78 lines
2.9 KiB
C
78 lines
2.9 KiB
C
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/*
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* Written by J.T. Conklin <jtc@netbsd.org>.
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* Public domain.
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*
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* Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
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*/
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/*
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* The 8087 method for the exponential function is to calculate
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* exp(x) = 2^(x log2(e))
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* after separating integer and fractional parts
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* x log2(e) = i + f, |f| <= .5
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* 2^i is immediate but f needs to be precise for long double accuracy.
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* Suppress range reduction error in computing f by the following.
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* Separate x into integer and fractional parts
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* x = xi + xf, |xf| <= .5
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* Separate log2(e) into the sum of an exact number c0 and small part c1.
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* c0 + c1 = log2(e) to extra precision
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* Then
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* f = (c0 xi - i) + c0 xf + c1 x
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* where c0 xi is exact and so also is (c0 xi - i).
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* -- moshier@na-net.ornl.gov
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*/
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#include <math.h>
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static long double c0 = 1.44268798828125L;
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static long double c1 = 7.05260771340735992468e-6L;
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long double
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expl (long double x)
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{
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long double res;
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/* I added the following ugly construct because expl(+-Inf) resulted
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in NaN. The ugliness results from the bright minds at Intel.
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For the i686 the code can be written better.
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-- drepper@cygnus.com. */
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asm ("fxam\n\t" /* Is NaN or +-Inf? */
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"fstsw %%ax\n\t"
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"movb $0x45, %%dh\n\t"
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"andb %%ah, %%dh\n\t"
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"cmpb $0x05, %%dh\n\t"
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"je 1f\n\t" /* Is +-Inf, jump. */
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"fldl2e\n\t" /* 1 log2(e) */
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"fmul %%st(1),%%st\n\t" /* 1 x log2(e) */
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"frndint\n\t" /* 1 i */
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"fld %%st(1)\n\t" /* 2 x */
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"frndint\n\t" /* 2 xi */
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"fld %%st(1)\n\t" /* 3 i */
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"fldt %2\n\t" /* 4 c0 */
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"fld %%st(2)\n\t" /* 5 xi */
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"fmul %%st(1),%%st\n\t" /* 5 c0 xi */
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"fsubp %%st,%%st(2)\n\t" /* 4 f = c0 xi - i */
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"fld %%st(4)\n\t" /* 5 x */
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"fsub %%st(3),%%st\n\t" /* 5 xf = x - xi */
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"fmulp %%st,%%st(1)\n\t" /* 4 c0 xf */
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"faddp %%st,%%st(1)\n\t" /* 3 f = f + c0 xf */
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"fldt %3\n\t" /* 4 */
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"fmul %%st(4),%%st\n\t" /* 4 c1 * x */
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"faddp %%st,%%st(1)\n\t" /* 3 f = f + c1 * x */
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"f2xm1\n\t" /* 3 2^(fract(x * log2(e))) - 1 */
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"fld1\n\t" /* 4 1.0 */
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"faddp\n\t" /* 3 2^(fract(x * log2(e))) */
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"fstp %%st(1)\n\t" /* 2 */
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"fscale\n\t" /* 2 scale factor is st(1); e^x */
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"fstp %%st(1)\n\t" /* 1 */
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"fstp %%st(1)\n\t" /* 0 */
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"jmp 2f\n\t"
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"1:\ttestl $0x200, %%eax\n\t" /* Test sign. */
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"jz 2f\n\t" /* If positive, jump. */
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"fstp %%st\n\t"
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"fldz\n\t" /* Set result to 0. */
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"2:\t\n"
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: "=t" (res) : "0" (x), "m" (c0), "m" (c1) : "ax", "dx");
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return res;
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}
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