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/* ix87 specific implementation of pow function.
Copyright (C) 1996-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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
<https://www.gnu.org/licenses/>. */
#include <machine/asm.h>
#include <i386-math-asm.h>
#include <libm-alias-finite.h>
.section .rodata.cst8,"aM",@progbits,8
.p2align 3
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
.type limit,@object
limit: .double 0.29
ASM_SIZE_DIRECTIVE(limit)
.type p63,@object
p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
ASM_SIZE_DIRECTIVE(p63)
.type p10,@object
p10: .byte 0, 0, 0, 0, 0, 0, 0x90, 0x40
ASM_SIZE_DIRECTIVE(p10)
.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)
DEFINE_DBL_MIN
#ifdef PIC
# define MO(op) op##@GOTOFF(%ecx)
# define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
#else
# define MO(op) op
# define MOX(op,x,f) op(,x,f)
#endif
.text
ENTRY(__ieee754_pow)
fldl 12(%esp) // y
fxam
#ifdef PIC
LOAD_PIC_REG (cx)
#endif
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
fldl 4(%esp) // x : y
subl $8,%esp
cfi_adjust_cfa_offset (8)
fxam
fnstsw
movb %ah, %dh
andb $0x45, %ah
cmpb $0x40, %ah
je 20f // x is ±0
cmpb $0x05, %ah
je 15f // x is ±inf
cmpb $0x01, %ah
je 32f // x is NaN
fxch // y : x
/* fistpll raises invalid exception for |y| >= 1L<<63. */
fld %st // y : y : x
fabs // |y| : y : x
fcompl MO(p63) // y : x
fnstsw
sahf
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 (%esp) // y : x
fildll (%esp) // int(y) : y : x
fucomp %st(1) // y : x
fnstsw
sahf
jne 3f
/* OK, we have an integer value for y. If large enough that
errors may propagate out of the 11 bits excess precision, use
the algorithm for real exponent instead. */
fld %st // y : y : x
fabs // |y| : y : x
fcompl MO(p10) // y : x
fnstsw
sahf
jnc 2f
popl %eax
cfi_adjust_cfa_offset (-4)
popl %edx
cfi_adjust_cfa_offset (-4)
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
/* If y is even, take the absolute value of x. Otherwise,
ensure all intermediate values that might overflow have the
sign of x. */
testb $1, %al
jnz 6f
fabs
6: shrdl $1, %edx, %eax
jnc 5f
fxch
fabs
fmul %st(1) // x : ST*x
fxch
5: fld %st // x : x : ST*x
fabs // |x| : x : ST*x
fmulp // |x|*x : ST*x
shrl $1, %edx
movl %eax, %ecx
orl %edx, %ecx
jnz 6b
fstp %st(0) // ST*x
#ifdef PIC
LOAD_PIC_REG (cx)
#endif
DBL_NARROW_EVAL_UFLOW_NONNAN
ret
/* y is ±NAN */
30: fldl 4(%esp) // x : y
fldl MO(one) // 1.0 : x : y
fucomp %st(1) // x : y
fnstsw
sahf
je 31f
fxch // y : x
31: fstp %st(1)
ret
cfi_adjust_cfa_offset (8)
32: addl $8, %esp
cfi_adjust_cfa_offset (-8)
fstp %st(1)
ret
cfi_adjust_cfa_offset (8)
.align ALIGNARG(4)
2: // y is a large integer (absolute value at least 1L<<10), 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
.align ALIGNARG(4)
3: /* 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
sahf
ja 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
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))
// Before scaling, we must negate if x is negative and y is an
// odd integer.
testb $2, %dh
jz 291f
// x is negative. If y is an odd integer, negate the result.
fldl 20(%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
fabs // |y| : y : 2^fract(y*log2(x)) : int(y*log2(x))
fcompl MO(p63) // y : 2^fract(y*log2(x)) : int(y*log2(x))
fnstsw
sahf
jnc 290f
// We must find out whether y is an odd integer.
fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
fistpll (%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
fildll (%esp) // int(y) : y : 2^fract(y*log2(x)) : int(y*log2(x))
fucompp // 2^fract(y*log2(x)) : int(y*log2(x))
fnstsw
sahf
jne 291f
// OK, the value is an integer, but is it odd?
popl %eax
cfi_adjust_cfa_offset (-4)
popl %edx
cfi_adjust_cfa_offset (-4)
andb $1, %al
jz 292f // jump if not odd
// It's an odd integer.
fchs
jmp 292f
cfi_adjust_cfa_offset (8)
290: fstp %st(0) // 2^fract(y*log2(x)) : int(y*log2(x))
291: addl $8, %esp
cfi_adjust_cfa_offset (-8)
292: 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))
DBL_NARROW_EVAL_UFLOW_NONNAN
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
fldl 4(%esp) // 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
fldl MOX(inf_zero, %edx, 4)
ret
.align ALIGNARG(4)
14: fldl MO(one)
ret
.align ALIGNARG(4)
13: fldl 4(%esp) // load x == NaN
ret
cfi_adjust_cfa_offset (8)
.align ALIGNARG(4)
// x is ±inf
15: fstp %st(0) // y
testb $2, %dh
jz 16f // jump if x == +inf
// fistpll raises invalid exception for |y| >= 1L<<63, so test
// that (in which case y is certainly even) before testing
// whether y is odd.
fld %st // y : y
fabs // |y| : y
fcompl MO(p63) // y
fnstsw
sahf
jnc 16f
// We must find out whether y is an odd integer.
fld %st // y : y
fistpll (%esp) // y
fildll (%esp) // int(y) : y
fucompp // <empty>
fnstsw
sahf
jne 17f
// OK, the value is an integer.
popl %eax
cfi_adjust_cfa_offset (-4)
popl %edx
cfi_adjust_cfa_offset (-4)
andb $1, %al
jz 18f // jump if not odd
// It's an odd integer.
shrl $31, %edx
fldl MOX(minf_mzero, %edx, 8)
ret
cfi_adjust_cfa_offset (8)
.align ALIGNARG(4)
16: fcompl MO(zero)
addl $8, %esp
cfi_adjust_cfa_offset (-8)
fnstsw
shrl $5, %eax
andl $8, %eax
fldl MOX(inf_zero, %eax, 1)
ret
cfi_adjust_cfa_offset (8)
.align ALIGNARG(4)
17: shll $30, %edx // sign bit for y in right position
addl $8, %esp
cfi_adjust_cfa_offset (-8)
18: shrl $31, %edx
fldl MOX(inf_zero, %edx, 8)
ret
cfi_adjust_cfa_offset (8)
.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
// fistpll raises invalid exception for |y| >= 1L<<63, so test
// that (in which case y is certainly even) before testing
// whether y is odd.
fld %st // y : y
fabs // |y| : y
fcompl MO(p63) // y
fnstsw
sahf
jnc 25f
fld %st // y : y
fistpll (%esp) // y
fildll (%esp) // int(y) : y
fucompp // <empty>
fnstsw
sahf
jne 26f
// OK, the value is an integer.
popl %eax
cfi_adjust_cfa_offset (-4)
popl %edx
cfi_adjust_cfa_offset (-4)
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
cfi_adjust_cfa_offset (8)
25: fstp %st(0)
26: addl $8, %esp
cfi_adjust_cfa_offset (-8)
27: // Raise divide-by-zero exception and get infinity value.
fldl MO(one)
fdivl MO(zero)
ret
cfi_adjust_cfa_offset (8)
.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
// fistpll raises invalid exception for |y| >= 1L<<63, so test
// that (in which case y is certainly even) before testing
// whether y is odd.
fcoml MO(p63) // y
fnstsw
sahf
jnc 22f
fld %st // y : y
fistpll (%esp) // y
fildll (%esp) // int(y) : y
fucompp // <empty>
fnstsw
sahf
jne 23f
// OK, the value is an integer.
popl %eax
cfi_adjust_cfa_offset (-4)
popl %edx
cfi_adjust_cfa_offset (-4)
andb $1, %al
jz 24f // jump if not odd
// It's an odd integer.
fldl MO(mzero)
ret
cfi_adjust_cfa_offset (8)
22: fstp %st(0)
23: addl $8, %esp // Don't use 2 x pop
cfi_adjust_cfa_offset (-8)
24: fldl MO(zero)
ret
END(__ieee754_pow)
libm_alias_finite (__ieee754_pow, __pow)
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