1/* Function exp10f vectorized with SSE4. 2 Copyright (C) 2021-2022 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 * exp10(x) = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y)) 23 * where 24 * x = m*log10(2)/K + y, y in [-log10(2)/K..log10(2)/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 exp10(x)-1 30 * on small interval [-log10(2)/K..log10(2)/K] 31 * 32 * Special cases: 33 * 34 * exp10(NaN) = NaN 35 * exp10(+INF) = +INF 36 * exp10(-INF) = 0 37 * exp10(x) = 1 for subnormals 38 * For IEEE float 39 * if x > 38.5318412780761720 then exp10f(x) overflow 40 * if x < -45.4555282592773440 then exp10f(x) underflow 41 * 42 */ 43 44/* Offsets for data table __svml_sexp10_data_internal 45 */ 46#define _sT 0 47#define _sLg2_10 128 48#define _sShifter 144 49#define _sInvLg2_10hi 160 50#define _sInvLg2_10lo 176 51#define _sPC0 192 52#define _sPC1 208 53#define _sPC2 224 54#define _iIndexMask 240 55#define _iAbsMask 256 56#define _iDomainRange 272 57 58#include <sysdep.h> 59 60 .section .text.sse4, "ax", @progbits 61ENTRY(_ZGVbN4v_exp10f_sse4) 62 subq $72, %rsp 63 cfi_def_cfa_offset(80) 64 movaps %xmm0, %xmm4 65 66 /* Load arument */ 67 movups _sLg2_10+__svml_sexp10_data_internal(%rip), %xmm2 68 lea __svml_sexp10_data_internal(%rip), %r8 69 mulps %xmm4, %xmm2 70 movups _sShifter+__svml_sexp10_data_internal(%rip), %xmm5 71 72 /* R */ 73 movups _sInvLg2_10hi+__svml_sexp10_data_internal(%rip), %xmm14 74 addps %xmm5, %xmm2 75 movaps %xmm2, %xmm1 76 movups _sInvLg2_10lo+__svml_sexp10_data_internal(%rip), %xmm15 77 subps %xmm5, %xmm1 78 mulps %xmm1, %xmm14 79 movaps %xmm4, %xmm5 80 mulps %xmm1, %xmm15 81 subps %xmm14, %xmm5 82 83 /* 84 * Polynomial 85 * exp10 = 2^N*(Tj+Tj*poly) 86 * poly(sN) = {1+later} a0+a1*sR 87 */ 88 movups _sPC2+__svml_sexp10_data_internal(%rip), %xmm1 89 subps %xmm15, %xmm5 90 mulps %xmm5, %xmm1 91 movdqu _iIndexMask+__svml_sexp10_data_internal(%rip), %xmm3 92 93 /* Index and lookup */ 94 movdqa %xmm3, %xmm10 95 96 /* remove index bits */ 97 pandn %xmm2, %xmm3 98 pand %xmm2, %xmm10 99 100 /* 2^N */ 101 pslld $18, %xmm3 102 103 /* iIndex *= sizeof(S); */ 104 pslld $2, %xmm10 105 addps _sPC1+__svml_sexp10_data_internal(%rip), %xmm1 106 movd %xmm10, %edx 107 pshufd $1, %xmm10, %xmm7 108 pshufd $2, %xmm10, %xmm9 109 pshufd $3, %xmm10, %xmm11 110 movd %xmm7, %ecx 111 movd %xmm9, %esi 112 movd %xmm11, %edi 113 114 /* Check for overflow\underflow */ 115 movdqu _iAbsMask+__svml_sexp10_data_internal(%rip), %xmm6 116 pand %xmm4, %xmm6 117 mulps %xmm1, %xmm5 118 movslq %edx, %rdx 119 addps _sPC0+__svml_sexp10_data_internal(%rip), %xmm5 120 movslq %ecx, %rcx 121 movslq %esi, %rsi 122 movslq %edi, %rdi 123 movd (%r8, %rdx), %xmm0 124 movd (%r8, %rcx), %xmm8 125 movd (%r8, %rsi), %xmm13 126 movd (%r8, %rdi), %xmm12 127 punpckldq %xmm8, %xmm0 128 punpckldq %xmm12, %xmm13 129 punpcklqdq %xmm13, %xmm0 130 131 /* Tj_l+Tj_h*poly */ 132 mulps %xmm0, %xmm5 133 pcmpgtd _iDomainRange+__svml_sexp10_data_internal(%rip), %xmm6 134 addps %xmm5, %xmm0 135 movmskps %xmm6, %eax 136 137 /* quick mul 2^N */ 138 paddd %xmm3, %xmm0 139 140 /* Finish */ 141 testl %eax, %eax 142 143 /* Go to special inputs processing branch */ 144 jne L(SPECIAL_VALUES_BRANCH) 145 # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm4 146 147 /* Restore registers 148 * and exit the function 149 */ 150 151L(EXIT): 152 addq $72, %rsp 153 cfi_def_cfa_offset(8) 154 ret 155 cfi_def_cfa_offset(80) 156 157 /* Branch to process 158 * special inputs 159 */ 160 161L(SPECIAL_VALUES_BRANCH): 162 movups %xmm4, 32(%rsp) 163 movups %xmm0, 48(%rsp) 164 # LOE rbx rbp r12 r13 r14 r15 eax 165 166 xorl %edx, %edx 167 movq %r12, 16(%rsp) 168 cfi_offset(12, -64) 169 movl %edx, %r12d 170 movq %r13, 8(%rsp) 171 cfi_offset(13, -72) 172 movl %eax, %r13d 173 movq %r14, (%rsp) 174 cfi_offset(14, -80) 175 # LOE rbx rbp r15 r12d r13d 176 177 /* Range mask 178 * bits check 179 */ 180 181L(RANGEMASK_CHECK): 182 btl %r12d, %r13d 183 184 /* Call scalar math function */ 185 jc L(SCALAR_MATH_CALL) 186 # LOE rbx rbp r15 r12d r13d 187 188 /* Special inputs 189 * processing loop 190 */ 191 192L(SPECIAL_VALUES_LOOP): 193 incl %r12d 194 cmpl $4, %r12d 195 196 /* Check bits in range mask */ 197 jl L(RANGEMASK_CHECK) 198 # LOE rbx rbp r15 r12d r13d 199 200 movq 16(%rsp), %r12 201 cfi_restore(12) 202 movq 8(%rsp), %r13 203 cfi_restore(13) 204 movq (%rsp), %r14 205 cfi_restore(14) 206 movups 48(%rsp), %xmm0 207 208 /* Go to exit */ 209 jmp L(EXIT) 210 cfi_offset(12, -64) 211 cfi_offset(13, -72) 212 cfi_offset(14, -80) 213 # LOE rbx rbp r12 r13 r14 r15 xmm0 214 215 /* Scalar math fucntion call 216 * to process special input 217 */ 218 219L(SCALAR_MATH_CALL): 220 movl %r12d, %r14d 221 movss 32(%rsp, %r14, 4), %xmm0 222 call exp10f@PLT 223 # LOE rbx rbp r14 r15 r12d r13d xmm0 224 225 movss %xmm0, 48(%rsp, %r14, 4) 226 227 /* Process special inputs in loop */ 228 jmp L(SPECIAL_VALUES_LOOP) 229 # LOE rbx rbp r15 r12d r13d 230END(_ZGVbN4v_exp10f_sse4) 231 232 .section .rodata, "a" 233 .align 16 234 235#ifdef __svml_sexp10_data_internal_typedef 236typedef unsigned int VUINT32; 237typedef struct { 238 __declspec(align(16)) VUINT32 _sT[(1<<5)][1]; 239 __declspec(align(16)) VUINT32 _sLg2_10[4][1]; 240 __declspec(align(16)) VUINT32 _sShifter[4][1]; 241 __declspec(align(16)) VUINT32 _sInvLg2_10hi[4][1]; 242 __declspec(align(16)) VUINT32 _sInvLg2_10lo[4][1]; 243 __declspec(align(16)) VUINT32 _sPC0[4][1]; 244 __declspec(align(16)) VUINT32 _sPC1[4][1]; 245 __declspec(align(16)) VUINT32 _sPC2[4][1]; 246 __declspec(align(16)) VUINT32 _iIndexMask[4][1]; 247 __declspec(align(16)) VUINT32 _iAbsMask[4][1]; 248 __declspec(align(16)) VUINT32 _iDomainRange[4][1]; 249} __svml_sexp10_data_internal; 250#endif 251__svml_sexp10_data_internal: 252 /* _sT */ 253 .long 0x3f800000 // 2^( 0 /32 ) 254 .long 0x3f82cd87 // 2^( 1 /32 ) 255 .long 0x3f85aac3 // 2^( 2 /32 ) 256 .long 0x3f88980f // 2^( 3 /32 ) 257 .long 0x3f8b95c2 // 2^( 4 /32 ) 258 .long 0x3f8ea43a // 2^( 5 /32 ) 259 .long 0x3f91c3d3 // 2^( 6 /32 ) 260 .long 0x3f94f4f0 // 2^( 7 /32 ) 261 .long 0x3f9837f0 // 2^( 8 /32 ) 262 .long 0x3f9b8d3a // 2^( 9 /32 ) 263 .long 0x3f9ef532 // 2^( 10/32 ) 264 .long 0x3fa27043 // 2^( 11/32 ) 265 .long 0x3fa5fed7 // 2^( 12/32 ) 266 .long 0x3fa9a15b // 2^( 13/32 ) 267 .long 0x3fad583f // 2^( 14/32 ) 268 .long 0x3fb123f6 // 2^( 15/32 ) 269 .long 0x3fb504f3 // 2^( 16/32 ) 270 .long 0x3fb8fbaf // 2^( 17/32 ) 271 .long 0x3fbd08a4 // 2^( 18/32 ) 272 .long 0x3fc12c4d // 2^( 19/32 ) 273 .long 0x3fc5672a // 2^( 20/32 ) 274 .long 0x3fc9b9be // 2^( 21/32 ) 275 .long 0x3fce248c // 2^( 22/32 ) 276 .long 0x3fd2a81e // 2^( 23/32 ) 277 .long 0x3fd744fd // 2^( 24/32 ) 278 .long 0x3fdbfbb8 // 2^( 25/32 ) 279 .long 0x3fe0ccdf // 2^( 26/32 ) 280 .long 0x3fe5b907 // 2^( 27/32 ) 281 .long 0x3feac0c7 // 2^( 28/32 ) 282 .long 0x3fefe4ba // 2^( 29/32 ) 283 .long 0x3ff5257d // 2^( 30/32 ) 284 .long 0x3ffa83b3 // 2^( 31/32 ) 285 .align 16 286 .long 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78 /* _sLg2_10*2^K */ 287 .align 16 288 .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter) */ 289 .align 16 290 .long 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000 /* _sInvLg2_10hi/2^K hi (24-K-7) bits */ 291 .align 16 292 .long 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc /* _sInvLg2_10lo/2^K lo bits */ 293 // otherwise exp10(0) won't produce exact 1.0 294 .align 16 295 .long 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868 /* _sPC0 */ 296 .align 16 297 .long 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b /* _sPC1 */ 298 .align 16 299 .long 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2 /* _sPC2 */ 300 .align 16 301 .long 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f /* _iIndexMask =(2^K-1) */ 302 //common 303 .align 16 304 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ 305 .align 16 306 .long 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818 /* _iDomainRange=-log10(max_denormal=0x007fffff) RZ */ 307 .align 16 308 .type __svml_sexp10_data_internal, @object 309 .size __svml_sexp10_data_internal, .-__svml_sexp10_data_internal 310