2014-10-31 11:29:18 +01:00
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/*
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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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// tanh(x)=(exp(x)-exp(-x))/(exp(x)+exp(-x))=(1-exp(-2*x))/(1+exp(-2*x))
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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)*2^8*2=int(xH*L2EH*2^9),
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// f=0.b1 b2 ... b8, k integer
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// 2^{-f} is approximated as Tn[f]+Dn[f]
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// Tn stores the high 53 bits, Dn stores (2^{-f}-Tn[f]) rounded to double precision
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//
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// r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-9}+2^{-14},
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// for |x| in [23/64,3*2^7)
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// e^{-2*|x|}=2^{-k-f}*2^{-r} ~ 2^{-k}*(Tn+Dn)*(1+p)=(T0+D0)*(1+p)
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//
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// For |x| in [2^{-4},2^5):
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// 2^{-r}-1 ~ p=c1*r+c2*r^2+..+c5*r^5
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// Let R=1/(1+T0+p*T0), truncated to 35 significant bits
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// R=1/(1+T0+D0+p*(T0+D0))*(1+eps), |eps|<2^{-33}
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// 1+T0+D0+p*(T0+D0)=KH+KL, where
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// KH=(1+T0+c1*r*T0)_high (leading 17 bits)
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// KL=T0_low+D0+(c1*r*T0)_low+c1*r*D0+(c2*r^2+..c5*r^5)*T0
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// eps ~ (R*KH-1)+R*KL
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// 1/(1+T0+D0+p*(T0+D0)) ~ R-R*eps
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// The result is approximated as (1-T0-D0-(T0+D0)*p)*(R-R*eps)
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// 1-T0-D0-(T0+D0)*p=-((KH-2)+KL)
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// The result is formed as
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// (KH-2)*R+(-(KH-2)*R*eps+(KL*R-KL*R*eps)), with the correct sign
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// set at the end
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//
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// For |x| in [2^{-64},2^{-4}):
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// A Taylor series expansion is used (x+p3*x^3+..+p13*x^{13})
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//
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// For |x|<2^{-64}: x is returned
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//
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// For |x|>=2^32: return +/-1
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//
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// Special cases:
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// tanh(NaN) = quiet NaN, and raise invalid exception
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// tanh(INF) = that INF
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// tanh(+/-0) = +/-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 tanh
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ENTRY(tanh)
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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, 40(%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 4256(%ebx), %xmm3
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xorpd %xmm4, %xmm4
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movsd 4112(%ebx), %xmm1
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movsd 4120(%ebx), %xmm2
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movl $32768, %eax
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pinsrw $3, %eax, %xmm4
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movsd 4096(%ebx), %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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movl $32768, %edx
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andl %ecx, %edx
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andl $32767, %ecx
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subl $16304, %ecx
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cmpl $144, %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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movapd %xmm3, %xmm7
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addsd %xmm6, %xmm3
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mulsd %xmm4, %xmm1
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movsd 4264(%ebx), %xmm4
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subsd %xmm6, %xmm3
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xorpd %xmm0, %xmm0
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addsd %xmm1, %xmm2
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subsd %xmm3, %xmm7
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movapd 4128(%ebx), %xmm6
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addsd %xmm7, %xmm2
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movl $255, %ecx
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andl %eax, %ecx
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addl %ecx, %ecx
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movapd (%ebx,%ecx,8), %xmm5
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shrl $4, %eax
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andl $65520, %eax
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subl $16368, %eax
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negl %eax
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pinsrw $3, %eax, %xmm0
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movapd 4144(%ebx), %xmm1
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pshufd $68, %xmm0, %xmm0
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mulpd %xmm5, %xmm0
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movsd 4160(%ebx), %xmm7
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pshufd $68, %xmm2, %xmm2
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movapd %xmm4, %xmm5
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addsd %xmm0, %xmm4
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mulpd %xmm2, %xmm6
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mulsd %xmm2, %xmm7
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mulpd %xmm2, %xmm2
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addpd %xmm6, %xmm1
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mulsd %xmm2, %xmm2
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movsd 4264(%ebx), %xmm3
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mulpd %xmm2, %xmm1
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pshufd $78, %xmm1, %xmm6
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addsd %xmm6, %xmm1
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movapd %xmm1, %xmm6
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addsd %xmm7, %xmm1
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mulsd %xmm0, %xmm1
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addsd %xmm4, %xmm1
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andpd 4224(%ebx), %xmm4
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divsd %xmm1, %xmm5
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subsd %xmm4, %xmm3
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pshufd $238, %xmm0, %xmm1
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addsd %xmm0, %xmm3
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movapd %xmm4, %xmm2
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addsd %xmm1, %xmm3
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mulsd %xmm7, %xmm1
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mulsd %xmm0, %xmm7
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addsd %xmm1, %xmm3
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addsd %xmm7, %xmm4
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movsd 4240(%ebx), %xmm1
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mulsd %xmm0, %xmm6
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andpd 4224(%ebx), %xmm4
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addsd %xmm6, %xmm3
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movapd %xmm4, %xmm6
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subsd %xmm4, %xmm2
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addsd %xmm7, %xmm2
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movsd 4264(%ebx), %xmm7
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andpd %xmm1, %xmm5
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addsd %xmm2, %xmm3
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mulsd %xmm5, %xmm4
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xorpd %xmm2, %xmm2
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mulsd %xmm5, %xmm3
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subsd 4272(%ebx), %xmm6
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subsd %xmm7, %xmm4
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xorl $32768, %edx
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pinsrw $3, %edx, %xmm2
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addsd %xmm3, %xmm4
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mulsd %xmm5, %xmm6
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movapd %xmm3, %xmm1
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mulsd %xmm4, %xmm3
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movapd %xmm6, %xmm0
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mulsd %xmm4, %xmm6
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subsd %xmm3, %xmm1
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subsd %xmm6, %xmm1
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addsd %xmm1, %xmm0
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xorpd %xmm2, %xmm0
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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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addl $960, %ecx
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cmpl $1104, %ecx
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jae .L_2TAG_PACKET_2.0.2
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movapd 4176(%ebx), %xmm2
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pshufd $68, %xmm0, %xmm1
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movapd 4192(%ebx), %xmm3
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mulpd %xmm1, %xmm1
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movapd 4208(%ebx), %xmm4
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mulpd %xmm1, %xmm2
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pshufd $68, %xmm1, %xmm5
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addpd %xmm3, %xmm2
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mulsd %xmm5, %xmm5
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mulpd %xmm1, %xmm2
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mulsd %xmm5, %xmm5
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addpd %xmm4, %xmm2
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mulpd %xmm5, %xmm2
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pshufd $238, %xmm2, %xmm5
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addsd %xmm5, %xmm2
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mulsd %xmm0, %xmm2
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addsd %xmm2, %xmm0
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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 $15344, %ecx
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cmpl $16448, %ecx
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jae .L_2TAG_PACKET_3.0.2
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cmpl $16, %ecx
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jb .L_2TAG_PACKET_4.0.2
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xorpd %xmm2, %xmm2
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movl $17392, %eax
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pinsrw $3, %eax, %xmm2
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mulsd %xmm0, %xmm2
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addsd %xmm0, %xmm2
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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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movapd %xmm0, %xmm2
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mulsd %xmm2, %xmm2
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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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cmpl $32752, %ecx
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jae .L_2TAG_PACKET_5.0.2
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xorpd %xmm2, %xmm2
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movl $15344, %ecx
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pinsrw $3, %ecx, %xmm2
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movapd %xmm2, %xmm3
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mulsd %xmm2, %xmm2
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addsd %xmm3, %xmm2
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.L_2TAG_PACKET_6.0.2:
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xorpd %xmm0, %xmm0
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orl $16368, %edx
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pinsrw $3, %edx, %xmm0
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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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movapd %xmm0, %xmm2
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movd %xmm0, %eax
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psrlq $20, %xmm2
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movd %xmm2, %ecx
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orl %eax, %ecx
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cmpl $0, %ecx
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je .L_2TAG_PACKET_6.0.2
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addsd %xmm0, %xmm0
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_1.0.2:
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movsd %xmm0, 24(%esp)
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fldl 24(%esp)
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.L_2TAG_PACKET_7.0.2:
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movl 40(%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(tanh)
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# -- End tanh
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# Start file scope ASM
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2015-03-14 01:43:52 +01:00
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ALIAS_SYMBOL(tanhl, tanh);
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2014-10-31 11:29:18 +01:00
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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 0
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.long 1072693248
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.long 0
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.long 0
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.long 1797923801
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.long 1072687577
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.long 1950547427
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.long 1013229059
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.long 730821105
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.long 1072681922
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.type static_const_table,@object
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.data
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|
|
|
.section .note.GNU-stack, ""
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# End
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