sysdeps/x86_64/fpu/multiarch/svml_d_exp22_core_sse4.S

   1 /* Function exp2 vectorized with SSE4.
   2    Copyright (C) 2021 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    https://www.gnu.org/licenses/.  */
  18
  19 /*
  20  * ALGORITHM DESCRIPTION:
  21  *
  22  *   exp2(x)  = 2^n * T[j] * (1 + P(y))
  23  *   where
  24  *        x = m*(1/K) + y,    y in [-1/K..1/K]
  25  *        m = n*K + j,           m,n,j - signed integer, j in [-K/2..K/2]
  26  *
  27  *        values of 2^j/K are tabulated
  28  *
  29  *        P(y) is a minimax polynomial approximation of exp2(x)-1
  30  *        on small interval [-1/K..1/K]
  31  *
  32  *  Special cases:
  33  *
  34  *   exp2(NaN)  = NaN
  35  *   exp2(+INF) = +INF
  36  *   exp2(-INF) = 0
  37  *   exp2(x)    = 1 for subnormals
  38  *   For IEEE double
  39  *     if x >= 1024.0 then exp2(x) overflows
  40  *     if x < -1076.0 then exp2(x) underflows
  41  *
  42  */
  43
  44 /* Offsets for data table __svml_dexp2_data_internal
  45  */
  46 #define _dbT                            0
  47 #define _dbShifter                      1024
  48 #define _dPC1                           1040
  49 #define _dPC2                           1056
  50 #define _dPC3                           1072
  51 #define _dPC4                           1088
  52 #define _lIndexMask                     1104
  53 #define _iAbsMask                       1120
  54 #define _iDomainRange                   1136
  55
  56 #include <sysdep.h>
  57
  58         .text
  59         .section .text.sse4,"ax",@progbits
  60 ENTRY(_ZGVbN2v_exp2_sse4)
  61         subq      $72, %rsp
  62         cfi_def_cfa_offset(80)
  63
  64 /*  R  */
  65         movaps    %xmm0, %xmm7
  66         movups    _dbShifter+__svml_dexp2_data_internal(%rip), %xmm1
  67
  68 /* out, basePtr, iIndex, iBaseOfs, iSize, iGran, iOfs */
  69         lea       __svml_dexp2_data_internal(%rip), %rsi
  70
  71 /*  Load arument  */
  72         movaps    %xmm1, %xmm10
  73         addpd     %xmm0, %xmm10
  74         movaps    %xmm10, %xmm6
  75         subpd     %xmm1, %xmm6
  76         subpd     %xmm6, %xmm7
  77
  78 /*
  79  *  Polynomial
  80  * poly(dN) = a1*dR+...+a4*dR^4
  81  */
  82         movups    _dPC4+__svml_dexp2_data_internal(%rip), %xmm8
  83         mulpd     %xmm7, %xmm8
  84         addpd     _dPC3+__svml_dexp2_data_internal(%rip), %xmm8
  85         mulpd     %xmm7, %xmm8
  86         addpd     _dPC2+__svml_dexp2_data_internal(%rip), %xmm8
  87         movdqu    _lIndexMask+__svml_dexp2_data_internal(%rip), %xmm9
  88
  89 /*  Index and lookup  */
  90         movdqa    %xmm9, %xmm5
  91         pandn     %xmm10, %xmm9
  92         pand      %xmm10, %xmm5
  93
  94 /*  2^N  */
  95         psllq     $45, %xmm9
  96         movd      %xmm5, %eax
  97         movq      _iAbsMask+__svml_dexp2_data_internal(%rip), %xmm2
  98
  99 /* Check for overflow\underflow  */
 100         pshufd    $221, %xmm0, %xmm4
 101         pextrw    $4, %xmm5, %ecx
 102
 103 /* a1+...+a4*dR^3 ! */
 104         mulpd     %xmm7, %xmm8
 105         shll      $3, %eax
 106         pand      %xmm2, %xmm4
 107         shll      $3, %ecx
 108         movq      (%rsi,%rax), %xmm1
 109         movhpd    (%rsi,%rcx), %xmm1
 110
 111 /* dR=dR*dT */
 112         mulpd     %xmm1, %xmm7
 113         addpd     _dPC1+__svml_dexp2_data_internal(%rip), %xmm8
 114
 115 /*
 116  *  Reconstruction
 117  * exp2 = {2^N later}*(Tj+Tj*poly)
 118  * dN = dT+dT*dR*(a1+...+a4*dR^3)
 119  */
 120         mulpd     %xmm7, %xmm8
 121         addpd     %xmm8, %xmm1
 122         movq      _iDomainRange+__svml_dexp2_data_internal(%rip), %xmm3
 123         pcmpgtd   %xmm3, %xmm4
 124         movmskps  %xmm4, %edx
 125
 126 /* quick 2^N */
 127         paddq     %xmm9, %xmm1
 128         andl      $3, %edx
 129
 130 /*  Finish   */
 131
 132 /* Go to special inputs processing branch */
 133         jne       L(SPECIAL_VALUES_BRANCH)
 134                                 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1
 135
 136 /* Restore registers
 137  * and exit the function
 138  */
 139
 140 L(EXIT):
 141         movaps    %xmm1, %xmm0
 142         addq      $72, %rsp
 143         cfi_def_cfa_offset(8)
 144         ret
 145         cfi_def_cfa_offset(80)
 146
 147 /* Branch to process
 148  * special inputs
 149  */
 150
 151 L(SPECIAL_VALUES_BRANCH):
 152         movups    %xmm0, 32(%rsp)
 153         movups    %xmm1, 48(%rsp)
 154                                 # LOE rbx rbp r12 r13 r14 r15 edx xmm1
 155
 156         xorl      %eax, %eax
 157         movq      %r12, 16(%rsp)
 158         cfi_offset(12, -64)
 159         movl      %eax, %r12d
 160         movq      %r13, 8(%rsp)
 161         cfi_offset(13, -72)
 162         movl      %edx, %r13d
 163         movq      %r14, (%rsp)
 164         cfi_offset(14, -80)
 165                                 # LOE rbx rbp r15 r12d r13d
 166
 167 /* Range mask
 168  * bits check
 169  */
 170
 171 L(RANGEMASK_CHECK):
 172         btl       %r12d, %r13d
 173
 174 /* Call scalar math function */
 175         jc        L(SCALAR_MATH_CALL)
 176                                 # LOE rbx rbp r15 r12d r13d
 177
 178 /* Special inputs
 179  * processing loop
 180  */
 181
 182 L(SPECIAL_VALUES_LOOP):
 183         incl      %r12d
 184         cmpl      $2, %r12d
 185
 186 /* Check bits in range mask */
 187         jl        L(RANGEMASK_CHECK)
 188                                 # LOE rbx rbp r15 r12d r13d
 189
 190         movq      16(%rsp), %r12
 191         cfi_restore(12)
 192         movq      8(%rsp), %r13
 193         cfi_restore(13)
 194         movq      (%rsp), %r14
 195         cfi_restore(14)
 196         movups    48(%rsp), %xmm1
 197
 198 /* Go to exit */
 199         jmp       L(EXIT)
 200         cfi_offset(12, -64)
 201         cfi_offset(13, -72)
 202         cfi_offset(14, -80)
 203                                 # LOE rbx rbp r12 r13 r14 r15 xmm1
 204
 205 /* Scalar math fucntion call
 206  * to process special input
 207  */
 208
 209 L(SCALAR_MATH_CALL):
 210         movl      %r12d, %r14d
 211         movsd     32(%rsp,%r14,8), %xmm0
 212         call      exp2@PLT
 213                                 # LOE rbx rbp r14 r15 r12d r13d xmm0
 214
 215         movsd     %xmm0, 48(%rsp,%r14,8)
 216
 217 /* Process special inputs in loop */
 218         jmp       L(SPECIAL_VALUES_LOOP)
 219                                 # LOE rbx rbp r15 r12d r13d
 220 END(_ZGVbN2v_exp2_sse4)
 221
 222         .section .rodata, "a"
 223         .align 16
 224
 225 #ifdef __svml_dexp2_data_internal_typedef
 226 typedef unsigned int VUINT32;
 227 typedef struct
 228 {
 229         __declspec(align(16)) VUINT32 _dbT[(1<<7)][2];
 230         __declspec(align(16)) VUINT32 _dbShifter[2][2];
 231         __declspec(align(16)) VUINT32 _dPC1[2][2];
 232         __declspec(align(16)) VUINT32 _dPC2[2][2];
 233         __declspec(align(16)) VUINT32 _dPC3[2][2];
 234         __declspec(align(16)) VUINT32 _dPC4[2][2];
 235         __declspec(align(16)) VUINT32 _lIndexMask[2][2];
 236         __declspec(align(16)) VUINT32 _iAbsMask[4][1];
 237         __declspec(align(16)) VUINT32 _iDomainRange[4][1];
 238 } __svml_dexp2_data_internal;
 239 #endif
 240 __svml_dexp2_data_internal:
 241         /*== _dbT ==*/
 242         .quad 0x3ff0000000000000, 0x3ff0163da9fb3335   /*2^( 0 /128),2^( 1 /128)*/
 243         .quad 0x3ff02c9a3e778061, 0x3ff04315e86e7f85   /*2^( 2 /128),2^( 3 /128)*/
 244         .quad 0x3ff059b0d3158574, 0x3ff0706b29ddf6de   /*2^( 4 /128),2^( 5 /128)*/
 245         .quad 0x3ff0874518759bc8, 0x3ff09e3ecac6f383   /*2^( 6 /128),2^( 7 /128)*/
 246         .quad 0x3ff0b5586cf9890f, 0x3ff0cc922b7247f7   /*2^( 8 /128),2^( 9 /128)*/
 247         .quad 0x3ff0e3ec32d3d1a2, 0x3ff0fb66affed31b   /*2^( 10 /128),2^( 11 /128)*/
 248         .quad 0x3ff11301d0125b51, 0x3ff12abdc06c31cc   /*2^( 12 /128),2^( 13 /128)*/
 249         .quad 0x3ff1429aaea92de0, 0x3ff15a98c8a58e51   /*2^( 14 /128),2^( 15 /128)*/
 250         .quad 0x3ff172b83c7d517b, 0x3ff18af9388c8dea   /*2^( 16 /128),2^( 17 /128)*/
 251         .quad 0x3ff1a35beb6fcb75, 0x3ff1bbe084045cd4   /*2^( 18 /128),2^( 19 /128)*/
 252         .quad 0x3ff1d4873168b9aa, 0x3ff1ed5022fcd91d   /*2^( 20 /128),2^( 21 /128)*/
 253         .quad 0x3ff2063b88628cd6, 0x3ff21f49917ddc96   /*2^( 22 /128),2^( 23 /128)*/
 254         .quad 0x3ff2387a6e756238, 0x3ff251ce4fb2a63f   /*2^( 24 /128),2^( 25 /128)*/
 255         .quad 0x3ff26b4565e27cdd, 0x3ff284dfe1f56381   /*2^( 26 /128),2^( 27 /128)*/
 256         .quad 0x3ff29e9df51fdee1, 0x3ff2b87fd0dad990   /*2^( 28 /128),2^( 29 /128)*/
 257         .quad 0x3ff2d285a6e4030b, 0x3ff2ecafa93e2f56   /*2^( 30 /128),2^( 31 /128)*/
 258         .quad 0x3ff306fe0a31b715, 0x3ff32170fc4cd831   /*2^( 32 /128),2^( 33 /128)*/
 259         .quad 0x3ff33c08b26416ff, 0x3ff356c55f929ff1   /*2^( 34 /128),2^( 35 /128)*/
 260         .quad 0x3ff371a7373aa9cb, 0x3ff38cae6d05d866   /*2^( 36 /128),2^( 37 /128)*/
 261         .quad 0x3ff3a7db34e59ff7, 0x3ff3c32dc313a8e5   /*2^( 38 /128),2^( 39 /128)*/
 262         .quad 0x3ff3dea64c123422, 0x3ff3fa4504ac801c   /*2^( 40 /128),2^( 41 /128)*/
 263         .quad 0x3ff4160a21f72e2a, 0x3ff431f5d950a897   /*2^( 42 /128),2^( 43 /128)*/
 264         .quad 0x3ff44e086061892d, 0x3ff46a41ed1d0057   /*2^( 44 /128),2^( 45 /128)*/
 265         .quad 0x3ff486a2b5c13cd0, 0x3ff4a32af0d7d3de   /*2^( 46 /128),2^( 47 /128)*/
 266         .quad 0x3ff4bfdad5362a27, 0x3ff4dcb299fddd0d   /*2^( 48 /128),2^( 49 /128)*/
 267         .quad 0x3ff4f9b2769d2ca7, 0x3ff516daa2cf6642   /*2^( 50 /128),2^( 51 /128)*/
 268         .quad 0x3ff5342b569d4f82, 0x3ff551a4ca5d920f   /*2^( 52 /128),2^( 53 /128)*/
 269         .quad 0x3ff56f4736b527da, 0x3ff58d12d497c7fd   /*2^( 54 /128),2^( 55 /128)*/
 270         .quad 0x3ff5ab07dd485429, 0x3ff5c9268a5946b7   /*2^( 56 /128),2^( 57 /128)*/
 271         .quad 0x3ff5e76f15ad2148, 0x3ff605e1b976dc09   /*2^( 58 /128),2^( 59 /128)*/
 272         .quad 0x3ff6247eb03a5585, 0x3ff6434634ccc320   /*2^( 60 /128),2^( 61 /128)*/
 273         .quad 0x3ff6623882552225, 0x3ff68155d44ca973   /*2^( 62 /128),2^( 63 /128)*/
 274         .quad 0x3ff6a09e667f3bcd, 0x3ff6c012750bdabf   /*2^( 64 /128),2^( 65 /128)*/
 275         .quad 0x3ff6dfb23c651a2f, 0x3ff6ff7df9519484   /*2^( 66 /128),2^( 67 /128)*/
 276         .quad 0x3ff71f75e8ec5f74, 0x3ff73f9a48a58174   /*2^( 68 /128),2^( 69 /128)*/
 277         .quad 0x3ff75feb564267c9, 0x3ff780694fde5d3f   /*2^( 70 /128),2^( 71 /128)*/
 278         .quad 0x3ff7a11473eb0187, 0x3ff7c1ed0130c132   /*2^( 72 /128),2^( 73 /128)*/
 279         .quad 0x3ff7e2f336cf4e62, 0x3ff80427543e1a12   /*2^( 74 /128),2^( 75 /128)*/
 280         .quad 0x3ff82589994cce13, 0x3ff8471a4623c7ad   /*2^( 76 /128),2^( 77 /128)*/
 281         .quad 0x3ff868d99b4492ed, 0x3ff88ac7d98a6699   /*2^( 78 /128),2^( 79 /128)*/
 282         .quad 0x3ff8ace5422aa0db, 0x3ff8cf3216b5448c   /*2^( 80 /128),2^( 81 /128)*/
 283         .quad 0x3ff8f1ae99157736, 0x3ff9145b0b91ffc6   /*2^( 82 /128),2^( 83 /128)*/
 284         .quad 0x3ff93737b0cdc5e5, 0x3ff95a44cbc8520f   /*2^( 84 /128),2^( 85 /128)*/
 285         .quad 0x3ff97d829fde4e50, 0x3ff9a0f170ca07ba   /*2^( 86 /128),2^( 87 /128)*/
 286         .quad 0x3ff9c49182a3f090, 0x3ff9e86319e32323   /*2^( 88 /128),2^( 89 /128)*/
 287         .quad 0x3ffa0c667b5de565, 0x3ffa309bec4a2d33   /*2^( 90 /128),2^( 91 /128)*/
 288         .quad 0x3ffa5503b23e255d, 0x3ffa799e1330b358   /*2^( 92 /128),2^( 93 /128)*/
 289         .quad 0x3ffa9e6b5579fdbf, 0x3ffac36bbfd3f37a   /*2^( 94 /128),2^( 95 /128)*/
 290         .quad 0x3ffae89f995ad3ad, 0x3ffb0e07298db666   /*2^( 96 /128),2^( 97 /128)*/
 291         .quad 0x3ffb33a2b84f15fb, 0x3ffb59728de5593a   /*2^( 98 /128),2^( 99 /128)*/
 292         .quad 0x3ffb7f76f2fb5e47, 0x3ffba5b030a1064a   /*2^( 100 /128),2^( 101 /128)*/
 293         .quad 0x3ffbcc1e904bc1d2, 0x3ffbf2c25bd71e09   /*2^( 102 /128),2^( 103 /128)*/
 294         .quad 0x3ffc199bdd85529c, 0x3ffc40ab5fffd07a   /*2^( 104 /128),2^( 105 /128)*/
 295         .quad 0x3ffc67f12e57d14b, 0x3ffc8f6d9406e7b5   /*2^( 106 /128),2^( 107 /128)*/
 296         .quad 0x3ffcb720dcef9069, 0x3ffcdf0b555dc3fa   /*2^( 108 /128),2^( 109 /128)*/
 297         .quad 0x3ffd072d4a07897c, 0x3ffd2f87080d89f2   /*2^( 110 /128),2^( 111 /128)*/
 298         .quad 0x3ffd5818dcfba487, 0x3ffd80e316c98398   /*2^( 112 /128),2^( 113 /128)*/
 299         .quad 0x3ffda9e603db3285, 0x3ffdd321f301b460   /*2^( 114 /128),2^( 115 /128)*/
 300         .quad 0x3ffdfc97337b9b5f, 0x3ffe264614f5a129   /*2^( 116 /128),2^( 117 /128)*/
 301         .quad 0x3ffe502ee78b3ff6, 0x3ffe7a51fbc74c83   /*2^( 118 /128),2^( 119 /128)*/
 302         .quad 0x3ffea4afa2a490da, 0x3ffecf482d8e67f1   /*2^( 120 /128),2^( 121 /128)*/
 303         .quad 0x3ffefa1bee615a27, 0x3fff252b376bba97   /*2^( 122 /128),2^( 123 /128)*/
 304         .quad 0x3fff50765b6e4540, 0x3fff7bfdad9cbe14   /*2^( 124 /128),2^( 125 /128)*/
 305         .quad 0x3fffa7c1819e90d8, 0x3fffd3c22b8f71f1 /*2^( 126 /128),2^( 127 /128)*/
 306         .align 16
 307         .quad 0x42c8000000000000, 0x42c8000000000000  /* _dbShifter - 0x433-7=0x42c shifted right on K!*/
 308         //log2(relerr) = -53.547756365162
 309         .align 16
 310         .quad 0x3fe62e42fefa3685, 0x3fe62e42fefa3685 /* _dPC1 */
 311         .align 16
 312         .quad 0x3fcebfbdff82ca48, 0x3fcebfbdff82ca48 /* _dPC2 */
 313         .align 16
 314         .quad 0x3fac6b09b180f045, 0x3fac6b09b180f045 /* _dPC3 */
 315         .align 16
 316         .quad 0x3f83b2ab5bb1268f, 0x3f83b2ab5bb1268f /* _dPC4 */
 317         .align 16
 318         .quad 0x000000000000007f, 0x000000000000007f          /* _lIndexMask =(2^K-1)*/
 319         .align 16
 320         .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff          /* _iAbsMask */
 321         .align 16
 322         .long 0x408fefff, 0x408fefff, 0x408fefff, 0x408fefff /* _iDomainRange */
 323         .align 16
 324         .type   __svml_dexp2_data_internal,@object
 325         .size   __svml_dexp2_data_internal,.-__svml_dexp2_data_internal