| /* |
| * 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> |
| |
| #ifdef USE_AS_EXP10L |
| # define IEEE754_EXPL __ieee754_exp10l |
| # define EXPL_FINITE __exp10l_finite |
| # define FLDLOG fldl2t |
| #elif defined USE_AS_EXPM1L |
| # define IEEE754_EXPL __expm1l |
| # undef EXPL_FINITE |
| # define FLDLOG fldl2e |
| #else |
| # define IEEE754_EXPL __ieee754_expl |
| # define EXPL_FINITE __expl_finite |
| # define FLDLOG fldl2e |
| #endif |
| |
| .section .rodata.cst16,"aM",@progbits,16 |
| |
| .p2align 4 |
| #ifdef USE_AS_EXP10L |
| .type c0,@object |
| c0: .byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40 |
| .byte 0, 0, 0, 0, 0, 0 |
| ASM_SIZE_DIRECTIVE(c0) |
| .type c1,@object |
| c1: .byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f |
| .byte 0, 0, 0, 0, 0, 0 |
| ASM_SIZE_DIRECTIVE(c1) |
| #else |
| .type 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) |
| .type 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) |
| #endif |
| #ifndef USE_AS_EXPM1L |
| .type 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) |
| #endif |
| |
| #ifdef PIC |
| # define MO(op) op##(%rip) |
| #else |
| # define MO(op) op |
| #endif |
| |
| .text |
| ENTRY(IEEE754_EXPL) |
| #ifdef USE_AS_EXPM1L |
| movzwl 8+8(%rsp), %eax |
| xorb $0x80, %ah // invert sign bit (now 1 is "positive") |
| cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)? |
| jae HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0) |
| #endif |
| 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? */ |
| #ifdef USE_AS_EXPM1L |
| xorb $0x80, %ah |
| cmpl $0xc006, %eax |
| fstsw %ax |
| movb $0x45, %dh |
| jb 4f |
| |
| /* Below -64.0 (may be -NaN or -Inf). */ |
| andb %ah, %dh |
| cmpb $0x01, %dh |
| je 2f /* Is +-NaN, jump. */ |
| jmp 1f /* -large, possibly -Inf. */ |
| |
| 4: /* In range -64.0 to 64.0 (may be +-0 but not NaN or +-Inf). */ |
| /* Test for +-0 as argument. */ |
| andb %ah, %dh |
| cmpb $0x40, %dh |
| je 2f |
| #else |
| 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 |
| #endif |
| 3: FLDLOG /* 1 log2(base) */ |
| fmul %st(1), %st /* 1 x log2(base) */ |
| /* Set round-to-nearest temporarily. */ |
| fstcw -4(%rsp) |
| movl $0xf3ff, %edx |
| andl -4(%rsp), %edx |
| movl %edx, -8(%rsp) |
| fldcw -8(%rsp) |
| frndint /* 1 i */ |
| fld %st(1) /* 2 x */ |
| frndint /* 2 xi */ |
| fldcw -4(%rsp) |
| 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(base))) - 1 */ |
| #ifdef USE_AS_EXPM1L |
| fstp %st(1) /* 2 */ |
| fscale /* 2 scale factor is st(1); base^x - 2^i */ |
| fxch /* 2 i */ |
| fld1 /* 3 1.0 */ |
| fscale /* 3 2^i */ |
| fld1 /* 4 1.0 */ |
| fsubrp %st, %st(1) /* 3 2^i - 1.0 */ |
| fstp %st(1) /* 2 */ |
| faddp %st, %st(1) /* 1 base^x - 1.0 */ |
| #else |
| fld1 /* 4 1.0 */ |
| faddp /* 3 2^(fract(x * log2(base))) */ |
| fstp %st(1) /* 2 */ |
| fscale /* 2 scale factor is st(1); base^x */ |
| fstp %st(1) /* 1 */ |
| #endif |
| fstp %st(1) /* 0 */ |
| jmp 2f |
| 1: |
| #ifdef USE_AS_EXPM1L |
| /* For expm1l, only negative sign gets here. */ |
| fstp %st |
| fld1 |
| fchs |
| #else |
| testl $0x200, %eax /* Test sign. */ |
| jz 2f /* If positive, jump. */ |
| fstp %st |
| fldz /* Set result to 0. */ |
| #endif |
| 2: ret |
| END(IEEE754_EXPL) |
| #ifdef USE_AS_EXPM1L |
| libm_hidden_def (__expm1l) |
| weak_alias (__expm1l, expm1l) |
| #else |
| strong_alias (IEEE754_EXPL, EXPL_FINITE) |
| #endif |
