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/*
* 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 <libm-alias-ldouble.h>
#include <machine/asm.h>
#include <x86_64-math-asm.h>
#include <libm-alias-finite.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)
libm_alias_ldouble (__expm1, expm1)
#elif defined USE_AS_EXP10L
libm_alias_finite (__ieee754_exp10l, __exp10l)
#else
libm_alias_finite (__ieee754_expl, __expl)
#endif
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