logf.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* 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
* 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.
*/
/*
* 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;
hx = *(int *)&x;
return ((hx < 0)? x * 0.0f : x * x);
exp = 0;
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;
}
ix &= 0x007fffff;
i = iy >> 17;
f = (float)(t + v);
return (f);
}