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/e_exp.S b/libm/x86_64/e_exp.S
new file mode 100644
index 0000000..6882dfc
--- /dev/null
+++ b/libm/x86_64/e_exp.S
@@ -0,0 +1,636 @@
+/*
+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).
+// x x/log(2) n
+// e = 2 = 2 * T[j] * (1 + P(y))
+// 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).
+//
+// 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]
+// where BIAS is a value of exponent bias.
+//
+// Special cases:
+// exp(NaN) = NaN
+// exp(+INF) = +INF
+// exp(-INF) = 0
+// exp(x) = 1 for subnormals
+// for finite argument, only exp(0)=1 is exact
+// For IEEE double
+// if x > 709.782712893383973096 then exp(x) overflow
+// if x < -745.133219101941108420 then exp(x) underflow
+//
+/******************************************************************************/
+
+#include <private/bionic_asm.h>
+# -- Begin exp
+ENTRY(exp)
+# parameter 1: %xmm0
+..B1.1:
+..___tag_value_exp.1:
+ subq $24, %rsp
+..___tag_value_exp.3:
+ movsd %xmm0, 8(%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 $15504, %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 64+cv(%rip), %xmm4
+ mulpd %xmm1, %xmm3
+ movapd 80+cv(%rip), %xmm5
+ subpd %xmm2, %xmm0
+ movd %xmm7, %eax
+ movl %eax, %ecx
+ andl $63, %ecx
+ shll $4, %ecx
+ sarl $6, %eax
+ movl %eax, %edx
+ movdqa mmask(%rip), %xmm6
+ pand %xmm6, %xmm7
+ movdqa bias(%rip), %xmm6
+ paddq %xmm6, %xmm7
+ psllq $46, %xmm7
+ subpd %xmm3, %xmm0
+ lea Tbl_addr(%rip), %r8
+ movapd (%rcx,%r8), %xmm2
+ mulpd %xmm0, %xmm4
+ movapd %xmm0, %xmm6
+ movapd %xmm0, %xmm1
+ mulpd %xmm6, %xmm6
+ mulpd %xmm6, %xmm0
+ addpd %xmm4, %xmm5
+ mulsd %xmm6, %xmm0
+ mulpd 48+cv(%rip), %xmm6
+ addsd %xmm2, %xmm1
+ unpckhpd %xmm2, %xmm2
+ mulpd %xmm5, %xmm0
+ addsd %xmm0, %xmm1
+ orpd %xmm7, %xmm2
+ unpckhpd %xmm0, %xmm0
+ addsd %xmm1, %xmm0
+ addsd %xmm6, %xmm0
+ addl $894, %edx
+ cmpl $1916, %edx
+ ja .L_2TAG_PACKET_1.0.2
+ mulsd %xmm2, %xmm0
+ addsd %xmm2, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_1.0.2:
+ xorpd %xmm3, %xmm3
+ movapd ALLONES(%rip), %xmm4
+ movl $-1022, %edx
+ subl %eax, %edx
+ movd %edx, %xmm5
+ psllq %xmm5, %xmm4
+ movl %eax, %ecx
+ sarl $1, %eax
+ pinsrw $3, %eax, %xmm3
+ movapd ebias(%rip), %xmm6
+ psllq $4, %xmm3
+ psubd %xmm3, %xmm2
+ mulsd %xmm2, %xmm0
+ cmpl $52, %edx
+ jg .L_2TAG_PACKET_2.0.2
+ andpd %xmm2, %xmm4
+ paddd %xmm6, %xmm3
+ subsd %xmm4, %xmm2
+ addsd %xmm2, %xmm0
+ cmpl $1023, %ecx
+ jge .L_2TAG_PACKET_3.0.2
+ pextrw $3, %xmm0, %ecx
+ andl $32768, %ecx
+ orl %ecx, %edx
+ cmpl $0, %edx
+ je .L_2TAG_PACKET_4.0.2
+ movapd %xmm0, %xmm6
+ addsd %xmm4, %xmm0
+ mulsd %xmm3, %xmm0
+ pextrw $3, %xmm0, %ecx
+ andl $32752, %ecx
+ cmpl $0, %ecx
+ je .L_2TAG_PACKET_5.0.2
+ jmp ..B1.5
+.L_2TAG_PACKET_5.0.2:
+ mulsd %xmm3, %xmm6
+ mulsd %xmm3, %xmm4
+ movq %xmm6, %xmm0
+ pxor %xmm4, %xmm6
+ psrad $31, %xmm6
+ pshufd $85, %xmm6, %xmm6
+ psllq $1, %xmm0
+ psrlq $1, %xmm0
+ pxor %xmm6, %xmm0
+ psrlq $63, %xmm6
+ paddq %xmm6, %xmm0
+ paddq %xmm4, %xmm0
+ movl $15, (%rsp)
+ jmp .L_2TAG_PACKET_6.0.2
+.L_2TAG_PACKET_4.0.2:
+ addsd %xmm4, %xmm0
+ mulsd %xmm3, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_3.0.2:
+ addsd %xmm4, %xmm0
+ mulsd %xmm3, %xmm0
+ pextrw $3, %xmm0, %ecx
+ andl $32752, %ecx
+ cmpl $32752, %ecx
+ jnb .L_2TAG_PACKET_7.0.2
+ jmp ..B1.5
+.L_2TAG_PACKET_2.0.2:
+ paddd %xmm6, %xmm3
+ addpd %xmm2, %xmm0
+ mulsd %xmm3, %xmm0
+ movl $15, (%rsp)
+ jmp .L_2TAG_PACKET_6.0.2
+.L_2TAG_PACKET_8.0.2:
+ cmpl $2146435072, %eax
+ jae .L_2TAG_PACKET_9.0.2
+ movl 12(%rsp), %eax
+ cmpl $-2147483648, %eax
+ jae .L_2TAG_PACKET_10.0.2
+ movsd XMAX(%rip), %xmm0
+ mulsd %xmm0, %xmm0
+.L_2TAG_PACKET_7.0.2:
+ movl $14, (%rsp)
+ jmp .L_2TAG_PACKET_6.0.2
+.L_2TAG_PACKET_10.0.2:
+ movsd XMIN(%rip), %xmm0
+ mulsd %xmm0, %xmm0
+ movl $15, (%rsp)
+ jmp .L_2TAG_PACKET_6.0.2
+.L_2TAG_PACKET_9.0.2:
+ movl 8(%rsp), %edx
+ cmpl $2146435072, %eax
+ ja .L_2TAG_PACKET_11.0.2
+ cmpl $0, %edx
+ jne .L_2TAG_PACKET_11.0.2
+ movl 12(%rsp), %eax
+ cmpl $2146435072, %eax
+ jne .L_2TAG_PACKET_12.0.2
+ movsd INF(%rip), %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_12.0.2:
+ movsd ZERO(%rip), %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_11.0.2:
+ movsd 8(%rsp), %xmm0
+ addsd %xmm0, %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_0.0.2:
+ movl 12(%rsp), %eax
+ andl $2147483647, %eax
+ cmpl $1083179008, %eax
+ jae .L_2TAG_PACKET_8.0.2
+ movsd 8(%rsp), %xmm0
+ addsd ONE_val(%rip), %xmm0
+ jmp ..B1.5
+.L_2TAG_PACKET_6.0.2:
+ movq %xmm0, 16(%rsp)
+..B1.3:
+ movq 16(%rsp), %xmm0
+.L_2TAG_PACKET_13.0.2:
+..B1.5:
+ addq $24, %rsp
+..___tag_value_exp.4:
+ ret
+..___tag_value_exp.5:
+END(exp)
+# -- End exp
+ .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 4294967294
+ .long 1071644671
+ .long 4294967294
+ .long 1071644671
+ .long 3811088480
+ .long 1062650204
+ .long 1432067621
+ .long 1067799893
+ .long 3230715663
+ .long 1065423125
+ .long 1431604129
+ .long 1069897045
+ .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
+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
+Tbl_addr:
+ .long 0
+ .long 0
+ .long 0
+ .long 0
+ .long 235107661
+ .long 1018002367
+ .long 1048019040
+ .long 11418
+ .long 896005651
+ .long 1015861842
+ .long 3541402996
+ .long 22960
+ .long 1642514529
+ .long 1012987726
+ .long 410360776
+ .long 34629
+ .long 1568897900
+ .long 1016568486
+ .long 1828292879
+ .long 46424
+ .long 1882168529
+ .long 1010744893
+ .long 852742562
+ .long 58348
+ .long 509852888
+ .long 1017336174
+ .long 3490863952
+ .long 70401
+ .long 653277307
+ .long 1017431380
+ .long 2930322911
+ .long 82586
+ .long 1649557430
+ .long 1017729363
+ .long 1014845818
+ .long 94904
+ .long 1058231231
+ .long 1015777676
+ .long 3949972341
+ .long 107355
+ .long 1044000607
+ .long 1016786167
+ .long 828946858
+ .long 119943
+ .long 1151779725
+ .long 1015705409
+ .long 2288159958
+ .long 132667
+ .long 3819481236
+ .long 1016499965
+ .long 1853186616
+ .long 145530
+ .long 2552227826
+ .long 1015039787
+ .long 1709341917
+ .long 158533
+ .long 1829350193
+ .long 1015216097
+ .long 4112506593
+ .long 171677
+ .long 1913391795
+ .long 1015756674
+ .long 2799960843
+ .long 184965
+ .long 1303423926
+ .long 1015238005
+ .long 171030293
+ .long 198398
+ .long 1574172746
+ .long 1016061241
+ .long 2992903935
+ .long 211976
+ .long 3424156969
+ .long 1017196428
+ .long 926591434
+ .long 225703
+ .long 1938513547
+ .long 1017631273
+ .long 887463926
+ .long 239579
+ .long 2804567149
+ .long 1015390024
+ .long 1276261410
+ .long 253606
+ .long 631083525
+ .long 1017690182
+ .long 569847337
+ .long 267786
+ .long 1623370770
+ .long 1011049453
+ .long 1617004845
+ .long 282120
+ .long 3667985273
+ .long 1013894369
+ .long 3049340112
+ .long 296610
+ .long 3145379760
+ .long 1014403278
+ .long 3577096743
+ .long 311258
+ .long 2603100681
+ .long 1017152460
+ .long 1990012070
+ .long 326066
+ .long 3249202951
+ .long 1017448880
+ .long 1453150081
+ .long 341035
+ .long 419288974
+ .long 1016280325
+ .long 917841882
+ .long 356167
+ .long 3793507337
+ .long 1016095713
+ .long 3712504873
+ .long 371463
+ .long 728023093
+ .long 1016345318
+ .long 363667784
+ .long 386927
+ .long 2582678538
+ .long 1017123460
+ .long 2956612996
+ .long 402558
+ .long 7592966
+ .long 1016721543
+ .long 2186617380
+ .long 418360
+ .long 228611441
+ .long 1016696141
+ .long 1719614412
+ .long 434334
+ .long 2261665670
+ .long 1017457593
+ .long 1013258798
+ .long 450482
+ .long 544148907
+ .long 1017323666
+ .long 3907805043
+ .long 466805
+ .long 2383914918
+ .long 1017143586
+ .long 1447192520
+ .long 483307
+ .long 1176412038
+ .long 1017267372
+ .long 1944781190
+ .long 499988
+ .long 2882956373
+ .long 1013312481
+ .long 919555682
+ .long 516851
+ .long 3154077648
+ .long 1016528543
+ .long 2571947538
+ .long 533897
+ .long 348651999
+ .long 1016405780
+ .long 2604962540
+ .long 551129
+ .long 3253791412
+ .long 1015920431
+ .long 1110089947
+ .long 568549
+ .long 1509121860
+ .long 1014756995
+ .long 2568320822
+ .long 586158
+ .long 2617649212
+ .long 1017340090
+ .long 2966275556
+ .long 603959
+ .long 553214634
+ .long 1016457425
+ .long 2682146383
+ .long 621954
+ .long 730975783
+ .long 1014083580
+ .long 2191782032
+ .long 640145
+ .long 1486499517
+ .long 1016818996
+ .long 2069751140
+ .long 658534
+ .long 2595788928
+ .long 1016407932
+ .long 2990417244
+ .long 677123
+ .long 1853053619
+ .long 1015310724
+ .long 1434058175
+ .long 695915
+ .long 2462790535
+ .long 1015814775
+ .long 2572866477
+ .long 714911
+ .long 3693944214
+ .long 1017259110
+ .long 3092190714
+ .long 734114
+ .long 2979333550
+ .long 1017188654
+ .long 4076559942
+ .long 753526
+ .long 174054861
+ .long 1014300631
+ .long 2420883922
+ .long 773150
+ .long 816778419
+ .long 1014197934
+ .long 3716502172
+ .long 792987
+ .long 3507050924
+ .long 1015341199
+ .long 777507147
+ .long 813041
+ .long 1821514088
+ .long 1013410604
+ .long 3706687593
+ .long 833312
+ .long 920623539
+ .long 1016295433
+ .long 1242007931
+ .long 853805
+ .long 2789017511
+ .long 1014276997
+ .long 3707479175
+ .long 874520
+ .long 3586233004
+ .long 1015962192
+ .long 64696965
+ .long 895462
+ .long 474650514
+ .long 1016642419
+ .long 863738718
+ .long 916631
+ .long 1614448851
+ .long 1014281732
+ .long 3884662774
+ .long 938030
+ .long 2450082086
+ .long 1016164135
+ .long 2728693977
+ .long 959663
+ .long 1101668360
+ .long 1015989180
+ .long 3999357479
+ .long 981531
+ .long 835814894
+ .long 1015702697
+ .long 1533953344
+ .long 1003638
+ .long 1301400989
+ .long 1014466875
+ .long 2174652632
+ .long 1025985
+ .type Tbl_addr,@object
+ .size Tbl_addr,1024
+ .align 16
+ALLONES:
+ .long 4294967295
+ .long 4294967295
+ .long 4294967295
+ .long 4294967295
+ .type ALLONES,@object
+ .size ALLONES,16
+ .align 16
+ebias:
+ .long 0
+ .long 1072693248
+ .long 0
+ .long 1072693248
+ .type ebias,@object
+ .size ebias,16
+ .align 4
+XMAX:
+ .long 4294967295
+ .long 2146435071
+ .type XMAX,@object
+ .size XMAX,8
+ .align 4
+XMIN:
+ .long 0
+ .long 1048576
+ .type XMIN,@object
+ .size XMIN,8
+ .align 4
+INF:
+ .long 0
+ .long 2146435072
+ .type INF,@object
+ .size INF,8
+ .align 4
+ZERO:
+ .long 0
+ .long 0
+ .type ZERO,@object
+ .size ZERO,8
+ .align 4
+ONE_val:
+ .long 0
+ .long 1072693248
+ .type ONE_val,@object
+ .size ONE_val,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_exp.1-.
+ .4byte ..___tag_value_exp.5-..___tag_value_exp.1
+ .2byte 0x0400
+ .4byte ..___tag_value_exp.3-..___tag_value_exp.1
+ .2byte 0x200e
+ .byte 0x04
+ .4byte ..___tag_value_exp.4-..___tag_value_exp.3
+ .2byte 0x080e
+ .byte 0x00
+# End