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1930 lines
40 KiB
1930 lines
40 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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// To compute acos(s), separate schemes are used when s is in different
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// intervals.
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//
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// |s| in [2^{-4}, sqrt(3)/2):
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// Let t=2^k*1.b1 b2..b6 1, where s=2^k*1.b1 b2 .. b52
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// acos(s)=pi/2-asin(t)-asin(r), where r=s*sqrt(1-t^2)-t*sqrt(1-s^2)
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// asin(r)-r evaluated as 7-degree polynomial (c3*r^3+c5*r^5+c7*r^7)
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// For the first degree term, r is evaluated as
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// R=(s^2-t^2)/(sqrt(1-t^2)*s+sqrt(1-s^2)*t)
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// (sqrt(1-t^2) read from table)
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// The main source of error is still R (may still be affected by up to 3 ulps
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// of rounding error). The table size must be sufficiently large, to minimize
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// this effect.
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//
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// |s| in [sqrt(3)/2, 255/256):
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// Let t=2^k*1.b1 b2..b6 1, where sqrt(1-s^2)=2^k*1.b1 b2 .. b52 (rounded)
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// acos(|s|)=asin(t)-asin(r), r=s*t-sqrt(1-s^2)*sqrt(1-t^2)
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// acos(-|s|)=pi-acos(|s|)
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// (The -PI constant, or 0, is added to the result. The sign is set at
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// the end)
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// asin(r) evaluated as a polynomial (same as above)
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// The first degree term is evaluated as
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// r=(s^2+t^2-1)/(s*t+sqrt(1-s^2)*sqrt(1-t^2))
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//
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// |s|<2^{-4}: acos(s)=pi/2-asin(s)
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// evaluate asin(s) as 13-degree polynomial
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//
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// |s| in [255/256,1): acos(|s|)=2*asin(q), where q=sqrt((1-|s|)/2)
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// asin(q) is evaluated as 13-degree polynomial
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// q^2=(1-|s|)/2 is obtained in advance
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// 2*q*eps ~ ((1-|s|)/2-q^2)/q used for first term
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// acos(-|s|)=pi-acos(|s|)
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// (The -PI constant, or 0, is added to the result. The sign is set at
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// the end)
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//
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// Special cases:
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// acos(NaN) = quiet NaN, and raise invalid exception
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// acos(INF) = QNaN and raise invalid exception
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// acos(x) = QNaN and raise invalid exception, for |x|>1.0
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// acos(1) = +0
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//
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/******************************************************************************/
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#include <private/bionic_asm.h>
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# -- Begin static_func
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.text
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.align __bionic_asm_align
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.type static_func, @function
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static_func:
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..B1.1:
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call ..L2
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..L2:
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popl %eax
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lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
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lea static_const_table@GOTOFF(%eax), %eax
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ret
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.size static_func,.-static_func
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# -- End static_func
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# -- Begin acos
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ENTRY(acos)
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# parameter 1: 8 + %ebp
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..B2.1:
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..B2.2:
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pushl %ebp
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movl %esp, %ebp
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subl $104, %esp
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movl %ebx, 48(%esp)
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call static_func
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movl %eax, %ebx
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movsd 112(%esp), %xmm0
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movsd 6048(%ebx), %xmm4
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movsd 6080(%ebx), %xmm3
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xorpd %xmm5, %xmm5
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movsd 6064(%ebx), %xmm2
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movapd %xmm0, %xmm1
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movsd %xmm0, 8(%esp)
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psrlq $44, %xmm0
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movd %xmm0, %edx
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movapd %xmm1, %xmm7
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movl $8192, %ecx
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pinsrw $2, %ecx, %xmm5
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movapd %xmm1, %xmm0
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movl $524287, %eax
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andl %edx, %eax
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subl $260864, %eax
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cmpl $955, %eax
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jae .L_2TAG_PACKET_0.0.2
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mulsd %xmm1, %xmm1
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andl $65535, %edx
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subsd %xmm1, %xmm3
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sqrtsd %xmm3, %xmm3
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andpd %xmm7, %xmm2
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andl $-4, %edx
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subl $64256, %edx
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movsd 3840(%ebx,%edx,2), %xmm1
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orpd %xmm5, %xmm2
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movapd (%ebx,%edx,4), %xmm4
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movapd %xmm7, %xmm6
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addsd %xmm2, %xmm7
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subsd %xmm2, %xmm0
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mulsd %xmm0, %xmm7
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mulsd %xmm1, %xmm6
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mulsd %xmm2, %xmm3
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movapd %xmm6, %xmm1
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addsd %xmm3, %xmm6
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divsd %xmm6, %xmm7
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movsd 5976(%ebx), %xmm0
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movsd 5960(%ebx), %xmm5
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subsd %xmm3, %xmm1
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psrlq $63, %xmm2
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movapd %xmm1, %xmm3
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psllq $63, %xmm2
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mulsd %xmm1, %xmm1
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pshufd $68, %xmm2, %xmm2
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movsd 5968(%ebx), %xmm6
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mulsd %xmm1, %xmm3
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mulsd %xmm1, %xmm0
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xorpd %xmm2, %xmm4
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mulsd %xmm3, %xmm5
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subpd 5888(%ebx), %xmm4
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mulsd %xmm1, %xmm3
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addsd %xmm6, %xmm0
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mulsd %xmm3, %xmm0
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subsd %xmm4, %xmm5
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pshufd $238, %xmm4, %xmm4
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addsd %xmm5, %xmm0
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subsd %xmm7, %xmm0
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subsd %xmm4, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_0.0.2:
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subl $955, %eax
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cmpl $65, %eax
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jae .L_2TAG_PACKET_2.0.2
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psrlq $38, %xmm7
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psllq $38, %xmm7
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pmovmskb %xmm0, %eax
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andnpd %xmm0, %xmm4
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subsd %xmm7, %xmm1
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movapd %xmm7, %xmm6
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mulsd %xmm7, %xmm7
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addsd %xmm6, %xmm0
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orpd %xmm4, %xmm5
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subsd %xmm7, %xmm3
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mulsd %xmm1, %xmm0
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movapd %xmm3, %xmm4
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subsd %xmm0, %xmm3
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sqrtsd %xmm3, %xmm3
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andl $128, %eax
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shrl $7, %eax
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negl %eax
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movapd %xmm3, %xmm7
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andpd %xmm3, %xmm2
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psllq $2, %xmm3
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pextrw $3, %xmm3, %edx
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orpd %xmm5, %xmm2
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movd %eax, %xmm3
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pshufd $0, %xmm3, %xmm3
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subl $65216, %edx
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addl %edx, %edx
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mulsd 3840(%ebx,%edx,4), %xmm7
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mulsd %xmm2, %xmm6
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mulsd %xmm2, %xmm1
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mulsd %xmm2, %xmm2
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subsd %xmm7, %xmm6
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andpd 5904(%ebx), %xmm3
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addsd %xmm1, %xmm6
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subsd %xmm2, %xmm4
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addsd %xmm7, %xmm7
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movsd 5960(%ebx), %xmm5
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subsd %xmm0, %xmm4
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addsd %xmm6, %xmm7
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movsd 5976(%ebx), %xmm0
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divsd %xmm7, %xmm4
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movsd 5968(%ebx), %xmm2
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addpd (%ebx,%edx,8), %xmm3
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movapd %xmm6, %xmm1
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mulsd %xmm6, %xmm6
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mulsd %xmm6, %xmm0
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mulsd %xmm6, %xmm1
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mulsd %xmm1, %xmm5
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mulsd %xmm6, %xmm1
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addsd %xmm2, %xmm0
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pxor %xmm6, %xmm6
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mulsd %xmm1, %xmm0
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addsd %xmm3, %xmm5
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addsd %xmm5, %xmm0
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andl $32768, %eax
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pinsrw $3, %eax, %xmm6
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movapd %xmm4, %xmm5
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pshufd $238, %xmm3, %xmm3
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addsd %xmm3, %xmm4
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subsd %xmm4, %xmm3
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addsd %xmm3, %xmm5
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addsd %xmm5, %xmm0
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addsd %xmm4, %xmm0
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xorpd %xmm6, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_2.0.2:
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addl $15291, %eax
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cmpl $14336, %eax
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jae .L_2TAG_PACKET_3.0.2
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unpcklpd %xmm0, %xmm0
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movapd 5984(%ebx), %xmm6
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unpcklpd %xmm0, %xmm1
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movapd 6000(%ebx), %xmm2
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movapd 6016(%ebx), %xmm4
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mulpd %xmm0, %xmm0
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movapd 5888(%ebx), %xmm5
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mulpd %xmm0, %xmm1
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mulpd %xmm0, %xmm6
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mulpd %xmm0, %xmm0
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movapd %xmm1, %xmm3
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mulsd %xmm1, %xmm1
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addpd %xmm2, %xmm6
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mulpd %xmm0, %xmm4
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mulsd %xmm3, %xmm1
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addpd %xmm4, %xmm6
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pshufd $238, %xmm5, %xmm0
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mulpd %xmm6, %xmm1
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pshufd $238, %xmm5, %xmm6
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subsd %xmm7, %xmm0
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pshufd $238, %xmm1, %xmm2
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subsd %xmm1, %xmm5
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subsd %xmm0, %xmm6
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subsd %xmm2, %xmm5
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subsd %xmm6, %xmm7
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subsd %xmm7, %xmm5
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addsd %xmm5, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_3.0.2:
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subl $15356, %eax
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cmpl $4, %eax
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jae .L_2TAG_PACKET_4.0.2
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xorpd %xmm6, %xmm6
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andpd 6048(%ebx), %xmm7
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movsd 6096(%ebx), %xmm4
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movapd 5984(%ebx), %xmm1
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mulsd %xmm4, %xmm7
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movapd 6000(%ebx), %xmm2
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subsd %xmm7, %xmm4
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movapd 6016(%ebx), %xmm3
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pshufd $68, %xmm4, %xmm7
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sqrtsd %xmm4, %xmm4
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mulpd %xmm7, %xmm1
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pshufd $68, %xmm7, %xmm5
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pextrw $3, %xmm0, %eax
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mulpd %xmm7, %xmm7
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addpd %xmm1, %xmm2
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movsd 5936(%ebx), %xmm1
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mulpd %xmm7, %xmm3
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cmpsd $1, %xmm6, %xmm0
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mulsd %xmm5, %xmm7
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addpd %xmm3, %xmm2
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pshufd $68, %xmm0, %xmm0
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mulsd %xmm7, %xmm2
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andpd 5904(%ebx), %xmm0
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mulpd %xmm5, %xmm2
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andpd %xmm4, %xmm1
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pshufd $68, %xmm4, %xmm3
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subsd %xmm1, %xmm4
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addsd %xmm3, %xmm3
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mulsd %xmm1, %xmm1
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subsd %xmm4, %xmm3
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subsd %xmm1, %xmm5
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mulsd %xmm3, %xmm4
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pshufd $238, %xmm3, %xmm3
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subsd %xmm4, %xmm5
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divsd %xmm3, %xmm5
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addpd %xmm3, %xmm3
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mulpd %xmm3, %xmm2
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pshufd $238, %xmm2, %xmm4
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addsd %xmm0, %xmm2
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andl $32768, %eax
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pinsrw $3, %eax, %xmm6
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pshufd $238, %xmm0, %xmm0
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addsd %xmm4, %xmm2
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addsd %xmm5, %xmm2
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addsd %xmm3, %xmm2
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addsd %xmm2, %xmm0
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xorpd %xmm6, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_4.0.2:
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addl $261884, %eax
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cmpl $261888, %eax
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jb .L_2TAG_PACKET_5.0.2
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movd %xmm7, %ecx
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psrlq $32, %xmm7
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movd %xmm7, %edx
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andl $2147483647, %edx
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movl $1072693248, %eax
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subl %edx, %eax
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orl %ecx, %eax
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cmpl $0, %eax
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je .L_2TAG_PACKET_6.0.2
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movq 8(%esp), %xmm2
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movd %xmm2, %edx
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psrlq $32, %xmm2
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movd %xmm2, %ecx
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andl $2147483647, %ecx
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subl $1, %edx
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sbbl $2146435072, %ecx
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cmpl $0, %ecx
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jge .L_2TAG_PACKET_7.0.2
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xorpd %xmm1, %xmm1
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xorpd %xmm0, %xmm0
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movl $32752, %edx
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pinsrw $3, %edx, %xmm1
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mulsd %xmm1, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_6.0.2:
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pextrw $1, %xmm7, %edx
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shrl $15, %edx
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negl %edx
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movd %edx, %xmm7
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pshufd $0, %xmm7, %xmm7
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movsd 5920(%ebx), %xmm2
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movsd 5928(%ebx), %xmm0
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andpd %xmm7, %xmm2
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andpd %xmm7, %xmm0
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addsd %xmm2, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_5.0.2:
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movsd 5888(%ebx), %xmm2
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movsd 5896(%ebx), %xmm0
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addsd %xmm2, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_7.0.2:
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xorpd %xmm6, %xmm6
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addsd %xmm6, %xmm0
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movsd %xmm0, (%esp)
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fldl (%esp)
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.L_2TAG_PACKET_1.0.2:
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movl 48(%esp), %ebx
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movl %ebp, %esp
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popl %ebp
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ret
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..B2.3:
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END(acos)
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# -- End acos
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# Start file scope ASM
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ALIAS_SYMBOL(acosl, acos);
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# End file scope ASM
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.section .rodata, "a"
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.align 16
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.align 16
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static_const_table:
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|
.long 3822952792
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|
.long 1021639372
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|
.long 182792448
|
|
.long 1068507836
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|
.long 2264213271
|
|
.long 1019558908
|
|
.long 649052928
|
|
.long 1068524253
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|
.long 1797139609
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|
.long 1022295143
|
|
.long 1243095296
|
|
.long 1068540671
|
|
.long 1415938756
|
|
.long 1021439537
|
|
.long 2033294592
|
|
.long 1068557090
|
|
.long 2356809978
|
|
.long 1021777916
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|
.long 3088063744
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|
.long 1068573510
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|
.long 2669055318
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|
.long 1022124482
|
|
.long 180888576
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|
.long 1068589932
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|
.long 3566445325
|
|
.long 1021358712
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|
.long 1970196992
|
|
.long 1068606354
|
|
.long 896980323
|
|
.long 1021319659
|
|
.long 4229555456
|
|
.long 1068622777
|
|
.long 436049712
|
|
.long 1021319758
|
|
.long 2732572160
|
|
.long 1068639202
|
|
.long 583123209
|
|
.long 1020797960
|
|
.long 1842831872
|
|
.long 1068655628
|
|
.long 1370449804
|
|
.long 1021429270
|
|
.long 1628994560
|
|
.long 1068672055
|
|
.long 2411391464
|
|
.long 1021057980
|
|
.long 2159763712
|
|
.long 1068688483
|
|
.long 1208692749
|
|
.long 1021943903
|
|
.long 3503886336
|
|
.long 1068704912
|
|
.long 538793309
|
|
.long 1019744063
|
|
.long 1435187200
|
|
.long 1068721343
|
|
.long 4085087612
|
|
.long 1020608419
|
|
.long 317469952
|
|
.long 1068737775
|
|
.long 144386942
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|
.long 1021440732
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.type static_const_table,@object
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.size static_const_table,6112
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.data
|
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.section .note.GNU-stack, "",@progbits
|
|
# End
|