diff options
Diffstat (limited to 'libc/sysdeps/x86_64/fpu/e_expl.S')
| -rw-r--r-- | libc/sysdeps/x86_64/fpu/e_expl.S | 106 |
1 files changed, 106 insertions, 0 deletions
diff --git a/libc/sysdeps/x86_64/fpu/e_expl.S b/libc/sysdeps/x86_64/fpu/e_expl.S new file mode 100644 index 000000000..d497b2897 --- /dev/null +++ b/libc/sysdeps/x86_64/fpu/e_expl.S @@ -0,0 +1,106 @@ +/* + * 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 <machine/asm.h> + + .section .rodata.cst16,"aM",@progbits,16 + + .p2align 4 + ASM_TYPE_DIRECTIVE(c0,@object) +c0: .byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f + .byte 0, 0, 0, 0, 0, 0 + ASM_SIZE_DIRECTIVE(c0) + ASM_TYPE_DIRECTIVE(c1,@object) +c1: .byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f + .byte 0, 0, 0, 0, 0, 0 + ASM_SIZE_DIRECTIVE(c1) + ASM_TYPE_DIRECTIVE(csat,@object) +csat: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40 + .byte 0, 0, 0, 0, 0, 0 + ASM_SIZE_DIRECTIVE(csat) + +#ifdef PIC +# define MO(op) op##(%rip) +#else +# define MO(op) op +#endif + + .text +ENTRY(__ieee754_expl) + fldt 8(%rsp) +/* 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? */ + movzwl 8+8(%rsp), %eax + andl $0x7fff, %eax + cmpl $0x400d, %eax + jle 3f + /* Overflow, underflow or infinity or NaN as argument. */ + fstsw %ax + movb $0x45, %dh + andb %ah, %dh + cmpb $0x05, %dh + je 1f /* Is +-Inf, jump. */ + cmpb $0x01, %dh + je 2f /* Is +-NaN, jump. */ + /* Overflow or underflow; saturate. */ + fstp %st + fldt MO(csat) + andb $2, %ah + jz 3f + fchs +3: fldl2e /* 1 log2(e) */ + fmul %st(1), %st /* 1 x log2(e) */ + frndint /* 1 i */ + fld %st(1) /* 2 x */ + frndint /* 2 xi */ + fld %st(1) /* 3 i */ + fldt MO(c0) /* 4 c0 */ + fld %st(2) /* 5 xi */ + fmul %st(1), %st /* 5 c0 xi */ + fsubp %st, %st(2) /* 4 f = c0 xi - i */ + fld %st(4) /* 5 x */ + fsub %st(3), %st /* 5 xf = x - xi */ + fmulp %st, %st(1) /* 4 c0 xf */ + faddp %st, %st(1) /* 3 f = f + c0 xf */ + fldt MO(c1) /* 4 */ + fmul %st(4), %st /* 4 c1 * x */ + faddp %st, %st(1) /* 3 f = f + c1 * x */ + f2xm1 /* 3 2^(fract(x * log2(e))) - 1 */ + fld1 /* 4 1.0 */ + faddp /* 3 2^(fract(x * log2(e))) */ + fstp %st(1) /* 2 */ + fscale /* 2 scale factor is st(1); e^x */ + fstp %st(1) /* 1 */ + fstp %st(1) /* 0 */ + jmp 2f +1: testl $0x200, %eax /* Test sign. */ + jz 2f /* If positive, jump. */ + fstp %st + fldz /* Set result to 0. */ +2: ret +END(__ieee754_expl) +strong_alias (__ieee754_expl, __expl_finite) |