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Diffstat (limited to 'libm/x86_64/e_log.S')
| -rw-r--r-- | libm/x86_64/e_log.S | 779 |
1 files changed, 779 insertions, 0 deletions
diff --git a/libm/x86_64/e_log.S b/libm/x86_64/e_log.S new file mode 100644 index 0000000..40cb5e2 --- /dev/null +++ b/libm/x86_64/e_log.S @@ -0,0 +1,779 @@ +/* +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 +// --------------------- +// +// x=2^k * mx, mx in [1,2) +// +// Get B~1/mx based on the output of rcpss instruction (B0) +// B = int((B0*2^7+0.5))/2^7 +// +// Reduced argument: r=B*mx-1.0 (computed accurately in high and low parts) +// +// Result: k*log(2) - log(B) + p(r) if |x-1| >= small value (2^-6) and +// p(r) is a degree 7 polynomial +// -log(B) read from data table (high, low parts) +// Result is formed from high and low parts +// +// Special cases: +// log(NaN) = quiet NaN, and raise invalid exception +// log(+INF) = that INF +// log(0) = -INF with divide-by-zero exception raised +// log(1) = +0 +// log(x) = NaN with invalid exception raised if x < -0, including -INF +// +/******************************************************************************/ + +#include <private/bionic_asm.h> +# -- Begin log +ENTRY(log) +# parameter 1: %xmm0 +..B1.1: +..___tag_value_log.1: + subq $24, %rsp +..___tag_value_log.3: + movsd %xmm0, (%rsp) +..B1.2: + movq $0x3ff0000000000000, %rax + movd %rax, %xmm2 + movq $0x77f0000000000000, %rdx + movd %rdx, %xmm3 + movl $32768, %ecx + movd %rcx, %xmm4 + movq $0xffffe00000000000, %r8 + movd %r8, %xmm5 + movq %xmm0, %xmm1 + pextrw $3, %xmm0, %eax + orpd %xmm2, %xmm0 + movl $16352, %ecx + psrlq $27, %xmm0 + lea L_tbl(%rip), %r11 + psrld $2, %xmm0 + rcpps %xmm0, %xmm0 + psllq $12, %xmm1 + pshufd $228, %xmm5, %xmm6 + psrlq $12, %xmm1 + subl $16, %eax + cmpl $32736, %eax + jae .L_2TAG_PACKET_0.0.2 +.L_2TAG_PACKET_1.0.2: + paddd %xmm4, %xmm0 + orpd %xmm3, %xmm1 + movd %xmm0, %edx + psllq $29, %xmm0 + andpd %xmm1, %xmm5 + andpd %xmm6, %xmm0 + subsd %xmm5, %xmm1 + mulpd %xmm0, %xmm5 + andl $32752, %eax + subl %ecx, %eax + cvtsi2sd %eax, %xmm7 + mulsd %xmm0, %xmm1 + movq log2(%rip), %xmm6 + movapd coeff(%rip), %xmm3 + subsd %xmm2, %xmm5 + andl $16711680, %edx + shrl $12, %edx + movapd (%r11,%rdx), %xmm0 + movapd 16+coeff(%rip), %xmm4 + addsd %xmm5, %xmm1 + movapd 32+coeff(%rip), %xmm2 + mulsd %xmm7, %xmm6 + movddup %xmm1, %xmm5 + mulsd 8+log2(%rip), %xmm7 + mulsd %xmm1, %xmm3 + addsd %xmm6, %xmm0 + mulpd %xmm5, %xmm4 + mulpd %xmm5, %xmm5 + movddup %xmm0, %xmm6 + addsd %xmm1, %xmm0 + addpd %xmm2, %xmm4 + mulpd %xmm5, %xmm3 + subsd %xmm0, %xmm6 + mulsd %xmm1, %xmm4 + pshufd $238, %xmm0, %xmm2 + addsd %xmm6, %xmm1 + mulsd %xmm5, %xmm5 + addsd %xmm2, %xmm7 + addpd %xmm3, %xmm4 + addsd %xmm7, %xmm1 + mulpd %xmm5, %xmm4 + addsd %xmm4, %xmm1 + pshufd $238, %xmm4, %xmm5 + addsd %xmm5, %xmm1 + addsd %xmm1, %xmm0 + jmp ..B1.5 +.L_2TAG_PACKET_0.0.2: + movq (%rsp), %xmm0 + movq (%rsp), %xmm1 + addl $16, %eax + cmpl $32768, %eax + jae .L_2TAG_PACKET_2.0.2 + cmpl $16, %eax + jb .L_2TAG_PACKET_3.0.2 +.L_2TAG_PACKET_4.0.2: + addsd %xmm0, %xmm0 + jmp ..B1.5 +.L_2TAG_PACKET_5.0.2: + ja .L_2TAG_PACKET_4.0.2 + cmpl $0, %edx + ja .L_2TAG_PACKET_4.0.2 + jmp .L_2TAG_PACKET_6.0.2 +.L_2TAG_PACKET_3.0.2: + xorpd %xmm1, %xmm1 + addsd %xmm0, %xmm1 + movd %xmm1, %edx + psrlq $32, %xmm1 + movd %xmm1, %ecx + orl %ecx, %edx + cmpl $0, %edx + je .L_2TAG_PACKET_7.0.2 + xorpd %xmm1, %xmm1 + movl $18416, %eax + pinsrw $3, %eax, %xmm1 + mulsd %xmm1, %xmm0 + movq %xmm0, %xmm1 + pextrw $3, %xmm0, %eax + orpd %xmm2, %xmm0 + psrlq $27, %xmm0 + movl $18416, %ecx + psrld $2, %xmm0 + rcpps %xmm0, %xmm0 + psllq $12, %xmm1 + pshufd $228, %xmm5, %xmm6 + psrlq $12, %xmm1 + jmp .L_2TAG_PACKET_1.0.2 +.L_2TAG_PACKET_2.0.2: + movd %xmm1, %edx + psrlq $32, %xmm1 + movd %xmm1, %ecx + addl %ecx, %ecx + cmpl $-2097152, %ecx + jae .L_2TAG_PACKET_5.0.2 + orl %ecx, %edx + cmpl $0, %edx + je .L_2TAG_PACKET_7.0.2 +.L_2TAG_PACKET_6.0.2: + xorpd %xmm1, %xmm1 + xorpd %xmm0, %xmm0 + movl $32752, %eax + pinsrw $3, %eax, %xmm1 + mulsd %xmm1, %xmm0 + movl $3, 16(%rsp) + jmp .L_2TAG_PACKET_8.0.2 +.L_2TAG_PACKET_7.0.2: + xorpd %xmm1, %xmm1 + xorpd %xmm0, %xmm0 + movl $49136, %eax + pinsrw $3, %eax, %xmm0 + divsd %xmm1, %xmm0 + movl $2, 16(%rsp) +.L_2TAG_PACKET_8.0.2: + movq %xmm0, 8(%rsp) +..B1.3: + movq 8(%rsp), %xmm0 +.L_2TAG_PACKET_9.0.2: +..B1.5: + addq $24, %rsp +..___tag_value_log.4: + ret +..___tag_value_log.5: +END(log) +# -- End log + .section .rodata, "a" + .align 16 + .align 16 +L_tbl: + .long 4277811200 + .long 1072049730 + .long 2479318832 + .long 1026487127 + .long 2854492160 + .long 1072033410 + .long 215631550 + .long 1025638968 + .long 1547061248 + .long 1072017216 + .long 2886781435 + .long 1026423395 + .long 649825280 + .long 1072001146 + .long 4281533405 + .long 1024038923 + .long 646346752 + .long 1071985198 + .long 1562735921 + .long 1023790276 + .long 2203734016 + .long 1071969370 + .long 1838397691 + .long 3173936209 + .long 1872169984 + .long 1071953661 + .long 3981202460 + .long 1022325013 + .long 669557760 + .long 1071938069 + .long 4182597802 + .long 3173174122 + .long 4076413952 + .long 1071922591 + .long 1209029111 + .long 3170736207 + .long 556125184 + .long 1071907228 + .long 821086028 + .long 3173437049 + .long 204914688 + .long 1071891976 + .long 2097025986 + .long 3171071798 + .long 387545088 + .long 1071876834 + .long 3142936996 + .long 3173092218 + .long 2912783360 + .long 1071861800 + .long 2502420140 + .long 1024505919 + .long 1144260608 + .long 1071846874 + .long 3315658140 + .long 3173469843 + .long 1471209472 + .long 1071832053 + .long 129621009 + .long 3172443877 + .long 1829683200 + .long 1071817336 + .long 3885467693 + .long 1025535275 + .long 288676864 + .long 1071802722 + .long 86139472 + .long 3171639793 + .long 3636378624 + .long 1071788208 + .long 1850238587 + .long 1024654342 + .long 1606817792 + .long 1071773795 + .long 3388899795 + .long 3173675586 + .long 1236164608 + .long 1071759480 + .long 3983599207 + .long 1020046558 + .long 1089616896 + .long 1071745262 + .long 4171974224 + .long 1024773198 + .long 4143093760 + .long 1071731139 + .long 2727587401 + .long 3173965207 + .long 600267776 + .long 1071717112 + .long 3147685042 + .long 3173353031 + .long 2249313280 + .long 1071703177 + .long 125835074 + .long 1025255832 + .long 3805303808 + .long 1071689334 + .long 2289991207 + .long 1025460331 + .long 87278592 + .long 1071675583 + .long 1106114045 + .long 1025933602 + .long 3195405312 + .long 1071661920 + .long 3885316576 + .long 3171206239 + .long 3853649920 + .long 1071648346 + .long 2977069852 + .long 3171236771 + .long 2944026624 + .long 1071625048 + .long 1008093493 + .long 1023444474 + .long 3993180160 + .long 1071598247 + .long 1862355595 + .long 1024642533 + .long 1454641152 + .long 1071571617 + .long 1514603089 + .long 1026500596 + .long 3286085632 + .long 1071545154 + .long 1400028424 + .long 3173279056 + .long 438773760 + .long 1071518858 + .long 120727864 + .long 3172148914 + .long 1212979200 + .long 1071492725 + .long 1625055594 + .long 3172901933 + .long 1189017600 + .long 1071466754 + .long 3920062376 + .long 1025727407 + .long 403064832 + .long 1071440943 + .long 1053271728 + .long 3171391427 + .long 3343210496 + .long 1071415289 + .long 3243395502 + .long 3173627613 + .long 1765777408 + .long 1071389792 + .long 2145968512 + .long 1026354304 + .long 461430784 + .long 1071364449 + .long 4094322285 + .long 1026021467 + .long 71706624 + .long 1071339258 + .long 763632021 + .long 1024496933 + .long 1380503552 + .long 1071314217 + .long 1383547992 + .long 3173088453 + .long 1015732224 + .long 1071289325 + .long 3198646877 + .long 1025390322 + .long 35977216 + .long 1071264580 + .long 2141026805 + .long 1025754693 + .long 3927306240 + .long 1071239979 + .long 282116272 + .long 3173394334 + .long 1125341184 + .long 1071215523 + .long 2768427504 + .long 3172279059 + .long 1666971648 + .long 1071191208 + .long 786837629 + .long 3172427445 + .long 2827694080 + .long 1071167033 + .long 3857122416 + .long 3173014241 + .long 2003683328 + .long 1071142997 + .long 859010954 + .long 1026545007 + .long 1004017664 + .long 1071119098 + .long 3356644970 + .long 3173458064 + .long 1753020416 + .long 1071095334 + .long 788338552 + .long 1026157693 + .long 1992718336 + .long 1071071704 + .long 1239179443 + .long 1026394889 + .long 3870234624 + .long 1071048206 + .long 2082614663 + .long 1024926053 + .long 1050437632 + .long 1071024840 + .long 660007840 + .long 1025548499 + .long 188395520 + .long 1071001603 + .long 3878792704 + .long 3173889571 + .long 3747176448 + .long 1070978493 + .long 144991708 + .long 3171552042 + .long 1405669376 + .long 1070955511 + .long 3999088879 + .long 1025486317 + .long 121151488 + .long 1070932654 + .long 2170865497 + .long 1026473584 + .long 2652319744 + .long 1070909920 + .long 453695652 + .long 3173916809 + .long 3262236672 + .long 1070887309 + .long 157800053 + .long 3173984206 + .long 601221120 + .long 1070864820 + .long 3968917661 + .long 1023992886 + .long 1999843328 + .long 1070842450 + .long 3053895004 + .long 1024998228 + .long 1992167424 + .long 1070820199 + .long 2968614856 + .long 1024552653 + .long 3788726272 + .long 1070798065 + .long 3542170808 + .long 3173573242 + .long 2094829568 + .long 1070776048 + .long 1246758132 + .long 1026202874 + .long 288675840 + .long 1070754146 + .long 3747328950 + .long 1026331585 + .long 1829681152 + .long 1070732357 + .long 3125197546 + .long 1024100318 + .long 1666869248 + .long 1070710681 + .long 1363656119 + .long 1026336493 + .long 3417110528 + .long 1070689116 + .long 4154791553 + .long 1026267853 + .long 2183653376 + .long 1070667662 + .long 1671819292 + .long 3173785870 + .long 1734434816 + .long 1070646317 + .long 373091049 + .long 1025972363 + .long 1615681536 + .long 1070625080 + .long 384650897 + .long 1022926043 + .long 1445382144 + .long 1070603950 + .long 344320330 + .long 3172397196 + .long 1823715328 + .long 1070569756 + .long 3389841200 + .long 1025231852 + .long 3839688704 + .long 1070527917 + .long 1706790417 + .long 3167363349 + .long 4293332992 + .long 1070486286 + .long 1614935088 + .long 1019351591 + .long 2966720512 + .long 1070444861 + .long 4145393717 + .long 3173711658 + .long 4066729984 + .long 1070403639 + .long 1974925028 + .long 3171437182 + .long 3337621504 + .long 1070362619 + .long 3314953170 + .long 3169971314 + .long 943448064 + .long 1070321799 + .long 1498682038 + .long 3173862340 + .long 1465634816 + .long 1070281176 + .long 1319952810 + .long 3171693965 + .long 1015734272 + .long 1070240749 + .long 1347821929 + .long 3173544515 + .long 118001664 + .long 1070200516 + .long 1751482746 + .long 1026134093 + .long 3707174912 + .long 1070160474 + .long 1486946159 + .long 1023930920 + .long 3946381312 + .long 1070120623 + .long 2867408081 + .long 3171368276 + .long 1699848192 + .long 1070080961 + .long 2590187139 + .long 1025379803 + .long 2235846656 + .long 1070041485 + .long 1888568069 + .long 3172754960 + .long 2339729408 + .long 1070002194 + .long 3852214753 + .long 3173323149 + .long 3196850176 + .long 1069963086 + .long 742141560 + .long 1025101707 + .long 1800683520 + .long 1069924160 + .long 3949500444 + .long 3172102179 + .long 3835801600 + .long 1069885413 + .long 3848895943 + .long 1025913832 + .long 2201202688 + .long 1069846845 + .long 1425913464 + .long 1025868665 + .long 2778279936 + .long 1069808453 + .long 2120889677 + .long 3173831128 + .long 2954203136 + .long 1069770236 + .long 592147081 + .long 1019621288 + .long 210141184 + .long 1069732193 + .long 3414275233 + .long 1023647084 + .long 709476352 + .long 1069694321 + .long 2413027164 + .long 1024462115 + .long 2116284416 + .long 1069656619 + .long 1144559924 + .long 1026336654 + .long 2183651328 + .long 1069619086 + .long 3459057650 + .long 1025634168 + .long 3047047168 + .long 1069581720 + .long 1879674924 + .long 3173508573 + .long 970711040 + .long 1069541521 + .long 1335954173 + .long 3173332182 + .long 2198478848 + .long 1069467449 + .long 2951103968 + .long 3173892200 + .long 1669611520 + .long 1069393703 + .long 531044147 + .long 1025149248 + .long 29114368 + .long 1069320280 + .long 3327831251 + .long 1025918673 + .long 2376949760 + .long 1069247176 + .long 737634533 + .long 3172176000 + .long 1085390848 + .long 1069174390 + .long 3108243400 + .long 3171828406 + .long 1566130176 + .long 1069101918 + .long 985483226 + .long 1025708380 + .long 792780800 + .long 1069029758 + .long 4184866295 + .long 1024426204 + .long 183156736 + .long 1068957907 + .long 2845699378 + .long 1022107277 + .long 1301782528 + .long 1068886362 + .long 1012735262 + .long 3173804294 + .long 1562411008 + .long 1068815121 + .long 2197086703 + .long 3170187813 + .long 2815549440 + .long 1068744181 + .long 2782613207 + .long 1026345054 + .long 2756124672 + .long 1068673540 + .long 2929486205 + .long 3173037800 + .long 3511050240 + .long 1068603195 + .long 1443733147 + .long 3173331549 + .long 3047047168 + .long 1068533144 + .long 1879674924 + .long 3172459997 + .long 3221667840 + .long 1068427825 + .long 1338588027 + .long 3171815742 + .long 3453861888 + .long 1068288883 + .long 1205348359 + .long 3172624626 + .long 3506110464 + .long 1068150514 + .long 893105198 + .long 1025571866 + .long 346013696 + .long 1068012714 + .long 3495569021 + .long 3172563349 + .long 4074029056 + .long 1067875476 + .long 3961106338 + .long 3171065595 + .long 3559784448 + .long 1067738798 + .long 1975385384 + .long 3173783155 + .long 797769728 + .long 1067602675 + .long 3760305787 + .long 1026047642 + .long 2313633792 + .long 1067467101 + .long 1559353171 + .long 1023480256 + .long 3960766464 + .long 1067213778 + .long 1067365107 + .long 1025865926 + .long 684261376 + .long 1066944805 + .long 844762164 + .long 3173687482 + .long 630718464 + .long 1066676905 + .long 2458269694 + .long 1024033081 + .long 1486061568 + .long 1066410070 + .long 115537874 + .long 3173243995 + .long 2743664640 + .long 1065886792 + .long 3665098304 + .long 3173471607 + .long 1971912704 + .long 1065357333 + .long 2577214440 + .long 3171993451 + .long 1498939392 + .long 1064306693 + .long 3409036923 + .long 1025599151 + .long 0 + .long 0 + .long 0 + .long 2147483648 + .type L_tbl,@object + .size L_tbl,2064 + .align 16 +log2: + .long 4277811200 + .long 1067855426 + .long 2479318832 + .long 1022292823 + .type log2,@object + .size log2,16 + .align 16 +coeff: + .long 2454267026 + .long 1069697316 + .long 0 + .long 3218079744 + .long 1030730101 + .long 3217380702 + .long 1431655765 + .long 1070945621 + .long 2576980378 + .long 1070176665 + .long 0 + .long 3219128320 + .type coeff,@object + .size coeff,48 + .data + .section .note.GNU-stack, "" +// -- Begin DWARF2 SEGMENT .eh_frame + .section .eh_frame,"a",@progbits +.eh_frame_seg: + .align 1 + .4byte 0x00000014 + .8byte 0x00527a0100000000 + .8byte 0x08070c1b01107801 + .4byte 0x00000190 + .4byte 0x0000001c + .4byte 0x0000001c + .4byte ..___tag_value_log.1-. + .4byte ..___tag_value_log.5-..___tag_value_log.1 + .2byte 0x0400 + .4byte ..___tag_value_log.3-..___tag_value_log.1 + .2byte 0x200e + .byte 0x04 + .4byte ..___tag_value_log.4-..___tag_value_log.3 + .2byte 0x080e + .byte 0x00 +# End |