usr/src/lib/libm/common/C/log10.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 __log10 = log10
  30
  31 /* INDENT OFF */
  32 /*
  33  * log10(x) = log(x)/log10
  34  *
  35  * Base on Table look-up algorithm with product polynomial
  36  * approximation for log(x).
  37  *
  38  * By K.C. Ng, Nov 29, 2004
  39  *
  40  * (a). For x in [1-0.125, 1+0.125], from log.c we have
  41  *      log(x) =  f + ((a1*f^2) *
  42  *                 ((a2 + (a3*f)*(a4+f)) + (f^3)*(a5+f))) *
  43  *                 (((a6 + f*(a7+f)) + (f^3)*(a8+f)) *
  44  *                 ((a9 + (a10*f)*(a11+f)) + (f^3)*(a12+f)))
  45  *      where f = x - 1.
  46  *      (i) modify a1 <- a1 / log10
  47  *      (ii) 1/log10 = 0.4342944819...
  48  *                   = 0.4375 - 0.003205518... (7 bit shift)
  49  *           Let lgv = 0.4375 - 1/log10, then
  50  *           lgv = 0.003205518096748172348871081083395...,
  51  *      (iii) f*0.4375 is exact because f has 3 trailing zero.
  52  *      (iv) Thus, log10(x) = f*0.4375 - (lgv*f - PPoly)
  53  *
  54  * (b). For 0.09375 <= x < 24
  55  *      Let j = (ix - 0x3fb80000) >> 15. Look up Y[j], 1/Y[j], and log(Y[j])
  56  *      from _TBL_log.c. Then
  57  *              log10(x)  = log10(Y[j]) + log10(1 + (x-Y[j])*(1/Y[j]))
  58  *                        = log(Y[j])(1/log10) + log10(1 + s)
  59  *      where
  60  *              s = (x-Y[j])*(1/Y[j])
  61  *      From log.c, we have log(1+s) =
  62  *                                2              2                     2
  63  *              (b s) (b + b s + s ) [b + b s + s (b + s)] (b + b s + s )
  64  *                1     2   3          4   5        6        7   8
  65  *
  66  *      By setting b1 <- b1/log10, we have
  67  *              log10(x) = 0.4375 * T - (lgv * T - POLY(s))
  68  *
  69  * (c). Otherwise, get "n", the exponent of x, and then normalize x to
  70  *      z in [1,2). Then similar to (b) find a Y[i] that matches z to 5.5
  71  *      significant bits. Then
  72  *          log(x) = n*ln2 + log(Y[i]) + log(z/Y[i]).
  73  *          log10(x) = n*(ln2/ln10) + log10(z).
  74  *
  75  * Special cases:
  76  *      log10(x) is NaN with signal if x < 0 (including -INF) ;
  77  *      log10(+INF) is +INF; log10(0) is -INF with signal;
  78  *      log10(NaN) is that NaN with no signal.
  79  *
  80  * Maximum error observed: less than 0.89 ulp
  81  *
  82  * Constants:
  83  * The hexadecimal values are the intended ones for the following constants.
  84  * The decimal values may be used, provided that the compiler will convert
  85  * from decimal to binary accurately enough to produce the hexadecimal values
  86  * shown.
  87  */
  88 /* INDENT ON */
  89
  90 #include "libm.h"
  91
  92 extern const double _TBL_log[];
  93
  94 static const double P[] = {
  95 /* ONE   */  1.0,
  96 /* TWO52 */  4503599627370496.0,
  97 /* LNAHI */  3.01029995607677847147e-01,        /* 3FD34413 50900000 */
  98 /* LNALO */  5.63033480667509769841e-11,        /* 3DCEF3FD E623E256 */
  99 /* A1    */ -2.9142521960136582507385480707044582802184e-02,
 100 /* A2    */  1.99628461483039965074226529395673424005508422852e+0000,
 101 /* A3    */  2.26812367662950720159642514772713184356689453125e+0000,
 102 /* A4    */ -9.05030639084976384900471657601883634924888610840e-0001,
 103 /* A5    */ -1.48275767132434044270894446526654064655303955078e+0000,
 104 /* A6    */  1.88158320939722756293122074566781520843505859375e+0000,
 105 /* A7    */  1.83309386046986411145098827546462416648864746094e+0000,
 106 /* A8    */  1.24847063988317086291601754055591300129890441895e+0000,
 107 /* A9    */  1.98372421445537705508854742220137268304824829102e+0000,
 108 /* A10   */ -3.94711735767898475035764249696512706577777862549e-0001,
 109 /* A11   */  3.07890395362954372160402272129431366920471191406e+0000,
 110 /* A12   */ -9.60099585275022149311041630426188930869102478027e-0001,
 111 /* B1    */ -5.4304894950350052960838096752491540286689e-02,
 112 /* B2    */  1.87161713283355151891381127914642725337613123482e+0000,
 113 /* B3    */ -1.89082956295731507978530316904652863740921020508e+0000,
 114 /* B4    */ -2.50562891673640253387134180229622870683670043945e+0000,
 115 /* B5    */  1.64822828085258366037635369139024987816810607910e+0000,
 116 /* B6    */ -1.24409107065868340669112512841820716857910156250e+0000,
 117 /* B7    */  1.70534231658220414296067701798165217041969299316e+0000,
 118 /* B8    */  1.99196833784655646937267192697618156671524047852e+0000,
 119 /* LGH   */  0.4375,
 120 /* LGL   */  0.003205518096748172348871081083395,
 121 /* LG10V */  0.43429448190325182765112891891660509576226,
 122 };
 123
 124 #define ONE   P[0]
 125 #define TWO52 P[1]
 126 #define LNAHI P[2]
 127 #define LNALO P[3]
 128 #define A1    P[4]
 129 #define A2    P[5]
 130 #define A3    P[6]
 131 #define A4    P[7]
 132 #define A5    P[8]
 133 #define A6    P[9]
 134 #define A7    P[10]
 135 #define A8    P[11]
 136 #define A9    P[12]
 137 #define A10   P[13]
 138 #define A11   P[14]
 139 #define A12   P[15]
 140 #define B1    P[16]
 141 #define B2    P[17]
 142 #define B3    P[18]
 143 #define B4    P[19]
 144 #define B5    P[20]
 145 #define B6    P[21]
 146 #define B7    P[22]
 147 #define B8    P[23]
 148 #define LGH   P[24]
 149 #define LGL   P[25]
 150 #define LG10V P[26]
 151
 152 double
 153 log10(double x) {
 154         double  *tb, dn, dn1, s, z, r, w;
 155         int     i, hx, ix, n, lx;
 156
 157         n = 0;
 158         hx = ((int *)&x)[HIWORD];
 159         ix = hx & 0x7fffffff;
 160         lx = ((int *)&x)[LOWORD];
 161
 162         /* subnormal,0,negative,inf,nan */
 163         if ((hx + 0x100000) < 0x200000) {
 164                 if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0)) /* nan */
 165                         return (x * x);
 166                 if (((hx << 1) | lx) == 0)              /* zero */
 167                         return (_SVID_libm_err(x, x, 18));
 168                 if (hx < 0)                             /* negative */
 169                         return (_SVID_libm_err(x, x, 19));
 170                 if (((hx - 0x7ff00000) | lx) == 0)      /* +inf */
 171                         return (x);
 172
 173                 /* x must be positive and subnormal */
 174                 x *= TWO52;
 175                 n = -52;
 176                 ix = ((int *)&x)[HIWORD];
 177                 lx = ((int *)&x)[LOWORD];
 178         }
 179
 180         i = ix >> 19;
 181         if (i >= 0x7f7 && i <= 0x806) {
 182                 /* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */
 183                 if (ix >= 0x3fec0000 && ix < 0x3ff20000) {
 184                         /* 0.875 <= x < 1.125 */
 185                         s = x - ONE;
 186                         z = s * s;
 187                         if (((ix - 0x3ff00000) | lx) == 0) /* x = 1 */
 188                                 return (z);
 189                         r = (A10 * s) * (A11 + s);
 190                         w = z * s;
 191                         return (LGH * s - (LGL * s - ((A1 * z) *
 192                                 ((A2 + (A3 * s) * (A4 + s)) + w * (A5 + s))) *
 193                                 (((A6 + s * (A7 + s)) + w * (A8 + s)) *
 194                                 ((A9 + r) + w * (A12 + s)))));
 195                 } else {
 196                         i = (ix - 0x3fb80000) >> 15;
 197                         tb = (double *)_TBL_log + (i + i + i);
 198                         s = (x - tb[0]) * tb[1];
 199                         return (LGH * tb[2] - (LGL * tb[2] - ((B1 * s) *
 200                                 (B2 + s * (B3 + s))) *
 201                                 (((B4 + s * B5) + (s * s) * (B6 + s)) *
 202                                 (B7 + s * (B8 + s)))));
 203                 }
 204         } else {
 205                 dn = (double)(n + ((ix >> 20) - 0x3ff));
 206                 dn1 = dn * LNAHI;
 207                 i = (ix & 0x000fffff) | 0x3ff00000;     /* scale x to [1,2] */
 208                 ((int *)&x)[HIWORD] = i;
 209                 i = (i - 0x3fb80000) >> 15;
 210                 tb = (double *)_TBL_log + (i + i + i);
 211                 s = (x - tb[0]) * tb[1];
 212                 dn = dn * LNALO + tb[2] * LG10V;
 213                 return (dn1 + (dn + ((B1 * s) *
 214                         (B2 + s * (B3 + s))) *
 215                         (((B4 + s * B5) + (s * s) * (B6 + s)) *
 216                         (B7 + s * (B8 + s)))));
 217         }
 218 }