mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-15 01:21:06 +00:00
79 lines
3.0 KiB
C
79 lines
3.0 KiB
C
/*
|
|
* Written by J.T. Conklin <jtc@netbsd.org>.
|
|
* Public domain.
|
|
*
|
|
* Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
|
|
*/
|
|
|
|
/*
|
|
* The 8087 method for the exponential function is to calculate
|
|
* exp(x) = 2^(x log2(e))
|
|
* after separating integer and fractional parts
|
|
* x log2(e) = i + f, |f| <= .5
|
|
* 2^i is immediate but f needs to be precise for long double accuracy.
|
|
* Suppress range reduction error in computing f by the following.
|
|
* Separate x into integer and fractional parts
|
|
* x = xi + xf, |xf| <= .5
|
|
* Separate log2(e) into the sum of an exact number c0 and small part c1.
|
|
* c0 + c1 = log2(e) to extra precision
|
|
* Then
|
|
* f = (c0 xi - i) + c0 xf + c1 x
|
|
* where c0 xi is exact and so also is (c0 xi - i).
|
|
* -- moshier@na-net.ornl.gov
|
|
*/
|
|
|
|
#include <math_private.h>
|
|
|
|
static const long double c0 = 1.44268798828125L;
|
|
static const long double c1 = 7.05260771340735992468e-6L;
|
|
|
|
long double
|
|
__ieee754_expl (long double x)
|
|
{
|
|
long double res;
|
|
|
|
/* I added the following ugly construct because expl(+-Inf) resulted
|
|
in NaN. The ugliness results from the bright minds at Intel.
|
|
For the i686 the code can be written better.
|
|
-- drepper@cygnus.com. */
|
|
asm ("fxam\n\t" /* Is NaN or +-Inf? */
|
|
"fstsw %%ax\n\t"
|
|
"movb $0x45, %%dh\n\t"
|
|
"andb %%ah, %%dh\n\t"
|
|
"cmpb $0x05, %%dh\n\t"
|
|
"je 1f\n\t" /* Is +-Inf, jump. */
|
|
"fldl2e\n\t" /* 1 log2(e) */
|
|
"fmul %%st(1),%%st\n\t" /* 1 x log2(e) */
|
|
"frndint\n\t" /* 1 i */
|
|
"fld %%st(1)\n\t" /* 2 x */
|
|
"frndint\n\t" /* 2 xi */
|
|
"fld %%st(1)\n\t" /* 3 i */
|
|
"fldt %2\n\t" /* 4 c0 */
|
|
"fld %%st(2)\n\t" /* 5 xi */
|
|
"fmul %%st(1),%%st\n\t" /* 5 c0 xi */
|
|
"fsubp %%st,%%st(2)\n\t" /* 4 f = c0 xi - i */
|
|
"fld %%st(4)\n\t" /* 5 x */
|
|
"fsub %%st(3),%%st\n\t" /* 5 xf = x - xi */
|
|
"fmulp %%st,%%st(1)\n\t" /* 4 c0 xf */
|
|
"faddp %%st,%%st(1)\n\t" /* 3 f = f + c0 xf */
|
|
"fldt %3\n\t" /* 4 */
|
|
"fmul %%st(4),%%st\n\t" /* 4 c1 * x */
|
|
"faddp %%st,%%st(1)\n\t" /* 3 f = f + c1 * x */
|
|
"f2xm1\n\t" /* 3 2^(fract(x * log2(e))) - 1 */
|
|
"fld1\n\t" /* 4 1.0 */
|
|
"faddp\n\t" /* 3 2^(fract(x * log2(e))) */
|
|
"fstp %%st(1)\n\t" /* 2 */
|
|
"fscale\n\t" /* 2 scale factor is st(1); e^x */
|
|
"fstp %%st(1)\n\t" /* 1 */
|
|
"fstp %%st(1)\n\t" /* 0 */
|
|
"jmp 2f\n\t"
|
|
"1:\ttestl $0x200, %%eax\n\t" /* Test sign. */
|
|
"jz 2f\n\t" /* If positive, jump. */
|
|
"fstp %%st\n\t"
|
|
"fldz\n\t" /* Set result to 0. */
|
|
"2:\t\n"
|
|
: "=t" (res) : "0" (x), "m" (c0), "m" (c1) : "ax", "dx");
|
|
return res;
|
|
}
|
|
strong_alias (__ieee754_expl, __expl_finite)
|