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/* ix87 specific implementation of pow function.
Copyright (C) 1996, 1997, 1998, 1999, 2001, 2004, 2007
Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <machine/asm.h>
#ifdef __ELF__
.section .rodata
#else
.text
#endif
.align ALIGNARG(4)
ASM_TYPE_DIRECTIVE(infinity,@object)
inf_zero:
infinity:
.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
ASM_SIZE_DIRECTIVE(infinity)
ASM_TYPE_DIRECTIVE(zero,@object)
zero: .double 0.0
ASM_SIZE_DIRECTIVE(zero)
ASM_TYPE_DIRECTIVE(minf_mzero,@object)
minf_mzero:
minfinity:
.byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
mzero:
.byte 0, 0, 0, 0, 0, 0, 0, 0x80
ASM_SIZE_DIRECTIVE(minf_mzero)
ASM_TYPE_DIRECTIVE(one,@object)
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
ASM_TYPE_DIRECTIVE(limit,@object)
limit: .double 0.29
ASM_SIZE_DIRECTIVE(limit)
ASM_TYPE_DIRECTIVE(p63,@object)
p63:
.byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
ASM_SIZE_DIRECTIVE(p63)
#ifdef PIC
#define MO(op) op##(%rip)
#else
#define MO(op) op
#endif
.text
ENTRY(__ieee754_powl)
fldt 24(%rsp) // y
fxam
fnstsw
movb %ah, %dl
andb $0x45, %ah
cmpb $0x40, %ah // is y == 0 ?
je 11f
cmpb $0x05, %ah // is y == ±inf ?
je 12f
cmpb $0x01, %ah // is y == NaN ?
je 30f
fldt 8(%rsp) // x : y
fxam
fnstsw
movb %ah, %dh
andb $0x45, %ah
cmpb $0x40, %ah
je 20f // x is ±0
cmpb $0x05, %ah
je 15f // x is ±inf
fxch // y : x
/* fistpll raises invalid exception for |y| >= 1L<<63. */
fldl MO(p63) // 1L<<63 : y : x
fld %st(1) // y : 1L<<63 : y : x
fabs // |y| : 1L<<63 : y : x
fcomip %st(1), %st // 1L<<63 : y : x
fstp %st(0) // y : x
jnc 2f
/* First see whether `y' is a natural number. In this case we
can use a more precise algorithm. */
fld %st // y : y : x
fistpll -8(%rsp) // y : x
fildll -8(%rsp) // int(y) : y : x
fucomip %st(1),%st // y : x
jne 2f
/* OK, we have an integer value for y. */
mov -8(%rsp),%eax
mov -4(%rsp),%edx
orl $0, %edx
fstp %st(0) // x
jns 4f // y >= 0, jump
fdivrl MO(one) // 1/x (now referred to as x)
negl %eax
adcl $0, %edx
negl %edx
4: fldl MO(one) // 1 : x
fxch
6: shrdl $1, %edx, %eax
jnc 5f
fxch
fmul %st(1) // x : ST*x
fxch
5: fmul %st(0), %st // x*x : ST*x
shrl $1, %edx
movl %eax, %ecx
orl %edx, %ecx
jnz 6b
fstp %st(0) // ST*x
ret
/* y is ±NAN */
30: fldt 8(%rsp) // x : y
fldl MO(one) // 1.0 : x : y
fucomip %st(1),%st // x : y
je 31f
fxch // y : x
31: fstp %st(1)
ret
.align ALIGNARG(4)
2: /* y is a real number. */
fxch // x : y
fldl MO(one) // 1.0 : x : y
fldl MO(limit) // 0.29 : 1.0 : x : y
fld %st(2) // x : 0.29 : 1.0 : x : y
fsub %st(2) // x-1 : 0.29 : 1.0 : x : y
fabs // |x-1| : 0.29 : 1.0 : x : y
fucompp // 1.0 : x : y
fnstsw
fxch // x : 1.0 : y
test $4500,%eax
jz 7f
fsub %st(1) // x-1 : 1.0 : y
fyl2xp1 // log2(x) : y
jmp 8f
7: fyl2x // log2(x) : y
8: fmul %st(1) // y*log2(x) : y
fxam
fnstsw
andb $0x45, %ah
cmpb $0x05, %ah // is y*log2(x) == ±inf ?
je 28f
fst %st(1) // y*log2(x) : y*log2(x)
frndint // int(y*log2(x)) : y*log2(x)
fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
fxch // fract(y*log2(x)) : int(y*log2(x))
f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
ret
28: fstp %st(1) // y*log2(x)
fldl MO(one) // 1 : y*log2(x)
fscale // 2^(y*log2(x)) : y*log2(x)
fstp %st(1) // 2^(y*log2(x))
ret
// pow(x,±0) = 1
.align ALIGNARG(4)
11: fstp %st(0) // pop y
fldl MO(one)
ret
// y == ±inf
.align ALIGNARG(4)
12: fstp %st(0) // pop y
fldl MO(one) // 1
fldt 8(%rsp) // x : 1
fabs // abs(x) : 1
fucompp // < 1, == 1, or > 1
fnstsw
andb $0x45, %ah
cmpb $0x45, %ah
je 13f // jump if x is NaN
cmpb $0x40, %ah
je 14f // jump if |x| == 1
shlb $1, %ah
xorb %ah, %dl
andl $2, %edx
#ifdef PIC
lea inf_zero(%rip),%rcx
fldl (%rcx, %rdx, 4)
#else
fldl inf_zero(,%rdx, 4)
#endif
ret
.align ALIGNARG(4)
14: fldl MO(one)
ret
.align ALIGNARG(4)
13: fldt 8(%rsp) // load x == NaN
ret
.align ALIGNARG(4)
// x is ±inf
15: fstp %st(0) // y
testb $2, %dh
jz 16f // jump if x == +inf
// We must find out whether y is an odd integer.
fld %st // y : y
fistpll -8(%rsp) // y
fildll -8(%rsp) // int(y) : y
fucomip %st(1),%st
ffreep %st // <empty>
jne 17f
// OK, the value is an integer, but is it odd?
mov -8(%rsp), %eax
mov -4(%rsp), %edx
andb $1, %al
jz 18f // jump if not odd
// It's an odd integer.
shrl $31, %edx
#ifdef PIC
lea minf_mzero(%rip),%rcx
fldl (%rcx, %rdx, 8)
#else
fldl minf_mzero(,%rdx, 8)
#endif
ret
.align ALIGNARG(4)
16: fcompl MO(zero)
fnstsw
shrl $5, %eax
andl $8, %eax
#ifdef PIC
lea inf_zero(%rip),%rcx
fldl (%rcx, %rax, 1)
#else
fldl inf_zero(,%rax, 1)
#endif
ret
.align ALIGNARG(4)
17: shll $30, %edx // sign bit for y in right position
18: shrl $31, %edx
#ifdef PIC
lea inf_zero(%rip),%rcx
fldl (%rcx, %rdx, 8)
#else
fldl inf_zero(,%rdx, 8)
#endif
ret
.align ALIGNARG(4)
// x is ±0
20: fstp %st(0) // y
testb $2, %dl
jz 21f // y > 0
// x is ±0 and y is < 0. We must find out whether y is an odd integer.
testb $2, %dh
jz 25f
fld %st // y : y
fistpll -8(%rsp) // y
fildll -8(%rsp) // int(y) : y
fucomip %st(1),%st
ffreep %st // <empty>
jne 26f
// OK, the value is an integer, but is it odd?
mov -8(%rsp),%eax
mov -4(%rsp),%edx
andb $1, %al
jz 27f // jump if not odd
// It's an odd integer.
// Raise divide-by-zero exception and get minus infinity value.
fldl MO(one)
fdivl MO(zero)
fchs
ret
25: fstp %st(0)
26:
27: // Raise divide-by-zero exception and get infinity value.
fldl MO(one)
fdivl MO(zero)
ret
.align ALIGNARG(4)
// x is ±0 and y is > 0. We must find out whether y is an odd integer.
21: testb $2, %dh
jz 22f
fld %st // y : y
fistpll -8(%rsp) // y
fildll -8(%rsp) // int(y) : y
fucomip %st(1),%st
ffreep %st // <empty>
jne 23f
// OK, the value is an integer, but is it odd?
mov -8(%rsp),%eax
mov -4(%rsp),%edx
andb $1, %al
jz 24f // jump if not odd
// It's an odd integer.
fldl MO(mzero)
ret
22: fstp %st(0)
23:
24: fldl MO(zero)
ret
END(__ieee754_powl)
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