| /* |
| * 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; |
| } |
