Add the optimized implementation of 18 math functions for x86 and x86_64 respectively
Change-Id: I31bf601448a9427f825517f3a0ff24de47f49bfa
Signed-off-by: Jingwei Zhang <jingwei.zhang@intel.com>
Signed-off-by: Mingwei Shi <mingwei.shi@intel.com>
diff --git a/libm/x86_64/s_expm1.S b/libm/x86_64/s_expm1.S
new file mode 100644
index 0000000..9da1d9d
--- /dev/null
+++ b/libm/x86_64/s_expm1.S
@@ -0,0 +1,727 @@
+/*
+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 expm1
+ENTRY(expm1)
+# parameter 1: %xmm0
+..B1.1:
+..___tag_value_expm1.1:
+ subq $56, %rsp
+..___tag_value_expm1.3:
+ movsd %xmm0, 32(%rsp)
+..B1.2:
+ unpcklpd %xmm0, %xmm0
+ movapd cv(%rip), %xmm1
+ movapd Shifter(%rip), %xmm6
+ movapd 16+cv(%rip), %xmm2
+ movapd 32+cv(%rip), %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 48+cv(%rip), %xmm4
+ mulpd %xmm1, %xmm3
+ movapd 64+cv(%rip), %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
+ lea Tbl_addr(%rip), %r11
+ movapd (%rcx,%r11), %xmm2
+ movq 80+cv(%rip), %xmm3
+ mulpd %xmm0, %xmm4
+ movapd %xmm0, %xmm1
+ mulpd %xmm0, %xmm0
+ mulsd %xmm0, %xmm3
+ addpd %xmm4, %xmm5
+ mulsd %xmm0, %xmm0
+ movq %xmm2, %xmm4
+ unpckhpd %xmm2, %xmm2
+ movdqa mmask(%rip), %xmm6
+ pand %xmm6, %xmm7
+ movdqa bias(%rip), %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
+ movq %xmm3, %xmm6
+ addsd %xmm1, %xmm3
+ pextrw $3, %xmm2, %edx
+ pshufd $238, %xmm0, %xmm5
+ psrlq $38, %xmm3
+ psllq $38, %xmm3
+ movq %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 ..B1.5
+.L_2TAG_PACKET_2.0.2:
+ cmpl $0, %edx
+ jl .L_2TAG_PACKET_4.0.2
+ mulsd %xmm4, %xmm0
+ subsd %xmm5, %xmm7
+ addsd %xmm7, %xmm0
+ addsd %xmm3, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_4.0.2:
+ mulsd %xmm4, %xmm0
+ addsd %xmm7, %xmm0
+ addsd %xmm3, %xmm0
+ subsd %xmm5, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_1.0.2:
+ movl 36(%rsp), %ecx
+ addsd %xmm0, %xmm1
+ unpckhpd %xmm0, %xmm0
+ addsd %xmm1, %xmm0
+ cmpl $0, %ecx
+ jl .L_2TAG_PACKET_5.0.2
+ fstcw (%rsp)
+ movw (%rsp), %dx
+ orw $768, %dx
+ movw %dx, 4(%rsp)
+ fldcw 4(%rsp)
+ movl %eax, %edx
+ sarl $1, %eax
+ subl %eax, %edx
+ movdqa emask(%rip), %xmm6
+ pandn %xmm2, %xmm6
+ addl $1023, %eax
+ movd %eax, %xmm3
+ psllq $52, %xmm3
+ orpd %xmm3, %xmm6
+ mulsd %xmm3, %xmm4
+ movsd %xmm0, 16(%rsp)
+ fldl 16(%rsp)
+ movsd %xmm6, 24(%rsp)
+ fldl 24(%rsp)
+ movsd %xmm4, 16(%rsp)
+ fldl 16(%rsp)
+ addl $1023, %edx
+ movd %edx, %xmm4
+ psllq $52, %xmm4
+ faddp %st, %st(1)
+ fmul %st, %st(1)
+ faddp %st, %st(1)
+ movsd %xmm4, 24(%rsp)
+ fldl 24(%rsp)
+ fmulp %st, %st(1)
+ fstpl 16(%rsp)
+ movsd 16(%rsp), %xmm0
+ fldcw (%rsp)
+ pextrw $3, %xmm0, %ecx
+ andl $32752, %ecx
+ cmpl $32752, %ecx
+ jae .L_2TAG_PACKET_6.0.2
+ jmp ..B1.5
+ cmpl $-2147483648, %ecx
+ jb .L_2TAG_PACKET_6.0.2
+ jmp ..B1.5
+.L_2TAG_PACKET_6.0.2:
+ movl $41, 8(%rsp)
+ jmp .L_2TAG_PACKET_7.0.2
+.L_2TAG_PACKET_8.0.2:
+ cmpl $2146435072, %eax
+ jae .L_2TAG_PACKET_9.0.2
+ movsd XMAX(%rip), %xmm0
+ mulsd %xmm0, %xmm0
+ movl $41, 8(%rsp)
+ jmp .L_2TAG_PACKET_7.0.2
+.L_2TAG_PACKET_9.0.2:
+ movl 36(%rsp), %eax
+ movl 32(%rsp), %edx
+ movl %eax, %ecx
+ andl $2147483647, %eax
+ cmpl $2146435072, %eax
+ ja .L_2TAG_PACKET_10.0.2
+ cmpl $0, %edx
+ jne .L_2TAG_PACKET_10.0.2
+ cmpl $0, %ecx
+ jl .L_2TAG_PACKET_11.0.2
+ movq INF(%rip), %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_11.0.2:
+ jmp .L_2TAG_PACKET_5.0.2
+.L_2TAG_PACKET_10.0.2:
+ movsd 32(%rsp), %xmm0
+ addsd %xmm0, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_12.0.2:
+ addl $16304, %eax
+ cmpl $15504, %eax
+ jb .L_2TAG_PACKET_13.0.2
+ movapd cvl(%rip), %xmm2
+ pshufd $68, %xmm0, %xmm1
+ movapd 16+cvl(%rip), %xmm3
+ movapd 32+cvl(%rip), %xmm4
+ movq 48+cvl(%rip), %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
+ movq %xmm7, %xmm4
+ addsd %xmm6, %xmm7
+ mulpd %xmm3, %xmm1
+ psrlq $27, %xmm7
+ psllq $27, %xmm7
+ movq HIGHMASK(%rip), %xmm3
+ subsd %xmm7, %xmm4
+ mulpd %xmm1, %xmm2
+ addsd %xmm4, %xmm6
+ pshufd $238, %xmm2, %xmm1
+ addsd %xmm2, %xmm6
+ andpd %xmm0, %xmm3
+ movq %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 ..B1.5
+.L_2TAG_PACKET_13.0.2:
+ cmpl $16, %eax
+ jae .L_2TAG_PACKET_3.0.2
+ movq %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, 8(%rsp)
+ jmp .L_2TAG_PACKET_7.0.2
+.L_2TAG_PACKET_0.0.2:
+ cmpl $0, %eax
+ jl .L_2TAG_PACKET_12.0.2
+ movl 36(%rsp), %eax
+ cmpl $1083179008, %eax
+ jge .L_2TAG_PACKET_8.0.2
+ cmpl $-1048576, %eax
+ jae .L_2TAG_PACKET_9.0.2
+.L_2TAG_PACKET_5.0.2:
+ xorpd %xmm0, %xmm0
+ movl $49136, %eax
+ pinsrw $3, %eax, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_7.0.2:
+ movq %xmm0, 40(%rsp)
+..B1.3:
+ movq 40(%rsp), %xmm0
+.L_2TAG_PACKET_14.0.2:
+..B1.5:
+ addq $56, %rsp
+..___tag_value_expm1.4:
+ ret
+..___tag_value_expm1.5:
+END(expm1)
+# -- End expm1
+ .section .rodata, "a"
+ .align 16
+ .align 16
+cv:
+ .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
+ .type cv,@object
+ .size cv,96
+ .align 16
+Shifter:
+ .long 0
+ .long 1127743488
+ .long 0
+ .long 1127743488
+ .type Shifter,@object
+ .size Shifter,16
+ .align 16
+Tbl_addr:
+ .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
+ .type Tbl_addr,@object
+ .size Tbl_addr,1024
+ .align 16
+mmask:
+ .long 4294967232
+ .long 0
+ .long 4294967232
+ .long 0
+ .type mmask,@object
+ .size mmask,16
+ .align 16
+bias:
+ .long 65472
+ .long 0
+ .long 65472
+ .long 0
+ .type bias,@object
+ .size bias,16
+ .align 16
+emask:
+ .long 0
+ .long 4293918720
+ .long 0
+ .long 4293918720
+ .type emask,@object
+ .size emask,16
+ .align 16
+cvl:
+ .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
+ .type cvl,@object
+ .size cvl,64
+ .align 8
+XMAX:
+ .long 4294967295
+ .long 2146435071
+ .type XMAX,@object
+ .size XMAX,8
+ .align 8
+INF:
+ .long 0
+ .long 2146435072
+ .type INF,@object
+ .size INF,8
+ .align 8
+HIGHMASK:
+ .long 4227858432
+ .long 4294967295
+ .type HIGHMASK,@object
+ .size HIGHMASK,8
+ .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_expm1.1-.
+ .4byte ..___tag_value_expm1.5-..___tag_value_expm1.1
+ .2byte 0x0400
+ .4byte ..___tag_value_expm1.3-..___tag_value_expm1.1
+ .2byte 0x400e
+ .byte 0x04
+ .4byte ..___tag_value_expm1.4-..___tag_value_expm1.3
+ .2byte 0x080e
+ .byte 0x00
+# End