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1958 lines
40 KiB
1958 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 acos
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ENTRY(acos)
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# parameter 1: %xmm0
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..B1.1:
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..___tag_value_acos.1:
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subq $24, %rsp
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..___tag_value_acos.3:
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movsd %xmm0, (%rsp)
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..B1.2:
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movsd ABSVALMASK(%rip), %xmm4
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movsd ONEMASK(%rip), %xmm3
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xorpd %xmm5, %xmm5
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movsd TMASK(%rip), %xmm2
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movq %xmm0, %xmm1
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psrlq $44, %xmm0
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movd %xmm0, %edx
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movq %xmm1, %xmm7
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movl $8192, %ecx
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pinsrw $2, %ecx, %xmm5
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movq %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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lea T_table(%rip), %r8
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movsd (%r8,%rdx,2), %xmm1
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orpd %xmm5, %xmm2
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lea Tbl_addr(%rip), %r8
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movapd (%r8,%rdx,4), %xmm4
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movq %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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movq %xmm6, %xmm1
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addsd %xmm3, %xmm6
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divsd %xmm6, %xmm7
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movsd 24+cv(%rip), %xmm0
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movsd 8+cv(%rip), %xmm5
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subsd %xmm3, %xmm1
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psrlq $63, %xmm2
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movq %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 16+cv(%rip), %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 PI_BY_2(%rip), %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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jmp ..B1.5
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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_1.0.2
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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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movq %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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movq %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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movq %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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lea T_table(%rip), %r8
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mulsd (%r8,%rdx,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 NEG_PI(%rip), %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 8+cv(%rip), %xmm5
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subsd %xmm0, %xmm4
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addsd %xmm6, %xmm7
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movsd 24+cv(%rip), %xmm0
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divsd %xmm7, %xmm4
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movsd 16+cv(%rip), %xmm2
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lea Tbl_addr(%rip), %r8
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addpd (%r8,%rdx,8), %xmm3
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movq %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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movq %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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jmp ..B1.5
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.L_2TAG_PACKET_1.0.2:
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addl $15291, %eax
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cmpl $14336, %eax
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jae .L_2TAG_PACKET_2.0.2
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unpcklpd %xmm0, %xmm0
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movapd cv2(%rip), %xmm6
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unpcklpd %xmm0, %xmm1
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movapd 16+cv2(%rip), %xmm2
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movapd 32+cv2(%rip), %xmm4
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mulpd %xmm0, %xmm0
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movapd PI_BY_2(%rip), %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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movq %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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jmp ..B1.5
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.L_2TAG_PACKET_2.0.2:
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subl $15356, %eax
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cmpl $4, %eax
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jae .L_2TAG_PACKET_3.0.2
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xorpd %xmm6, %xmm6
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andpd ABSVALMASK(%rip), %xmm7
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movsd ONE_BY_2(%rip), %xmm4
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movapd cv2(%rip), %xmm1
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mulsd %xmm4, %xmm7
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movapd 16+cv2(%rip), %xmm2
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subsd %xmm7, %xmm4
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movapd 32+cv2(%rip), %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 HALFMASK(%rip), %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 NEG_PI(%rip), %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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jmp ..B1.5
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.L_2TAG_PACKET_3.0.2:
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addl $261884, %eax
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cmpl $261888, %eax
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jb .L_2TAG_PACKET_4.0.2
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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_5.0.2
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movsd (%rsp), %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_6.0.2
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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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jmp .L_2TAG_PACKET_7.0.2
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.L_2TAG_PACKET_5.0.2:
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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 PI(%rip), %xmm2
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movsd 8+PI(%rip), %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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jmp ..B1.5
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.L_2TAG_PACKET_4.0.2:
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movsd PI_BY_2(%rip), %xmm2
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movsd 8+PI_BY_2(%rip), %xmm0
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addsd %xmm2, %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_6.0.2:
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xorpd %xmm6, %xmm6
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addsd %xmm6, %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_7.0.2:
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movq %xmm0, 8(%rsp)
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..B1.3:
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movq 8(%rsp), %xmm0
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.L_2TAG_PACKET_8.0.2:
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..B1.5:
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addq $24, %rsp
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..___tag_value_acos.4:
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ret
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..___tag_value_acos.5:
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END(acos)
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# -- End acos
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.section .rodata, "a"
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.align 16
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.align 16
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ABSVALMASK:
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.long 4294967295
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.long 2147483647
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.long 0
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.long 0
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.type ABSVALMASK,@object
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.size ABSVALMASK,16
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.align 16
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T_table:
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.long 2642784509
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.long 1072689083
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.long 1514442531
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.long 1072688953
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.long 333108933
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.long 1072688821
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.long 3392112024
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.long 1072688686
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.long 2099852862
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.long 1072688550
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.long 749609004
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.long 1072688412
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.long 3634632596
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.long 1072688271
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.long 2163248461
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.long 1072688129
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.long 628657846
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.long 1072687985
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.long 3324036511
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.long 1072687838
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.long 1657632815
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.long 1072687690
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.long 4217538760
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.long 1072687539
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.long 2411951597
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|
.long 1072687387
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.long 533944872
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|
.long 1072687233
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.long 2876566508
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|
.long 1072687076
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.long 847936891
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.long 1072686918
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.long 3036019913
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.long 1072686757
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.long 848884575
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.long 1072686595
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.long 2874443326
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.long 1072686430
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.long 520713666
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.long 1072686264
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.long 2375556481
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.long 1072686095
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.long 4141904948
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.long 1072685924
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.long 1522666382
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.long 1072685752
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.long 3105624104
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.long 1072685577
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.long 298666327
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.long 1072685401
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.long 1689524500
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.long 1072685222
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.long 2981002200
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.long 1072685041
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.long 4170844284
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.long 1072684858
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.long 961802263
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.long 1072684674
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.long 1941503454
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.long 1072684487
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.long 2812647170
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.long 1072684298
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.long 3572873869
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.long 1072684107
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.long 4219797823
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.long 1072683914
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.long 456039788
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.long 1072683720
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.long 869096151
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.long 1072683523
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.long 1161535119
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.long 1072683324
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.long 1330865866
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.long 1072683123
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.long 1374571204
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.long 1072682920
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.long 1290107538
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.long 1072682715
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.long 1074904836
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.long 1072682508
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.long 726366587
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.long 1072682299
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.long 241869763
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.long 1072682088
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.long 3913732079
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.long 1072681874
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.long 3149342765
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.long 1072681659
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.type Tbl_addr,@object
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|
.size Tbl_addr,3840
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.space 768, 0x00 # pad
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|
.align 16
|
|
cv:
|
|
.long 0
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.type cv,@object
|
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.size cv,32
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.align 16
|
|
PI_BY_2:
|
|
.long 856972295
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|
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.type PI_BY_2,@object
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|
.size PI_BY_2,16
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.align 16
|
|
NEG_PI:
|
|
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|
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|
|
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|
|
cv2:
|
|
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|
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|
|
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.type cv2,@object
|
|
.size cv2,64
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.align 16
|
|
HALFMASK:
|
|
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|
|
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|
|
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|
|
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|
.type HALFMASK,@object
|
|
.size HALFMASK,16
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|
.align 16
|
|
PI:
|
|
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|
|
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|
|
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|
|
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|
|
.type PI,@object
|
|
.size PI,16
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|
.align 4
|
|
ONEMASK:
|
|
.long 0
|
|
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|
.type ONEMASK,@object
|
|
.size ONEMASK,8
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.align 4
|
|
TMASK:
|
|
.long 0
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|
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.type TMASK,@object
|
|
.size TMASK,8
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|
.align 4
|
|
ONE_BY_2:
|
|
.long 0
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.type ONE_BY_2,@object
|
|
.size ONE_BY_2,8
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|
.data
|
|
.section .note.GNU-stack, "",@progbits
|
|
// -- Begin DWARF2 SEGMENT .eh_frame
|
|
.section .eh_frame,"a",@progbits
|
|
.eh_frame_seg:
|
|
.align 1
|
|
.4byte 0x00000014
|
|
.8byte 0x00527a0100000000
|
|
.8byte 0x08070c1b01107801
|
|
.4byte 0x00000190
|
|
.4byte 0x0000001c
|
|
.4byte 0x0000001c
|
|
.4byte ..___tag_value_acos.1-.
|
|
.4byte ..___tag_value_acos.5-..___tag_value_acos.1
|
|
.2byte 0x0400
|
|
.4byte ..___tag_value_acos.3-..___tag_value_acos.1
|
|
.2byte 0x200e
|
|
.byte 0x04
|
|
.4byte ..___tag_value_acos.4-..___tag_value_acos.3
|
|
.2byte 0x080e
|
|
.byte 0x00
|
|
# End
|