squilu/mpdecimal

libmpdec
========

libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision
decimal floating point arithmetic. It is a complete implementation of
Mike Cowlishaw/IBM's General Decimal Arithmetic Specification.


Core files for small and medium precision arithmetic
----------------------------------------------------

basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19.
bits.h -> Portable detection of least/most significant one-bit.
constants.{c,h} -> Constants that are used in multiple files.
context.c -> Context functions.
io.{c,h} -> Conversions between mpd_t and ASCII strings,
mpd_t formatting (allows UTF-8 fill character).
memory.{c,h} -> Allocation handlers with overflow detection
and functions for switching between static
and dynamic mpd_t.
mpdecimal.{c,h} -> All (quiet) functions of the specification.
typearith.h -> Fast primitives for double word multiplication,
division etc.

Visual Studio only:
~~~~~~~~~~~~~~~~~~~
vccompat.h -> snprintf <==> sprintf_s and similar things.
vcstdint.h -> stdint.h (included in VS 2010 but not in VS 2008).
vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does
not allow inline asm for x64. Also, it does not provide
an intrinsic for double word division.

Files for bignum arithmetic:
----------------------------

The following files implement the Fast Number Theoretic Transform
used for multiplying coefficients with more than 1024 words (see
mpdecimal.c: _mpd_fntmul()).

umodarith.h -> Fast low level routines for unsigned modular arithmetic.
numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform.
difradix2.{c,h} -> Decimation in frequency transform, used as the
"base case" by the following three files:

fnt.{c,h} -> Transform arrays up to 4096 words.
sixstep.{c,h} -> Transform larger arrays of length 2**n.
fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n.

convolute.{c,h} -> Fast convolution using one of the three transform
functions.
transpose.{c,h} -> Transpositions needed for the sixstep algorithm.
crt.{c,h} -> Chinese Remainder Theorem: use information from three
transforms modulo three different primes to get the
final result.


Pointers to literature, proofs and more
=======================================

literature/
-----------

REFERENCES.txt -> List of relevant papers.
bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT).
fnt.py -> Verify constants used in the FNT; Python demo for the
O(N**2) discrete transform.

matrix-transform.txt -> Proof for the Matrix Fourier Transform used in
fourstep.c.
six-step.txt -> Show that the algorithm used in sixstep.c is
a variant of the Matrix Fourier Transform.
mulmod-64.txt -> Proof for the mulmod64 algorithm from
umodarith.h.
mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication
from umodarith.h.
umodarith.lisp -> ACL2 proofs for many functions from umodarith.h.


Library Author
==============

Stefan Krah