/*
* 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]
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* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __log2 = log2
/* INDENT OFF */
/*
* log2(x) = log(x)/log2
*
* 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 / log2
* (ii) 1/log2 = 1.4426950408889634...
* = 1.5 - 0.057304959... (4 bit shift)
* Let lv = 1.5 - 1/log2, then
* lv = 0.057304959111036592640075318998107956665325,
* (iii) f*1.5 is exact because f has 3 trailing zero.
* (iv) Thus, log2(x) = f*1.5 - (lv*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
* log2(x) = log2(Y[j]) + log2(1 + (x-Y[j])*(1/Y[j]))
* = log(Y[j])(1/log2) + log2(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/log2, we have
* log2(x) = 1.5 * T - (lv * 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
* log2(x) = n + log2(z).
*
* Special cases:
* log2(x) is NaN with signal if x < 0 (including -INF) ;
* log2(+INF) is +INF; log2(0) is -INF with signal;
* log2(NaN) is that NaN with no signal.
*
* Maximum error observed: less than 0.84 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"
#include "libm_protos.h"
extern const double _TBL_log[];
static const double P[] = {
/* ONE */ 1.0,
/* TWO52 */ 4503599627370496.0,
/* LN10V */ 1.4426950408889634073599246810018920433347, /* 1/log10 */
/* ZERO */ 0.0,
/* A1 */ -9.6809362455249638217841932228967194640116e-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 */ -1.8039695622547469514898963204616532885451e-01,
/* 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 */ 1.5,
/* LGL */ 0.057304959111036592640075318998107956665325,
};
#define ONE P[0]
#define TWO52 P[1]
#define LN10V P[2]
#define ZERO 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]
double
log2(double x) {
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 defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
return (x); /* for Cheetah when x is QNaN */
#endif
if (((hx << 1) | lx) == 0) /* log(0.0) = -inf */
return (A5 / fabs(x));
if (hx < 0) { /* x < 0 */
if (ix >= 0x7ff00000)
return (x - x); /* x is -inf or NaN */
else
return (ZERO / (x - x));
}
if (((hx - 0x7ff00000) | lx) == 0) /* log(inf) = inf */
return (x);
if (ix >= 0x7ff00000) /* log(NaN) = NaN */
return (x - x);
x *= TWO52;
n = -52;
hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff;
lx = ((int *) &x)[LOWORD];
}
/* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */
i = ix >> 19;
if (i >= 0x7f7 && i <= 0x806) {
/* 0.875 <= x < 1.125 */
if (ix >= 0x3fec0000 && ix < 0x3ff20000) {
double s, z, r, w;
s = x - ONE; z = s * s; r = (A10 * s) * (A11 + s);
w = z * s;
if (((ix << 12) | lx) == 0)
return (z);
else
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 {
double *tb, s;
i = (ix - 0x3fb80000) >> 15;
tb = (double *) _TBL_log + (i + i + i);
if (((ix << 12) | lx) == 0) /* 2's power */
return ((double) ((ix >> 20) - 0x3ff));
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 {
double *tb, dn, s;
dn = (double) (n + ((ix >> 20) - 0x3ff));
ix <<= 12;
if ((ix | lx) == 0)
return (dn);
i = ((unsigned) ix >> 12) | 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];
return (dn + (tb[2] * LN10V + ((B1 * s) *
(B2 + s * (B3 + s))) *
(((B4 + s * B5) + (s * s) * (B6 + s)) *
(B7 + s * (B8 + s)))));
}
}