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 } 219