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457 lines
9.6 KiB
ArmAsm
457 lines
9.6 KiB
ArmAsm
/* ix87 specific implementation of pow function.
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Copyright (C) 1996-2023 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include <machine/asm.h>
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#include <i386-math-asm.h>
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#include <libm-alias-finite.h>
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.section .rodata.cst8,"aM",@progbits,8
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.p2align 3
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.type one,@object
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one: .double 1.0
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ASM_SIZE_DIRECTIVE(one)
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.type limit,@object
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limit: .double 0.29
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ASM_SIZE_DIRECTIVE(limit)
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.type p63,@object
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p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
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ASM_SIZE_DIRECTIVE(p63)
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.type p10,@object
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p10: .byte 0, 0, 0, 0, 0, 0, 0x90, 0x40
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ASM_SIZE_DIRECTIVE(p10)
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.section .rodata.cst16,"aM",@progbits,16
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.p2align 3
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.type infinity,@object
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inf_zero:
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infinity:
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.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
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ASM_SIZE_DIRECTIVE(infinity)
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.type zero,@object
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zero: .double 0.0
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ASM_SIZE_DIRECTIVE(zero)
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.type minf_mzero,@object
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minf_mzero:
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minfinity:
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.byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
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mzero:
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.byte 0, 0, 0, 0, 0, 0, 0, 0x80
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ASM_SIZE_DIRECTIVE(minf_mzero)
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DEFINE_DBL_MIN
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#ifdef PIC
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# define MO(op) op##@GOTOFF(%ecx)
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# define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
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#else
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# define MO(op) op
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# define MOX(op,x,f) op(,x,f)
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#endif
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.text
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ENTRY(__ieee754_pow)
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fldl 12(%esp) // y
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fxam
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#ifdef PIC
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LOAD_PIC_REG (cx)
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#endif
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fnstsw
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movb %ah, %dl
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andb $0x45, %ah
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cmpb $0x40, %ah // is y == 0 ?
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je 11f
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cmpb $0x05, %ah // is y == ±inf ?
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je 12f
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cmpb $0x01, %ah // is y == NaN ?
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je 30f
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fldl 4(%esp) // x : y
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subl $8,%esp
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cfi_adjust_cfa_offset (8)
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fxam
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fnstsw
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movb %ah, %dh
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andb $0x45, %ah
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cmpb $0x40, %ah
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je 20f // x is ±0
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cmpb $0x05, %ah
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je 15f // x is ±inf
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cmpb $0x01, %ah
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je 32f // x is NaN
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fxch // y : x
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/* fistpll raises invalid exception for |y| >= 1L<<63. */
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fld %st // y : y : x
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fabs // |y| : y : x
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fcompl MO(p63) // y : x
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fnstsw
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sahf
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jnc 2f
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/* First see whether `y' is a natural number. In this case we
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can use a more precise algorithm. */
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fld %st // y : y : x
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fistpll (%esp) // y : x
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fildll (%esp) // int(y) : y : x
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fucomp %st(1) // y : x
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fnstsw
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sahf
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jne 3f
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/* OK, we have an integer value for y. If large enough that
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errors may propagate out of the 11 bits excess precision, use
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the algorithm for real exponent instead. */
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fld %st // y : y : x
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fabs // |y| : y : x
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fcompl MO(p10) // y : x
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fnstsw
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sahf
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jnc 2f
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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orl $0, %edx
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fstp %st(0) // x
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jns 4f // y >= 0, jump
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fdivrl MO(one) // 1/x (now referred to as x)
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negl %eax
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adcl $0, %edx
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negl %edx
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4: fldl MO(one) // 1 : x
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fxch
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/* If y is even, take the absolute value of x. Otherwise,
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ensure all intermediate values that might overflow have the
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sign of x. */
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testb $1, %al
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jnz 6f
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fabs
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6: shrdl $1, %edx, %eax
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jnc 5f
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fxch
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fabs
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fmul %st(1) // x : ST*x
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fxch
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5: fld %st // x : x : ST*x
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fabs // |x| : x : ST*x
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fmulp // |x|*x : ST*x
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shrl $1, %edx
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movl %eax, %ecx
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orl %edx, %ecx
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jnz 6b
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fstp %st(0) // ST*x
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#ifdef PIC
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LOAD_PIC_REG (cx)
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#endif
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DBL_NARROW_EVAL_UFLOW_NONNAN
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ret
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/* y is ±NAN */
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30: fldl 4(%esp) // x : y
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fldl MO(one) // 1.0 : x : y
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fucomp %st(1) // x : y
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fnstsw
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sahf
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je 31f
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fxch // y : x
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31: fstp %st(1)
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ret
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cfi_adjust_cfa_offset (8)
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32: addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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fstp %st(1)
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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2: // y is a large integer (absolute value at least 1L<<10), but
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// may be odd unless at least 1L<<64. So it may be necessary
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// to adjust the sign of a negative result afterwards.
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fxch // x : y
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fabs // |x| : y
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fxch // y : x
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.align ALIGNARG(4)
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3: /* y is a real number. */
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fxch // x : y
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fldl MO(one) // 1.0 : x : y
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fldl MO(limit) // 0.29 : 1.0 : x : y
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fld %st(2) // x : 0.29 : 1.0 : x : y
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fsub %st(2) // x-1 : 0.29 : 1.0 : x : y
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fabs // |x-1| : 0.29 : 1.0 : x : y
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fucompp // 1.0 : x : y
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fnstsw
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fxch // x : 1.0 : y
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sahf
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ja 7f
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fsub %st(1) // x-1 : 1.0 : y
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fyl2xp1 // log2(x) : y
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jmp 8f
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7: fyl2x // log2(x) : y
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8: fmul %st(1) // y*log2(x) : y
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fst %st(1) // y*log2(x) : y*log2(x)
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frndint // int(y*log2(x)) : y*log2(x)
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fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
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fxch // fract(y*log2(x)) : int(y*log2(x))
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f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
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faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
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// Before scaling, we must negate if x is negative and y is an
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// odd integer.
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testb $2, %dh
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jz 291f
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// x is negative. If y is an odd integer, negate the result.
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fldl 20(%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fabs // |y| : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fcompl MO(p63) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fnstsw
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sahf
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jnc 290f
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// We must find out whether y is an odd integer.
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fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fistpll (%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fildll (%esp) // int(y) : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fucompp // 2^fract(y*log2(x)) : int(y*log2(x))
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fnstsw
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sahf
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jne 291f
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// OK, the value is an integer, but is it odd?
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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andb $1, %al
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jz 292f // jump if not odd
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// It's an odd integer.
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fchs
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jmp 292f
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cfi_adjust_cfa_offset (8)
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290: fstp %st(0) // 2^fract(y*log2(x)) : int(y*log2(x))
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291: addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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292: fscale // +/- 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
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fstp %st(1) // +/- 2^fract(y*log2(x))*2^int(y*log2(x))
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DBL_NARROW_EVAL_UFLOW_NONNAN
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ret
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// pow(x,±0) = 1
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.align ALIGNARG(4)
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11: fstp %st(0) // pop y
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fldl MO(one)
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ret
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// y == ±inf
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.align ALIGNARG(4)
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12: fstp %st(0) // pop y
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fldl MO(one) // 1
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fldl 4(%esp) // x : 1
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fabs // abs(x) : 1
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fucompp // < 1, == 1, or > 1
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fnstsw
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andb $0x45, %ah
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cmpb $0x45, %ah
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je 13f // jump if x is NaN
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cmpb $0x40, %ah
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je 14f // jump if |x| == 1
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shlb $1, %ah
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xorb %ah, %dl
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andl $2, %edx
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fldl MOX(inf_zero, %edx, 4)
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ret
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.align ALIGNARG(4)
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14: fldl MO(one)
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ret
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.align ALIGNARG(4)
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13: fldl 4(%esp) // load x == NaN
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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// x is ±inf
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15: fstp %st(0) // y
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testb $2, %dh
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jz 16f // jump if x == +inf
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// fistpll raises invalid exception for |y| >= 1L<<63, so test
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// that (in which case y is certainly even) before testing
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// whether y is odd.
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fld %st // y : y
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fabs // |y| : y
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fcompl MO(p63) // y
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fnstsw
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sahf
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jnc 16f
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// We must find out whether y is an odd integer.
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fld %st // y : y
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fistpll (%esp) // y
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fildll (%esp) // int(y) : y
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fucompp // <empty>
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fnstsw
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sahf
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jne 17f
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// OK, the value is an integer.
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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andb $1, %al
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jz 18f // jump if not odd
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// It's an odd integer.
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shrl $31, %edx
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fldl MOX(minf_mzero, %edx, 8)
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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16: fcompl MO(zero)
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addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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fnstsw
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shrl $5, %eax
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andl $8, %eax
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fldl MOX(inf_zero, %eax, 1)
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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17: shll $30, %edx // sign bit for y in right position
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addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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18: shrl $31, %edx
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fldl MOX(inf_zero, %edx, 8)
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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// x is ±0
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20: fstp %st(0) // y
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testb $2, %dl
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jz 21f // y > 0
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// x is ±0 and y is < 0. We must find out whether y is an odd integer.
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testb $2, %dh
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jz 25f
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// fistpll raises invalid exception for |y| >= 1L<<63, so test
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// that (in which case y is certainly even) before testing
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// whether y is odd.
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fld %st // y : y
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fabs // |y| : y
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fcompl MO(p63) // y
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fnstsw
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sahf
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jnc 25f
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fld %st // y : y
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fistpll (%esp) // y
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fildll (%esp) // int(y) : y
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fucompp // <empty>
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fnstsw
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sahf
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jne 26f
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// OK, the value is an integer.
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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andb $1, %al
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jz 27f // jump if not odd
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// It's an odd integer.
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// Raise divide-by-zero exception and get minus infinity value.
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fldl MO(one)
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fdivl MO(zero)
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fchs
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ret
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cfi_adjust_cfa_offset (8)
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25: fstp %st(0)
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26: addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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27: // Raise divide-by-zero exception and get infinity value.
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fldl MO(one)
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fdivl MO(zero)
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ret
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cfi_adjust_cfa_offset (8)
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.align ALIGNARG(4)
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// x is ±0 and y is > 0. We must find out whether y is an odd integer.
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21: testb $2, %dh
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jz 22f
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// fistpll raises invalid exception for |y| >= 1L<<63, so test
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// that (in which case y is certainly even) before testing
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// whether y is odd.
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fcoml MO(p63) // y
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fnstsw
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sahf
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jnc 22f
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fld %st // y : y
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fistpll (%esp) // y
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fildll (%esp) // int(y) : y
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fucompp // <empty>
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fnstsw
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sahf
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jne 23f
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// OK, the value is an integer.
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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andb $1, %al
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jz 24f // jump if not odd
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// It's an odd integer.
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fldl MO(mzero)
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ret
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cfi_adjust_cfa_offset (8)
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22: fstp %st(0)
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23: addl $8, %esp // Don't use 2 x pop
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cfi_adjust_cfa_offset (-8)
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24: fldl MO(zero)
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ret
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END(__ieee754_pow)
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libm_alias_finite (__ieee754_pow, __pow)
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