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755 lines
16 KiB
755 lines
16 KiB
/*
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Copyright (c) 2014, Intel Corporation
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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* Neither the name of Intel Corporation nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/******************************************************************************/
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// ALGORITHM DESCRIPTION
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// ---------------------
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//
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// Assume x=2^{3*k+j} * 1.b1 b2 ... b5 b6 ... b52, where j = 0,1,2.
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// Let r=(x*2^{-3k-j} - 1.b1 b2 ... b5 1)* rcp[b1 b2 ..b5],
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// where rcp[b1 b2 .. b5]=1/(1.b1 b2 b3 b4 b5 1) in double precision
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// cbrt(2^j * 1. b1 b2 .. b5 1) is approximated as T[j][b1..b5]+D[j][b1..b5]
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// (T stores the high 53 bits, D stores the low order bits)
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// Result=2^k*T+(2^k*T*r)*P+2^k*D
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// where P=p1+p2*r+..+p8*r^7
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//
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// Special cases:
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// cbrt(NaN) = quiet NaN, and raise invalid exception
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// cbrt(INF) = that INF
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// cbrt(+/-0) = +/-0
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//
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/******************************************************************************/
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#include <private/bionic_asm.h>
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# -- Begin cbrt
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ENTRY(cbrt)
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# parameter 1: %xmm0
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..B1.1:
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..___tag_value_cbrt.1:
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subq $24, %rsp
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..___tag_value_cbrt.3:
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movsd %xmm0, (%rsp)
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..B1.2:
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movq %xmm0, %xmm7
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movl $524032, %edx
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movsd EXP_MSK3(%rip), %xmm5
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movsd EXP_MSK2(%rip), %xmm3
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psrlq $44, %xmm7
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pextrw $0, %xmm7, %ecx
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movd %xmm7, %eax
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movsd EXP_MASK(%rip), %xmm1
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movsd SIG_MASK(%rip), %xmm2
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andl $248, %ecx
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lea rcp_table(%rip), %r8
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movsd (%rcx,%r8), %xmm4
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movq %rax, %r9
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andl %eax, %edx
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cmpl $0, %edx
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je .L_2TAG_PACKET_0.0.1
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cmpl $524032, %edx
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je .L_2TAG_PACKET_1.0.1
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shrl $8, %edx
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shrq $8, %r9
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andpd %xmm0, %xmm2
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andpd %xmm5, %xmm0
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orpd %xmm2, %xmm3
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orpd %xmm0, %xmm1
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movapd coeff_table(%rip), %xmm5
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movl $5462, %eax
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movapd 16+coeff_table(%rip), %xmm6
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mull %edx
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movq %r9, %rdx
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andq $2047, %r9
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shrl $14, %eax
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andl $2048, %edx
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subq %rax, %r9
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subq %rax, %r9
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subq %rax, %r9
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shlq $8, %r9
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addl $682, %eax
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orl %edx, %eax
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movd %eax, %xmm7
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addq %r9, %rcx
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psllq $52, %xmm7
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.L_2TAG_PACKET_2.0.1:
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movapd 32+coeff_table(%rip), %xmm2
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movapd 48+coeff_table(%rip), %xmm0
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subsd %xmm3, %xmm1
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movq %xmm7, %xmm3
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lea cbrt_table(%rip), %r8
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mulsd (%rcx,%r8), %xmm7
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mulsd %xmm4, %xmm1
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lea D_table(%rip), %r8
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mulsd (%rcx,%r8), %xmm3
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movapd %xmm1, %xmm4
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unpcklpd %xmm1, %xmm1
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mulpd %xmm1, %xmm5
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mulpd %xmm1, %xmm6
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mulpd %xmm1, %xmm1
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addpd %xmm5, %xmm2
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addpd %xmm6, %xmm0
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mulpd %xmm1, %xmm2
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mulpd %xmm1, %xmm1
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mulsd %xmm7, %xmm4
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addpd %xmm2, %xmm0
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mulsd %xmm0, %xmm1
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unpckhpd %xmm0, %xmm0
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addsd %xmm1, %xmm0
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mulsd %xmm4, %xmm0
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addsd %xmm3, %xmm0
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addsd %xmm7, %xmm0
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jmp ..B1.4
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.L_2TAG_PACKET_0.0.1:
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mulsd SCALE63(%rip), %xmm0
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movq %xmm0, %xmm7
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movl $524032, %edx
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psrlq $44, %xmm7
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pextrw $0, %xmm7, %ecx
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movd %xmm7, %eax
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andl $248, %ecx
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lea rcp_table(%rip), %r8
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movsd (%rcx,%r8), %xmm4
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movq %rax, %r9
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andl %eax, %edx
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shrl $8, %edx
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shrq $8, %r9
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cmpl $0, %edx
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je .L_2TAG_PACKET_3.0.1
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andpd %xmm0, %xmm2
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andpd %xmm5, %xmm0
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orpd %xmm2, %xmm3
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orpd %xmm0, %xmm1
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movapd coeff_table(%rip), %xmm5
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movl $5462, %eax
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movapd 16+coeff_table(%rip), %xmm6
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mull %edx
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movq %r9, %rdx
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andq $2047, %r9
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shrl $14, %eax
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andl $2048, %edx
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subq %rax, %r9
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subq %rax, %r9
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subq %rax, %r9
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shlq $8, %r9
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addl $661, %eax
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orl %edx, %eax
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movd %eax, %xmm7
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addq %r9, %rcx
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psllq $52, %xmm7
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jmp .L_2TAG_PACKET_2.0.1
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.L_2TAG_PACKET_3.0.1:
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cmpq $0, %r9
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jne .L_2TAG_PACKET_4.0.1
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xorpd %xmm0, %xmm0
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jmp ..B1.4
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.L_2TAG_PACKET_4.0.1:
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movsd ZERON(%rip), %xmm0
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jmp ..B1.4
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.L_2TAG_PACKET_1.0.1:
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movl 4(%rsp), %eax
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movl (%rsp), %edx
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movl %eax, %ecx
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andl $2147483647, %ecx
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cmpl $2146435072, %ecx
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ja .L_2TAG_PACKET_5.0.1
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cmpl $0, %edx
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jne .L_2TAG_PACKET_5.0.1
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cmpl $2146435072, %eax
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jne .L_2TAG_PACKET_6.0.1
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movsd INF(%rip), %xmm0
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jmp ..B1.4
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.L_2TAG_PACKET_6.0.1:
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movsd NEG_INF(%rip), %xmm0
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jmp ..B1.4
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.L_2TAG_PACKET_5.0.1:
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movsd (%rsp), %xmm0
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addsd %xmm0, %xmm0
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movq %xmm0, 8(%rsp)
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.L_2TAG_PACKET_7.0.1:
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..B1.4:
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addq $24, %rsp
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..___tag_value_cbrt.4:
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ret
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..___tag_value_cbrt.5:
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END(cbrt)
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# -- End cbrt
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.section .rodata, "a"
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.align 16
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.align 16
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coeff_table:
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.long 1553778919
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.long 3213899486
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.long 3534952507
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.long 3215266280
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.long 1646371399
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.long 3214412045
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.long 477218588
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.long 3216798151
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.long 3582521621
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.long 1066628362
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.long 1007461464
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.long 1068473053
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.long 889629714
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.long 1067378449
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.long 1431655765
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.long 1070945621
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.type coeff_table,@object
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.size coeff_table,64
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.align 4
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EXP_MSK3:
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.long 4294967295
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.long 1048575
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.type EXP_MSK3,@object
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.size EXP_MSK3,8
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.align 4
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EXP_MSK2:
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.long 0
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.long 3220193280
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.type EXP_MSK2,@object
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.size EXP_MSK2,8
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.align 4
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EXP_MASK:
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.long 0
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.long 3220176896
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.type EXP_MASK,@object
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.size EXP_MASK,8
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.align 4
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SIG_MASK:
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.long 0
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.long 1032192
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.type SIG_MASK,@object
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.size SIG_MASK,8
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.align 4
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rcp_table:
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.long 528611360
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.long 3220144632
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.long 2884679527
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.long 3220082993
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.long 1991868891
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.long 3220024928
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.long 2298714891
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.long 3219970134
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.long 58835168
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.long 3219918343
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.long 3035110223
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.long 3219869313
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.long 1617585086
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.long 3219822831
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.long 2500867033
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.long 3219778702
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.long 4241943008
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.long 3219736752
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.long 258732970
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.long 3219696825
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.long 404232216
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.long 3219658776
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.long 2172167368
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.long 3219622476
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.long 1544257904
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.long 3219587808
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.long 377579543
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.long 3219554664
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.long 1616385542
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.long 3219522945
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.long 813783277
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.long 3219492562
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.long 3940743189
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.long 3219463431
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.long 2689777499
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.long 3219435478
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.long 1700977147
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.long 3219408632
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.long 3169102082
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.long 3219382828
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.long 327235604
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.long 3219358008
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.long 1244336319
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.long 3219334115
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.long 1300311200
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.long 3219311099
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.long 3095471925
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.long 3219288912
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.long 2166487928
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.long 3219267511
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.long 2913108253
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.long 3219246854
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.long 293672978
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.long 3219226904
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.long 288737297
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.long 3219207624
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.long 1810275472
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.long 3219188981
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.long 174592167
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.long 3219170945
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.long 3539053052
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.long 3219153485
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.long 2164392968
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.long 3219136576
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.type rcp_table,@object
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.size rcp_table,256
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.align 4
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cbrt_table:
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.long 572345495
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.long 1072698681
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.long 1998204467
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.long 1072709382
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.long 3861501553
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.long 1072719872
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.long 2268192434
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.long 1072730162
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.long 2981979308
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.long 1072740260
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.long 270859143
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.long 1072750176
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.long 2958651392
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.long 1072759916
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.long 313113243
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.long 1072769490
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.long 919449400
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.long 1072778903
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.long 2809328903
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.long 1072788162
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.long 2222981587
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.long 1072797274
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.long 2352530781
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.long 1072806244
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.long 594152517
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.long 1072815078
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.long 1555767199
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.long 1072823780
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.long 4282421314
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.long 1072832355
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.long 2355578597
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.long 1072840809
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.long 1162590619
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.long 1072849145
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.long 797864051
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.long 1072857367
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.long 431273680
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.long 1072865479
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.long 2669831148
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.long 1072873484
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.long 733477752
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.long 1072881387
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.long 4280220604
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.long 1072889189
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.long 801961634
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.long 1072896896
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.long 2915370760
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.long 1072904508
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.long 1159613482
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.long 1072912030
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.long 2689944798
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.long 1072919463
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.long 1248687822
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.long 1072926811
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.long 2967951030
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.long 1072934075
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.long 630170432
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.long 1072941259
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.long 3760898254
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.long 1072948363
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.long 0
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.long 1072955392
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.long 2370273294
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.long 1072962345
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.long 1261754802
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.long 1072972640
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.long 546334065
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.long 1072986123
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.long 1054893830
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.long 1072999340
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.long 1571187597
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.long 1073012304
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.long 1107975175
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.long 1073025027
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.long 3606909377
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.long 1073037519
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.long 1113616747
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.long 1073049792
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.long 4154744632
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.long 1073061853
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.long 3358931423
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.long 1073073713
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.long 4060702372
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|
.long 1073085379
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.long 747576176
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.long 1073096860
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.long 3023138255
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|
.long 1073108161
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.long 1419988548
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|
.long 1073119291
|
|
.long 1914185305
|
|
.long 1073130255
|
|
.long 294389948
|
|
.long 1073141060
|
|
.long 3761802570
|
|
.long 1073151710
|
|
.long 978281566
|
|
.long 1073162213
|
|
.long 823148820
|
|
.long 1073172572
|
|
.long 2420954441
|
|
.long 1073182792
|
|
.long 3815449908
|
|
.long 1073192878
|
|
.long 2046058587
|
|
.long 1073202835
|
|
.long 1807524753
|
|
.long 1073212666
|
|
.long 2628681401
|
|
.long 1073222375
|
|
.long 3225667357
|
|
.long 1073231966
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|
.long 1555307421
|
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.long 1073241443
|
|
.long 3454043099
|
|
.long 1073250808
|
|
.long 1208137896
|
|
.long 1073260066
|
|
.long 3659916772
|
|
.long 1073269218
|
|
.long 1886261264
|
|
.long 1073278269
|
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.long 3593647839
|
|
.long 1073287220
|
|
.long 3086012205
|
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.long 1073296075
|
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.long 2769796922
|
|
.long 1073304836
|
|
.long 888716057
|
|
.long 1073317807
|
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.long 2201465623
|
|
.long 1073334794
|
|
.long 164369365
|
|
.long 1073351447
|
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.long 3462666733
|
|
.long 1073367780
|
|
.long 2773905457
|
|
.long 1073383810
|
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.long 1342879088
|
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.long 1073399550
|
|
.long 2543933975
|
|
.long 1073415012
|
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.long 1684477781
|
|
.long 1073430209
|
|
.long 3532178543
|
|
.long 1073445151
|
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.long 1147747300
|
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.long 1073459850
|
|
.long 1928031793
|
|
.long 1073474314
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.long 2079717015
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.long 1073488553
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.long 4016765315
|
|
.long 1073502575
|
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.long 3670431139
|
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.long 1073516389
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.long 3549227225
|
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.long 1073530002
|
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.long 11637607
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.long 1073543422
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.long 588220169
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.long 1073556654
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.long 2635407503
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.long 1073569705
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.long 2042029317
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.long 1073582582
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.long 1925128962
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.long 1073595290
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.long 4136375664
|
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.long 1073607834
|
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.long 759964600
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.long 1073620221
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.long 4257606771
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.long 1073632453
|
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.long 297278907
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.long 1073644538
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.long 3655053093
|
|
.long 1073656477
|
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.long 2442253172
|
|
.long 1073668277
|
|
.long 1111876799
|
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.long 1073679941
|
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.long 3330973139
|
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.long 1073691472
|
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.long 3438879452
|
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.long 1073702875
|
|
.long 3671565478
|
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.long 1073714153
|
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.long 1317849547
|
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.long 1073725310
|
|
.long 1642364115
|
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.long 1073736348
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|
.type cbrt_table,@object
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.size cbrt_table,768
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|
.align 4
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D_table:
|
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.long 4050900474
|
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.long 1014427190
|
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.long 1157977860
|
|
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SCALE63:
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ZERON:
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INF:
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NEG_INF:
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.data
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|
.section .note.GNU-stack, "",@progbits
|
|
// -- Begin DWARF2 SEGMENT .eh_frame
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|
.section .eh_frame,"a",@progbits
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.eh_frame_seg:
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.align 1
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.2byte 0x080e
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.byte 0x00
|
|
# End
|