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@@ -597,6 +597,204 @@ type
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{$ifndef FPC_SYSTEM_HAS_EXP}
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+{$ifdef SUPPORT_DOUBLE}
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+ {
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+ This code was translated from uclib code, the original code
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+ had the following copyright notice:
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+
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+ *
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+ * ====================================================
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+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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+ *
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+ * Developed at SunPro, a Sun Microsystems, Inc. business.
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+ * Permission to use, copy, modify, and distribute this
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+ * software is freely granted, provided that this notice
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+ * is preserved.
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+ * ====================================================
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+ *}
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+
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+ {*
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+ * Returns the exponential of x.
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+ *
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+ * Method
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+ * 1. Argument reduction:
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+ * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
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+ * Given x, find r and integer k such that
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+ *
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+ * x = k*ln2 + r, |r| <= 0.5*ln2.
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+ *
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+ * Here r will be represented as r = hi-lo for better
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+ * accuracy.
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+ *
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+ * 2. Approximation of exp(r) by a special rational function on
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+ * the interval [0,0.34658]:
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+ * Write
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+ * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
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+ * We use a special Reme algorithm on [0,0.34658] to generate
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+ * a polynomial of degree 5 to approximate R. The maximum error
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+ * of this polynomial approximation is bounded by 2**-59. In
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+ * other words,
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+ * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
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+ * (where z=r*r, and the values of P1 to P5 are listed below)
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+ * and
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+ * | 5 | -59
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+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
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+ * | |
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+ * The computation of exp(r) thus becomes
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+ * 2*r
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+ * exp(r) = 1 + -------
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+ * R - r
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+ * r*R1(r)
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+ * = 1 + r + ----------- (for better accuracy)
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+ * 2 - R1(r)
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+ * where
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+ * 2 4 10
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+ * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
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+ *
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+ * 3. Scale back to obtain exp(x):
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+ * From step 1, we have
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+ * exp(x) = 2^k * exp(r)
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+ *
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+ * Special cases:
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+ * exp(INF) is INF, exp(NaN) is NaN;
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+ * exp(-INF) is 0, and
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+ * for finite argument, only exp(0)=1 is exact.
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+ *
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+ * Accuracy:
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+ * according to an error analysis, the error is always less than
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+ * 1 ulp (unit in the last place).
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+ *
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+ * Misc. info.
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+ * For IEEE double
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+ * if x > 7.09782712893383973096e+02 then exp(x) overflow
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+ * if x < -7.45133219101941108420e+02 then exp(x) underflow
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+ *
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+ * Constants:
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+ * The hexadecimal values are the intended ones for the following
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+ * constants. The decimal values may be used, provided that the
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+ * compiler will convert from decimal to binary accurately enough
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+ * to produce the hexadecimal values shown.
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+ *
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+ }
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+ function fpc_exp_real(x: Double):Double;compilerproc;
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+ const
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+ one = 1.0,
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+ halF : array[0..1] of double = (0.5,-0.5);
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+ huge = 1.0e+300;
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+ twom1000 = 9.33263618503218878990e-302; { 2**-1000=0x01700000,0}
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+ o_threshold = 7.09782712893383973096e+02; { 0x40862E42, 0xFEFA39EF }
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+ u_threshold = -7.45133219101941108420e+02; { 0xc0874910, 0xD52D3051 }
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+ ln2HI : array[0..1] of double = ( 6.93147180369123816490e-01: { 0x3fe62e42, 0xfee00000 }
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+ -6.93147180369123816490e-01); { 0xbfe62e42, 0xfee00000 }
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+ ln2LO : array[0..1] of double = (1.90821492927058770002e-10; { 0x3dea39ef, 0x35793c76 }
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+ -1.90821492927058770002e-10); { 0xbdea39ef, 0x35793c76 }
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+ invln2 = 1.44269504088896338700e+00; { 0x3ff71547, 0x652b82fe }
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+ P1 = 1.66666666666666019037e-01; { 0x3FC55555, 0x5555553E }
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+ P2 = -2.77777777770155933842e-03; { 0xBF66C16C, 0x16BEBD93 }
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+ P3 = 6.61375632143793436117e-05; { 0x3F11566A, 0xAF25DE2C }
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+ P4 = -1.65339022054652515390e-06; { 0xBEBBBD41, 0xC5D26BF1 }
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+ P5 = 4.13813679705723846039e-08; { 0x3E663769, 0x72BEA4D0 }
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+ var
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+ double hi : double = 0.0;
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+ double lo = 0.0;
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+ c : double;
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+ t : double;
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+ int32_t k=0;
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+ xsb : longint;
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+ hx,hy,lx : dword;
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+ begin
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+ hx:=float64(x).high;
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+ xsb := (hx shr 31) and 1; { sign bit of x }
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+ hx := hx and $7fffffff; { high word of |x| }
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+
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+ { filter out non-finite argument }
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+ if hx >= $40862E42 then
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+ begin { if |x|>=709.78... }
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+ if hx >= $7ff00000
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+ begin
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+ lx:=float64(x).low;
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+ if ((hx and $fffff) or lx)<>0 then
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+ begin
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+ result:=x+x; { NaN }
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+ exit;
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+ else
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+ else
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+ begin
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+ if xsb=0 then
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+ result:=x
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+ else
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+ result:=0.0; { exp(+-inf)=begininf,0end }
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+ exit;
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+ end;
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+ end;
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+ if x > o_threshold then
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+ begin
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+ result:=huge*huge; { overflow }
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+ exit;
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+ end;
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+ if x < u_threshold then
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+ begin
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+ result:=twom1000*twom1000; { underflow }
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+ exit;
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+ end;
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+ end;
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+
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+ { argument reduction }
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+ if hx > $3fd62e42 then
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+ begin { if |x| > 0.5 ln2 }
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+ if hx < $3FF0A2B2 then { and |x| < 1.5 ln2 }
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+ begin
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+ hi := x-ln2HI[xsb];
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+ lo:=ln2LO[xsb];
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+ k := 1-xsb-xsb;
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+ end
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+ else
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+ begin
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+ k := invln2*x+halF[xsb];
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+ t := k;
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+ hi := x - t*ln2HI[0]; { t*ln2HI is exact here }
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+ lo := t*ln2LO[0];
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+ end;
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+ x := hi - lo;
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+ end
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+ else if hx < $3e300000 then
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+ begin { when |x|<2**-28 }
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+ if huge+x>one then
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+ begin
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+ result:=one+x;{ trigger inexact }
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+ exit;
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+ end;
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+ end
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+ else
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+ k := 0;
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+
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+ { x is now in primary range }
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+ t:=x*x;
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+ c:=x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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+ if k=0 then
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+ begin
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+ result:=one-((x*c)/(c-2.0)-x);
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+ exit;
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+ end
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+ else
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+ y := one-((lo-(x*c)/(2.0-c))-hi);
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+
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+ if k >= -1021
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+ begin
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+ hy:=float64(y).high;
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+ float64(y).high:=hy+(k shl 20); { add k to y's exponent }
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+ result:=y;
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+ end
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+ else
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+ begin
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+ hy:=float64(y).high;
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+ float64(y).high:=hy+((k+1000) shl 20); { add k to y's exponent }
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+ result:=y*twom1000;
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+ end;
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+ end;
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+
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+{$else SUPPORT_DOUBLE}
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+
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function fpc_exp_real(d: ValReal):ValReal;compilerproc;
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{*****************************************************************}
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{ Exponential Function }
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@@ -668,6 +866,8 @@ type
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result := d;
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end;
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end;
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+{$endif SUPPORT_DOUBLE}
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+
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{$endif}
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@@ -695,7 +895,7 @@ type
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else
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result:=tr;
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end;
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-{$endif}
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+{$endif FPC_SYSTEM_HAS_EXP}
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{$ifdef FPC_CURRENCY_IS_INT64}
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florian