diff options
Diffstat (limited to 'sysdeps/i386')
| -rw-r--r-- | sysdeps/i386/fpu/e_expl.S | 43 | ||||
| -rw-r--r-- | sysdeps/i386/fpu/e_expl.c | 75 | ||||
| -rw-r--r-- | sysdeps/i386/fpu/libm-test-ulps | 20 |
3 files changed, 85 insertions, 53 deletions
diff --git a/sysdeps/i386/fpu/e_expl.S b/sysdeps/i386/fpu/e_expl.S deleted file mode 100644 index 2bcdf58c58..0000000000 --- a/sysdeps/i386/fpu/e_expl.S +++ /dev/null @@ -1,43 +0,0 @@ -/* - * Written by J.T. Conklin <jtc@netbsd.org>. - * Public domain. - * - * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>. - */ - -#include <machine/asm.h> - -RCSID("$NetBSD: $") - -/* e^x = 2^(x * log2l(e)) */ -ENTRY(__ieee754_expl) - fldt 4(%esp) -/* 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. */ - fxam /* Is NaN or +-Inf? */ - fstsw %ax - movb $0x45, %dh - andb %ah, %dh - cmpb $0x05, %dh - je 1f /* Is +-Inf, jump. */ - fldl2e - fmulp /* x * log2(e) */ - fld %st - frndint /* int(x * log2(e)) */ - fsubr %st,%st(1) /* fract(x * log2(e)) */ - fxch - f2xm1 /* 2^(fract(x * log2(e))) - 1 */ - fld1 - faddp /* 2^(fract(x * log2(e))) */ - fscale /* e^x */ - fstp %st(1) - ret - -1: testl $0x200, %eax /* Test sign. */ - jz 2f /* If positive, jump. */ - fstp %st - fldz /* Set result to 0. */ -2: ret -END (__ieee754_expl) 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; +} diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 7c60eea593..82d167cd18 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -484,13 +484,13 @@ ldouble: 128 # ctan Test "Real part of: ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i": -ildouble: 437 -ldouble: 437 +ildouble: 439 +ldouble: 439 Test "Imaginary part of: ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i": float: 1 ifloat: 1 -ildouble: 1 -ldouble: 1 +ildouble: 2 +ldouble: 2 Test "Real part of: ctan (0.7 + 1.2 i) == 0.1720734197630349001 + 0.9544807059989405538 i": double: 1 float: 1 @@ -506,13 +506,13 @@ ldouble: 367 # ctanh Test "Real part of: ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i": -ildouble: 2 -ldouble: 2 +ildouble: 5 +ldouble: 5 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i": float: 1 ifloat: 1 -ildouble: 23 -ldouble: 23 +ildouble: 25 +ldouble: 25 Test "Real part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i": Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i": float: 1 @@ -551,8 +551,8 @@ double: 24 float: 12 idouble: 24 ifloat: 12 -ldouble: 4 -ildouble: 4 +ldouble: 12 +ildouble: 12 Test "erfc (9) == 0.41370317465138102381e-36": ldouble: 36 ildouble: 36 |