glibc/sysdeps/x86_64/fpu/e_powl.S

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/* ix87 specific implementation of pow function.
Copyright (C) 1996-2014 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, see
<http://www.gnu.org/licenses/>. */
#include <machine/asm.h>
.section .rodata.cst8,"aM",@progbits,8
.p2align 3
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
.type p3,@object
p3: .byte 0, 0, 0, 0, 0, 0, 0x20, 0x40
ASM_SIZE_DIRECTIVE(p3)
.type p63,@object
p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
ASM_SIZE_DIRECTIVE(p63)
.type p64,@object
p64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
ASM_SIZE_DIRECTIVE(p64)
.type p78,@object
p78: .byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
ASM_SIZE_DIRECTIVE(p78)
.type pm79,@object
pm79: .byte 0, 0, 0, 0, 0, 0, 0, 0x3b
ASM_SIZE_DIRECTIVE(pm79)
.section .rodata.cst16,"aM",@progbits,16
.p2align 3
.type infinity,@object
inf_zero:
infinity:
.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
ASM_SIZE_DIRECTIVE(infinity)
.type zero,@object
zero: .double 0.0
ASM_SIZE_DIRECTIVE(zero)
.type 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)
#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 == <EFBFBD>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 <EFBFBD>0
cmpb $0x05, %ah
je 15f // x is <EFBFBD>inf
cmpb $0x01, %ah
je 31f // x is NaN
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
je 9f
// If y has absolute value at most 0x1p-79, then any finite
// nonzero x will result in 1. Saturate y to those bounds to
// avoid underflow in the calculation of y*log2(x).
fldl MO(pm79) // 0x1p-79 : y : x
fld %st(1) // y : 0x1p-79 : y : x
fabs // |y| : 0x1p-79 : y : x
fcomip %st(1), %st // 0x1p-79 : y : x
fstp %st(0) // y : x
jnc 3f
fstp %st(0) // pop y
fldl MO(pm79) // 0x1p-79 : x
testb $2, %dl
jnz 3f // y > 0
fchs // -0x1p-79 : x
jmp 3f
9: /* OK, we have an integer value for y. Unless very small
(we use < 8), use the algorithm for real exponent to avoid
accumulation of errors. */
fldl MO(p3) // 8 : y : x
fld %st(1) // y : 8 : y : x
fabs // |y| : 8 : y : x
fcomip %st(1), %st // 8 : y : x
fstp %st(0) // y : x
jnc 2f
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 <20>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 large integer (absolute value at least 8), but
// may be odd unless at least 1L<<64. So it may be necessary
// to adjust the sign of a negative result afterwards.
fxch // x : y
fabs // |x| : y
fxch // y : |x|
// If y has absolute value at least 1L<<78, then any finite
// nonzero x will result in 0 (underflow), 1 or infinity (overflow).
// Saturate y to those bounds to avoid overflow in the calculation
// of y*log2(x).
fldl MO(p78) // 1L<<78 : y : |x|
fld %st(1) // y : 1L<<78 : y : |x|
fabs // |y| : 1L<<78 : y : |x|
fcomip %st(1), %st // 1L<<78 : y : |x|
fstp %st(0) // y : |x|
jc 3f
fstp %st(0) // pop y
fldl MO(p78) // 1L<<78 : |x|
testb $2, %dl
jz 3f // y > 0
fchs // -(1L<<78) : |x|
.align ALIGNARG(4)
3: /* y is a real number. */
subq $40, %rsp
cfi_adjust_cfa_offset (40)
fstpt 16(%rsp) // x
fstpt (%rsp) // <empty>
mov %edx, 32(%rsp)
call HIDDEN_JUMPTARGET (__powl_helper) // <result>
mov 32(%rsp), %edx
addq $40, %rsp
cfi_adjust_cfa_offset (-40)
testb $2, %dh
jz 292f
// x is negative. If y is an odd integer, negate the result.
fldt 24(%rsp) // y : abs(result)
fldl MO(p64) // 1L<<64 : y : abs(result)
fld %st(1) // y : 1L<<64 : y : abs(result)
fabs // |y| : 1L<<64 : y : abs(result)
fcomip %st(1), %st // 1L<<64 : y : abs(result)
fstp %st(0) // y : abs(result)
jnc 291f
fldl MO(p63) // p63 : y : abs(result)
fxch // y : p63 : abs(result)
fprem // y%p63 : p63 : abs(result)
fstp %st(1) // y%p63 : abs(result)
// We must find out whether y is an odd integer.
fld %st // y : y : abs(result)
fistpll -8(%rsp) // y : abs(result)
fildll -8(%rsp) // int(y) : y : abs(result)
fucomip %st(1),%st // y : abs(result)
ffreep %st // abs(result)
jne 292f
// OK, the value is an integer, but is it odd?
mov -8(%rsp), %eax
mov -4(%rsp), %edx
andb $1, %al
jz 290f // jump if not odd
// It's an odd integer.
fchs
290: ret
291: fstp %st(0) // abs(result)
292: ret
// pow(x,<EFBFBD>0) = 1
.align ALIGNARG(4)
11: fstp %st(0) // pop y
fldl MO(one)
ret
// y == <EFBFBD>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 <EFBFBD>inf
15: fstp %st(0) // y
testb $2, %dh
jz 16f // jump if x == +inf
// fistpll raises invalid exception for |y| >= 1L<<63, but y
// may be odd unless we know |y| >= 1L<<64.
fldl MO(p64) // 1L<<64 : y
fld %st(1) // y : 1L<<64 : y
fabs // |y| : 1L<<64 : y
fcomip %st(1), %st // 1L<<64 : y
fstp %st(0) // y
jnc 16f
fldl MO(p63) // p63 : y
fxch // y : p63
fprem // y%p63 : p63
fstp %st(1) // y%p63
// 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 <EFBFBD>0
20: fstp %st(0) // y
testb $2, %dl
jz 21f // y > 0
// x is <EFBFBD>0 and y is < 0. We must find out whether y is an odd integer.
testb $2, %dh
jz 25f
// fistpll raises invalid exception for |y| >= 1L<<63, but y
// may be odd unless we know |y| >= 1L<<64.
fldl MO(p64) // 1L<<64 : y
fld %st(1) // y : 1L<<64 : y
fabs // |y| : 1L<<64 : y
fcomip %st(1), %st // 1L<<64 : y
fstp %st(0) // y
jnc 25f
fldl MO(p63) // p63 : y
fxch // y : p63
fprem // y%p63 : p63
fstp %st(1) // y%p63
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 <EFBFBD>0 and y is > 0. We must find out whether y is an odd integer.
21: testb $2, %dh
jz 22f
// fistpll raises invalid exception for |y| >= 1L<<63, but y
// may be odd unless we know |y| >= 1L<<64.
fldl MO(p64) // 1L<<64 : y
fxch // y : 1L<<64
fcomi %st(1), %st // y : 1L<<64
fstp %st(1) // y
jnc 22f
fldl MO(p63) // p63 : y
fxch // y : p63
fprem // y%p63 : p63
fstp %st(1) // y%p63
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)
strong_alias (__ieee754_powl, __powl_finite)