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c898991d8b
Bug 19848 reports cases where powl on x86 / x86_64 has error accumulation, for small integer exponents, larger than permitted by glibc's accuracy goals, at least in some rounding modes. This patch further restricts the exponent range for which the small-integer-exponent logic is used to limit the possible error accumulation. Tested for x86_64 and x86 and ulps updated accordingly. [BZ #19848] * sysdeps/i386/fpu/e_powl.S (p3): Rename to p2 and change value from 8 to 4. (__ieee754_powl): Compare integer exponent against 4 not 8. * sysdeps/x86_64/fpu/e_powl.S (p3): Rename to p2 and change value from 8 to 4. (__ieee754_powl): Compare integer exponent against 4 not 8. * math/auto-libm-test-in: Add more tests of pow. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
415 lines
8.8 KiB
ArmAsm
415 lines
8.8 KiB
ArmAsm
/* ix87 specific implementation of pow function.
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Copyright (C) 1996-2016 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
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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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<http://www.gnu.org/licenses/>. */
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#include <machine/asm.h>
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#include <x86_64-math-asm.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 p2,@object
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p2: .byte 0, 0, 0, 0, 0, 0, 0x10, 0x40
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ASM_SIZE_DIRECTIVE(p2)
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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 p64,@object
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p64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
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ASM_SIZE_DIRECTIVE(p64)
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.type p78,@object
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p78: .byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
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ASM_SIZE_DIRECTIVE(p78)
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.type pm79,@object
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pm79: .byte 0, 0, 0, 0, 0, 0, 0, 0x3b
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ASM_SIZE_DIRECTIVE(pm79)
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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_LDBL_MIN
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#ifdef PIC
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# define MO(op) op##(%rip)
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#else
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# define MO(op) op
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#endif
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.text
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ENTRY(__ieee754_powl)
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fldt 24(%rsp) // y
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fxam
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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 == <EFBFBD>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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fldt 8(%rsp) // x : y
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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 <EFBFBD>0
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cmpb $0x05, %ah
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je 15f // x is <EFBFBD>inf
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cmpb $0x01, %ah
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je 31f // 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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fldl MO(p63) // 1L<<63 : y : x
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fld %st(1) // y : 1L<<63 : y : x
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fabs // |y| : 1L<<63 : y : x
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fcomip %st(1), %st // 1L<<63 : y : x
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fstp %st(0) // y : x
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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 -8(%rsp) // y : x
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fildll -8(%rsp) // int(y) : y : x
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fucomip %st(1),%st // y : x
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je 9f
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// If y has absolute value at most 0x1p-79, then any finite
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// nonzero x will result in 1. Saturate y to those bounds to
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// avoid underflow in the calculation of y*log2(x).
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fldl MO(pm79) // 0x1p-79 : y : x
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fld %st(1) // y : 0x1p-79 : y : x
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fabs // |y| : 0x1p-79 : y : x
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fcomip %st(1), %st // 0x1p-79 : y : x
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fstp %st(0) // y : x
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jnc 3f
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fstp %st(0) // pop y
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fldl MO(pm79) // 0x1p-79 : x
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testb $2, %dl
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jnz 3f // y > 0
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fchs // -0x1p-79 : x
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jmp 3f
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9: /* OK, we have an integer value for y. Unless very small
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(we use < 4), use the algorithm for real exponent to avoid
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accumulation of errors. */
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fldl MO(p2) // 4 : y : x
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fld %st(1) // y : 4 : y : x
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fabs // |y| : 4 : y : x
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fcomip %st(1), %st // 4 : y : x
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fstp %st(0) // y : x
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jnc 3f
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mov -8(%rsp),%eax
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mov -4(%rsp),%edx
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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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LDBL_CHECK_FORCE_UFLOW_NONNAN
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ret
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/* y is <20>NAN */
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30: fldt 8(%rsp) // x : y
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fldl MO(one) // 1.0 : x : y
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fucomip %st(1),%st // x : y
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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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.align ALIGNARG(4)
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2: // y is a large integer (absolute value at least 1L<<63).
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// If y has absolute value at least 1L<<78, then any finite
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// nonzero x will result in 0 (underflow), 1 or infinity (overflow).
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// Saturate y to those bounds to avoid overflow in the calculation
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// of y*log2(x).
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fldl MO(p78) // 1L<<78 : y : x
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fld %st(1) // y : 1L<<78 : y : x
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fabs // |y| : 1L<<78 : y : x
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fcomip %st(1), %st // 1L<<78 : y : x
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fstp %st(0) // y : x
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jc 3f
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fstp %st(0) // pop y
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fldl MO(p78) // 1L<<78 : x
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testb $2, %dl
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jz 3f // y > 0
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fchs // -(1L<<78) : x
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.align ALIGNARG(4)
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3: /* y is a real number. */
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subq $40, %rsp
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cfi_adjust_cfa_offset (40)
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fstpt 16(%rsp) // x
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fstpt (%rsp) // <empty>
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call HIDDEN_JUMPTARGET (__powl_helper) // <result>
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addq $40, %rsp
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cfi_adjust_cfa_offset (-40)
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ret
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// pow(x,<EFBFBD>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 == <EFBFBD>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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fldt 8(%rsp) // 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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#ifdef PIC
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lea inf_zero(%rip),%rcx
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fldl (%rcx, %rdx, 4)
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#else
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fldl inf_zero(,%rdx, 4)
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#endif
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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: fldt 8(%rsp) // load x == NaN
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ret
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.align ALIGNARG(4)
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// x is <EFBFBD>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, but y
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// may be odd unless we know |y| >= 1L<<64.
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fldl MO(p64) // 1L<<64 : y
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fld %st(1) // y : 1L<<64 : y
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fabs // |y| : 1L<<64 : y
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fcomip %st(1), %st // 1L<<64 : y
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fstp %st(0) // y
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jnc 16f
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fldl MO(p63) // p63 : y
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fxch // y : p63
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fprem // y%p63 : p63
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fstp %st(1) // y%p63
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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 -8(%rsp) // y
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fildll -8(%rsp) // int(y) : y
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fucomip %st(1),%st
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ffreep %st // <empty>
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jne 17f
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// OK, the value is an integer, but is it odd?
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mov -8(%rsp), %eax
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mov -4(%rsp), %edx
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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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#ifdef PIC
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lea minf_mzero(%rip),%rcx
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fldl (%rcx, %rdx, 8)
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#else
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fldl minf_mzero(,%rdx, 8)
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#endif
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ret
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.align ALIGNARG(4)
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16: fcompl MO(zero)
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fnstsw
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shrl $5, %eax
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andl $8, %eax
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#ifdef PIC
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lea inf_zero(%rip),%rcx
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fldl (%rcx, %rax, 1)
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#else
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fldl inf_zero(,%rax, 1)
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#endif
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ret
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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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18: shrl $31, %edx
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#ifdef PIC
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lea inf_zero(%rip),%rcx
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fldl (%rcx, %rdx, 8)
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#else
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fldl inf_zero(,%rdx, 8)
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#endif
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ret
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.align ALIGNARG(4)
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// x is <EFBFBD>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 <EFBFBD>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, but y
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// may be odd unless we know |y| >= 1L<<64.
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fldl MO(p64) // 1L<<64 : y
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fld %st(1) // y : 1L<<64 : y
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fabs // |y| : 1L<<64 : y
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fcomip %st(1), %st // 1L<<64 : y
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fstp %st(0) // y
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jnc 25f
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fldl MO(p63) // p63 : y
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fxch // y : p63
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fprem // y%p63 : p63
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fstp %st(1) // y%p63
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fld %st // y : y
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fistpll -8(%rsp) // y
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fildll -8(%rsp) // int(y) : y
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fucomip %st(1),%st
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ffreep %st // <empty>
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jne 26f
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// OK, the value is an integer, but is it odd?
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mov -8(%rsp),%eax
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mov -4(%rsp),%edx
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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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25: fstp %st(0)
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26:
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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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.align ALIGNARG(4)
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// x is <EFBFBD>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, but y
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// may be odd unless we know |y| >= 1L<<64.
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fldl MO(p64) // 1L<<64 : y
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fxch // y : 1L<<64
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fcomi %st(1), %st // y : 1L<<64
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fstp %st(1) // y
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jnc 22f
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fldl MO(p63) // p63 : y
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fxch // y : p63
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fprem // y%p63 : p63
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fstp %st(1) // y%p63
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fld %st // y : y
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fistpll -8(%rsp) // y
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fildll -8(%rsp) // int(y) : y
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fucomip %st(1),%st
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ffreep %st // <empty>
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jne 23f
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// OK, the value is an integer, but is it odd?
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mov -8(%rsp),%eax
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mov -4(%rsp),%edx
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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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22: fstp %st(0)
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23:
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24: fldl MO(zero)
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ret
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END(__ieee754_powl)
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strong_alias (__ieee754_powl, __powl_finite)
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