/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2005 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak log10 = __log10 /* INDENT OFF */ /* * log10(x) = log(x)/log10 * * Base on Table look-up algorithm with product polynomial * approximation for log(x). * * By K.C. Ng, Nov 29, 2004 * * (a). For x in [1-0.125, 1+0.125], from log.c we have * log(x) = f + ((a1*f^2) * * ((a2 + (a3*f)*(a4+f)) + (f^3)*(a5+f))) * * (((a6 + f*(a7+f)) + (f^3)*(a8+f)) * * ((a9 + (a10*f)*(a11+f)) + (f^3)*(a12+f))) * where f = x - 1. * (i) modify a1 <- a1 / log10 * (ii) 1/log10 = 0.4342944819... * = 0.4375 - 0.003205518... (7 bit shift) * Let lgv = 0.4375 - 1/log10, then * lgv = 0.003205518096748172348871081083395..., * (iii) f*0.4375 is exact because f has 3 trailing zero. * (iv) Thus, log10(x) = f*0.4375 - (lgv*f - PPoly) * * (b). For 0.09375 <= x < 24 * Let j = (ix - 0x3fb80000) >> 15. Look up Y[j], 1/Y[j], and log(Y[j]) * from _TBL_log.c. Then * log10(x) = log10(Y[j]) + log10(1 + (x-Y[j])*(1/Y[j])) * = log(Y[j])(1/log10) + log10(1 + s) * where * s = (x-Y[j])*(1/Y[j]) * From log.c, we have log(1+s) = * 2 2 2 * (b s) (b + b s + s ) [b + b s + s (b + s)] (b + b s + s ) * 1 2 3 4 5 6 7 8 * * By setting b1 <- b1/log10, we have * log10(x) = 0.4375 * T - (lgv * T - POLY(s)) * * (c). Otherwise, get "n", the exponent of x, and then normalize x to * z in [1,2). Then similar to (b) find a Y[i] that matches z to 5.5 * significant bits. Then * log(x) = n*ln2 + log(Y[i]) + log(z/Y[i]). * log10(x) = n*(ln2/ln10) + log10(z). * * Special cases: * log10(x) is NaN with signal if x < 0 (including -INF) ; * log10(+INF) is +INF; log10(0) is -INF with signal; * log10(NaN) is that NaN with no signal. * * Maximum error observed: less than 0.89 ulp * * Constants: * The hexadecimal values are the intended ones for the following constants. * The decimal values may be used, provided that the compiler will convert * from decimal to binary accurately enough to produce the hexadecimal values * shown. */ /* INDENT ON */ #include "libm.h" extern const double _TBL_log[]; static const double P[] = { /* ONE */ 1.0, /* TWO52 */ 4503599627370496.0, /* LNAHI */ 3.01029995607677847147e-01, /* 3FD34413 50900000 */ /* LNALO */ 5.63033480667509769841e-11, /* 3DCEF3FD E623E256 */ /* A1 */ -2.9142521960136582507385480707044582802184e-02, /* A2 */ 1.99628461483039965074226529395673424005508422852e+0000, /* A3 */ 2.26812367662950720159642514772713184356689453125e+0000, /* A4 */ -9.05030639084976384900471657601883634924888610840e-0001, /* A5 */ -1.48275767132434044270894446526654064655303955078e+0000, /* A6 */ 1.88158320939722756293122074566781520843505859375e+0000, /* A7 */ 1.83309386046986411145098827546462416648864746094e+0000, /* A8 */ 1.24847063988317086291601754055591300129890441895e+0000, /* A9 */ 1.98372421445537705508854742220137268304824829102e+0000, /* A10 */ -3.94711735767898475035764249696512706577777862549e-0001, /* A11 */ 3.07890395362954372160402272129431366920471191406e+0000, /* A12 */ -9.60099585275022149311041630426188930869102478027e-0001, /* B1 */ -5.4304894950350052960838096752491540286689e-02, /* B2 */ 1.87161713283355151891381127914642725337613123482e+0000, /* B3 */ -1.89082956295731507978530316904652863740921020508e+0000, /* B4 */ -2.50562891673640253387134180229622870683670043945e+0000, /* B5 */ 1.64822828085258366037635369139024987816810607910e+0000, /* B6 */ -1.24409107065868340669112512841820716857910156250e+0000, /* B7 */ 1.70534231658220414296067701798165217041969299316e+0000, /* B8 */ 1.99196833784655646937267192697618156671524047852e+0000, /* LGH */ 0.4375, /* LGL */ 0.003205518096748172348871081083395, /* LG10V */ 0.43429448190325182765112891891660509576226, }; #define ONE P[0] #define TWO52 P[1] #define LNAHI P[2] #define LNALO P[3] #define A1 P[4] #define A2 P[5] #define A3 P[6] #define A4 P[7] #define A5 P[8] #define A6 P[9] #define A7 P[10] #define A8 P[11] #define A9 P[12] #define A10 P[13] #define A11 P[14] #define A12 P[15] #define B1 P[16] #define B2 P[17] #define B3 P[18] #define B4 P[19] #define B5 P[20] #define B6 P[21] #define B7 P[22] #define B8 P[23] #define LGH P[24] #define LGL P[25] #define LG10V P[26] double log10(double x) { double *tb, dn, dn1, s, z, r, w; int i, hx, ix, n, lx; n = 0; hx = ((int *)&x)[HIWORD]; ix = hx & 0x7fffffff; lx = ((int *)&x)[LOWORD]; /* subnormal,0,negative,inf,nan */ if ((hx + 0x100000) < 0x200000) { if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0)) /* nan */ return (x * x); if (((hx << 1) | lx) == 0) /* zero */ return (_SVID_libm_err(x, x, 18)); if (hx < 0) /* negative */ return (_SVID_libm_err(x, x, 19)); if (((hx - 0x7ff00000) | lx) == 0) /* +inf */ return (x); /* x must be positive and subnormal */ x *= TWO52; n = -52; ix = ((int *)&x)[HIWORD]; lx = ((int *)&x)[LOWORD]; } i = ix >> 19; if (i >= 0x7f7 && i <= 0x806) { /* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */ if (ix >= 0x3fec0000 && ix < 0x3ff20000) { /* 0.875 <= x < 1.125 */ s = x - ONE; z = s * s; if (((ix - 0x3ff00000) | lx) == 0) /* x = 1 */ return (z); r = (A10 * s) * (A11 + s); w = z * s; return (LGH * s - (LGL * s - ((A1 * z) * ((A2 + (A3 * s) * (A4 + s)) + w * (A5 + s))) * (((A6 + s * (A7 + s)) + w * (A8 + s)) * ((A9 + r) + w * (A12 + s))))); } else { i = (ix - 0x3fb80000) >> 15; tb = (double *)_TBL_log + (i + i + i); s = (x - tb[0]) * tb[1]; return (LGH * tb[2] - (LGL * tb[2] - ((B1 * s) * (B2 + s * (B3 + s))) * (((B4 + s * B5) + (s * s) * (B6 + s)) * (B7 + s * (B8 + s))))); } } else { dn = (double)(n + ((ix >> 20) - 0x3ff)); dn1 = dn * LNAHI; i = (ix & 0x000fffff) | 0x3ff00000; /* scale x to [1,2] */ ((int *)&x)[HIWORD] = i; i = (i - 0x3fb80000) >> 15; tb = (double *)_TBL_log + (i + i + i); s = (x - tb[0]) * tb[1]; dn = dn * LNALO + tb[2] * LG10V; return (dn1 + (dn + ((B1 * s) * (B2 + s * (B3 + s))) * (((B4 + s * B5) + (s * s) * (B6 + s)) * (B7 + s * (B8 + s))))); } }