usr/src/lib/libmvec/common/__vexpf.c

   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 expf(float x)
  37  *
  38  * Method :
  39  *      1. Special cases:
  40  *              for x > 88.722839355...(0x42B17218) => Inf + overflow;
  41  *              for x < -103.97207642..(0xc2CFF1B4) => 0 + underflow;
  42  *              for x = Inf                         => Inf;
  43  *              for x = -Inf                        => 0;
  44  *              for x = +-NaN                       => QNaN.
  45  *      2. Computes exponential from:
  46  *              exp(x) = 2**a  *  2**(k/256)  *  2**(y/256)
  47  *      Where:
  48  *              a    =    int  ( 256 * log2(e) * x ) >> 8;
  49  *              k    =    int  ( 256 * log2(e) * x ) & 0xFF;
  50  *              y    =    frac ( 256 * x * log2(e)).
  51  *      Note that:
  52  *              k = 0, 1, ..., 255;
  53  *              y = (-1, 1).
  54  *      Then:
  55  *              2**(k/256) is looked up in a table of 2**0, 2**1/256, ...
  56  *              2**(y/256) is computed using approximation:
  57  *                      2**(y/256) =  a0 + a1 * y + a2 * y**2
  58  *              Multiplication by 2**a is done by adding "a" to
  59  *              the biased exponent.
  60  * Accuracy:
  61  *      The maximum relative error for the approximating
  62  *      polynomial is 2**(-29.18).  All calculations are of
  63  *      double precision.
  64  *      Maximum error observed: less than 0.528 ulp for the whole
  65  *      float type range.
  66  *
  67  * NOTE: This implementation has been modified for SPARC to deliver
  68  * zero instead of a subnormal result whenever the argument is less
  69  * than log(2^-126).  Therefore the worst case relative error is 1.
  70  */
  71
  72 static const double __TBL_exp2f[] = {
  73         /* 2^(i/256) - (((i & 0xff) << 44), i = [0, 255] */
  74 1.000000000000000000e+00, 9.994025125251012609e-01, 9.988087005564013632e-01,
  75 9.982185740592087742e-01, 9.976321430258502376e-01, 9.970494174757447148e-01,
  76 9.964704074554765478e-01, 9.958951230388689568e-01, 9.953235743270583136e-01,
  77 9.947557714485678604e-01, 9.941917245593818730e-01, 9.936314438430204898e-01,
  78 9.930749395106142074e-01, 9.925222218009785990e-01, 9.919733009806893653e-01,
  79 9.914281873441580517e-01, 9.908868912137068774e-01, 9.903494229396448967e-01,
  80 9.898157929003436051e-01, 9.892860115023132117e-01, 9.887600891802785785e-01,
  81 9.882380363972563808e-01, 9.877198636446310465e-01, 9.872055814422322495e-01,
  82 9.866952003384118486e-01, 9.861887309101209365e-01, 9.856861837629877776e-01,
  83 9.851875695313955239e-01, 9.846928988785599302e-01, 9.842021824966076249e-01,
  84 9.837154311066546031e-01, 9.832326554588848300e-01, 9.827538663326288448e-01,
  85 9.822790745364429199e-01, 9.818082909081884413e-01, 9.813415263151109569e-01,
  86 9.808787916539204454e-01, 9.804200978508705866e-01, 9.799654558618393629e-01,
  87 9.795148766724087741e-01, 9.790683712979462161e-01, 9.786259507836846394e-01,
  88 9.781876262048033732e-01, 9.777534086665099489e-01, 9.773233093041209241e-01,
  89 9.768973392831440394e-01, 9.764755097993595978e-01, 9.760578320789027318e-01,
  90 9.756443173783457823e-01, 9.752349769847807881e-01, 9.748298222159020865e-01,
  91 9.744288644200894689e-01, 9.740321149764913367e-01, 9.736395852951079677e-01,
  92 9.732512868168755604e-01, 9.728672310137493895e-01, 9.724874293887887378e-01,
  93 9.721118934762408292e-01, 9.717406348416250950e-01, 9.713736650818186602e-01,
  94 9.710109958251406104e-01, 9.706526387314379223e-01, 9.702986054921705072e-01,
  95 9.699489078304969203e-01, 9.696035575013605134e-01, 9.692625662915755891e-01,
  96 9.689259460199136642e-01, 9.685937085371902899e-01, 9.682658657263515378e-01,
  97 9.679424295025619296e-01, 9.676234118132908124e-01, 9.673088246384006217e-01,
  98 9.669986799902344776e-01, 9.666929899137042259e-01, 9.663917664863788115e-01,
  99 9.660950218185727634e-01, 9.658027680534350123e-01, 9.655150173670379310e-01,
 100 9.652317819684667066e-01, 9.649530740999082701e-01, 9.646789060367420010e-01,
 101 9.644092900876289898e-01, 9.641442385946024096e-01, 9.638837639331581109e-01,
 102 9.636278785123455481e-01, 9.633765947748582636e-01, 9.631299251971253694e-01,
 103 9.628878822894031408e-01, 9.626504785958666099e-01, 9.624177266947013809e-01,
 104 9.621896391981960006e-01, 9.619662287528346623e-01, 9.617475080393891318e-01,
 105 9.615334897730127839e-01, 9.613241867033328614e-01, 9.611196116145447332e-01,
 106 9.609197773255048203e-01, 9.607246966898252971e-01, 9.605343825959679060e-01,
 107 9.603488479673386591e-01, 9.601681057623822069e-01, 9.599921689746773179e-01,
 108 9.598210506330320246e-01, 9.596547638015787696e-01, 9.594933215798706616e-01,
 109 9.593367371029771773e-01, 9.591850235415807502e-01, 9.590381941020729162e-01,
 110 9.588962620266514580e-01, 9.587592405934176609e-01, 9.586271431164729018e-01,
 111 9.584999829460172371e-01, 9.583777734684463256e-01, 9.582605281064505709e-01,
 112 9.581482603191123770e-01, 9.580409836020059577e-01, 9.579387114872952580e-01,
 113 9.578414575438342071e-01, 9.577492353772650846e-01, 9.576620586301189952e-01,
 114 9.575799409819160113e-01, 9.575028961492645374e-01, 9.574309378859631181e-01,
 115 9.573640799831001358e-01, 9.573023362691556182e-01, 9.572457206101023797e-01,
 116 9.571942469095077177e-01, 9.571479291086353314e-01, 9.571067811865475727e-01,
 117 9.570708171602075875e-01, 9.570400510845827879e-01, 9.570144970527471040e-01,
 118 9.569941691959850116e-01, 9.569790816838944503e-01, 9.569692487244911838e-01,
 119 9.569646845643128286e-01, 9.569654034885233251e-01, 9.569714198210175216e-01,
 120 9.569827479245263113e-01, 9.569994022007218826e-01, 9.570213970903235223e-01,
 121 9.570487470732028656e-01, 9.570814666684909211e-01, 9.571195704346837640e-01,
 122 9.571630729697496731e-01, 9.572119889112359337e-01, 9.572663329363761964e-01,
 123 9.573261197621985019e-01, 9.573913641456324175e-01, 9.574620808836177277e-01,
 124 9.575382848132127922e-01, 9.576199908117032367e-01, 9.577072137967114207e-01,
 125 9.577999687263049067e-01, 9.578982705991073709e-01, 9.580021344544072948e-01,
 126 9.581115753722692086e-01, 9.582266084736434930e-01, 9.583472489204779565e-01,
 127 9.584735119158284133e-01, 9.586054127039703721e-01, 9.587429665705107240e-01,
 128 9.588861888424999869e-01, 9.590350948885443261e-01, 9.591897001189184646e-01,
 129 9.593500199856788146e-01, 9.595160699827764983e-01, 9.596878656461707013e-01,
 130 9.598654225539432483e-01, 9.600487563264122892e-01, 9.602378826262468747e-01,
 131 9.604328171585819751e-01, 9.606335756711334994e-01, 9.608401739543135367e-01,
 132 9.610526278413467072e-01, 9.612709532083855146e-01, 9.614951659746271417e-01,
 133 9.617252821024303566e-01, 9.619613175974318642e-01, 9.622032885086644338e-01,
 134 9.624512109286739170e-01, 9.627051009936374859e-01, 9.629649748834822054e-01,
 135 9.632308488220031606e-01, 9.635027390769824729e-01, 9.637806619603088709e-01,
 136 9.640646338280971506e-01, 9.643546710808080791e-01, 9.646507901633681881e-01,
 137 9.649530075652912320e-01, 9.652613398207983142e-01, 9.655758035089392344e-01,
 138 9.658964152537145020e-01, 9.662231917241966839e-01, 9.665561496346526393e-01,
 139 9.668953057446663113e-01, 9.672406768592617388e-01, 9.675922798290256255e-01,
 140 9.679501315502314629e-01, 9.683142489649629869e-01, 9.686846490612389671e-01,
 141 9.690613488731369962e-01, 9.694443654809188349e-01, 9.698337160111555333e-01,
 142 9.702294176368531087e-01, 9.706314875775782225e-01, 9.710399430995845238e-01,
 143 9.714548015159391037e-01, 9.718760801866497268e-01, 9.723037965187919518e-01,
 144 9.727379679666363632e-01, 9.731786120317773570e-01, 9.736257462632605941e-01,
 145 9.740793882577122309e-01, 9.745395556594674824e-01, 9.750062661607005188e-01,
 146 9.754795375015535841e-01, 9.759593874702675587e-01, 9.764458339033119660e-01,
 147 9.769388946855159794e-01, 9.774385877501994280e-01, 9.779449310793042471e-01,
 148 9.784579427035267063e-01, 9.789776407024486371e-01, 9.795040432046712153e-01,
 149 9.800371683879468554e-01, 9.805770344793129922e-01, 9.811236597552254191e-01,
 150 9.816770625416927354e-01, 9.822372612144102400e-01, 9.828042741988944897e-01,
 151 9.833781199706193021e-01, 9.839588170551499813e-01, 9.845463840282800971e-01,
 152 9.851408395161672660e-01, 9.857422021954695968e-01, 9.863504907934828037e-01,
 153 9.869657240882776517e-01, 9.875879209088370692e-01, 9.882171001351949258e-01,
 154 9.888532806985737000e-01, 9.894964815815237014e-01, 9.901467218180625141e-01,
 155 9.908040204938135531e-01, 9.914683967461471736e-01, 9.921398697643202258e-01,
 156 9.928184587896166091e-01, 9.935041831154891590e-01, 9.941970620877000897e-01,
 157 9.948971151044636585e-01, 9.956043616165879406e-01, 9.963188211276171602e-01,
 158 9.970405131939754639e-01, 9.977694574251096959e-01, 9.985056734836331715e-01,
 159 9.992491810854701173e-01
 160 };
 161
 162 static const double
 163         K256ONLN2 = 369.3299304675746271,
 164         KA2 = 3.66556671660783833261e-06,
 165         KA1 = 2.70760782821392980564e-03,
 166         KA0 = 1.0;
 167
 168 static const float extreme[2] = { 1.0e30f, 1.0e-30f };
 169
 170 #define PROCESS(N)                                              \
 171         x##N *= K256ONLN2;                                      \
 172         k##N = (int) x##N;                                      \
 173         x##N -= (double) k##N;                                  \
 174         x##N = (KA2 * x##N + KA1) * x##N + KA0;                 \
 175         lres##N = ((long long *)__TBL_exp2f)[k##N & 0xff];      \
 176         lres##N += (long long)k##N << 44;                       \
 177         *y = (float) (x##N * *(double *)&lres##N);              \
 178         y += stridey
 179
 180
 181 #define PREPROCESS(N, index, label)                             \
 182         xi = *(int *)x;                                         \
 183         ax = xi & ~0x80000000;                                  \
 184         fx = *x;                                                \
 185         x += stridex;                                           \
 186         if (ax > 0x42cff1b4)    /* 103.972076f */               \
 187         {                                                       \
 188                 sign = (unsigned)xi >> 31;                      \
 189                 if (ax >= 0x7f800000)   /* |x| = inf or nan */  \
 190                 {                                               \
 191                         if (ax > 0x7f800000)    /* nan */       \
 192                         {                                       \
 193                                 y[index] = fx * fx;             \
 194                                 goto label;                     \
 195                         }                                       \
 196                         y[index] = (sign) ? 0.0f : fx;          \
 197                         goto label;                             \
 198                 }                                               \
 199                 fx = extreme[sign];                             \
 200                 y[index] = fx * fx;                             \
 201                 goto label;                                     \
 202         }                                                       \
 203         x##N = fx
 204
 205
 206 void
 207 __vexpf(int n, float * restrict x, int stridex, float * restrict y,
 208         int stridey)
 209 {
 210         double          x0, x1, x2, x3, x4;
 211         double          res0, res1, res2, res3, res4;
 212         float           fx;
 213         long long       lres0, lres1, lres2, lres3, lres4;
 214         int             k0, k1, k2, k3, k4;
 215         int             xi, ax, sign;
 216
 217         y -= stridey;
 218
 219         for (; ;)
 220         {
 221 begin:
 222                 if (--n < 0)
 223                         break;
 224                 y += stridey;
 225
 226                 PREPROCESS(0, 0, begin);
 227
 228                 if (--n < 0)
 229                         goto process1;
 230
 231                 PREPROCESS(1, stridey, process1);
 232
 233                 if (--n < 0)
 234                         goto process2;
 235
 236                 PREPROCESS(2, stridey << 1, process2);
 237
 238                 if (--n < 0)
 239                         goto process3;
 240
 241                 PREPROCESS(3, (stridey << 1) + stridey, process3);
 242
 243                 if (--n < 0)
 244                         goto process4;
 245
 246                 PREPROCESS(4, (stridey << 2), process4);
 247
 248                 x0 *= K256ONLN2;
 249                 x1 *= K256ONLN2;
 250                 x2 *= K256ONLN2;
 251                 x3 *= K256ONLN2;
 252                 x4 *= K256ONLN2;
 253
 254                 k0 = (int)x0;
 255                 k1 = (int)x1;
 256                 k2 = (int)x2;
 257                 k3 = (int)x3;
 258                 k4 = (int)x4;
 259
 260                 x0 -= (double)k0;
 261                 x1 -= (double)k1;
 262                 x2 -= (double)k2;
 263                 x3 -= (double)k3;
 264                 x4 -= (double)k4;
 265
 266                 x0 = (KA2 * x0 + KA1) * x0 + KA0;
 267                 x1 = (KA2 * x1 + KA1) * x1 + KA0;
 268                 x2 = (KA2 * x2 + KA1) * x2 + KA0;
 269                 x3 = (KA2 * x3 + KA1) * x3 + KA0;
 270                 x4 = (KA2 * x4 + KA1) * x4 + KA0;
 271
 272                 lres0 = ((long long *)__TBL_exp2f)[k0 & 255];
 273                 lres1 = ((long long *)__TBL_exp2f)[k1 & 255];
 274                 lres2 = ((long long *)__TBL_exp2f)[k2 & 255];
 275                 lres3 = ((long long *)__TBL_exp2f)[k3 & 255];
 276                 lres4 = ((long long *)__TBL_exp2f)[k4 & 255];
 277
 278                 lres0 += (long long)k0 << 44;
 279                 res0 = *(double *)&lres0;
 280                 lres1 += (long long)k1 << 44;
 281                 res1 = *(double *)&lres1;
 282                 lres2 += (long long)k2 << 44;
 283                 res2 = *(double *)&lres2;
 284                 lres3 += (long long)k3 << 44;
 285                 res3 = *(double *)&lres3;
 286                 lres4 += (long long)k4 << 44;
 287                 res4 = *(double *)&lres4;
 288
 289                 *y = (float)(res0 * x0);
 290                 y += stridey;
 291                 *y = (float)(res1 * x1);
 292                 y += stridey;
 293                 *y = (float)(res2 * x2);
 294                 y += stridey;
 295                 *y = (float)(res3 * x3);
 296                 y += stridey;
 297                 *y = (float)(res4 * x4);
 298                 continue;
 299
 300 process1:
 301                 PROCESS(0);
 302                 continue;
 303
 304 process2:
 305                 PROCESS(0);
 306                 PROCESS(1);
 307                 continue;
 308
 309 process3:
 310                 PROCESS(0);
 311                 PROCESS(1);
 312                 PROCESS(2);
 313                 continue;
 314
 315 process4:
 316                 PROCESS(0);
 317                 PROCESS(1);
 318                 PROCESS(2);
 319                 PROCESS(3);
 320         }
 321 }