diff options
Diffstat (limited to 'sysdeps/i386/fpu/e_expl.c')
| -rw-r--r-- | sysdeps/i386/fpu/e_expl.c | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/sysdeps/i386/fpu/e_expl.c b/sysdeps/i386/fpu/e_expl.c new file mode 100644 index 0000000000..d9c6476e11 --- /dev/null +++ b/sysdeps/i386/fpu/e_expl.c @@ -0,0 +1,75 @@ +/* + * 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 + */ + +static long double c0 = 1.44268798828125L; +static long double c1 = 7.05260771340735992468e-6L; + +long double +__ieee754_expl (long double x) +{ + long double res, t; + +/* 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 c0\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 c1\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) : "ax", "dx"); + return res; +} |