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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
// ---------------------
//
// Description:
// Let K = 64 (table size).
//
// Four sub-domains:
// 1. |x| < 1/(2*K)
// expm1(x) ~ P(x)
// 2. 1/(2*K) <= |x| <= 56*log(2)
// x x/log(2) n
// e - 1 = 2 = 2 * T[j] * (1 + P(y)) - 1
// 3. 56*log(2) < x < MAX_LOG
// x x x/log(2) n
// e - 1 ~ e = 2 = 2 * T[j] * (1 + P(y))
// 4. x < -56*log(2)
// x x
// e - 1 = -1 + e ~ -1
// where
// x = m*log(2)/K + y, y in [-log(2)/K..log(2)/K]
// m = n*K + j, m,n,j - signed integer, j in [-K/2..K/2]
// j/K
// values of 2 are tabulated as T[j] = T_hi[j] ( 1 + T_lo[j]).
//
// P(y) is a minimax polynomial approximation of exp(x)-1
// on small interval [-log(2)/K..log(2)/K] (were calculated by Maple V).
//
// In case 3, to avoid problems with arithmetic overflow and underflow,
// n n1 n2
// value of 2 is safely computed as 2 * 2 where n1 in [-BIAS/2..BIAS/2]
// and BIAS is a value of exponent bias.
//
// Special cases:
// expm1(NaN) is NaN
// expm1(+INF) is +INF
// expm1(-INF) is -1
// expm1(x) is x for subnormals
// for finite argument, only expm1(0)=0 is exact.
// For IEEE double
// if x > 709.782712893383973096 then expm1(x) overflow
//
/******************************************************************************/
#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 expm1
ENTRY(expm1)
# parameter 1: 8 + %ebp
..B2.1:
..B2.2:
pushl %ebp
movl %esp, %ebp
subl $120, %esp
movl %ebx, 64(%esp)
call static_func
movl %eax, %ebx
movsd 128(%esp), %xmm0
unpcklpd %xmm0, %xmm0
movapd 64(%ebx), %xmm1
movapd 48(%ebx), %xmm6
movapd 80(%ebx), %xmm2
movapd 96(%ebx), %xmm3
pextrw $3, %xmm0, %eax
andl $32767, %eax
movl $16527, %edx
subl %eax, %edx
subl $16304, %eax
orl %eax, %edx
cmpl $-2147483648, %edx
jae .L_2TAG_PACKET_0.0.2
mulpd %xmm0, %xmm1
addpd %xmm6, %xmm1
movapd %xmm1, %xmm7
subpd %xmm6, %xmm1
mulpd %xmm1, %xmm2
movapd 112(%ebx), %xmm4
mulpd %xmm1, %xmm3
movapd 128(%ebx), %xmm5
subpd %xmm2, %xmm0
movd %xmm7, %eax
movl %eax, %ecx
andl $63, %ecx
shll $4, %ecx
sarl $6, %eax
movl %eax, %edx
subpd %xmm3, %xmm0
movapd 160(%ebx,%ecx), %xmm2
movsd 144(%ebx), %xmm3
mulpd %xmm0, %xmm4
movapd %xmm0, %xmm1
mulpd %xmm0, %xmm0
mulsd %xmm0, %xmm3
addpd %xmm4, %xmm5
mulsd %xmm0, %xmm0
movapd %xmm2, %xmm4
unpckhpd %xmm2, %xmm2
movdqa 16(%ebx), %xmm6
pand %xmm6, %xmm7
movdqa 32(%ebx), %xmm6
paddq %xmm6, %xmm7
psllq $46, %xmm7
mulsd %xmm0, %xmm3
mulpd %xmm5, %xmm0
addl $894, %edx
cmpl $1916, %edx
ja .L_2TAG_PACKET_1.0.2
addsd %xmm3, %xmm0
xorpd %xmm3, %xmm3
movl $16368, %eax
pinsrw $3, %eax, %xmm3
orpd %xmm7, %xmm2
mulsd %xmm4, %xmm7
movapd %xmm3, %xmm6
addsd %xmm1, %xmm3
pextrw $3, %xmm2, %edx
pshufd $238, %xmm0, %xmm5
psrlq $38, %xmm3
psllq $38, %xmm3
movapd %xmm2, %xmm4
subsd %xmm3, %xmm6
addsd %xmm5, %xmm0
addsd %xmm6, %xmm1
addsd %xmm7, %xmm4
mulsd %xmm3, %xmm7
mulsd %xmm2, %xmm3
xorpd %xmm5, %xmm5
movl $16368, %eax
pinsrw $3, %eax, %xmm5
addsd %xmm1, %xmm0
movl $17184, %ecx
subl %edx, %ecx
subl $16256, %edx
orl %edx, %ecx
jl .L_2TAG_PACKET_2.0.2
mulsd %xmm4, %xmm0
subsd %xmm5, %xmm3
addsd %xmm7, %xmm0
addsd %xmm3, %xmm0
.L_2TAG_PACKET_3.0.2:
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_2.0.2:
cmpl $0, %edx
jl .L_2TAG_PACKET_5.0.2
mulsd %xmm4, %xmm0
subsd %xmm5, %xmm7
addsd %xmm7, %xmm0
addsd %xmm3, %xmm0
jmp .L_2TAG_PACKET_3.0.2
.L_2TAG_PACKET_5.0.2:
mulsd %xmm4, %xmm0
addsd %xmm7, %xmm0
addsd %xmm3, %xmm0
subsd %xmm5, %xmm0
jmp .L_2TAG_PACKET_3.0.2
.L_2TAG_PACKET_1.0.2:
movl 132(%esp), %ecx
addsd %xmm0, %xmm1
unpckhpd %xmm0, %xmm0
addsd %xmm1, %xmm0
cmpl $0, %ecx
jl .L_2TAG_PACKET_6.0.2
fstcw 24(%esp)
movzwl 24(%esp), %edx
orl $768, %edx
movw %dx, 28(%esp)
fldcw 28(%esp)
movl %eax, %edx
sarl $1, %eax
subl %eax, %edx
movdqa (%ebx), %xmm6
pandn %xmm2, %xmm6
addl $1023, %eax
movd %eax, %xmm3
psllq $52, %xmm3
orpd %xmm3, %xmm6
mulsd %xmm3, %xmm4
movsd %xmm0, 8(%esp)
fldl 8(%esp)
movsd %xmm6, 16(%esp)
fldl 16(%esp)
movsd %xmm4, 16(%esp)
fldl 16(%esp)
addl $1023, %edx
movd %edx, %xmm4
psllq $52, %xmm4
faddp %st, %st(1)
fmul %st, %st(1)
faddp %st, %st(1)
movsd %xmm4, 8(%esp)
fldl 8(%esp)
fmulp %st, %st(1)
fstpl 8(%esp)
movsd 8(%esp), %xmm0
fldcw 24(%esp)
pextrw $3, %xmm0, %ecx
andl $32752, %ecx
cmpl $32752, %ecx
jae .L_2TAG_PACKET_7.0.2
jmp .L_2TAG_PACKET_4.0.2
cmpl $-2147483648, %ecx
jb .L_2TAG_PACKET_7.0.2
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_7.0.2:
movl $41, %edx
.L_2TAG_PACKET_8.0.2:
movsd %xmm0, (%esp)
movsd 128(%esp), %xmm0
fldl (%esp)
jmp .L_2TAG_PACKET_9.0.2
.L_2TAG_PACKET_10.0.2:
cmpl $2146435072, %eax
jae .L_2TAG_PACKET_11.0.2
movsd 1272(%ebx), %xmm0
mulsd %xmm0, %xmm0
movl $41, %edx
jmp .L_2TAG_PACKET_8.0.2
.L_2TAG_PACKET_11.0.2:
movl 132(%esp), %eax
movl 128(%esp), %edx
movl %eax, %ecx
andl $2147483647, %eax
cmpl $2146435072, %eax
ja .L_2TAG_PACKET_12.0.2
cmpl $0, %edx
jne .L_2TAG_PACKET_12.0.2
cmpl $0, %ecx
jl .L_2TAG_PACKET_13.0.2
movsd 1256(%ebx), %xmm0
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_13.0.2:
jmp .L_2TAG_PACKET_6.0.2
.L_2TAG_PACKET_12.0.2:
movsd 128(%esp), %xmm0
addsd %xmm0, %xmm0
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_14.0.2:
addl $16304, %eax
cmpl $15504, %eax
jb .L_2TAG_PACKET_15.0.2
movapd 1184(%ebx), %xmm2
pshufd $68, %xmm0, %xmm1
movapd 1200(%ebx), %xmm3
movapd 1216(%ebx), %xmm4
movsd 1232(%ebx), %xmm5
mulsd %xmm1, %xmm1
xorpd %xmm6, %xmm6
movl $16352, %eax
pinsrw $3, %eax, %xmm6
mulpd %xmm0, %xmm2
xorpd %xmm7, %xmm7
movl $16368, %edx
pinsrw $3, %edx, %xmm7
addpd %xmm3, %xmm2
mulsd %xmm1, %xmm5
pshufd $228, %xmm1, %xmm3
mulpd %xmm1, %xmm1
mulsd %xmm0, %xmm6
mulpd %xmm0, %xmm2
addpd %xmm4, %xmm2
movapd %xmm7, %xmm4
addsd %xmm6, %xmm7
mulpd %xmm3, %xmm1
psrlq $27, %xmm7
psllq $27, %xmm7
movsd 1288(%ebx), %xmm3
subsd %xmm7, %xmm4
mulpd %xmm1, %xmm2
addsd %xmm4, %xmm6
pshufd $238, %xmm2, %xmm1
addsd %xmm2, %xmm6
andpd %xmm0, %xmm3
movapd %xmm0, %xmm4
addsd %xmm6, %xmm1
subsd %xmm3, %xmm0
addsd %xmm5, %xmm1
mulsd %xmm7, %xmm3
mulsd %xmm7, %xmm0
mulsd %xmm1, %xmm4
addsd %xmm4, %xmm0
addsd %xmm3, %xmm0
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_15.0.2:
cmpl $16, %eax
jae .L_2TAG_PACKET_3.0.2
movapd %xmm0, %xmm2
movd %xmm0, %eax
psrlq $31, %xmm2
movd %xmm2, %ecx
orl %ecx, %eax
je .L_2TAG_PACKET_3.0.2
movl $16, %edx
xorpd %xmm1, %xmm1
pinsrw $3, %edx, %xmm1
mulsd %xmm1, %xmm1
movl $42, %edx
jmp .L_2TAG_PACKET_8.0.2
.L_2TAG_PACKET_0.0.2:
cmpl $0, %eax
jl .L_2TAG_PACKET_14.0.2
movl 132(%esp), %eax
cmpl $1083179008, %eax
jge .L_2TAG_PACKET_10.0.2
cmpl $-1048576, %eax
jae .L_2TAG_PACKET_11.0.2
.L_2TAG_PACKET_6.0.2:
xorpd %xmm0, %xmm0
movl $49136, %eax
pinsrw $3, %eax, %xmm0
jmp .L_2TAG_PACKET_4.0.2
.L_2TAG_PACKET_4.0.2:
movsd %xmm0, 48(%esp)
fldl 48(%esp)
.L_2TAG_PACKET_9.0.2:
movl 64(%esp), %ebx
movl %ebp, %esp
popl %ebp
ret
..B2.3:
END(expm1)
# -- End expm1
# Start file scope ASM
ALIAS_SYMBOL(expm1l, expm1);
# End file scope ASM
.section .rodata, "a"
.align 16
.align 16
static_const_table:
.long 0
.long 4293918720
.long 0
.long 4293918720
.long 4294967232
.long 0
.long 4294967232
.long 0
.long 65472
.long 0
.long 65472
.long 0
.long 0
.long 1127743488
.long 0
.long 1127743488
.long 1697350398
.long 1079448903
.long 1697350398
.long 1079448903
.long 4277796864
.long 1065758274
.long 4277796864
.long 1065758274
.long 3164486458
.long 1025308570
.long 3164486458
.long 1025308570
.long 1963358694
.long 1065423121
.long 1431655765
.long 1069897045
.long 1431655765
.long 1067799893
.long 0
.long 1071644672
.long 381774871
.long 1062650220
.long 381774871
.long 1062650220
.long 0
.long 0
.long 0
.long 0
.long 1000070955
.long 1042145304
.long 1040187392
.long 11418
.long 988267849
.long 1039500660
.long 3539992576
.long 22960
.long 36755401
.long 1042114290
.long 402653184
.long 34629
.long 3634769483
.long 1042178627
.long 1820327936
.long 46424
.long 2155991225
.long 1041560680
.long 847249408
.long 58348
.long 2766913307
.long 1039293264
.long 3489660928
.long 70401
.long 3651174602
.long 1040488175
.long 2927624192
.long 82586
.long 3073892131
.long 1042240606
.long 1006632960
.long 94904
.long 1328391742
.long 1042019037
.long 3942645760
.long 107355
.long 2650893825
.long 1041903210
.long 822083584
.long 119943
.long 2397289153
.long 1041802037
.long 2281701376
.long 132667
.long 430997175
.long 1042110606
.long 1845493760
.long 145530
.long 1230936525
.long 1041801015
.long 1702887424
.long 158533
.long 740675935
.long 1040178913
.long 4110417920
.long 171677
.long 3489810261
.long 1041825986
.long 2793406464
.long 184965
.long 2532600530
.long 1040767882
.long 167772160
.long 198398
.long 3542557060
.long 1041827263
.long 2986344448
.long 211976
.long 1401563777
.long 1041061093
.long 922746880
.long 225703
.long 3129406026
.long 1041852413
.long 880803840
.long 239579
.long 900993572
.long 1039283234
.long 1275068416
.long 253606
.long 2115029358
.long 1042140042
.long 562036736
.long 267786
.long 1086643152
.long 1041785419
.long 1610612736
.long 282120
.long 82864366
.long 1041256244
.long 3045064704
.long 296610
.long 2392968152
.long 1040913683
.long 3573547008
.long 311258
.long 2905856183
.long 1040002214
.long 1988100096
.long 326066
.long 3742008261
.long 1040011137
.long 1451229184
.long 341035
.long 863393794
.long 1040880621
.long 914358272
.long 356167
.long 1446136837
.long 1041372426
.long 3707764736
.long 371463
.long 927855201
.long 1040617636
.long 360710144
.long 386927
.long 1492679939
.long 1041050306
.long 2952790016
.long 402558
.long 608827001
.long 1041582217
.long 2181038080
.long 418360
.long 606260204
.long 1042271987
.long 1711276032
.long 434334
.long 3163044019
.long 1041843851
.long 1006632960
.long 450482
.long 4148747325
.long 1041962972
.long 3900702720
.long 466805
.long 802924201
.long 1041275378
.long 1442840576
.long 483307
.long 3052749833
.long 1041940577
.long 1937768448
.long 499988
.long 2216116399
.long 1041486744
.long 914358272
.long 516851
.long 2729697836
.long 1041445764
.long 2566914048
.long 533897
.long 540608356
.long 1041310907
.long 2600468480
.long 551129
.long 2916344493
.long 1040535661
.long 1107296256
.long 568549
.long 731391814
.long 1039497014
.long 2566914048
.long 586158
.long 1024722704
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.type static_const_table,@object
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.data
.section .note.GNU-stack, "",@progbits
# End
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