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/*
Copyright (c) 2014, Intel Corporation
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/******************************************************************************/
// ALGORITHM DESCRIPTION
// ---------------------
//
// cosh(x)=(exp(x)+exp(-x))/2
//
// Let |x|=xH+xL (upper 26 bits, lower 27 bits)
// log2(e) rounded to 26 bits (high part) plus a double precision low part is
// L2EH+L2EL (upper 26, lower 53 bits)
//
// Let xH*L2EH=k+f+r`, where (k+f)*2^7=int(xH*L2EH*2^7),
// f=0.b1 b2 ... b7, k integer
// 2^f is approximated as Tp[f]+Dp[f], and 2^{-f} as Tn[f]+Dn[f]
// Tp stores higher 53 bits, Dp stores (2^f-Tp[f]) rounded to double precision
//
// e^|x|=2^{k+f}*2^r, r=r`+xL*L2EH+|x|*L2EL, |r|<2^{-8}+2^{-14},
// for |x| in [1/8,3*2^8)
// e^{-|x|}=2^{-k-f}*2^{-r}
//
// e^|x| is approximated as 2^k*Tp+2^k*Tp*c1*r(1+c2*r+..+c5*r^4)+2^k*Dp=
// =2^k*Tp+2^k*Tp*P15+2^k*Dp
// e^{-|x|} approximated as 2^{-k}*Tn-2^{-k}*Tn*c1*r(1-c2*r+..+c5*r^4)
//
// For |x| in [1/8, 3*2^7), cosh(x) is formed as
// 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
//
// For |x| in [3*2^7, 3*2^8), (e^|x|)/2 is returned, and
// the result is checked for overflow.
//
// For |x|<1/8, a Taylor polynomial expansion is used (degree 10)
// (error bound for polynomial expansion is below 0.501 ulp)
//
// Special cases:
// cosh(NaN) = quiet NaN, and raise invalid exception
// cosh(INF) = that INF
// cosh(0)=1
// for finite argument, only cosh(0)=1 is exact
// For IEEE double
// cosh(x) overflows
// for x > 710.47586007394386342639336362481117248535156250 = MAXLOG+log(2)
//
/******************************************************************************/
#include <private/bionic_asm.h>
# -- Begin static_func
.text
.align __bionic_asm_align
.type static_func, @function
static_func:
..B1.1:
call ..L2
..L2:
popl %eax
lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
lea static_const_table@GOTOFF(%eax), %eax
ret
.size static_func,.-static_func
# -- End static_func
# -- Begin cosh
ENTRY(cosh)
# parameter 1: 8 + %ebp
..B2.1:
..B2.2:
pushl %ebp
movl %esp, %ebp
subl $104, %esp
movl %ebx, 40(%esp)
call static_func
movl %eax, %ebx
movsd 112(%esp), %xmm0
movsd 4240(%ebx), %xmm3
xorpd %xmm4, %xmm4
movsd 4192(%ebx), %xmm1
movsd 4200(%ebx), %xmm2
movl $32768, %eax
pinsrw $3, %eax, %xmm4
movsd 4096(%ebx), %xmm6
pextrw $3, %xmm0, %ecx
andpd %xmm0, %xmm3
andnpd %xmm0, %xmm4
pshufd $68, %xmm4, %xmm5
andl $32767, %ecx
subl $16320, %ecx
cmpl $200, %ecx
jae .L_2TAG_PACKET_0.0.2
subsd %xmm3, %xmm4
mulsd %xmm1, %xmm3
mulsd %xmm5, %xmm2
cvtsd2si %xmm3, %eax
movapd %xmm3, %xmm7
addsd %xmm6, %xmm3
mulsd %xmm4, %xmm1
xorpd %xmm5, %xmm5
subsd %xmm6, %xmm3
movapd 4112(%ebx), %xmm4
addsd %xmm1, %xmm2
movapd 4128(%ebx), %xmm6
subsd %xmm3, %xmm7
movl $32704, %edx
pinsrw $3, %edx, %xmm5
movapd 4144(%ebx), %xmm1
addsd %xmm7, %xmm2
movl $127, %edx
andl %eax, %edx
addl %edx, %edx
shrl $3, %eax
andl $65520, %eax
addl $16352, %eax
xorpd %xmm0, %xmm0
cmpl $184, %ecx
jae .L_2TAG_PACKET_1.0.2
pshufd $68, %xmm5, %xmm5
pinsrw $3, %eax, %xmm0
pshufd $68, %xmm0, %xmm0
psubw %xmm0, %xmm5
mulpd (%ebx,%edx,8), %xmm0
mulpd 2048(%ebx,%edx,8), %xmm5
pshufd $68, %xmm2, %xmm3
movapd 4160(%ebx), %xmm7
pshufd $68, %xmm2, %xmm2
mulpd %xmm3, %xmm3
mulpd %xmm2, %xmm4
mulpd %xmm2, %xmm6
mulpd 4176(%ebx), %xmm2
mulpd %xmm3, %xmm1
mulpd %xmm3, %xmm7
mulpd %xmm3, %xmm4
mulpd %xmm3, %xmm1
addpd %xmm7, %xmm6
movapd %xmm0, %xmm7
addpd %xmm1, %xmm4
shufpd $0, %xmm5, %xmm7
addpd %xmm5, %xmm0
mulpd %xmm7, %xmm2
addpd %xmm6, %xmm4
subsd %xmm0, %xmm7
mulpd %xmm2, %xmm4
pshufd $238, %xmm0, %xmm6
addsd %xmm5, %xmm7
addpd %xmm2, %xmm4
addsd %xmm6, %xmm7
pshufd $238, %xmm4, %xmm2
addsd %xmm7, %xmm2
addsd %xmm4, %xmm2
addsd %xmm2, %xmm0
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_0.0.2:
addl $16320, %ecx
cmpl $16320, %ecx
ja .L_2TAG_PACKET_3.0.2
cmpl $15952, %ecx
jae .L_2TAG_PACKET_4.0.2
addsd %xmm2, %xmm6
movsd 4248(%ebx), %xmm0
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_1.0.2:
subl $16352, %eax
movl %eax, %ecx
andl $32752, %eax
shrl $1, %eax
andl $65520, %eax
subl %eax, %ecx
addl $16352, %eax
pinsrw $3, %eax, %xmm0
pshufd $68, %xmm0, %xmm0
mulpd (%ebx,%edx,8), %xmm0
pshufd $68, %xmm2, %xmm3
movsd 4160(%ebx), %xmm7
mulsd %xmm3, %xmm3
mulsd %xmm2, %xmm4
mulsd %xmm2, %xmm6
mulsd 4176(%ebx), %xmm2
mulsd %xmm3, %xmm1
mulsd %xmm3, %xmm7
mulsd %xmm3, %xmm4
addl $16368, %ecx
pinsrw $3, %ecx, %xmm5
mulsd %xmm3, %xmm1
addsd %xmm7, %xmm6
addsd %xmm1, %xmm4
mulsd %xmm0, %xmm2
addsd %xmm6, %xmm4
mulsd %xmm2, %xmm4
pshufd $238, %xmm0, %xmm6
addsd %xmm6, %xmm4
addsd %xmm4, %xmm2
addsd %xmm2, %xmm0
mulsd %xmm5, %xmm0
pextrw $3, %xmm0, %eax
andl $32752, %eax
movl $64, %edx
cmpl $32752, %eax
je .L_2TAG_PACKET_5.0.2
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_4.0.2:
movapd 4208(%ebx), %xmm1
mulpd %xmm5, %xmm5
movapd 4224(%ebx), %xmm2
xorpd %xmm3, %xmm3
movapd %xmm5, %xmm0
mulpd %xmm5, %xmm1
movsd 4248(%ebx), %xmm6
mulpd %xmm5, %xmm5
movl $16352, %eax
pinsrw $3, %eax, %xmm3
addpd %xmm2, %xmm1
mulpd %xmm5, %xmm1
pshufd $238, %xmm1, %xmm2
mulsd %xmm1, %xmm5
mulsd %xmm3, %xmm0
addsd %xmm5, %xmm2
addsd %xmm2, %xmm0
addsd %xmm6, %xmm0
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_3.0.2:
cmpl $32752, %ecx
jae .L_2TAG_PACKET_6.0.2
xorpd %xmm0, %xmm0
movl $32736, %eax
pinsrw $3, %eax, %xmm0
mulsd %xmm0, %xmm0
movl $64, %edx
.L_2TAG_PACKET_5.0.2:
movsd %xmm0, (%esp)
movsd 112(%esp), %xmm0
fldl (%esp)
jmp .L_2TAG_PACKET_7.0.2
.L_2TAG_PACKET_6.0.2:
mulsd %xmm0, %xmm0
jmp .L_2TAG_PACKET_2.0.2
.L_2TAG_PACKET_2.0.2:
movsd %xmm0, 24(%esp)
fldl 24(%esp)
.L_2TAG_PACKET_7.0.2:
movl 40(%esp), %ebx
movl %ebp, %esp
popl %ebp
ret
..B2.3:
END(cosh)
# -- End cosh
# Start file scope ASM
.weak coshl
.equ coshl, cosh
# End file scope ASM
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.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
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.long 3212193346
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.long 1053077003
.long 3078135644
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.long 381774870
.long 1062650220
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.long 0
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.type static_const_table,@object
.size static_const_table,4256
.data
.section .note.GNU-stack, ""
# End
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