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Diffstat (limited to 'usr/src/lib/libm/common/R/logf.c')
| -rw-r--r-- | usr/src/lib/libm/common/R/logf.c | 148 |
1 files changed, 148 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/R/logf.c b/usr/src/lib/libm/common/R/logf.c new file mode 100644 index 0000000000..d746260917 --- /dev/null +++ b/usr/src/lib/libm/common/R/logf.c @@ -0,0 +1,148 @@ +/* + * 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 logf = __logf + +/* + * Algorithm: + * + * Let y = x rounded to six significant bits. Then for any choice + * of e and z such that y = 2^e z, we have + * + * log(x) = e log(2) + log(z) + log(1+(x-y)/y) + * + * Note that (x-y)/y = (x'-y')/y' for any scaled x' = sx, y' = sy; + * in particular, we can take s to be the power of two that makes + * ulp(x') = 1. + * + * From a table, obtain l = log(z) and r = 1/y'. For |s| <= 2^-6, + * approximate log(1+s) by a polynomial p(s) where p(s) := s+s*s* + * (K1+s*(K2+s*K3)). Then we compute the expression above as + * e*ln2 + l + p(r*(x'-y')) all evaluated in double precision. + * + * When x is subnormal, we first scale it to the normal range, + * adjusting e accordingly. + * + * Accuracy: + * + * The largest error is less than 0.6 ulps. + */ + +#include "libm.h" + +/* + * For i = 0, ..., 12, + * TBL[2i] = log(1 + i/32) and TBL[2i+1] = 2^-23 / (1 + i/32) + * + * For i = 13, ..., 32, + * TBL[2i] = log(1/2 + i/64) and TBL[2i+1] = 2^-23 / (1 + i/32) + */ +static const double TBL[] = { + 0.000000000000000000e+00, 1.192092895507812500e-07, + 3.077165866675368733e-02, 1.155968868371212153e-07, + 6.062462181643483994e-02, 1.121969784007352926e-07, + 8.961215868968713805e-02, 1.089913504464285680e-07, + 1.177830356563834557e-01, 1.059638129340277719e-07, + 1.451820098444978890e-01, 1.030999260979729787e-07, + 1.718502569266592284e-01, 1.003867701480263102e-07, + 1.978257433299198675e-01, 9.781275040064102225e-08, + 2.231435513142097649e-01, 9.536743164062500529e-08, + 2.478361639045812692e-01, 9.304139672256097884e-08, + 2.719337154836417580e-01, 9.082612537202380448e-08, + 2.954642128938358980e-01, 8.871388989825581272e-08, + 3.184537311185345887e-01, 8.669766512784091150e-08, + -3.522205935893520934e-01, 8.477105034722222546e-08, + -3.302416868705768671e-01, 8.292820142663043248e-08, + -3.087354816496132859e-01, 8.116377160904255122e-08, + -2.876820724517809014e-01, 7.947285970052082892e-08, + -2.670627852490452536e-01, 7.785096460459183052e-08, + -2.468600779315257843e-01, 7.629394531250000159e-08, + -2.270574506353460753e-01, 7.479798560049019504e-08, + -2.076393647782444896e-01, 7.335956280048077330e-08, + -1.885911698075500298e-01, 7.197542010613207272e-08, + -1.698990367953974734e-01, 7.064254195601851460e-08, + -1.515498981272009327e-01, 6.935813210227272390e-08, + -1.335313926245226268e-01, 6.811959402901785336e-08, + -1.158318155251217008e-01, 6.692451343201754014e-08, + -9.844007281325252434e-02, 6.577064251077586116e-08, + -8.134563945395240081e-02, 6.465588585805084723e-08, + -6.453852113757117814e-02, 6.357828776041666578e-08, + -4.800921918636060631e-02, 6.253602074795082293e-08, + -3.174869831458029812e-02, 6.152737525201612732e-08, + -1.574835696813916761e-02, 6.055075024801586965e-08, + 0.000000000000000000e+00, 5.960464477539062500e-08, +}; + +static const double C[] = { + 6.931471805599452862e-01, + -2.49887584306188944706e-01, + 3.33368809981254554946e-01, + -5.00000008402474976565e-01 +}; + +#define ln2 C[0] +#define K3 C[1] +#define K2 C[2] +#define K1 C[3] + +float +logf(float x) +{ + double v, t; + float f; + int hx, ix, i, exp, iy; + + hx = *(int *)&x; + ix = hx & ~0x80000000; + + if (ix >= 0x7f800000) /* nan or inf */ + return ((hx < 0)? x * 0.0f : x * x); + + exp = 0; + if (hx < 0x00800000) { /* negative, zero, or subnormal */ + if (hx <= 0) { + f = 0.0f; + return ((ix == 0)? -1.0f / f : f / f); + } + + /* subnormal; scale by 2^149 */ + f = (float)ix; + ix = *(int *)&f; + exp = -149; + } + + exp += (ix - 0x3f320000) >> 23; + ix &= 0x007fffff; + iy = (ix + 0x20000) & 0xfffc0000; + i = iy >> 17; + t = ln2 * (double)exp + TBL[i]; + v = (double)(ix - iy) * TBL[i + 1]; + v += (v * v) * (K1 + v * (K2 + v * K3)); + f = (float)(t + v); + return (f); +} |