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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
| .long 1041461625
| .long 2961178624
| .long 603959
| .long 3806831748
| .long 1041732499
| .long 2675965952
| .long 621954
| .long 238953304
| .long 1040316488
| .long 2189426688
| .long 640145
| .long 749123235
| .long 1041725785
| .long 2063597568
| .long 658534
| .long 1168187977
| .long 1041175214
| .long 2986344448
| .long 677123
| .long 3506096399
| .long 1042186095
| .long 1426063360
| .long 695915
| .long 1470221620
| .long 1041675499
| .long 2566914048
| .long 714911
| .long 3182425146
| .long 1041483134
| .long 3087007744
| .long 734114
| .long 3131698208
| .long 1042208657
| .long 4068474880
| .long 753526
| .long 2300504125
| .long 1041428596
| .long 2415919104
| .long 773150
| .long 2290297931
| .long 1037388400
| .long 3716153344
| .long 792987
| .long 3532148223
| .long 1041626194
| .long 771751936
| .long 813041
| .long 1161884404
| .long 1042015258
| .long 3699376128
| .long 833312
| .long 876383176
| .long 1037968878
| .long 1241513984
| .long 853805
| .long 3379986796
| .long 1042213153
| .long 3699376128
| .long 874520
| .long 1545797737
| .long 1041681569
| .long 58720256
| .long 895462
| .long 2925146801
| .long 1042212567
| .long 855638016
| .long 916631
| .long 1316627971
| .long 1038516204
| .long 3883925504
| .long 938030
| .long 3267869137
| .long 1040337004
| .long 2726297600
| .long 959663
| .long 3720868999
| .long 1041782409
| .long 3992977408
| .long 981531
| .long 433316142
| .long 1041994064
| .long 1526726656
| .long 1003638
| .long 781232103
| .long 1040093400
| .long 2172649472
| .long 1025985
| .long 2773927732
| .long 1053236707
| .long 381774871
| .long 1062650220
| .long 379653899
| .long 1056571845
| .long 286331153
| .long 1065423121
| .long 436314138
| .long 1059717536
| .long 1431655765
| .long 1067799893
| .long 1431655765
| .long 1069897045
| .long 0
| .long 1071644672
| .long 0
| .long 1072693248
| .long 0
| .long 2146435072
| .long 0
| .long 0
| .long 4294967295
| .long 2146435071
| .long 0
| .long 1048576
| .long 4227858432
| .long 4294967295
| .type static_const_table,@object
| .size static_const_table,1296
| .data
| .section .note.GNU-stack, ""
| # End
|
|
