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Diffstat (limited to 'REORG.TODO/sysdeps/x86_64/fpu/e_expl.S')
| -rw-r--r-- | REORG.TODO/sysdeps/x86_64/fpu/e_expl.S | 219 |
1 files changed, 219 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/x86_64/fpu/e_expl.S b/REORG.TODO/sysdeps/x86_64/fpu/e_expl.S new file mode 100644 index 0000000000..a4ef023b2b --- /dev/null +++ b/REORG.TODO/sysdeps/x86_64/fpu/e_expl.S @@ -0,0 +1,219 @@ +/* + * 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> +#include <x86_64-math-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) +DEFINE_LDBL_MIN +#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 6f /* 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 + + /* Test for arguments that are small but not subnormal. */ + movzwl 8+8(%rsp), %eax + andl $0x7fff, %eax + cmpl $0x3fbf, %eax + jge 3f + /* Argument's exponent below -64; avoid spurious underflow if + normal. */ + cmpl $0x0001, %eax + jge 2f + /* Force underflow and return the argument, to avoid wrong signs + of zero results from the code below in some rounding modes. */ + fld %st + fmul %st + fstp %st + jmp 2f +#else + movzwl 8+8(%rsp), %eax + andl $0x7fff, %eax + cmpl $0x400d, %eax + jg 5f + cmpl $0x3fbc, %eax + jge 3f + /* Argument's exponent below -67, result rounds to 1. */ + fld1 + faddp + jmp 2f +5: /* 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 6f /* 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 */ + LDBL_CHECK_FORCE_UFLOW_NONNEG +#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 +6: /* NaN argument. */ + fadd %st + ret +END(IEEE754_EXPL) +#ifdef USE_AS_EXPM1L +libm_hidden_def (__expm1l) +weak_alias (__expm1l, expm1l) +#else +strong_alias (IEEE754_EXPL, EXPL_FINITE) +#endif |