1/* Function exp2f 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 * 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 float 39 * if x >= 128.0 then exp2f(x) overflow 40 * if x < -151.0 then exp2f(x) underflow 41 * 42 */ 43 44/* Offsets for data table __svml_sexp2_data_internal 45 */ 46#define _sShifter 0 47#define _sPC0 16 48#define _sPC1 32 49#define _sPC2 48 50#define _sPC3 64 51#define _sPC4 80 52#define _sPC5 96 53#define _sPC6 112 54#define _iAbsMask 128 55#define _iDomainRange 144 56 57#include <sysdep.h> 58 59 .section .text.sse4, "ax", @progbits 60ENTRY(_ZGVbN4v_exp2f_sse4) 61 subq $72, %rsp 62 cfi_def_cfa_offset(80) 63 64 /* Check for overflow\underflow */ 65 movups __svml_sexp2_data_internal(%rip), %xmm1 66 67 /* Implementation */ 68 movaps %xmm1, %xmm5 69 70 /* Polynomial */ 71 movups _sPC6+__svml_sexp2_data_internal(%rip), %xmm4 72 addps %xmm0, %xmm5 73 movaps %xmm5, %xmm3 74 75 /* 2^N */ 76 pslld $23, %xmm5 77 78 /* Check for overflow\underflow */ 79 movdqu _iAbsMask+__svml_sexp2_data_internal(%rip), %xmm2 80 subps %xmm1, %xmm3 81 82 /* R */ 83 movaps %xmm0, %xmm1 84 pand %xmm0, %xmm2 85 pcmpgtd _iDomainRange+__svml_sexp2_data_internal(%rip), %xmm2 86 subps %xmm3, %xmm1 87 movmskps %xmm2, %edx 88 mulps %xmm1, %xmm4 89 addps _sPC5+__svml_sexp2_data_internal(%rip), %xmm4 90 mulps %xmm1, %xmm4 91 addps _sPC4+__svml_sexp2_data_internal(%rip), %xmm4 92 mulps %xmm1, %xmm4 93 addps _sPC3+__svml_sexp2_data_internal(%rip), %xmm4 94 mulps %xmm1, %xmm4 95 addps _sPC2+__svml_sexp2_data_internal(%rip), %xmm4 96 mulps %xmm1, %xmm4 97 addps _sPC1+__svml_sexp2_data_internal(%rip), %xmm4 98 mulps %xmm4, %xmm1 99 addps _sPC0+__svml_sexp2_data_internal(%rip), %xmm1 100 101 /* Reconstruction */ 102 paddd %xmm5, %xmm1 103 testl %edx, %edx 104 105 /* Go to special inputs processing branch */ 106 jne L(SPECIAL_VALUES_BRANCH) 107 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 108 109 /* Restore registers 110 * and exit the function 111 */ 112 113L(EXIT): 114 movaps %xmm1, %xmm0 115 addq $72, %rsp 116 cfi_def_cfa_offset(8) 117 ret 118 cfi_def_cfa_offset(80) 119 120 /* Branch to process 121 * special inputs 122 */ 123 124L(SPECIAL_VALUES_BRANCH): 125 movups %xmm0, 32(%rsp) 126 movups %xmm1, 48(%rsp) 127 # LOE rbx rbp r12 r13 r14 r15 edx 128 129 xorl %eax, %eax 130 movq %r12, 16(%rsp) 131 cfi_offset(12, -64) 132 movl %eax, %r12d 133 movq %r13, 8(%rsp) 134 cfi_offset(13, -72) 135 movl %edx, %r13d 136 movq %r14, (%rsp) 137 cfi_offset(14, -80) 138 # LOE rbx rbp r15 r12d r13d 139 140 /* Range mask 141 * bits check 142 */ 143 144L(RANGEMASK_CHECK): 145 btl %r12d, %r13d 146 147 /* Call scalar math function */ 148 jc L(SCALAR_MATH_CALL) 149 # LOE rbx rbp r15 r12d r13d 150 151 /* Special inputs 152 * processing loop 153 */ 154 155L(SPECIAL_VALUES_LOOP): 156 incl %r12d 157 cmpl $4, %r12d 158 159 /* Check bits in range mask */ 160 jl L(RANGEMASK_CHECK) 161 # LOE rbx rbp r15 r12d r13d 162 163 movq 16(%rsp), %r12 164 cfi_restore(12) 165 movq 8(%rsp), %r13 166 cfi_restore(13) 167 movq (%rsp), %r14 168 cfi_restore(14) 169 movups 48(%rsp), %xmm1 170 171 /* Go to exit */ 172 jmp L(EXIT) 173 cfi_offset(12, -64) 174 cfi_offset(13, -72) 175 cfi_offset(14, -80) 176 # LOE rbx rbp r12 r13 r14 r15 xmm1 177 178 /* Scalar math fucntion call 179 * to process special input 180 */ 181 182L(SCALAR_MATH_CALL): 183 movl %r12d, %r14d 184 movss 32(%rsp, %r14, 4), %xmm0 185 call exp2f@PLT 186 # LOE rbx rbp r14 r15 r12d r13d xmm0 187 188 movss %xmm0, 48(%rsp, %r14, 4) 189 190 /* Process special inputs in loop */ 191 jmp L(SPECIAL_VALUES_LOOP) 192 # LOE rbx rbp r15 r12d r13d 193END(_ZGVbN4v_exp2f_sse4) 194 195 .section .rodata, "a" 196 .align 16 197 198#ifdef __svml_sexp2_data_internal_typedef 199typedef unsigned int VUINT32; 200typedef struct { 201 __declspec(align(16)) VUINT32 _sShifter[4][1]; 202 __declspec(align(16)) VUINT32 _sPC0[4][1]; 203 __declspec(align(16)) VUINT32 _sPC1[4][1]; 204 __declspec(align(16)) VUINT32 _sPC2[4][1]; 205 __declspec(align(16)) VUINT32 _sPC3[4][1]; 206 __declspec(align(16)) VUINT32 _sPC4[4][1]; 207 __declspec(align(16)) VUINT32 _sPC5[4][1]; 208 __declspec(align(16)) VUINT32 _sPC6[4][1]; 209 __declspec(align(16)) VUINT32 _iAbsMask[4][1]; 210 __declspec(align(16)) VUINT32 _iDomainRange[4][1]; 211} __svml_sexp2_data_internal; 212#endif 213__svml_sexp2_data_internal: 214 .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter */ 215 .align 16 216 .long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC0 */ 217 .align 16 218 .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 /* _sPC1 */ 219 .align 16 220 .long 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef /* _sPC2 */ 221 .align 16 222 .long 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf /* _sPC3 */ 223 .align 16 224 .long 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c /* _sPC4 */ 225 .align 16 226 .long 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51 /* _sPC5 */ 227 .align 16 228 .long 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c /* _sPC6 */ 229 //common 230 .align 16 231 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ 232 .align 16 233 .long 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000 /* _iDomainRange=126.0 */ 234 .align 16 235 .type __svml_sexp2_data_internal, @object 236 .size __svml_sexp2_data_internal, .-__svml_sexp2_data_internal 237