_qcompare(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+	return c;
+}
+
+int
+mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	int c;
+	c = mpd_qcompare_signal(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+	return c;
+}
+
+void
+mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_ssize(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_i32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_i64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_uint(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_u32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qadd_u64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_ssize(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_i32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_i64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_uint(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_u32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsub_u64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv(q, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_ssize(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_i32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_i64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_uint(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_u32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdiv_u64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdivmod(q, r, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qdivint(q, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qexp(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
+        mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qfma(result, a, b, c, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qln(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qlog10(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmax(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmax_mag(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmin(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmin_mag(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qminus(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_ssize(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_i32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_i64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_uint(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_u32(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qmul_u64(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+#endif
+
+void
+mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qnext_minus(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qnext_plus(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qnext_toward(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qplus(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qpow(result, base, exp, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod,
+           mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qpowmod(result, base, exp, mod, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qquantize(result, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qrescale(result, a, exp, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qreduce(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qrem(r, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qrem_near(r, a, b, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qround_to_intx(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qround_to_int(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qtrunc(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qfloor(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qceil(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qsqrt(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+void
+mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx)
+{
+	uint32_t status = 0;
+	mpd_qinvroot(result, a, ctx, &status);
+	mpd_addstatus_raise(ctx, status);
+}
+
+
+

ext/mpdecimal/mptest.h

@@ -0,0 +1,56 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MPTEST_H
+#define MPTEST_H
+
+
+#include "mpdecimal.h"
+#ifndef _MSC_VER
+  #define IMPORTEXPORT
+#endif
+
+
+/* newton division undergoes the same rigorous tests as standard division */
+IMPORTEXPORT void mpd_test_newtondiv(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+IMPORTEXPORT void mpd_test_newtondivint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+IMPORTEXPORT void mpd_test_newtonrem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+IMPORTEXPORT void mpd_test_newtondivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx);
+
+/* fenv */
+IMPORTEXPORT unsigned int mpd_set_fenv(void);
+IMPORTEXPORT void mpd_restore_fenv(unsigned int);
+
+IMPORTEXPORT mpd_uint_t *_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v, mpd_size_t ulen, mpd_size_t vlen, mpd_size_t *rsize);
+IMPORTEXPORT mpd_uint_t *_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v, mpd_size_t ulen, mpd_size_t vlen, mpd_size_t *rsize);
+IMPORTEXPORT mpd_uint_t *_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v, mpd_size_t ulen, mpd_size_t vlen, mpd_size_t *rsize);
+
+
+#endif
+
+

ext/mpdecimal/mptypes.h

@@ -0,0 +1,80 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef MPTYPES_H
+#define MPTYPES_H
+
+#if defined(_MSC_VER)
+  #define PRIi64 "lld"
+  #define PRIu64 "llu"
+  #define PRIi32 "d"
+  #define PRIu32 "u"
+#endif
+
+#if defined(CONFIG_64)
+  #if defined(_MSC_VER) || defined(__OpenBSD__) || defined(__APPLE__)
+    #define PRI_mpd_uint_t "llu"
+    #define PRI_mpd_size_t "llu"
+    #define PRI_mpd_ssize_t "lld"
+  #else
+    #define PRI_mpd_uint_t "lu"
+    #define PRI_mpd_size_t "lu"
+    #define PRI_mpd_ssize_t "ld"
+  #endif
+  #define PRI_time_t "ld"
+  #define CONV_mpd_ssize_t "L"
+  #define ONE_UM 1ULL
+#elif defined(CONFIG_32)
+  #define PRI_mpd_uint_t "u"
+  #define PRI_mpd_size_t "u"
+  #define PRI_mpd_ssize_t "d"
+  #if defined (__OpenBSD__)
+    #undef PRI_mpd_size_t
+    #define PRI_mpd_size_t "lu"
+    #define PRI_time_t "d"
+  #elif defined(__FreeBSD__)
+    #if defined(__x86_64__)
+      #define PRI_time_t "ld"
+    #else
+      #define PRI_time_t "d"
+    #endif
+  #else
+    #define PRI_time_t "ld"
+  #endif
+  #if MPD_SSIZE_MAX != INT_MAX
+    #error "define CONV_mpd_ssize_t"
+  #endif
+  #define CONV_mpd_ssize_t "i"
+  #define ONE_UM 1UL
+#else
+  #error "define CONFIG_64 or CONFIG_32"
+#endif
+
+#endif
+
+

ext/mpdecimal/numbertheory.c

@@ -0,0 +1,119 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "umodarith.h"
+#include "numbertheory.h"
+
+
+/* transform kernel */
+mpd_uint_t
+_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
+{
+	mpd_uint_t umod, p, r, xi;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+
+	SETMODULUS(modnum);
+	r = mpd_roots[modnum];
+	p = umod;
+	xi = (p-1) / n;
+
+	if (sign == -1)
+		return POWMOD(r, (p-1-xi));
+	else
+		return POWMOD(r, xi);
+}
+
+/* initialize transform parameters */
+struct fnt_params *
+_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
+{
+	struct fnt_params *tparams;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t kernel, imag, w;
+	mpd_uint_t i;
+	mpd_size_t nhalf;
+
+	assert(ispower2(n));
+	assert(sign == -1 || sign == 1);
+	assert(P1 <= modnum && modnum <= P3);
+
+	nhalf = n/2;
+	tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
+	if (tparams == NULL) {
+		return NULL;
+	}
+
+	SETMODULUS(modnum);
+	kernel = _mpd_getkernel(n, sign, modnum);
+	imag = _mpd_getkernel(4, -sign, modnum);
+
+	tparams->modnum = modnum;
+	tparams->modulus = umod;
+	tparams->imag = imag;
+	tparams->kernel = kernel;
+
+	w  = 1;
+	for (i = 0; i < nhalf; i++) {
+		tparams->wtable[i] = w;
+		w = MULMOD(w, kernel);
+	}
+
+	return tparams;
+}
+
+/* initialize wtable of size three */
+void
+_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
+{
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t kernel;
+
+	SETMODULUS(modnum);
+	kernel = _mpd_getkernel(3, sign, modnum);
+
+	w3table[0] = 1;
+	w3table[1] = kernel;
+	w3table[2] = POWMOD(kernel, 2);
+}
+
+

ext/mpdecimal/numbertheory.h

@@ -0,0 +1,72 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef NUMBER_THEORY_H
+#define NUMBER_THEORY_H
+
+
+#include "constants.h"
+#include "mpdecimal.h"
+
+
+/* transform parameters */
+struct fnt_params {
+	int modnum;
+	mpd_uint_t modulus;
+	mpd_uint_t imag;
+	mpd_uint_t kernel;
+	mpd_uint_t wtable[];
+};
+
+
+mpd_uint_t _mpd_getkernel(mpd_uint_t n, int sign, int modnum);
+struct fnt_params *_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum);
+void _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum);
+
+
+#ifdef PPRO
+static inline void
+ppro_setmodulus(int modnum, mpd_uint_t *umod, double *dmod, uint32_t dinvmod[3])
+{
+	*dmod = *umod =  mpd_moduli[modnum];
+	dinvmod[0] = mpd_invmoduli[modnum][0];
+	dinvmod[1] = mpd_invmoduli[modnum][1];
+	dinvmod[2] = mpd_invmoduli[modnum][2];
+}
+#else
+static inline void
+std_setmodulus(int modnum, mpd_uint_t *umod)
+{
+	*umod =  mpd_moduli[modnum];
+}
+#endif
+
+
+#endif
+
+

ext/mpdecimal/sixstep.c

@@ -0,0 +1,219 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "difradix2.h"
+#include "mptypes.h"
+#include "numbertheory.h"
+#include "transpose.h"
+#include "umodarith.h"
+#include "sixstep.h"
+
+
+/*
+ * A variant of the six-step algorithm from:
+ *
+ * David H. Bailey: FFTs in External or Hierarchical Memory, Journal of
+ * Supercomputing, vol. 4, no. 1 (March 1990), p. 23-35.
+ *
+ * URL: http://crd.lbl.gov/~dhbailey/dhbpapers/
+ */
+
+
+/* forward transform with sign = -1 */
+int
+six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	struct fnt_params *tparams;
+	mpd_size_t log2n, C, R;
+	mpd_uint_t kernel;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t *x, w0, w1, wstep;
+	mpd_size_t i, k;
+
+
+	assert(ispower2(n));
+	assert(n >= 16);
+	assert(n <= MPD_MAXTRANSFORM_2N);
+
+	log2n = mpd_bsr(n);
+	C = (ONE_UM << (log2n / 2));  /* number of columns */
+	R = (ONE_UM << (log2n - (log2n / 2))); /* number of rows */
+
+
+	/* view 'a' as an RxC matrix, transpose */
+	if (!transpose_pow2(a, R, C)) {
+		return 0;
+	}
+
+	if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {
+		return 0;
+	}
+	for (x = a; x < a+n; x += R) {
+		fnt_dif2(x, R, tparams);
+	}
+
+	if (!transpose_pow2(a, C, R)) {
+		mpd_free(tparams);
+		return 0;
+	}
+
+
+	SETMODULUS(modnum);
+	kernel = _mpd_getkernel(n, -1, modnum);
+	for (i = 1; i < R; i++) {
+		w0 = 1;
+		w1 = POWMOD(kernel, i);
+		wstep = MULMOD(w1, w1);
+		for (k = 0; k < C; k += 2) {
+			mpd_uint_t x0 = a[i*C+k];
+			mpd_uint_t x1 = a[i*C+k+1];
+			MULMOD2(&x0, w0, &x1, w1);
+			MULMOD2C(&w0, &w1, wstep);
+			a[i*C+k] = x0;
+			a[i*C+k+1] = x1;
+		}
+	}
+
+
+	if (C != R) {
+		mpd_free(tparams);
+		if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {
+			return 0;
+		}
+	}
+	for (x = a; x < a+n; x += C) {
+		fnt_dif2(x, C, tparams);
+	}
+	mpd_free(tparams);
+
+
+#if 0
+	/* An unordered transform is sufficient for convolution. */
+	if (ordered) {
+		if (!transpose_pow2(a, R, C)) {
+			return 0;
+		}
+	}
+#endif
+
+	return 1;
+}
+
+
+/* reverse transform, sign = 1 */
+int
+inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
+{
+	struct fnt_params *tparams;
+	mpd_size_t log2n, C, R;
+	mpd_uint_t kernel;
+	mpd_uint_t umod;
+#ifdef PPRO
+	double dmod;
+	uint32_t dinvmod[3];
+#endif
+	mpd_uint_t *x, w0, w1, wstep;
+	mpd_size_t i, k;
+
+
+	assert(ispower2(n));
+	assert(n >= 16);
+	assert(n <= MPD_MAXTRANSFORM_2N);
+
+	log2n = mpd_bsr(n);
+	C = (ONE_UM << (log2n / 2)); /* number of columns */
+	R = (ONE_UM << (log2n - (log2n / 2))); /* number of rows */
+
+
+#if 0
+	/* An unordered transform is sufficient for convolution. */
+	if (ordered) {
+		if (!transpose_pow2(a, C, R)) {
+			return 0;
+		}
+	}
+#endif
+
+	if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {
+		return 0;
+	}
+	for (x = a; x < a+n; x += C) {
+		fnt_dif2(x, C, tparams);
+	}
+
+	if (!transpose_pow2(a, R, C)) {
+		mpd_free(tparams);
+		return 0;
+	}
+
+
+	SETMODULUS(modnum);
+	kernel = _mpd_getkernel(n, 1, modnum);
+	for (i = 1; i < C; i++) {
+		w0 = 1;
+		w1 = POWMOD(kernel, i);
+		wstep = MULMOD(w1, w1);
+		for (k = 0; k < R; k += 2) {
+			mpd_uint_t x0 = a[i*R+k];
+			mpd_uint_t x1 = a[i*R+k+1];
+			MULMOD2(&x0, w0, &x1, w1);
+			MULMOD2C(&w0, &w1, wstep);
+			a[i*R+k] = x0;
+			a[i*R+k+1] = x1;
+		}
+	}
+
+
+	if (R != C) {
+		mpd_free(tparams);
+		if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {
+			return 0;
+		}
+	}
+	for (x = a; x < a+n; x += R) {
+		fnt_dif2(x, R, tparams);
+	}
+	mpd_free(tparams);
+
+	if (!transpose_pow2(a, C, R)) {
+		return 0;
+	}
+
+	return 1;
+}
+
+

ext/mpdecimal/sixstep.h

@@ -0,0 +1,41 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef SIX_STEP_H
+#define SIX_STEP_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+int six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+int inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum);
+
+
+#endif

ext/mpdecimal/transpose.c

@@ -0,0 +1,272 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <assert.h>
+#include "bits.h"
+#include "constants.h"
+#include "typearith.h"
+#include "transpose.h"
+
+
+#define BUFSIZE 4096
+#define SIDE 128
+
+
+/* Definition of the matrix transpose */
+void
+std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols)
+{
+	mpd_size_t idest, isrc;
+	mpd_size_t r, c;
+
+	for (r = 0; r < rows; r++) {
+		isrc = r * cols;
+		idest = r;
+		for (c = 0; c < cols; c++) {
+			dest[idest] = src[isrc];
+			isrc += 1;
+			idest += rows;
+		}
+	}
+}
+
+/*
+ * Swap half-rows of 2^n * (2*2^n) matrix.
+ * FORWARD_CYCLE: even/odd permutation of the halfrows.
+ * BACKWARD_CYCLE: reverse the even/odd permutation.
+ */
+static int
+swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir)
+{
+	mpd_uint_t buf1[BUFSIZE];
+	mpd_uint_t buf2[BUFSIZE];
+	mpd_uint_t *readbuf, *writebuf, *hp;
+	mpd_size_t *done, dbits;
+	mpd_size_t b = BUFSIZE, stride;
+	mpd_size_t hn, hmax; /* halfrow number */
+	mpd_size_t m, r=0;
+	mpd_size_t offset;
+	mpd_size_t next;
+
+
+	assert(cols == mul_size_t(2, rows));
+
+	if (dir == FORWARD_CYCLE) {
+		r = rows;
+	}
+	else if (dir == BACKWARD_CYCLE) {
+		r = 2;
+	}
+	else {
+		abort(); /* GCOV_NOT_REACHED */
+	}
+
+	m = cols - 1;
+	hmax = rows; /* cycles start at odd halfrows */
+	dbits = 8 * sizeof *done;
+	if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) {
+		return 0;
+	}
+
+	for (hn = 1; hn <= hmax; hn += 2) {
+
+		if (done[hn/dbits] & mpd_bits[hn%dbits]) {
+			continue;
+		}
+
+		readbuf = buf1; writebuf = buf2;
+
+		for (offset = 0; offset < cols/2; offset += b) {
+
+			stride = (offset + b < cols/2) ? b : cols/2-offset;
+
+			hp = matrix + hn*cols/2;
+			memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
+			pointerswap(&readbuf, &writebuf);
+
+			next = mulmod_size_t(hn, r, m);
+			hp = matrix + next*cols/2;
+
+			while (next != hn) {
+
+				memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
+				memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
+				pointerswap(&readbuf, &writebuf);
+
+				done[next/dbits] |= mpd_bits[next%dbits];
+
+				next = mulmod_size_t(next, r, m);
+			        hp = matrix + next*cols/2;
+
+			}
+
+			memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
+
+			done[hn/dbits] |= mpd_bits[hn%dbits];
+		}
+	}
+
+	mpd_free(done);
+	return 1;
+}
+
+/* In-place transpose of a square matrix */
+static inline void
+squaretrans(mpd_uint_t *buf, mpd_size_t cols)
+{
+	mpd_uint_t tmp;
+	mpd_size_t idest, isrc;
+	mpd_size_t r, c;
+
+	for (r = 0; r < cols; r++) {
+		c = r+1;
+		isrc = r*cols + c;
+		idest = c*cols + r;
+		for (c = r+1; c < cols; c++) {
+			tmp = buf[isrc];
+			buf[isrc] = buf[idest];
+			buf[idest] = tmp;
+			isrc += 1;
+			idest += cols;
+		}
+	}
+}
+
+/*
+ * Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into
+ * square blocks with side length 'SIDE'. First, the blocks are transposed,
+ * then a square tranposition is done on each individual block.
+ */
+static void
+squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size)
+{
+	mpd_uint_t buf1[SIDE*SIDE];
+	mpd_uint_t buf2[SIDE*SIDE];
+	mpd_uint_t *to, *from;
+	mpd_size_t b = size;
+	mpd_size_t r, c;
+	mpd_size_t i;
+
+	while (b > SIDE) b >>= 1;
+
+	for (r = 0; r < size; r += b) {
+
+		for (c = r; c < size; c += b) {
+
+			from = matrix + r*size + c;
+			to = buf1;
+			for (i = 0; i < b; i++) {
+				memcpy(to, from, b*(sizeof *to));
+				from += size;
+				to += b;
+			}
+			squaretrans(buf1, b);
+
+			if (r == c) {
+				to = matrix + r*size + c;
+				from = buf1;
+				for (i = 0; i < b; i++) {
+					memcpy(to, from, b*(sizeof *to));
+					from += b;
+					to += size;
+				}
+				continue;
+			}
+			else {
+				from = matrix + c*size + r;
+				to = buf2;
+				for (i = 0; i < b; i++) {
+					memcpy(to, from, b*(sizeof *to));
+					from += size;
+					to += b;
+				}
+				squaretrans(buf2, b);
+
+				to = matrix + c*size + r;
+				from = buf1;
+				for (i = 0; i < b; i++) {
+					memcpy(to, from, b*(sizeof *to));
+					from += b;
+					to += size;
+				}
+
+				to = matrix + r*size + c;
+				from = buf2;
+				for (i = 0; i < b; i++) {
+					memcpy(to, from, b*(sizeof *to));
+					from += b;
+					to += size;
+				}
+			}
+		}
+	}
+
+}
+
+/*
+ * In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
+ * or a (2*2^n) x 2^n matrix.
+ */
+int
+transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols)
+{
+	mpd_size_t size = mul_size_t(rows, cols);
+
+	assert(ispower2(rows));
+	assert(ispower2(cols));
+
+	if (cols == rows) {
+		squaretrans_pow2(matrix, rows);
+	}
+	else if (cols == mul_size_t(2, rows)) {
+		if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) {
+			return 0;
+		}
+		squaretrans_pow2(matrix, rows);
+		squaretrans_pow2(matrix+(size/2), rows);
+	}
+	else if (rows == mul_size_t(2, cols)) {
+		squaretrans_pow2(matrix, cols);
+		squaretrans_pow2(matrix+(size/2), cols);
+		if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) {
+			return 0;
+		}
+	}
+	else {
+		abort(); /* GCOV_NOT_REACHED */
+	}
+
+	return 1;
+}
+
+

ext/mpdecimal/transpose.h

@@ -0,0 +1,55 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef TRANSPOSE_H
+#define TRANSPOSE_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+
+
+enum {FORWARD_CYCLE, BACKWARD_CYCLE};
+
+
+void std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols);
+int transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
+void transpose_3xpow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols);
+
+
+static inline void pointerswap(mpd_uint_t **a, mpd_uint_t **b)
+{
+	mpd_uint_t *tmp;
+
+	tmp = *b;
+	*b = *a;
+	*a = tmp;
+}
+
+
+#endif

ext/mpdecimal/typearith.h

@@ -0,0 +1,639 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef TYPEARITH_H
+#define TYPEARITH_H
+
+
+#include "mpdecimal.h"
+
+
+/*****************************************************************************/
+/*                      Native arithmetic on basic types                     */
+/*****************************************************************************/
+
+
+/** ------------------------------------------------------------
+ **           Double width multiplication and division
+ ** ------------------------------------------------------------
+ */
+
+#if defined(CONFIG_64)
+#if defined(ANSI)
+#if defined(HAVE_UINT128_T)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	__uint128_t hl;
+
+	hl = (__uint128_t)a * b;
+
+	*hi = hl >> 64;
+	*lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+	__uint128_t hl;
+
+	hl = ((__uint128_t)hi<<64) + lo;
+	*q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+	*r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d);
+}
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	uint32_t w[4], carry;
+	uint32_t ah, al, bh, bl;
+	uint64_t hl;
+
+	ah = (uint32_t)(a>>32); al = (uint32_t)a;
+	bh = (uint32_t)(b>>32); bl = (uint32_t)b;
+
+	hl = (uint64_t)al * bl;
+	w[0] = (uint32_t)hl;
+	carry = (uint32_t)(hl>>32);
+
+	hl = (uint64_t)ah * bl + carry;
+	w[1] = (uint32_t)hl;
+	w[2] = (uint32_t)(hl>>32);
+
+	hl = (uint64_t)al * bh + w[1];
+	w[1] = (uint32_t)hl;
+	carry = (uint32_t)(hl>>32);
+
+	hl = ((uint64_t)ah * bh + w[2]) + carry;
+	w[2] = (uint32_t)hl;
+	w[3] = (uint32_t)(hl>>32);
+
+	*hi = ((uint64_t)w[3]<<32) + w[2];
+	*lo = ((uint64_t)w[1]<<32) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ *  site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint64_t x)
+{
+	int n;
+
+	if (x == 0) return(64);
+
+	n = 0;
+	if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;}
+	if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;}
+	if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;}
+	if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;}
+	if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;}
+	if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;}
+
+	return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+               mpd_uint_t v)
+{
+	const mpd_uint_t b = 4294967296;
+	mpd_uint_t un1, un0,
+	           vn1, vn0,
+	           q1, q0,
+	           un32, un21, un10,
+	           rhat, t;
+	int s;
+
+	assert(u1 < v);
+
+	s = nlz(v);
+	v = v << s;
+	vn1 = v >> 32;
+	vn0 = v & 0xFFFFFFFF;
+
+	t = (s == 0) ? 0 : u0 >> (64 - s);
+	un32 = (u1 << s) | t;
+	un10 = u0 << s;
+
+	un1 = un10 >> 32;
+	un0 = un10 & 0xFFFFFFFF;
+
+	q1 = un32 / vn1;
+	rhat = un32 - q1*vn1;
+again1:
+	if (q1 >= b || q1*vn0 > b*rhat + un1) {
+		q1 = q1 - 1;
+		rhat = rhat + vn1;
+		if (rhat < b) goto again1;
+	}
+
+	/*
+	 *  Before again1 we had:
+	 *      (1) q1*vn1   + rhat         = un32
+	 *      (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+	 *
+	 *  The statements inside the if-clause do not change the value
+	 *  of the left-hand side of (2), and the loop is only exited
+	 *  if q1*vn0 <= rhat*b + un1, so:
+	 *
+	 *      (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+	 *      (4)              q1*v <= un32*b + un1
+	 *      (5)                 0 <= un32*b + un1 - q1*v
+	 *
+	 *  By (5) we are certain that the possible add-back step from
+	 *  Knuth's algorithm D is never required.
+	 *
+	 *  Since the final quotient is less than 2**64, the following
+	 *  must be true:
+	 *
+	 *      (6) un32*b + un1 - q1*v <= UINT64_MAX
+	 *
+	 *  This means that in the following line, the high words
+	 *  of un32*b and q1*v can be discarded without any effect
+	 *  on the result.
+	 */
+	un21 = un32*b + un1 - q1*v;
+
+	q0 = un21 / vn1;
+	rhat = un21 - q0*vn1;
+again2:
+	if (q0 >= b || q0*vn0 > b*rhat + un0) {
+		q0 = q0 - 1;
+		rhat = rhat + vn1;
+		if (rhat < b) goto again2;
+	}
+
+	*q = q1*b + q0;
+	*r = (un21*b + un0 - q0*v) >> s;
+}
+#endif
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	mpd_uint_t h, l;
+
+	asm (	"mulq %3\n\t"
+		: "=d" (h), "=a" (l)
+		: "%a" (a), "rm" (b)
+		: "cc"
+	);
+
+	*hi = h;
+	*lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+	mpd_uint_t qq, rr;
+
+	asm (	"divq %4\n\t"
+		: "=a" (qq), "=d" (rr)
+		: "a" (lo), "d" (hi), "rm" (d)
+		: "cc"
+	);
+
+	*q = qq;
+	*r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+#include <intrin.h>
+#pragma intrinsic(_umul128)
+
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	*lo = _umul128(a, b, hi);
+}
+
+void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+                    mpd_uint_t d);
+
+/* END MASM (_MSC_VER) */
+#else
+  #error "need platform specific 128 bit multiplication and division"
+#endif
+
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+  assert(exp <= 19);
+
+  if (exp <= 9) {
+    if (exp <= 4) {
+      switch (exp) {
+      case 0: *q = v; *r = 0; break;
+      case 1: *q = v / 10ULL; *r = v - *q * 10ULL; break;
+      case 2: *q = v / 100ULL; *r = v - *q * 100ULL; break;
+      case 3: *q = v / 1000ULL; *r = v - *q * 1000ULL; break;
+      case 4: *q = v / 10000ULL; *r = v - *q * 10000ULL; break;
+      }
+    }
+    else {
+      switch (exp) {
+      case 5: *q = v / 100000ULL; *r = v - *q * 100000ULL; break;
+      case 6: *q = v / 1000000ULL; *r = v - *q * 1000000ULL; break;
+      case 7: *q = v / 10000000ULL; *r = v - *q * 10000000ULL; break;
+      case 8: *q = v / 100000000ULL; *r = v - *q * 100000000ULL; break;
+      case 9: *q = v / 1000000000ULL; *r = v - *q * 1000000000ULL; break;
+      }
+    }
+  }
+  else {
+    if (exp <= 14) {
+      switch (exp) {
+      case 10: *q = v / 10000000000ULL; *r = v - *q * 10000000000ULL; break;
+      case 11: *q = v / 100000000000ULL; *r = v - *q * 100000000000ULL; break;
+      case 12: *q = v / 1000000000000ULL; *r = v - *q * 1000000000000ULL; break;
+      case 13: *q = v / 10000000000000ULL; *r = v - *q * 10000000000000ULL; break;
+      case 14: *q = v / 100000000000000ULL; *r = v - *q * 100000000000000ULL; break;
+      }
+    }
+    else {
+      switch (exp) {
+      case 15: *q = v / 1000000000000000ULL; *r = v - *q * 1000000000000000ULL; break;
+      case 16: *q = v / 10000000000000000ULL; *r = v - *q * 10000000000000000ULL; break;
+      case 17: *q = v / 100000000000000000ULL; *r = v - *q * 100000000000000000ULL; break;
+      case 18: *q = v / 1000000000000000000ULL; *r = v - *q * 1000000000000000000ULL; break;
+      case 19: *q = v / 10000000000000000000ULL; *r = v - *q * 10000000000000000000ULL; break; /* GCOV_NOT_REACHED */
+      }
+    }
+  }
+}
+
+/* END CONFIG_64 */
+#elif defined(CONFIG_32)
+#if defined(ANSI)
+#if !defined(LEGACY_COMPILER)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	mpd_uuint_t hl;
+
+	hl = (mpd_uuint_t)a * b;
+
+	*hi = hl >> 32;
+	*lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+	mpd_uuint_t hl;
+
+	hl = ((mpd_uuint_t)hi<<32) + lo;
+	*q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+	*r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d);
+}
+/* END ANSI + uint64_t */
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	uint16_t w[4], carry;
+	uint16_t ah, al, bh, bl;
+	uint32_t hl;
+
+	ah = (uint16_t)(a>>16); al = (uint16_t)a;
+	bh = (uint16_t)(b>>16); bl = (uint16_t)b;
+
+	hl = (uint32_t)al * bl;
+	w[0] = (uint16_t)hl;
+	carry = (uint16_t)(hl>>16);
+
+	hl = (uint32_t)ah * bl + carry;
+	w[1] = (uint16_t)hl;
+	w[2] = (uint16_t)(hl>>16);
+
+	hl = (uint32_t)al * bh + w[1];
+	w[1] = (uint16_t)hl;
+	carry = (uint16_t)(hl>>16);
+
+	hl = ((uint32_t)ah * bh + w[2]) + carry;
+	w[2] = (uint16_t)hl;
+	w[3] = (uint16_t)(hl>>16);
+
+	*hi = ((uint32_t)w[3]<<16) + w[2];
+	*lo = ((uint32_t)w[1]<<16) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ *  site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint32_t x)
+{
+	int n;
+
+	if (x == 0) return(32);
+
+	n = 0;
+	if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
+	if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
+	if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
+	if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
+	if (x <= 0x7FFFFFFF) {n = n + 1;}
+
+	return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+               mpd_uint_t v)
+{
+	const mpd_uint_t b = 65536;
+	mpd_uint_t un1, un0,
+	           vn1, vn0,
+	           q1, q0,
+	           un32, un21, un10,
+	           rhat, t;
+	int s;
+
+	assert(u1 < v);
+
+	s = nlz(v);
+	v = v << s;
+	vn1 = v >> 16;
+	vn0 = v & 0xFFFF;
+
+	t = (s == 0) ? 0 : u0 >> (32 - s);
+	un32 = (u1 << s) | t;
+	un10 = u0 << s;
+
+	un1 = un10 >> 16;
+	un0 = un10 & 0xFFFF;
+
+	q1 = un32 / vn1;
+	rhat = un32 - q1*vn1;
+again1:
+	if (q1 >= b || q1*vn0 > b*rhat + un1) {
+		q1 = q1 - 1;
+		rhat = rhat + vn1;
+		if (rhat < b) goto again1;
+	}
+
+	/*
+	 *  Before again1 we had:
+	 *      (1) q1*vn1   + rhat         = un32
+	 *      (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+	 *
+	 *  The statements inside the if-clause do not change the value
+	 *  of the left-hand side of (2), and the loop is only exited
+	 *  if q1*vn0 <= rhat*b + un1, so:
+	 *
+	 *      (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+	 *      (4)              q1*v <= un32*b + un1
+	 *      (5)                 0 <= un32*b + un1 - q1*v
+	 *
+	 *  By (5) we are certain that the possible add-back step from
+	 *  Knuth's algorithm D is never required.
+	 *
+	 *  Since the final quotient is less than 2**32, the following
+	 *  must be true:
+	 *
+	 *      (6) un32*b + un1 - q1*v <= UINT32_MAX
+	 *
+	 *  This means that in the following line, the high words
+	 *  of un32*b and q1*v can be discarded without any effect
+	 *  on the result.
+	 */
+	un21 = un32*b + un1 - q1*v;
+
+	q0 = un21 / vn1;
+	rhat = un21 - q0*vn1;
+again2:
+	if (q0 >= b || q0*vn0 > b*rhat + un0) {
+		q0 = q0 - 1;
+		rhat = rhat + vn1;
+		if (rhat < b) goto again2;
+	}
+
+	*q = q1*b + q0;
+	*r = (un21*b + un0 - q0*v) >> s;
+}
+#endif /* END ANSI + LEGACY_COMPILER */
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	mpd_uint_t h, l;
+
+	asm (	"mull %3\n\t"
+		: "=d" (h), "=a" (l)
+		: "%a" (a), "rm" (b)
+		: "cc"
+	);
+
+	*hi = h;
+	*lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+	mpd_uint_t qq, rr;
+
+	asm (	"divl %4\n\t"
+		: "=a" (qq), "=d" (rr)
+		: "a" (lo), "d" (hi), "rm" (d)
+		: "cc"
+	);
+
+	*q = qq;
+	*r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+static inline void __cdecl
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+	mpd_uint_t h, l;
+
+	__asm {
+		mov eax, a
+		mul b
+		mov h, edx
+		mov l, eax
+	}
+
+	*hi = h;
+	*lo = l;
+}
+
+static inline void __cdecl
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+               mpd_uint_t d)
+{
+	mpd_uint_t qq, rr;
+
+	__asm {
+		mov eax, lo
+		mov edx, hi
+		div d
+		mov qq, eax
+		mov rr, edx
+	}
+
+	*q = qq;
+	*r = rr;
+}
+/* END MASM (_MSC_VER) */
+#else
+  #error "need platform specific 64 bit multiplication and division"
+#endif
+
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+  assert(exp <= 9);
+
+  if (exp <= 4) {
+    switch (exp) {
+    case 0: *q = v; *r = 0; break;
+    case 1: *q = v / 10UL; *r = v - *q * 10UL; break;
+    case 2: *q = v / 100UL; *r = v - *q * 100UL; break;
+    case 3: *q = v / 1000UL; *r = v - *q * 1000UL; break;
+    case 4: *q = v / 10000UL; *r = v - *q * 10000UL; break;
+    }
+  }
+  else {
+    switch (exp) {
+    case 5: *q = v / 100000UL; *r = v - *q * 100000UL; break;
+    case 6: *q = v / 1000000UL; *r = v - *q * 1000000UL; break;
+    case 7: *q = v / 10000000UL; *r = v - *q * 10000000UL; break;
+    case 8: *q = v / 100000000UL; *r = v - *q * 100000000UL; break;
+    case 9: *q = v / 1000000000UL; *r = v - *q * 1000000000UL; break; /* GCOV_NOT_REACHED */
+    }
+  }
+}
+/* END CONFIG_32 */
+
+/* NO CONFIG */
+#else
+  #error "define CONFIG_64 or CONFIG_32"
+#endif /* CONFIG */
+
+
+static inline void
+_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d)
+{
+	*q = v / d;
+	*r = v - *q * d;
+}
+
+static inline void
+_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d)
+{
+	*q = v / d;
+	*r = v - *q * d;
+}
+
+
+/** ------------------------------------------------------------
+ **              Arithmetic with overflow checking
+ ** ------------------------------------------------------------
+ */
+static inline mpd_size_t
+add_size_t(mpd_size_t a, mpd_size_t b)
+{
+	if (a > MPD_SIZE_MAX - b) {
+		mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+	}
+	return a + b;
+}
+
+static inline mpd_size_t
+sub_size_t(mpd_size_t a, mpd_size_t b)
+{
+	if (b > a) {
+		mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+	}
+	return a - b;
+}
+
+#if MPD_SIZE_MAX != MPD_UINT_MAX
+  #error "adapt mul_size_t() and mulmod_size_t()"
+#endif
+
+static inline mpd_size_t
+mul_size_t(mpd_size_t a, mpd_size_t b)
+{
+	mpd_uint_t hi, lo;
+
+	_mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+	if (hi) {
+		mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+	}
+	return lo;
+}
+
+static inline mpd_ssize_t
+mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m)
+{
+	mpd_ssize_t r = a % m;
+	return (r < 0) ? r + m : r;
+}
+
+static inline mpd_size_t
+mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m)
+{
+	mpd_uint_t hi, lo;
+	mpd_uint_t q, r;
+
+	_mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+	_mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m);
+
+	return r;
+}
+
+
+#endif /* TYPEARITH_H */
+
+
+

ext/mpdecimal/umodarith.h

@@ -0,0 +1,602 @@
+/*
+ * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#ifndef UMODARITH_H
+#define UMODARITH_H
+
+
+#include "constants.h"
+#include "mpdecimal.h"
+#include "typearith.h"
+
+
+/**************************************************************************/
+/*                      ANSI C99 modular arithmetic                       */
+/**************************************************************************/
+
+
+/*
+ * Restrictions: a < m and b < m
+ * ACL2 proof: umodarith.lisp: addmod-correct
+ */
+static inline mpd_uint_t
+addmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	mpd_uint_t s;
+
+	s = a + b;
+	s = (s < a) ? s - m : s;
+	s = (s >= m) ? s - m : s;
+
+	return s;
+}
+
+/*
+ * Restrictions: a < m and b < m
+ * ACL2 proof: umodarith.lisp: submod-2-correct
+ */
+static inline mpd_uint_t
+submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	mpd_uint_t d;
+
+	d = a - b;
+	d = (a < b) ? d + m : d;
+
+	return d;
+}
+
+/*
+ * Restrictions: a < 2m and b < 2m
+ * ACL2 proof: umodarith.lisp: ext-submod-2-correct
+ */
+static inline mpd_uint_t
+ext_submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	mpd_uint_t d;
+
+	a = (a >= m) ? a - m : a;
+	b = (b >= m) ? b - m : b;
+
+	d = a - b;
+	d = (a < b) ? d + m : d;
+
+	return d;
+}
+
+/* divide 2 words by v, return remainder */
+static inline mpd_uint_t
+bigmod2(mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t v)
+{
+	mpd_uint_t r1, r2, w;
+
+	_mpd_div_word(&w, &r1, hi, v);
+	_mpd_div_words(&w, &r2, r1, lo, v);
+
+	return r2;
+}
+
+/* subtract double word hi,lo from a */
+static inline mpd_uint_t
+dw_submod(mpd_uint_t a, mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m)
+{
+	mpd_uint_t d, r;
+
+	r = bigmod2(hi, lo, m);
+	d = a - r;
+	d = (a < r) ? d + m : d;
+
+	return d;
+}
+
+#ifdef CONFIG_64
+
+/**************************************************************************/
+/*                        64-bit modular arithmetic                       */
+/**************************************************************************/
+
+/*
+ * Description of the algorithm in apfloat.pdf, Chapter 7.1.1,
+ * by Mikko Tommila:  http://www.apfloat.org/apfloat/2.41/
+ *
+ * ACL2 proof: umodarith.lisp: section "Fast modular reduction"
+ */
+
+static inline mpd_uint_t
+x64_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	mpd_uint_t hi, lo, x, y;
+
+
+	_mpd_mul_words(&hi, &lo, a, b);
+
+	if (m & (1ULL<<32)) { /* P1 */
+
+		/* first reduction */
+		x = y = hi;
+		hi >>= 32;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 32;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		/* second reduction */
+		x = y = hi;
+		hi >>= 32;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 32;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		return (hi || lo >= m ? lo - m : lo);
+	}
+	else if (m & (1ULL<<34)) { /* P2 */
+
+		/* first reduction */
+		x = y = hi;
+		hi >>= 30;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 34;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		/* second reduction */
+		x = y = hi;
+		hi >>= 30;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 34;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		/* third reduction */
+		x = y = hi;
+		hi >>= 30;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 34;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		return (hi || lo >= m ? lo - m : lo);
+	}
+	else { /* P3 */
+
+		/* first reduction */
+		x = y = hi;
+		hi >>= 24;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 40;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		/* second reduction */
+		x = y = hi;
+		hi >>= 24;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 40;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		/* third reduction */
+		x = y = hi;
+		hi >>= 24;
+
+		x = lo - x;
+		if (x > lo) hi--;
+
+		y <<= 40;
+		lo = y + x;
+		if (lo < y) hi++;
+
+		return (hi || lo >= m ? lo - m : lo);
+	}
+}
+
+static inline void
+x64_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+	*a = x64_mulmod(*a, w, m);
+	*b = x64_mulmod(*b, w, m);
+}
+
+static inline void
+x64_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+	*a0 = x64_mulmod(*a0, b0, m);
+	*a1 = x64_mulmod(*a1, b1, m);
+}
+
+static inline mpd_uint_t
+x64_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
+{
+	mpd_uint_t r = 1;
+
+	while (exp > 0) {
+		if (exp & 1)
+			r = x64_mulmod(r, base, umod);
+		base = x64_mulmod(base, base, umod);
+		exp >>= 1;
+	}
+
+	return r;
+}
+
+/* END CONFIG_64 */
+#else /* CONFIG_32 */
+
+
+/**************************************************************************/
+/*                        32-bit modular arithmetic                       */
+/**************************************************************************/
+
+#if defined(ANSI)
+#if !defined(LEGACY_COMPILER)
+/* HAVE_UINT64_T */
+static inline mpd_uint_t
+std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	return ((mpd_uuint_t) a * b) % m;
+}
+
+static inline void
+std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+	*a = ((mpd_uuint_t) *a * w) % m;
+	*b = ((mpd_uuint_t) *b * w) % m;
+}
+
+static inline void
+std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+	*a0 = ((mpd_uuint_t) *a0 * b0) % m;
+	*a1 = ((mpd_uuint_t) *a1 * b1) % m;
+}
+/* END HAVE_UINT64_T */
+#else
+/* LEGACY_COMPILER */
+static inline mpd_uint_t
+std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m)
+{
+	mpd_uint_t hi, lo, q, r;
+	_mpd_mul_words(&hi, &lo, a, b);
+	_mpd_div_words(&q, &r, hi, lo, m);
+	return r;
+}
+
+static inline void
+std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m)
+{
+	*a = std_mulmod(*a, w, m);
+	*b = std_mulmod(*b, w, m);
+}
+
+static inline void
+std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+            mpd_uint_t m)
+{
+	*a0 = std_mulmod(*a0, b0, m);
+	*a1 = std_mulmod(*a1, b1, m);
+}
+/* END LEGACY_COMPILER */
+#endif
+
+static inline mpd_uint_t
+std_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod)
+{
+	mpd_uint_t r = 1;
+
+	while (exp > 0) {
+		if (exp & 1)
+			r = std_mulmod(r, base, umod);
+		base = std_mulmod(base, base, umod);
+		exp >>= 1;
+	}
+
+	return r;
+}
+#endif /* ANSI CONFIG_32 */
+
+
+/**************************************************************************/
+/*                    Pentium Pro modular arithmetic                      */
+/**************************************************************************/
+
+/*
+ * Description of the algorithm in apfloat.pdf, Chapter 7.1.1, by Mikko Tommila.
+ * http://www.apfloat.org/apfloat/2.41/
+ *
+ * Remarks:
+ *
+ *   - dinvmod points to an array of three uint32_t, which is interpreted
+ *     as an 80 bit long double.
+ *   - Intel compilers prior to version 11 do not seem to handle the
+ *     __GNUC__ inline assembly correctly.
+ *   - random tests are provided in tests/extended/ppro_mulmod.c
+ */
+
+#if defined(PPRO)
+#if defined(ASM)
+
+/* all operands < dmod */
+static inline mpd_uint_t
+ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
+{
+	mpd_uint_t retval;
+
+	asm (
+		"fildl	%2\n\t"
+		"fildl	%1\n\t"
+		"fmulp	%%st, %%st(1)\n\t"
+		"fldt	(%4)\n\t"
+		"fmul	%%st(1), %%st\n\t"
+		"flds	%5\n\t"
+		"fadd	%%st, %%st(1)\n\t"
+		"fsubrp	%%st, %%st(1)\n\t"
+		"fldl	(%3)\n\t"
+		"fmulp	%%st, %%st(1)\n\t"
+		"fsubrp	%%st, %%st(1)\n\t"
+		"fistpl	%0\n\t"
+		: "=m" (retval)
+		: "m" (a), "m" (b), "r" (dmod), "r" (dinvmod), "m" (MPD_TWO63)
+		: "st", "memory"
+	);
+
+	return retval;
+}
+
+/* all operands < dmod */
+static inline void
+ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
+              double *dmod, uint32_t *dinvmod)
+{
+	asm (
+		"fildl	%2\n\t"
+		"fildl	(%1)\n\t"
+		"fmul	%%st(1), %%st\n\t"
+		"fxch	%%st(1)\n\t"
+		"fildl	(%0)\n\t"
+		"fmulp	%%st, %%st(1) \n\t"
+		"fldt	(%4)\n\t"
+		"flds	%5\n\t"
+		"fld	%%st(2)\n\t"
+		"fmul	%%st(2)\n\t"
+		"fadd	%%st(1)\n\t"
+		"fsub	%%st(1)\n\t"
+		"fmull	(%3)\n\t"
+		"fsubrp %%st, %%st(3)\n\t"
+		"fxch   %%st(2)\n\t"
+		"fistpl	(%0)\n\t"
+		"fmul	%%st(2)\n\t"
+		"fadd	%%st(1)\n\t"
+		"fsubp  %%st, %%st(1)\n\t"
+		"fmull  (%3)\n\t"
+		"fsubrp %%st, %%st(1)\n\t"
+		"fistpl (%1)\n\t"
+		: : "r" (a0), "r" (a1), "m" (w),
+		    "r" (dmod), "r" (dinvmod),
+		    "m" (MPD_TWO63)
+		: "st", "memory"
+	);
+}
+
+/* all operands < dmod */
+static inline void
+ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+             double *dmod, uint32_t *dinvmod)
+{
+	asm (
+		"fildl	%3\n\t"
+		"fildl	(%2)\n\t"
+		"fmulp	%%st, %%st(1)\n\t"
+		"fildl	%1\n\t"
+		"fildl	(%0)\n\t"
+		"fmulp	%%st, %%st(1)\n\t"
+		"fldt	(%5)\n\t"
+		"fld	%%st(2)\n\t"
+		"fmul	%%st(1), %%st\n\t"
+		"fxch	%%st(1)\n\t"
+		"fmul	%%st(2), %%st\n\t"
+		"flds	%6\n\t"
+		"fldl	(%4)\n\t"
+		"fxch	%%st(3)\n\t"
+		"fadd	%%st(1), %%st\n\t"
+		"fxch	%%st(2)\n\t"
+		"fadd	%%st(1), %%st\n\t"
+		"fxch	%%st(2)\n\t"
+		"fsub	%%st(1), %%st\n\t"
+		"fxch	%%st(2)\n\t"
+		"fsubp	%%st, %%st(1)\n\t"
+		"fxch	%%st(1)\n\t"
+		"fmul	%%st(2), %%st\n\t"
+		"fxch	%%st(1)\n\t"
+		"fmulp	%%st, %%st(2)\n\t"
+		"fsubrp	%%st, %%st(3)\n\t"
+		"fsubrp	%%st, %%st(1)\n\t"
+		"fxch	%%st(1)\n\t"
+		"fistpl	(%2)\n\t"
+		"fistpl	(%0)\n\t"
+		: : "r" (a0), "m" (b0), "r" (a1), "m" (b1),
+		    "r" (dmod), "r" (dinvmod),
+		    "m" (MPD_TWO63)
+		: "st", "memory"
+	);
+}
+/* END PPRO GCC ASM */
+#elif defined(MASM)
+
+/* all operands < dmod */
+static inline mpd_uint_t __cdecl
+ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod)
+{
+	mpd_uint_t retval;
+
+	__asm {
+		mov	eax, dinvmod
+		mov	edx, dmod
+		fild	b
+		fild	a
+		fmulp	st(1), st
+		fld	TBYTE PTR [eax]
+		fmul	st, st(1)
+		fld	MPD_TWO63
+		fadd	st(1), st
+		fsubp	st(1), st
+		fld	QWORD PTR [edx]
+		fmulp	st(1), st
+		fsubp	st(1), st
+		fistp	retval
+	}
+
+	return retval;
+}
+
+/* all operands < dmod */
+static inline mpd_uint_t __cdecl
+ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w,
+              double *dmod, uint32_t *dinvmod)
+{
+	__asm {
+		mov	ecx, dmod
+		mov	edx, a1
+		mov	ebx, dinvmod
+		mov	eax, a0
+		fild	w
+		fild	DWORD PTR [edx]
+		fmul	st, st(1)
+		fxch	st(1)
+		fild	DWORD PTR [eax]
+		fmulp	st(1), st
+		fld	TBYTE PTR [ebx]
+		fld	MPD_TWO63
+		fld	st(2)
+		fmul	st, st(2)
+		fadd	st, st(1)
+		fsub	st, st(1)
+		fmul	QWORD PTR [ecx]
+		fsubp	st(3), st
+		fxch	st(2)
+		fistp	DWORD PTR [eax]
+		fmul	st, st(2)
+		fadd	st, st(1)
+		fsubrp	st(1), st
+		fmul	QWORD PTR [ecx]
+		fsubp	st(1), st
+		fistp	DWORD PTR [edx]
+	}
+}
+
+/* all operands < dmod */
+static inline void __cdecl
+ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1,
+             double *dmod, uint32_t *dinvmod)
+{
+	__asm {
+		mov	ecx, dmod
+		mov	edx, a1
+		mov	ebx, dinvmod
+		mov	eax, a0
+		fild	b1
+		fild	DWORD PTR [edx]
+		fmulp	st(1), st
+		fild	b0
+		fild	DWORD PTR [eax]
+		fmulp	st(1), st
+		fld	TBYTE PTR [ebx]
+		fld	st(2)
+		fmul	st, st(1)
+		fxch	st(1)
+		fmul	st, st(2)
+		fld	DWORD PTR MPD_TWO63
+		fld	QWORD PTR [ecx]
+		fxch	st(3)
+		fadd	st, st(1)
+		fxch	st(2)
+		fadd	st, st(1)
+		fxch	st(2)
+		fsub	st, st(1)
+		fxch	st(2)
+		fsubrp	st(1), st
+		fxch	st(1)
+		fmul	st, st(2)
+		fxch	st(1)
+		fmulp	st(2), st
+		fsubp	st(3), st
+		fsubp	st(1), st
+		fxch	st(1)
+		fistp	DWORD PTR [edx]
+		fistp	DWORD PTR [eax]
+	}
+}
+#endif /* PPRO MASM (_MSC_VER) */
+
+
+/* all operands < dmod */
+static inline mpd_uint_t
+ppro_powmod(mpd_uint_t base, mpd_uint_t exp, double *dmod, uint32_t *dinvmod)
+{
+	mpd_uint_t r = 1;
+
+	while (exp > 0) {
+		if (exp & 1)
+			r = ppro_mulmod(r, base, dmod, dinvmod);
+		base = ppro_mulmod(base, base, dmod, dinvmod);
+		exp >>= 1;
+	}
+
+	return r;
+}
+#endif /* PPRO */
+#endif /* CONFIG_32 */
+
+
+#endif /* UMODARITH_H */
+
+
+

ext/sq_decimal.cpp

@@ -0,0 +1,451 @@
+#include "mpdecimal.h"
+#include "squirrel.h"
+#include <string.h>
+SQ_OPT_STRING_STRLEN();
+
+static const SQChar sq_decimal_ctx_TAG[] = _SC("DecimalCtx");
+static const SQChar sq_decimal_TAG[] = _SC("Decimal");
+
+#define GET_DecimalCtx_INSTANCE(v, idx) SQ_GET_INSTANCE_VAR(v, idx, mpd_context_t, ctx, sq_decimal_ctx_TAG)
+#define GET_Decimal_INSTANCE(v, idx) SQ_GET_INSTANCE_VAR(v, idx, mpd_t, dec, sq_decimal_TAG)
+#define GET_Decimal_INSTANCE2(v, idx) SQ_GET_INSTANCE_VAR(v, idx, mpd_t, dec2, sq_decimal_TAG)
+
+
+static SQRESULT sq_DecimalCtx_release_hook(SQUserPointer p, SQInteger size, HSQUIRRELVM v) {
+    mpd_context_t *ctx = (mpd_context_t *)p;
+    if(ctx) sq_free(ctx, sizeof(mpd_context_t));
+    return 0;
+}
+
+/*
+** Creates a new DecimalCtx.
+*/
+static SQRESULT sq_DecimalCtx_constructor (HSQUIRRELVM v) {
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    SQ_OPT_INTEGER(v, 2, prec, 8);
+    if(prec < 0) return sq_throwerror(v, _SC("invalid precision (%d)"), prec);
+    ctx = (mpd_context_t *)sq_malloc(sizeof(mpd_context_t));
+    mpd_init(ctx, prec);
+    sq_setinstanceup(v, 1, ctx);
+    sq_setreleasehook(v, 1, sq_DecimalCtx_release_hook);
+    return 1;
+}
+
+static SQRESULT sq_DecimalCtx_prec(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, prec);
+        if(prec < 0) return sq_throwerror(v, _SC("invalid precision (%d)"), prec);
+        mpd_qsetprec(ctx, prec);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getprec(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_emax(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, emax);
+        if(emax < 0) return sq_throwerror(v, _SC("invalid emax (%d)"), emax);
+        mpd_qsetemax(ctx, emax);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getemax(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_emin(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, emin);
+        if(emin < 0) return sq_throwerror(v, _SC("invalid emin (%d)"), emin);
+        mpd_qsetemin(ctx, emin);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getemin(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_round(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, round);
+        if(round < 0) return sq_throwerror(v, _SC("invalid round (%d)"), round);
+        mpd_qsetround(ctx, round);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getround(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_traps(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, flags);
+        if(flags < 0) return sq_throwerror(v, _SC("invalid traps (%d)"), flags);
+        mpd_qsettraps(ctx, flags);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_gettraps(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_status(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, status);
+        if(status < 0) return sq_throwerror(v, _SC("invalid status (%d)"), status);
+        mpd_qsetstatus(ctx, status);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getstatus(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_clamp(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, clamp);
+        if(clamp < 0) return sq_throwerror(v, _SC("invalid clamp (%d)"), clamp);
+        mpd_qsetclamp(ctx, clamp);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getclamp(ctx));
+	return 1;
+}
+
+static SQRESULT sq_DecimalCtx_cr(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS(v);
+    GET_DecimalCtx_INSTANCE(v, 1);
+    if(_top_ > 1){
+        SQ_GET_INTEGER(v, 2, cr);
+        if(cr < 0) return sq_throwerror(v, _SC("invalid cr (%d)"), cr);
+        mpd_qsetcr(ctx, cr);
+        return 0;
+    }
+    else sq_pushinteger(v, mpd_getcr(ctx));
+	return 1;
+}
+
+#define _DECL_FUNC(name,nparams,tycheck) {_SC(#name),sq_DecimalCtx_##name,nparams,tycheck}
+static SQRegFunction DecimalCtx_methods[] =
+{
+    _DECL_FUNC(constructor,-1,_SC("xi")),
+    _DECL_FUNC(prec,-1,_SC("xi")),
+    _DECL_FUNC(emax,-1,_SC("xi")),
+    _DECL_FUNC(emin,-1,_SC("xi")),
+    _DECL_FUNC(round,-1,_SC("xi")),
+    _DECL_FUNC(traps,-1,_SC("xi")),
+    _DECL_FUNC(status,-1,_SC("xi")),
+    _DECL_FUNC(clamp,-1,_SC("xi")),
+    _DECL_FUNC(cr,-1,_SC("xi")),
+    {0,0}
+};
+#undef _DECL_FUNC
+
+static mpd_context_t * sq_get_global_ctx(HSQUIRRELVM v, SQInteger idx)
+{
+    sq_pushliteral(v, _SC("gctx"));
+    sq_get(v, idx);
+    mpd_context_t *ctx = 0;
+    sq_getinstanceup(v, -1, (void**)&ctx, (void*)sq_decimal_ctx_TAG);
+    sq_poptop(v);
+	return ctx;
+}
+
+static SQRESULT sq_Decimal_release_hook(SQUserPointer p, SQInteger size, HSQUIRRELVM v) {
+    mpd_t *dec = (mpd_t *)p;
+    if(dec) mpd_del(dec);
+    return 0;
+}
+
+/*
+** Creates a new Decimal.
+*/
+static SQRESULT sq_Decimal_constructor (HSQUIRRELVM v) {
+    SQ_FUNC_VARS(v);
+    GET_Decimal_INSTANCE(v, 1);
+    if(_top_ > 1){
+        switch(sq_gettype(v, 2)){
+            case OT_INSTANCE:{
+                GET_DecimalCtx_INSTANCE(v, 2);
+                dec = mpd_new(ctx);
+            }
+            case OT_INTEGER:{
+                SQ_GET_INTEGER(v, 2, iparam);
+                mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+                dec = mpd_new(ctx);
+                uint32_t status;
+                mpd_qset_i32(dec, iparam, ctx, &status);
+            }
+            break;
+            case OT_STRING:{
+                SQ_GET_STRING(v, 2, str);
+                mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+                dec = mpd_new(ctx);
+                uint32_t status;
+                mpd_qset_string(dec, str, ctx, &status);
+            }
+            break;
+            case OT_FLOAT:{
+                SQ_GET_FLOAT(v, 2, fparam);
+                mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+                dec = mpd_new(ctx);
+                uint32_t status;
+                char buf[32];
+                snprintf(buf, sizeof(buf), "%f", fparam);
+                mpd_qset_string(dec, buf, ctx, &status);
+            }
+            break;
+        }
+    }
+    else dec = mpd_qnew();
+    sq_setinstanceup(v, 1, dec);
+    sq_setreleasehook(v, 1, sq_Decimal_release_hook);
+    return 1;
+}
+
+static SQRESULT sq_Decimal_new_for_dec (HSQUIRRELVM v, mpd_t *dec, mpd_context_t *ctx, uint32_t status) {
+    //mpd_addstatus_raise(ctx, status);
+    sq_pushstring(v, sq_decimal_TAG, -1);
+    sq_getonroottable(v);
+    sq_createinstance(v, -1);
+    sq_setinstanceup(v, -1, dec);
+    sq_setreleasehook(v, -1, sq_Decimal_release_hook);
+    return 1;
+}
+
+static SQRESULT sq_Decimal_tostring(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    char *decstring =  mpd_to_eng(dec, 1);
+    sq_pushstring(v, decstring, -1);
+    if (decstring) mpd_free(decstring);
+	return 1;
+}
+
+static SQRESULT sq_Decimal__add(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qadd(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__sub(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qsub(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__mul(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qmul(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__div(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qdiv(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__modulo(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qrem(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__unm(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qminus(result, dec, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal__cmp(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    sq_pushinteger(v, mpd_cmp(dec, dec2, ctx));
+	return 1;
+}
+
+static SQRESULT sq_Decimal_abs(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qabs(result, dec, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal_max(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qmax(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal_min(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qmin(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal_next_minus(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qnext_minus(result, dec, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal_next_plus(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qnext_plus(result, dec, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+static SQRESULT sq_Decimal_next_toward(HSQUIRRELVM v)
+{
+    SQ_FUNC_VARS_NO_TOP(v);
+    GET_Decimal_INSTANCE(v, 1);
+    GET_Decimal_INSTANCE2(v, 2);
+    mpd_context_t *ctx = sq_get_global_ctx(v, 1);
+    mpd_t *result = mpd_new(ctx);
+    uint32_t status;
+    mpd_qnext_toward(result, dec, dec2, ctx, &status);
+	return sq_Decimal_new_for_dec(v, result, ctx, status);
+}
+
+#define _DECL_FUNC(name,nparams,tycheck) {_SC(#name),sq_Decimal_##name,nparams,tycheck}
+static SQRegFunction Decimal_methods[] =
+{
+    _DECL_FUNC(constructor,-1,_SC("x x|n|s")),
+    {_SC("_tostring"),sq_Decimal_tostring, 1,_SC("x")},
+    _DECL_FUNC(tostring,1,_SC("x")),
+    _DECL_FUNC(_add, 2,_SC("xx")),
+    _DECL_FUNC(_sub, 2,_SC("xx")),
+    _DECL_FUNC(_mul, 2,_SC("xx")),
+    _DECL_FUNC(_div, 2,_SC("xx")),
+    _DECL_FUNC(_modulo, 2,_SC("xx")),
+    _DECL_FUNC(_unm, 1,_SC("x")),
+    _DECL_FUNC(_cmp, 2,_SC("xx")),
+    _DECL_FUNC(abs, 1,_SC("x")),
+    _DECL_FUNC(max, 2,_SC("xx")),
+    _DECL_FUNC(min, 2,_SC("xx")),
+    _DECL_FUNC(next_minus, 1,_SC("x")),
+    _DECL_FUNC(next_plus, 1,_SC("x")),
+    _DECL_FUNC(next_toward, 2,_SC("xx")),
+    {0,0}
+};
+#undef _DECL_FUNC
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+SQRESULT sqext_register_decimal(HSQUIRRELVM v)
+{
+    sq_pushstring(v,sq_decimal_ctx_TAG,-1);
+	sq_newclass(v,SQFalse);
+	sq_settypetag(v,-1,(void*)sq_decimal_ctx_TAG);
+    sq_insert_reg_funcs(v, DecimalCtx_methods);
+    sq_newslot(v,-3,SQTrue);
+
+    sq_pushstring(v,sq_decimal_TAG,-1);
+	sq_newclass(v,SQFalse);
+	sq_settypetag(v,-1,(void*)sq_decimal_TAG);
+
+	sq_pushliteral(v, _SC("gctx"));
+	sq_pushstring(v,sq_decimal_ctx_TAG,-1);
+	sq_getonroottable(v);
+	sq_pushroottable(v);
+	sq_call(v, 1, SQTrue, SQFalse);
+	sq_remove(v, -2);
+    sq_newslot(v,-3,SQTrue);
+
+    sq_insert_reg_funcs(v, Decimal_methods);
+    sq_newslot(v,-3,SQTrue);
+
+    return 0;
+}
+
+#ifdef __cplusplus
+}
+#endif

sq/sq.c

@@ -319,6 +319,7 @@ SQRESULT sqext_register_SQLite3(HSQUIRRELVM v);
 SQRESULT sqext_register_mix (HSQUIRRELVM sqvm);
 SQRESULT sqext_register_rs232(HSQUIRRELVM v);
 SQRESULT sqext_register_tinyxml2(HSQUIRRELVM v);
+SQRESULT sqext_register_decimal(HSQUIRRELVM v);
 
 int sq_main_argc = 0;
 char** sq_main_argv = 0;
@@ -360,6 +361,7 @@ int main(int argc, char* argv[])
 	sqrat_register_importlib(v);
 	sqext_register_sq_slave_vm(v);
 	sqext_register_tinyxml2(v);
+	sqext_register_decimal(v);
 
 	sqext_register_sq_zmq3(v);
 

squilu.cbp

@@ -11,7 +11,7 @@
 				<Option object_output="obj/Debug/" />
 				<Option type="1" />
 				<Option compiler="gcc" />
-				<Option parameters="hello5.nut" />
+				<Option parameters="ourbiz-client.nut" />
 				<Compiler>
 					<Add option="-g" />
 					<Add directory="../zeromq-3.2.2/include" />
@@ -190,12 +190,15 @@
 			<Add directory="ext" />
 			<Add directory="ext/myaxtls" />
 			<Add directory="../dadbiz++/third-party/sqlite3" />
+			<Add directory="ext/mpdecimal" />
 		</Compiler>
 		<Linker>
+			<Add library="mpdecimal" />
 			<Add library="m" />
 			<Add library="z" />
 			<Add directory="lib" />
 			<Add directory="ext/myaxtls" />
+			<Add directory="ext/mpdecimal" />
 		</Linker>
 		<Unit filename="ext/fpdf.cpp" />
 		<Unit filename="ext/fpdf.h" />
@@ -214,6 +217,7 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="ext/sq_base64.cpp" />
+		<Unit filename="ext/sq_decimal.cpp" />
 		<Unit filename="ext/sq_fltk.cpp" />
 		<Unit filename="ext/sq_fpdf.cpp" />
 		<Unit filename="ext/sq_fs.c">