72 lines
2.6 KiB
C
72 lines
2.6 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.h>
|
|
#include "cephes_mconf.h" /* for max and min log thresholds */
|
|
|
|
static long double c0 = 1.44268798828125L;
|
|
static long double c1 = 7.05260771340735992468e-6L;
|
|
|
|
static long double
|
|
__expl (long double x)
|
|
{
|
|
long double res;
|
|
asm ("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 */
|
|
: "=t" (res) : "0" (x), "m" (c0), "m" (c1) : "ax", "dx");
|
|
return res;
|
|
}
|
|
|
|
long double expl (long double x)
|
|
{
|
|
if (x > MAXLOGL)
|
|
return INFINITY;
|
|
else if (x < MINLOGL)
|
|
return 0.0L;
|
|
else
|
|
return __expl (x);
|
|
}
|