| /* |
| 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 |
