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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 <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)
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