1373 lines
28 KiB
ArmAsm
1373 lines
28 KiB
ArmAsm
|
/*
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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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// cosh(x)=(exp(x)+exp(-x))/2
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//
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// Let |x|=xH+xL (upper 26 bits, lower 27 bits)
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// log2(e) rounded to 26 bits (high part) plus a double precision low part is
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// L2EH+L2EL (upper 26, lower 53 bits)
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//
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// Let xH*L2EH=k+f+r`, where (k+f)*2^7=int(xH*L2EH*2^7),
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// f=0.b1 b2 ... b7, k integer
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// 2^f is approximated as Tp[f]+Dp[f], and 2^{-f} as Tn[f]+Dn[f]
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// Tp stores higher 53 bits, Dp stores (2^f-Tp[f]) rounded to double precision
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//
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// e^|x|=2^{k+f}*2^r, r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-8}+2^{-14},
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// for |x| in [1/8,3*2^8)
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// e^{-|x|}=2^{-k-f}*2^{-r}
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//
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// e^|x| is approximated as 2^k*Tp+2^k*Tp*c1*r(1+c2*r+..+c5*r^4)+2^k*Dp=
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// =2^k*Tp+2^k*Tp*P15+2^k*Dp
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// e^{-|x|} approximated as 2^{-k}*Tn-2^{-k}*Tn*c1*r(1-c2*r+..+c5*r^4)
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//
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// For |x| in [1/8, 3*2^7), cosh(x) is formed as
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// RN(2^k*Tp+2^{-k}*Tn)+2^k*Tp*P15+2^{-k}*Tn*P`15+2^{-k}*TnL+2^{-k}*Dn+2^k*Dp
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//
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// For |x| in [3*2^7, 3*2^8), (e^|x|)/2 is returned, and
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// the result is checked for overflow.
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//
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// For |x|<1/8, a Taylor polynomial expansion is used (degree 10)
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// (error bound for polynomial expansion is below 0.501 ulp)
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//
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// Special cases:
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// cosh(NaN) = quiet NaN, and raise invalid exception
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// cosh(INF) = that INF
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// cosh(0)=1
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// for finite argument, only cosh(0)=1 is exact
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// For IEEE double
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// cosh(x) overflows
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// for x > 710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
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//
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/******************************************************************************/
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#include <private/bionic_asm.h>
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# -- Begin cosh
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ENTRY(cosh)
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# parameter 1: %xmm0
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..B1.1:
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..___tag_value_cosh.1:
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pushq %rsi
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..___tag_value_cosh.3:
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..B1.2:
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movsd HALFMASK(%rip), %xmm3
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xorpd %xmm4, %xmm4
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movsd L2E(%rip), %xmm1
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movsd 8+L2E(%rip), %xmm2
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movl $32768, %eax
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pinsrw $3, %eax, %xmm4
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movsd Shifter(%rip), %xmm6
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pextrw $3, %xmm0, %ecx
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andpd %xmm0, %xmm3
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andnpd %xmm0, %xmm4
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pshufd $68, %xmm4, %xmm5
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andl $32767, %ecx
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subl $16320, %ecx
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cmpl $200, %ecx
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jae .L_2TAG_PACKET_0.0.2
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subsd %xmm3, %xmm4
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mulsd %xmm1, %xmm3
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mulsd %xmm5, %xmm2
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cvtsd2si %xmm3, %eax
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movq %xmm3, %xmm7
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addsd %xmm6, %xmm3
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mulsd %xmm4, %xmm1
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xorpd %xmm5, %xmm5
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subsd %xmm6, %xmm3
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movapd cv(%rip), %xmm4
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addsd %xmm1, %xmm2
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movapd 16+cv(%rip), %xmm6
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subsd %xmm3, %xmm7
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movl $32704, %edx
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pinsrw $3, %edx, %xmm5
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movapd 32+cv(%rip), %xmm1
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addsd %xmm7, %xmm2
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movl $127, %edx
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andl %eax, %edx
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addl %edx, %edx
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shrl $3, %eax
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andl $65520, %eax
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addl $16352, %eax
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xorpd %xmm0, %xmm0
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cmpl $184, %ecx
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jae .L_2TAG_PACKET_1.0.2
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pshufd $68, %xmm5, %xmm5
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pinsrw $3, %eax, %xmm0
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pshufd $68, %xmm0, %xmm0
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psubw %xmm0, %xmm5
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lea T2f(%rip), %r8
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mulpd (%r8,%rdx,8), %xmm0
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lea T2_neg_f(%rip), %r8
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mulpd (%r8,%rdx,8), %xmm5
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pshufd $68, %xmm2, %xmm3
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movapd 48+cv(%rip), %xmm7
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pshufd $68, %xmm2, %xmm2
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mulpd %xmm3, %xmm3
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mulpd %xmm2, %xmm4
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mulpd %xmm2, %xmm6
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mulpd 64+cv(%rip), %xmm2
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mulpd %xmm3, %xmm1
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mulpd %xmm3, %xmm7
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mulpd %xmm3, %xmm4
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mulpd %xmm3, %xmm1
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addpd %xmm7, %xmm6
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movq %xmm0, %xmm7
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addpd %xmm1, %xmm4
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shufpd $0, %xmm5, %xmm7
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addpd %xmm5, %xmm0
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mulpd %xmm7, %xmm2
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addpd %xmm6, %xmm4
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subsd %xmm0, %xmm7
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mulpd %xmm2, %xmm4
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pshufd $238, %xmm0, %xmm6
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addsd %xmm5, %xmm7
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addpd %xmm2, %xmm4
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addsd %xmm6, %xmm7
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pshufd $238, %xmm4, %xmm2
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addsd %xmm7, %xmm2
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addsd %xmm4, %xmm2
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addsd %xmm2, %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_0.0.2:
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addl $16320, %ecx
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cmpl $16320, %ecx
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ja .L_2TAG_PACKET_2.0.2
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cmpl $15952, %ecx
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jae .L_2TAG_PACKET_3.0.2
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addsd %xmm2, %xmm6
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movq ONEMASK(%rip), %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_1.0.2:
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subl $16352, %eax
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movl %eax, %ecx
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andl $32752, %eax
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shrl $1, %eax
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andl $65520, %eax
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subl %eax, %ecx
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addl $16352, %eax
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pinsrw $3, %eax, %xmm0
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pshufd $68, %xmm0, %xmm0
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lea T2f(%rip), %r8
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mulpd (%r8,%rdx,8), %xmm0
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pshufd $68, %xmm2, %xmm3
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movsd 48+cv(%rip), %xmm7
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mulsd %xmm3, %xmm3
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mulsd %xmm2, %xmm4
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mulsd %xmm2, %xmm6
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mulsd 64+cv(%rip), %xmm2
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mulsd %xmm3, %xmm1
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mulsd %xmm3, %xmm7
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mulsd %xmm3, %xmm4
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addl $16368, %ecx
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pinsrw $3, %ecx, %xmm5
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mulsd %xmm3, %xmm1
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addsd %xmm7, %xmm6
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addsd %xmm1, %xmm4
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mulsd %xmm0, %xmm2
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addsd %xmm6, %xmm4
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mulsd %xmm2, %xmm4
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pshufd $238, %xmm0, %xmm6
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addsd %xmm6, %xmm4
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addsd %xmm4, %xmm2
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addsd %xmm2, %xmm0
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mulsd %xmm5, %xmm0
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pextrw $3, %xmm0, %eax
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andl $32752, %eax
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cmpl $32752, %eax
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je .L_2TAG_PACKET_4.0.2
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jmp ..B1.5
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.L_2TAG_PACKET_3.0.2:
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movapd pv(%rip), %xmm1
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mulpd %xmm5, %xmm5
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movapd 16+pv(%rip), %xmm2
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xorpd %xmm3, %xmm3
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movq %xmm5, %xmm0
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mulpd %xmm5, %xmm1
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movsd ONEMASK(%rip), %xmm6
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mulpd %xmm5, %xmm5
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movl $16352, %eax
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pinsrw $3, %eax, %xmm3
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addpd %xmm2, %xmm1
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mulpd %xmm5, %xmm1
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pshufd $238, %xmm1, %xmm2
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mulsd %xmm1, %xmm5
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mulsd %xmm3, %xmm0
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addsd %xmm5, %xmm2
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addsd %xmm2, %xmm0
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addsd %xmm6, %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_2.0.2:
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cmpl $32752, %ecx
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jae .L_2TAG_PACKET_5.0.2
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xorpd %xmm0, %xmm0
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movl $32736, %eax
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pinsrw $3, %eax, %xmm0
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mulsd %xmm0, %xmm0
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jmp .L_2TAG_PACKET_4.0.2
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.L_2TAG_PACKET_5.0.2:
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mulsd %xmm0, %xmm0
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jmp ..B1.5
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.L_2TAG_PACKET_4.0.2:
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movq %xmm0, (%rsp)
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..B1.3:
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movq (%rsp), %xmm0
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.L_2TAG_PACKET_6.0.2:
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..B1.5:
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popq %rcx
|
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..___tag_value_cosh.4:
|
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|
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ret
|
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..___tag_value_cosh.5:
|
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END(cosh)
|
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|
|
# -- End cosh
|
||
|
|
.section .rodata, "a"
|
||
|
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.align 16
|
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|
|
.align 16
|
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|
|
L2E:
|
||
|
|
.long 1610612736
|
||
|
|
.long 1080497479
|
||
|
|
.long 4166901572
|
||
|
|
.long 1053077003
|
||
|
|
.type L2E,@object
|
||
|
|
.size L2E,16
|
||
|
|
.align 16
|
||
|
|
Shifter:
|
||
|
|
.long 0
|
||
|
|
.long 1127743488
|
||
|
|
.long 0
|
||
|
|
.long 3275227136
|
||
|
|
.type Shifter,@object
|
||
|
|
.size Shifter,16
|
||
|
|
.align 16
|
||
|
|
cv:
|
||
|
|
.long 3607404736
|
||
|
|
.long 1044146952
|
||
|
|
.long 3607404736
|
||
|
|
.long 3191630600
|
||
|
|
.long 4277811695
|
||
|
|
.long 1063661122
|
||
|
|
.long 4277811695
|
||
|
|
.long 3211144770
|
||
|
|
.long 2140175755
|
||
|
|
.long 1033864261
|
||
|
|
.long 2140175755
|
||
|
|
.long 1033864261
|
||
|
|
.long 4289495988
|
||
|
|
.long 1054113747
|
||
|
|
.long 4289495988
|
||
|
|
.long 1054113747
|
||
|
|
.long 4277811695
|
||
|
|
.long 1064709698
|
||
|
|
.long 4277811695
|
||
|
|
.long 3212193346
|
||
|
|
.type cv,@object
|
||
|
|
.size cv,80
|
||
|
|
.align 16
|
||
|
|
T2f:
|
||
|
|
.long 0
|
||
|
|
.long 1072693248
|
||
|
|
.long 0
|
||
|
|
.long 0
|
||
|
|
.long 2851812149
|
||
|
|
.long 1072698941
|
||
|
|
.long 2595802551
|
||
|
|
.long 1016815913
|
||
|
|
.long 1048019041
|
||
|
|
.long 1072704666
|
||
|
|
.long 1398474845
|
||
|
|
.long 3161559171
|
||
|
|
.long 3899555717
|
||
|
|
.long 1072710421
|
||
|
|
.long 427280750
|
||
|
|
.long 3163595548
|
||
|
|
.long 3541402996
|
||
|
|
.long 1072716208
|
||
|
|
.long 2759177317
|
||
|
|
.long 1015903202
|
||
|
|
.long 702412510
|
||
|
|
.long 1072722027
|
||
|
|
.long 3803266087
|
||
|
|
.long 3163328991
|
||
|
|
.long 410360776
|
||
|
|
.long 1072727877
|
||
|
|
.long 1269990655
|
||
|
|
.long 1013024446
|
||
|
|
.long 3402036099
|
||
|
|
.long 1072733758
|
||
|
|
.long 405889334
|
||
|
|
.long 1016154232
|
||
|
|
.long 1828292879
|
||
|
|
.long 1072739672
|
||
|
|
.long 1255956747
|
||
|
|
.long 1016636974
|
||
|
|
.long 728909815
|
||
|
|
.long 1072745618
|
||
|
|
.long 383930225
|
||
|
|
.long 1016078044
|
||
|
|
.long 852742562
|
||
|
|
.long 1072751596
|
||
|
|
.long 667253586
|
||
|
|
.long 1010842135
|
||
|
|
.long 2952712987
|
||
|
|
.long 1072757606
|
||
|
|
.long 3293494651
|
||
|
|
.long 3161168877
|
||
|
|
.long 3490863953
|
||
|
|
.long 1072763649
|
||
|
|
.long 960797498
|
||
|
|
.long 3163997456
|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
|
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|
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|
|
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|
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|
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|
|
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|
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|
|
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|
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|
|
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|
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|
|
.long 3162948880
|
||
|
|
.long 2952712987
|
||
|
|
.long 1071709030
|
||
|
|
.long 3293494651
|
||
|
|
.long 3160120301
|
||
|
|
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|
||
|
|
.long 1071703020
|
||
|
|
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|
||
|
|
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|
||
|
|
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|
||
|
|
.long 1071697042
|
||
|
|
.long 383930225
|
||
|
|
.long 1015029468
|
||
|
|
.long 1828292879
|
||
|
|
.long 1071691096
|
||
|
|
.long 1255956747
|
||
|
|
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|
||
|
|
.long 3402036099
|
||
|
|
.long 1071685182
|
||
|
|
.long 405889334
|
||
|
|
.long 1015105656
|
||
|
|
.long 410360776
|
||
|
|
.long 1071679301
|
||
|
|
.long 1269990655
|
||
|
|
.long 1011975870
|
||
|
|
.long 702412510
|
||
|
|
.long 1071673451
|
||
|
|
.long 3803266087
|
||
|
|
.long 3162280415
|
||
|
|
.long 3541402996
|
||
|
|
.long 1071667632
|
||
|
|
.long 2759177317
|
||
|
|
.long 1014854626
|
||
|
|
.long 3899555717
|
||
|
|
.long 1071661845
|
||
|
|
.long 427280750
|
||
|
|
.long 3162546972
|
||
|
|
.long 1048019041
|
||
|
|
.long 1071656090
|
||
|
|
.long 1398474845
|
||
|
|
.long 3160510595
|
||
|
|
.long 2851812149
|
||
|
|
.long 1071650365
|
||
|
|
.long 2595802551
|
||
|
|
.long 1015767337
|
||
|
|
.type T2_neg_f,@object
|
||
|
|
.size T2_neg_f,2048
|
||
|
|
.align 16
|
||
|
|
pv:
|
||
|
|
.long 3078135644
|
||
|
|
.long 1049787983
|
||
|
|
.long 381774870
|
||
|
|
.long 1062650220
|
||
|
|
.long 436314137
|
||
|
|
.long 1056571808
|
||
|
|
.long 1431655765
|
||
|
|
.long 1067799893
|
||
|
|
.type pv,@object
|
||
|
|
.size pv,32
|
||
|
|
.align 4
|
||
|
|
HALFMASK:
|
||
|
|
.long 4160749568
|
||
|
|
.long 2147483647
|
||
|
|
.type HALFMASK,@object
|
||
|
|
.size HALFMASK,8
|
||
|
|
.align 4
|
||
|
|
ONEMASK:
|
||
|
|
.long 0
|
||
|
|
.long 1072693248
|
||
|
|
.type ONEMASK,@object
|
||
|
|
.size ONEMASK,8
|
||
|
|
.data
|
||
|
|
.section .note.GNU-stack, ""
|
||
|
|
// -- 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_cosh.1-.
|
||
|
|
.4byte ..___tag_value_cosh.5-..___tag_value_cosh.1
|
||
|
|
.2byte 0x0400
|
||
|
|
.4byte ..___tag_value_cosh.3-..___tag_value_cosh.1
|
||
|
|
.2byte 0x100e
|
||
|
|
.byte 0x04
|
||
|
|
.4byte ..___tag_value_cosh.4-..___tag_value_cosh.3
|
||
|
|
.2byte 0x080e
|
||
|
|
.byte 0x00
|
||
|
|
# End
|