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/*
* 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 long double c0 = 1.44268798828125L;
static 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;
}
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