log10.c revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af
/*
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*
* The contents of this file are subject to the terms of the
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*
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* See the License for the specific language governing permissions
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*
* When distributing Covered Code, include this CDDL HEADER in each
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* If applicable, add the following below this CDDL HEADER, with the
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* information: Portions Copyright [yyyy] [name of copyright owner]
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*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/* 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
*
* 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]).
*
* 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) {
n = 0;
/* subnormal,0,negative,inf,nan */
return (x * x);
return (_SVID_libm_err(x, x, 18));
if (hx < 0) /* negative */
return (_SVID_libm_err(x, x, 19));
return (x);
/* x must be positive and subnormal */
x *= TWO52;
n = -52;
}
i = ix >> 19;
if (i >= 0x7f7 && i <= 0x806) {
/* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */
/* 0.875 <= x < 1.125 */
s = x - ONE;
z = s * s;
return (z);
w = z * s;
} else {
}
} else {
((int *)&x)[HIWORD] = i;
i = (i - 0x3fb80000) >> 15;
}
}