usr/src/lib/libm/common/R/logf.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  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28
  29 #pragma weak __logf = logf
  30
  31 /*
  32  * Algorithm:
  33  *
  34  * Let y = x rounded to six significant bits.  Then for any choice
  35  * of e and z such that y = 2^e z, we have
  36  *
  37  * log(x) = e log(2) + log(z) + log(1+(x-y)/y)
  38  *
  39  * Note that (x-y)/y = (x'-y')/y' for any scaled x' = sx, y' = sy;
  40  * in particular, we can take s to be the power of two that makes
  41  * ulp(x') = 1.
  42  *
  43  * From a table, obtain l = log(z) and r = 1/y'.  For |s| <= 2^-6,
  44  * approximate log(1+s) by a polynomial p(s) where p(s) := s+s*s*
  45  * (K1+s*(K2+s*K3)).  Then we compute the expression above as
  46  * e*ln2 + l + p(r*(x'-y')) all evaluated in double precision.
  47  *
  48  * When x is subnormal, we first scale it to the normal range,
  49  * adjusting e accordingly.
  50  *
  51  * Accuracy:
  52  *
  53  * The largest error is less than 0.6 ulps.
  54  */
  55
  56 #include "libm.h"
  57
  58 /*
  59  * For i = 0, ..., 12,
  60  *   TBL[2i] = log(1 + i/32) and TBL[2i+1] = 2^-23 / (1 + i/32)
  61  *
  62  * For i = 13, ..., 32,
  63  *   TBL[2i] = log(1/2 + i/64) and TBL[2i+1] = 2^-23 / (1 + i/32)
  64  */
  65 static const double TBL[] = {
  66         0.000000000000000000e+00, 1.192092895507812500e-07,
  67         3.077165866675368733e-02, 1.155968868371212153e-07,
  68         6.062462181643483994e-02, 1.121969784007352926e-07,
  69         8.961215868968713805e-02, 1.089913504464285680e-07,
  70         1.177830356563834557e-01, 1.059638129340277719e-07,
  71         1.451820098444978890e-01, 1.030999260979729787e-07,
  72         1.718502569266592284e-01, 1.003867701480263102e-07,
  73         1.978257433299198675e-01, 9.781275040064102225e-08,
  74         2.231435513142097649e-01, 9.536743164062500529e-08,
  75         2.478361639045812692e-01, 9.304139672256097884e-08,
  76         2.719337154836417580e-01, 9.082612537202380448e-08,
  77         2.954642128938358980e-01, 8.871388989825581272e-08,
  78         3.184537311185345887e-01, 8.669766512784091150e-08,
  79         -3.522205935893520934e-01, 8.477105034722222546e-08,
  80         -3.302416868705768671e-01, 8.292820142663043248e-08,
  81         -3.087354816496132859e-01, 8.116377160904255122e-08,
  82         -2.876820724517809014e-01, 7.947285970052082892e-08,
  83         -2.670627852490452536e-01, 7.785096460459183052e-08,
  84         -2.468600779315257843e-01, 7.629394531250000159e-08,
  85         -2.270574506353460753e-01, 7.479798560049019504e-08,
  86         -2.076393647782444896e-01, 7.335956280048077330e-08,
  87         -1.885911698075500298e-01, 7.197542010613207272e-08,
  88         -1.698990367953974734e-01, 7.064254195601851460e-08,
  89         -1.515498981272009327e-01, 6.935813210227272390e-08,
  90         -1.335313926245226268e-01, 6.811959402901785336e-08,
  91         -1.158318155251217008e-01, 6.692451343201754014e-08,
  92         -9.844007281325252434e-02, 6.577064251077586116e-08,
  93         -8.134563945395240081e-02, 6.465588585805084723e-08,
  94         -6.453852113757117814e-02, 6.357828776041666578e-08,
  95         -4.800921918636060631e-02, 6.253602074795082293e-08,
  96         -3.174869831458029812e-02, 6.152737525201612732e-08,
  97         -1.574835696813916761e-02, 6.055075024801586965e-08,
  98         0.000000000000000000e+00, 5.960464477539062500e-08,
  99 };
 100
 101 static const double C[] = {
 102         6.931471805599452862e-01,
 103         -2.49887584306188944706e-01,
 104         3.33368809981254554946e-01,
 105         -5.00000008402474976565e-01
 106 };
 107
 108 #define ln2     C[0]
 109 #define K3      C[1]
 110 #define K2      C[2]
 111 #define K1      C[3]
 112
 113 float
 114 logf(float x)
 115 {
 116         double  v, t;
 117         float   f;
 118         int     hx, ix, i, exp, iy;
 119
 120         hx = *(int *)&x;
 121         ix = hx & ~0x80000000;
 122
 123         if (ix >= 0x7f800000)   /* nan or inf */
 124                 return ((hx < 0)? x * 0.0f : x * x);
 125
 126         exp = 0;
 127         if (hx < 0x00800000) { /* negative, zero, or subnormal */
 128                 if (hx <= 0) {
 129                         f = 0.0f;
 130                         return ((ix == 0)? -1.0f / f : f / f);
 131                 }
 132
 133                 /* subnormal; scale by 2^149 */
 134                 f = (float)ix;
 135                 ix = *(int *)&f;
 136                 exp = -149;
 137         }
 138
 139         exp += (ix - 0x3f320000) >> 23;
 140         ix &= 0x007fffff;
 141         iy = (ix + 0x20000) & 0xfffc0000;
 142         i = iy >> 17;
 143         t = ln2 * (double)exp + TBL[i];
 144         v = (double)(ix - iy) * TBL[i + 1];
 145         v += (v * v) * (K1 + v * (K2 + v * K3));
 146         f = (float)(t + v);
 147         return (f);
 148 }