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>

1 files changed, 935 insertions, 0 deletions

diff --git a/libm/x86/s_atan.S b/libm/x86/s_atan.S
new file mode 100644
index 0000000..67d8c02
--- /dev/null
+++ b/libm/x86/s_atan.S
@@ -0,0 +1,935 @@
+/*
+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
+//                     ---------------------
+//
+// This implementation uses the main path for |x| in [2^{-5},2^65).
+// For |x| in [2^{-64},2^{-5}), a secondary path is used.
+// For the biased exponent of X within 3FFH-64 and 3FF+64, we use one branch.
+// We use the following definition of B and X` so that the formula
+// atan(X) = Tau + atan( (X`-B) / (One + BX) ) is correct
+//
+// X = (-1)^s * 2^k * 1. x1 x2 ... x52
+//
+// Define X`  = 0 if k >= 5; and X`  = |X| otherwise
+// Define One = 0 if k >= 5; and One = 1 otherwise
+// Define B  = 0 if k <= -6; B =  2^k * 1.x1 x2 x3 x4 1  if -5 <= k <= 4
+// Define B  =  2^5 * 1.0 0 ... 0   if  k >= 5
+//
+// Tau is 0 if k <= -6;
+// Tau is atan( B )  if -5 <= k <= 4
+// Tau is pi/2 if k >= 5
+//
+// Special cases:
+//  atan(NaN) = quiet NaN
+//  atan(+/-INF) = +/-Pi/2
+//  atan(+/-0) = +/-0
+//
+/******************************************************************************/
+
+#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  atan
+ENTRY(atan)
+# parameter 1: 8 + %ebp
+..B2.1:
+..B2.2:
+        pushl     %ebp
+        movl      %esp, %ebp
+        subl      $104, %esp
+        movl      %ebx, 48(%esp)
+        call      static_func
+        movl      %eax, %ebx
+        movsd     112(%esp), %xmm0
+        movsd     2640(%ebx), %xmm3
+        movsd     2624(%ebx), %xmm5
+        movsd     2656(%ebx), %xmm4
+        movsd     %xmm0, 8(%esp)
+        pextrw    $3, %xmm0, %edx
+        andpd     %xmm0, %xmm3
+        pshufd    $68, %xmm0, %xmm1
+        orpd      %xmm4, %xmm3
+        movl      %edx, %eax
+        andl      $32767, %edx
+        subl      $16288, %edx
+        cmpl      $159, %edx
+        ja        .L_2TAG_PACKET_0.0.2
+        mulsd     %xmm3, %xmm1
+        subsd     %xmm3, %xmm0
+        addsd     %xmm5, %xmm1
+        divsd     %xmm1, %xmm0
+        addl      $1, %edx
+        movsd     2672(%ebx), %xmm2
+        movsd     2688(%ebx), %xmm4
+        andl      $32768, %eax
+        xorpd     %xmm7, %xmm7
+        pinsrw    $3, %eax, %xmm7
+        addl      %edx, %edx
+        movsd     (%ebx,%edx,8), %xmm6
+        movsd     8(%ebx,%edx,8), %xmm5
+        xorpd     %xmm7, %xmm5
+        xorpd     %xmm7, %xmm6
+        movsd     2680(%ebx), %xmm7
+        pshufd    $68, %xmm0, %xmm1
+        mulsd     %xmm0, %xmm0
+        pshufd    $68, %xmm1, %xmm3
+        addsd     %xmm6, %xmm1
+        mulsd     %xmm0, %xmm2
+        addsd     %xmm0, %xmm4
+        subsd     %xmm1, %xmm6
+        mulsd     %xmm0, %xmm4
+        addsd     %xmm7, %xmm2
+        mulsd     %xmm3, %xmm0
+        addsd     %xmm3, %xmm6
+        mulsd     %xmm2, %xmm0
+        addsd     2696(%ebx), %xmm4
+        addsd     %xmm5, %xmm6
+        mulsd     %xmm4, %xmm0
+        addsd     %xmm6, %xmm0
+        addsd     %xmm1, %xmm0
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+        jmp       .L_2TAG_PACKET_1.0.2
+.L_2TAG_PACKET_0.0.2:
+        addl      $944, %edx
+        cmpl      $1103, %edx
+        ja        .L_2TAG_PACKET_2.0.2
+        movsd     2672(%ebx), %xmm4
+        movsd     2688(%ebx), %xmm7
+        movsd     8(%esp), %xmm0
+        mulsd     %xmm1, %xmm1
+        movsd     2680(%ebx), %xmm2
+        movsd     2696(%ebx), %xmm5
+        mulsd     %xmm1, %xmm4
+        addsd     %xmm1, %xmm7
+        movapd    %xmm1, %xmm6
+        mulsd     %xmm0, %xmm1
+        addsd     %xmm4, %xmm2
+        mulsd     %xmm6, %xmm7
+        mulsd     %xmm1, %xmm2
+        addsd     %xmm5, %xmm7
+        mulsd     %xmm7, %xmm2
+        addsd     %xmm2, %xmm0
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+        jmp       .L_2TAG_PACKET_1.0.2
+.L_2TAG_PACKET_2.0.2:
+        addl      $15344, %edx
+        cmpl      $16368, %edx
+        ja        .L_2TAG_PACKET_3.0.2
+        movsd     8(%esp), %xmm0
+        movsd     8(%esp), %xmm1
+        cmpl      $16, %edx
+        jae       .L_2TAG_PACKET_4.0.2
+        mulsd     %xmm0, %xmm1
+.L_2TAG_PACKET_4.0.2:
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+        jmp       .L_2TAG_PACKET_1.0.2
+.L_2TAG_PACKET_3.0.2:
+        cmpl      $17392, %edx
+        jae       .L_2TAG_PACKET_5.0.2
+        xorpd     %xmm1, %xmm1
+        movl      $49136, %ecx
+        pinsrw    $3, %ecx, %xmm1
+        divsd     %xmm0, %xmm1
+        movsd     2672(%ebx), %xmm2
+        movsd     2688(%ebx), %xmm4
+        andl      $32768, %eax
+        xorpd     %xmm7, %xmm7
+        pinsrw    $3, %eax, %xmm7
+        addl      %edx, %edx
+        movsd     2592(%ebx), %xmm6
+        movsd     2600(%ebx), %xmm5
+        xorpd     %xmm7, %xmm5
+        xorpd     %xmm7, %xmm6
+        movsd     2680(%ebx), %xmm7
+        pshufd    $68, %xmm1, %xmm0
+        mulsd     %xmm1, %xmm1
+        pshufd    $68, %xmm0, %xmm3
+        addsd     %xmm6, %xmm0
+        mulsd     %xmm1, %xmm2
+        addsd     %xmm1, %xmm4
+        subsd     %xmm0, %xmm6
+        mulsd     %xmm1, %xmm4
+        addsd     %xmm7, %xmm2
+        mulsd     %xmm3, %xmm1
+        addsd     %xmm3, %xmm6
+        mulsd     %xmm2, %xmm1
+        addsd     2696(%ebx), %xmm4
+        addsd     %xmm5, %xmm6
+        mulsd     %xmm4, %xmm1
+        addsd     %xmm6, %xmm1
+        addsd     %xmm1, %xmm0
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+        jmp       .L_2TAG_PACKET_1.0.2
+.L_2TAG_PACKET_5.0.2:
+        movsd     8(%esp), %xmm4
+        movsd     2608(%ebx), %xmm0
+        movsd     2592(%ebx), %xmm2
+        movsd     2600(%ebx), %xmm3
+        movd      %xmm1, %eax
+        psrlq     $32, %xmm1
+        movd      %xmm1, %edx
+        andl      $2147483647, %edx
+        cmpl      $2146435072, %edx
+        jae       .L_2TAG_PACKET_6.0.2
+.L_2TAG_PACKET_7.0.2:
+        andnpd    %xmm4, %xmm0
+        orpd      %xmm0, %xmm2
+        orpd      %xmm3, %xmm0
+        addsd     %xmm2, %xmm0
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+        jmp       .L_2TAG_PACKET_1.0.2
+.L_2TAG_PACKET_6.0.2:
+        subl      $2146435072, %edx
+        orl       %edx, %eax
+        cmpl      $0, %eax
+        je        .L_2TAG_PACKET_7.0.2
+        movapd    %xmm4, %xmm0
+        addsd     %xmm0, %xmm0
+        movsd     %xmm0, (%esp)
+        fldl      (%esp)
+.L_2TAG_PACKET_1.0.2:
+        movl      48(%esp), %ebx
+        movl      %ebp, %esp
+        popl      %ebp
+        ret       
+..B2.3:
+END(atan)
+# -- End  atan
+
+# Start file scope ASM
+.weak atanl
+.equ atanl, atan
+# End file scope ASM
+	.section .rodata, "a"
+	.align 16
+	.align 16
+static_const_table:
+	.long	0
+	.long	0
+	.long	0
+	.long	0
+	.long	3819695742
+	.long	1067482761
+	.long	2398680355
+	.long	3155462074
+	.long	2998791009
+	.long	1067548225
+	.long	3868465248
+	.long	3157182472
+	.long	3339424991
+	.long	1067613680
+	.long	3296670360
+	.long	1010752543
+	.long	2710002256
+	.long	1067679126
+	.long	3403896007
+	.long	1010910768
+	.long	3275701428
+	.long	1067744562
+	.long	119959933
+	.long	1011482843
+	.long	2908636881
+	.long	1067809988
+	.long	2464489612
+	.long	1011545526
+	.long	3777889398
+	.long	1067875403
+	.long	3262682165
+	.long	1009703919
+	.long	3759667419
+	.long	1067940807
+	.long	1838130851
+	.long	3157373556
+	.long	732369940
+	.long	1068006200
+	.long	1203428313
+	.long	1010055371
+	.long	1166616461
+	.long	1068071580
+	.long	2901274051
+	.long	3158549977
+	.long	2945472892
+	.long	1068136947
+	.long	3726120658
+	.long	1009762715
+	.long	3954480976
+	.long	1068202301
+	.long	1289173457
+	.long	1009429861
+	.long	2081752829
+	.long	1068267642
+	.long	1836909874
+	.long	1006212095
+	.long	3807999788
+	.long	1068332968
+	.long	2172459940
+	.long	3156162078
+	.long	2731789884
+	.long	1068398280
+	.long	3450718392
+	.long	3159216547
+	.long	1044477961
+	.long	1068463577
+	.long	2230553229
+	.long	1011424339
+	.long	1486930287
+	.long	1068530218
+	.long	2861547474
+	.long	1012041376
+	.long	2293016881
+	.long	1068595466
+	.long	136843272
+	.long	1012684797
+	.long	201518157
+	.long	1068660680
+	.long	63231984
+	.long	1012427198
+	.long	4054234584
+	.long	1068725856
+	.long	3927006960
+	.long	1011878955
+	.long	1246477213
+	.long	1068790995
+	.long	1494265652
+	.long	3155219350
+	.long	678186699
+	.long	1068856093
+	.long	1264361424
+	.long	3159256693
+	.long	2690594995
+	.long	1068921148
+	.long	3906996379
+	.long	1009288267
+	.long	3362611517
+	.long	1068986159
+	.long	1650970041
+	.long	3158331771
+	.long	3102162111
+	.long	1069051124
+	.long	365917035
+	.long	3160264153
+	.long	2352611067
+	.long	1069116041
+	.long	4008970190
+	.long	3159478182
+	.long	1594134794
+	.long	1069180908
+	.long	466690178
+	.long	1012526501
+	.long	1345079306
+	.long	1069245723
+	.long	2268273568
+	.long	3160164092
+	.long	2163300970
+	.long	1069310484
+	.long	2750834800
+	.long	3158113482
+	.long	352522716
+	.long	1069375190
+	.long	1750411372
+	.long	1011790845
+	.long	848541647
+	.long	1069439838
+	.long	2164207573
+	.long	1011698350
+	.long	40647312
+	.long	1069504427
+	.long	2949165434
+	.long	3159107267
+	.long	2216766270
+	.long	1069574357
+	.long	2197920765
+	.long	3161055954
+	.long	1090914384
+	.long	1069638757
+	.long	2330454674
+	.long	1013365998
+	.long	387601244
+	.long	1069703022
+	.long	3185681168
+	.long	1013434071
+	.long	3991640484
+	.long	1069767144
+	.long	1313211590
+	.long	3161087959
+	.long	3322489502
+	.long	1069831118
+	.long	3013977995
+	.long	1013053011
+	.long	3121698570
+	.long	1069894936
+	.long	4069015667
+	.long	1013023362
+	.long	4289964660
+	.long	1069958591
+	.long	1736191156
+	.long	3158266731
+	.long	3903312386
+	.long	1070022077
+	.long	1833592413
+	.long	3159731471
+	.long	3818449864
+	.long	1070085387
+	.long	851036429
+	.long	3159730451
+	.long	2097480306
+	.long	1070148515
+	.long	3506390884
+	.long	3160462302
+	.long	1611694502
+	.long	1070211454
+	.long	2785735540
+	.long	3160465144
+	.long	1464694796
+	.long	1070274198
+	.long	4229277299
+	.long	3159907000
+	.long	1299612775
+	.long	1070336741
+	.long	4116653788
+	.long	3160427739
+	.long	1310544789
+	.long	1070399077
+	.long	1064430331
+	.long	1013218202
+	.long	2253168030
+	.long	1070461200
+	.long	1405044609
+	.long	3157623179
+	.long	1159567373
+	.long	1070523105
+	.long	2353445521
+	.long	3159992176
+	.long	1359373750
+	.long	1070605818
+	.long	1748171336
+	.long	3161879263
+	.long	908341706
+	.long	1070667034
+	.long	3372710815
+	.long	3161775245
+	.long	1743027350
+	.long	1070727765
+	.long	687089934
+	.long	3160507171
+	.long	2055355646
+	.long	1070787992
+	.long	2392855242
+	.long	1013682469
+	.long	690426164
+	.long	1070847697
+	.long	1103926666
+	.long	1014052810
+	.long	1483247847
+	.long	1070906862
+	.long	2082645847
+	.long	3161345479
+	.long	392040270
+	.long	1070965472
+	.long	2407720023
+	.long	1014053754
+	.long	2673846014
+	.long	1071023511
+	.long	1293605532
+	.long	3158464385
+	.long	1384215810
+	.long	1071080967
+	.long	2446095872
+	.long	3159216407
+	.long	3101660631
+	.long	1071137826
+	.long	698040758
+	.long	1014855328
+	.long	2094057058
+	.long	1071194078
+	.long	2282048339
+	.long	1014040385
+	.long	1712750594
+	.long	1071249712
+	.long	1204372378
+	.long	3162276464
+	.long	1411515787
+	.long	1071304719
+	.long	949080808
+	.long	1015006403
+	.long	931538085
+	.long	1071359091
+	.long	3027127039
+	.long	1014307233
+	.long	179139065
+	.long	1071412821
+	.long	4285547492
+	.long	3161934731
+	.long	3387721259
+	.long	1071465902
+	.long	373225773
+	.long	1013486625
+	.long	2132236852
+	.long	1071544299
+	.long	3250533429
+	.long	1014031677
+	.long	1942070284
+	.long	1071645596
+	.long	1237964179
+	.long	3163239113
+	.long	1532707802
+	.long	1071695380
+	.long	330645583
+	.long	1012495610
+	.long	2294184979
+	.long	1071743834
+	.long	3959472897
+	.long	1015833116
+	.long	3805060714
+	.long	1071790961
+	.long	2671256142
+	.long	1013727772
+	.long	2215037898
+	.long	1071836770
+	.long	2683359117
+	.long	1015831902
+	.long	483661594
+	.long	1071881273
+	.long	836288326
+	.long	3162648643
+	.long	1534679894
+	.long	1071924486
+	.long	373258696
+	.long	3162470096
+	.long	1538714628
+	.long	1071966430
+	.long	3199433068
+	.long	1015325501
+	.long	527642555
+	.long	1072007128
+	.long	3636832592
+	.long	3161843145
+	.long	291339150
+	.long	1072046605
+	.long	890169537
+	.long	3160586117
+	.long	2450210201
+	.long	1072084888
+	.long	1636353294
+	.long	3163193400
+	.long	2411367951
+	.long	1072122007
+	.long	374899873
+	.long	1011331750
+	.long	681549971
+	.long	1072157992
+	.long	506411689
+	.long	1015373954
+	.long	1466745541
+	.long	1072192873
+	.long	2143860931
+	.long	1013364334
+	.long	2845622366
+	.long	1072226682
+	.long	2869178209
+	.long	3162423682
+	.long	2838871438
+	.long	1072275456
+	.long	3742223599
+	.long	1014338577
+	.long	4200275274
+	.long	1072337034
+	.long	1566539915
+	.long	3161839550
+	.long	3034733530
+	.long	1072394897
+	.long	652621408
+	.long	3162261964
+	.long	3207412993
+	.long	1072449290
+	.long	3206124665
+	.long	1014408733
+	.long	624461478
+	.long	1072500450
+	.long	932437485
+	.long	1015204343
+	.long	767665908
+	.long	1072548600
+	.long	1037911952
+	.long	3163527627
+	.long	1110773639
+	.long	1072593952
+	.long	2371517912
+	.long	3160465741
+	.long	1940828530
+	.long	1072636704
+	.long	2731408428
+	.long	3162895795
+	.long	1911329388
+	.long	1072677041
+	.long	1773089615
+	.long	3159569267
+	.long	1764715788
+	.long	1072704191
+	.long	691346949
+	.long	3164069946
+	.long	3332979233
+	.long	1072722195
+	.long	3550733983
+	.long	1014770628
+	.long	1321870254
+	.long	1072739231
+	.long	1415315820
+	.long	1016224052
+	.long	3657429030
+	.long	1072755365
+	.long	3910539033
+	.long	1015966402
+	.long	4197624557
+	.long	1072770661
+	.long	2333399254
+	.long	3164546480
+	.long	1512059493
+	.long	1072785177
+	.long	2701510318
+	.long	1016178092
+	.long	453379037
+	.long	1072798965
+	.long	4046344253
+	.long	3162814364
+	.long	1942345162
+	.long	1072818388
+	.long	621134147
+	.long	1016335195
+	.long	4210176273
+	.long	1072842164
+	.long	2701013387
+	.long	3164326619
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+	.type	static_const_table,@object
+	.size	static_const_table,2704
+	.data
+	.section .note.GNU-stack, ""
+# End