1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #ifdef __RESTRICT 31 #define restrict _Restrict 32 #else 33 #define restrict 34 #endif 35 36 /* float logf(float x) 37 * 38 * Method : 39 * 1. Special cases: 40 * for x is negative, -Inf => QNaN + invalid; 41 * for x = 0 => -Inf + divide-by-zero; 42 * for x = +Inf => Inf; 43 * for x = NaN => QNaN. 44 * 2. Computes logarithm from: 45 * x = m * 2**n => log(x) = n * log(2) + log(m), 46 * m = [1, 2). 47 * Let m = m0 + dm, where m0 = 1 + k / 32, 48 * k = [0, 32], 49 * dm = [-1/64, 1/64]. 50 * Then log(m) = log(m0 + dm) = log(m0) + log(1+y), 51 * where y = dm*(1/m0), y = [-1/66, 1/64]. 52 * Then 53 * 1/m0 is looked up in a table of 1, 1/(1+1/32), ..., 1/(1+32/32); 54 * log(m0) is looked up in a table of log(1), log(1+1/32), 55 * ..., log(1+32/32). 56 * log(1+y) is computed using approximation: 57 * log(1+y) = ((a3*y + a2)*y + a1)*y*y + y. 58 * Accuracy: 59 * The maximum relative error for the approximating 60 * polynomial is 2**(-28.41). All calculations are of 61 * double precision. 62 * Maximum error observed: less than 0.545 ulp for the 63 * whole float type range. 64 */ 65 66 static const double __TBL_logf[] = { 67 /* __TBL_logf[2*i] = log(1+i/32), i = [0, 32] */ 68 /* __TBL_logf[2*i+1] = 2**(-23)/(1+i/32), i = [0, 32] */ 69 0.000000000000000000e+00, 1.192092895507812500e-07, 3.077165866675368733e-02, 70 1.155968868371212153e-07, 6.062462181643483994e-02, 1.121969784007352926e-07, 71 8.961215868968713805e-02, 1.089913504464285680e-07, 1.177830356563834557e-01, 72 1.059638129340277719e-07, 1.451820098444978890e-01, 1.030999260979729787e-07, 73 1.718502569266592284e-01, 1.003867701480263102e-07, 1.978257433299198675e-01, 74 9.781275040064102225e-08, 2.231435513142097649e-01, 9.536743164062500529e-08, 75 2.478361639045812692e-01, 9.304139672256097884e-08, 2.719337154836417580e-01, 76 9.082612537202380448e-08, 2.954642128938358980e-01, 8.871388989825581272e-08, 77 3.184537311185345887e-01, 8.669766512784091150e-08, 3.409265869705931928e-01, 78 8.477105034722222546e-08, 3.629054936893684746e-01, 8.292820142663043248e-08, 79 3.844116989103320559e-01, 8.116377160904255122e-08, 4.054651081081643849e-01, 80 7.947285970052082892e-08, 4.260843953109000881e-01, 7.785096460459183052e-08, 81 4.462871026284195297e-01, 7.629394531250000159e-08, 4.660897299245992387e-01, 82 7.479798560049019504e-08, 4.855078157817008244e-01, 7.335956280048077330e-08, 83 5.045560107523953119e-01, 7.197542010613207272e-08, 5.232481437645478684e-01, 84 7.064254195601851460e-08, 5.415972824327444091e-01, 6.935813210227272390e-08, 85 5.596157879354226594e-01, 6.811959402901785336e-08, 5.773153650348236132e-01, 86 6.692451343201754014e-08, 5.947071077466927758e-01, 6.577064251077586116e-08, 87 6.118015411059929409e-01, 6.465588585805084723e-08, 6.286086594223740942e-01, 88 6.357828776041666578e-08, 6.451379613735847007e-01, 6.253602074795082293e-08, 89 6.613984822453650159e-01, 6.152737525201612732e-08, 6.773988235918061429e-01, 90 6.055075024801586965e-08, 6.931471805599452862e-01, 5.960464477539062500e-08 91 }; 92 93 static const double 94 K3 = -2.49887584306188944706e-01, 95 K2 = 3.33368809981254554946e-01, 96 K1 = -5.00000008402474976565e-01; 97 98 static const union { 99 int i; 100 float f; 101 } inf = { 0x7f800000 }; 102 103 #define INF inf.f 104 105 #define PROCESS(N) \ 106 iy##N = ival##N & 0x007fffff; \ 107 ival##N = (iy##N + 0x20000) & 0xfffc0000; \ 108 i##N = ival##N >> 17; \ 109 iy##N = iy##N - ival##N; \ 110 ty##N = LN2 * (double) exp##N + __TBL_logf[i##N]; \ 111 yy##N = (double) iy##N * __TBL_logf[i##N + 1]; \ 112 yy##N = ((K3 * yy##N + K2) * yy##N + K1) * yy##N * yy##N + yy##N; \ 113 y[0] = (float)(yy##N + ty##N); \ 114 y += stridey; 115 116 #define PREPROCESS(N, index, label) \ 117 ival##N = *(int*)x; \ 118 value = x[0]; \ 119 x += stridex; \ 120 exp##N = (ival##N >> 23) - 127; \ 121 if ((ival##N & 0x7fffffff) >= 0x7f800000) /* X = NaN or Inf */ \ 122 { \ 123 y[index] = value + INF; \ 124 goto label; \ 125 } \ 126 if (ival##N < 0x00800000) \ 127 { \ 128 if (ival##N > 0) /* X = denormal */ \ 129 { \ 130 value = (float) ival##N; \ 131 ival##N = *(int*) &value; \ 132 exp##N = (ival##N >> 23) - (127 + 149); \ 133 } \ 134 else \ 135 { \ 136 value = 0.0f; \ 137 y[index] = ((ival##N & 0x7fffffff) == 0) ? \ 138 -1.0f / value : value / value; \ 139 goto label; \ 140 } \ 141 } 142 143 void 144 __vlogf(int n, float * restrict x, int stridex, float * restrict y, 145 int stridey) 146 { 147 double LN2 = __TBL_logf[64]; /* log(2) = 0.6931471805599453094 */ 148 double yy0, yy1, yy2, yy3, yy4; 149 double ty0, ty1, ty2, ty3, ty4; 150 float value; 151 int i0, i1, i2, i3, i4; 152 int ival0, ival1, ival2, ival3, ival4; 153 int exp0, exp1, exp2, exp3, exp4; 154 int iy0, iy1, iy2, iy3, iy4; 155 156 y -= stridey; 157 158 for (; ;) 159 { 160 begin: 161 y += stridey; 162 163 if (--n < 0) 164 break; 165 166 PREPROCESS(0, 0, begin) 167 168 if (--n < 0) 169 goto process1; 170 171 PREPROCESS(1, stridey, process1) 172 173 if (--n < 0) 174 goto process2; 175 176 PREPROCESS(2, (stridey << 1), process2) 177 178 if (--n < 0) 179 goto process3; 180 181 PREPROCESS(3, (stridey << 1) + stridey, process3) 182 183 if (--n < 0) 184 goto process4; 185 186 PREPROCESS(4, (stridey << 2), process4) 187 188 iy0 = ival0 & 0x007fffff; 189 iy1 = ival1 & 0x007fffff; 190 iy2 = ival2 & 0x007fffff; 191 iy3 = ival3 & 0x007fffff; 192 iy4 = ival4 & 0x007fffff; 193 194 ival0 = (iy0 + 0x20000) & 0xfffc0000; 195 ival1 = (iy1 + 0x20000) & 0xfffc0000; 196 ival2 = (iy2 + 0x20000) & 0xfffc0000; 197 ival3 = (iy3 + 0x20000) & 0xfffc0000; 198 ival4 = (iy4 + 0x20000) & 0xfffc0000; 199 200 i0 = ival0 >> 17; 201 i1 = ival1 >> 17; 202 i2 = ival2 >> 17; 203 i3 = ival3 >> 17; 204 i4 = ival4 >> 17; 205 206 iy0 = iy0 - ival0; 207 iy1 = iy1 - ival1; 208 iy2 = iy2 - ival2; 209 iy3 = iy3 - ival3; 210 iy4 = iy4 - ival4; 211 212 ty0 = LN2 * (double) exp0 + __TBL_logf[i0]; 213 ty1 = LN2 * (double) exp1 + __TBL_logf[i1]; 214 ty2 = LN2 * (double) exp2 + __TBL_logf[i2]; 215 ty3 = LN2 * (double) exp3 + __TBL_logf[i3]; 216 ty4 = LN2 * (double) exp4 + __TBL_logf[i4]; 217 218 yy0 = (double) iy0 * __TBL_logf[i0 + 1]; 219 yy1 = (double) iy1 * __TBL_logf[i1 + 1]; 220 yy2 = (double) iy2 * __TBL_logf[i2 + 1]; 221 yy3 = (double) iy3 * __TBL_logf[i3 + 1]; 222 yy4 = (double) iy4 * __TBL_logf[i4 + 1]; 223 224 yy0 = ((K3 * yy0 + K2) * yy0 + K1) * yy0 * yy0 + yy0; 225 yy1 = ((K3 * yy1 + K2) * yy1 + K1) * yy1 * yy1 + yy1; 226 yy2 = ((K3 * yy2 + K2) * yy2 + K1) * yy2 * yy2 + yy2; 227 yy3 = ((K3 * yy3 + K2) * yy3 + K1) * yy3 * yy3 + yy3; 228 yy4 = ((K3 * yy4 + K2) * yy4 + K1) * yy4 * yy4 + yy4; 229 230 y[0] = (float)(yy0 + ty0); 231 y += stridey; 232 y[0] = (float)(yy1 + ty1); 233 y += stridey; 234 y[0] = (float)(yy2 + ty2); 235 y += stridey; 236 y[0] = (float)(yy3 + ty3); 237 y += stridey; 238 y[0] = (float)(yy4 + ty4); 239 continue; 240 241 process1: 242 PROCESS(0) 243 continue; 244 245 process2: 246 PROCESS(0) 247 PROCESS(1) 248 continue; 249 250 process3: 251 PROCESS(0) 252 PROCESS(1) 253 PROCESS(2) 254 continue; 255 256 process4: 257 PROCESS(0) 258 PROCESS(1) 259 PROCESS(2) 260 PROCESS(3) 261 } 262 } 263