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250 lines
5 KiB
C
250 lines
5 KiB
C
/* log10.c
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*
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* Common logarithm
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, log10();
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*
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* y = log10( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns logarithm to the base 10 of x.
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*
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* The argument is separated into its exponent and fractional
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* parts. The logarithm of the fraction is approximated by
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*
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* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
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* IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
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* DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
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*
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* In the tests over the interval [1, MAXNUM], the logarithms
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* of the random arguments were uniformly distributed over
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* [0, MAXLOG].
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*
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* ERROR MESSAGES:
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*
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* log10 singularity: x = 0; returns -INFINITY
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* log10 domain: x < 0; returns NAN
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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*/
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#include "mconf.h"
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static char fname[] = {"log10"};
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/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
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* 1/sqrt(2) <= x < sqrt(2)
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*/
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#ifdef UNK
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static double P[] = {
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4.58482948458143443514E-5,
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4.98531067254050724270E-1,
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6.56312093769992875930E0,
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2.97877425097986925891E1,
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6.06127134467767258030E1,
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5.67349287391754285487E1,
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1.98892446572874072159E1
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};
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static double Q[] = {
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/* 1.00000000000000000000E0, */
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1.50314182634250003249E1,
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8.27410449222435217021E1,
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2.20664384982121929218E2,
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3.07254189979530058263E2,
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2.14955586696422947765E2,
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5.96677339718622216300E1
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};
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0034500,0046473,0051374,0135174,
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0037777,0037566,0145712,0150321,
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0040722,0002426,0031543,0123107,
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0041356,0046513,0170752,0004346,
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0041562,0071553,0023536,0163343,
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0041542,0170221,0024316,0114216,
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0041237,0016454,0046611,0104602
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0041160,0100260,0067736,0102424,
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0041645,0075552,0036563,0147072,
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0042134,0125025,0021132,0025320,
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0042231,0120211,0046030,0103271,
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0042126,0172241,0052151,0120426,
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0041556,0125702,0072116,0047103
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};
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0x974f,0x6a5f,0x09a7,0x3f08,
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0x5a1a,0xd979,0xe7ee,0x3fdf,
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0x74c9,0xc66c,0x40a2,0x401a,
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0x411d,0x7e3d,0xc9a9,0x403d,
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0xdcdc,0x64eb,0x4e6d,0x404e,
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0xd312,0x2519,0x5e12,0x404c,
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0x3130,0x89b1,0xe3a5,0x4033
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0xd0a2,0x0dfb,0x1016,0x402e,
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0x79c7,0x47ae,0xaf6d,0x4054,
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0x455a,0xa44b,0x9542,0x406b,
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0x10d7,0x2983,0x3411,0x4073,
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0x3423,0x2a8d,0xde94,0x406a,
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0xc9c8,0x4e89,0xd578,0x404d
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};
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0x3f08,0x09a7,0x6a5f,0x974f,
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0x3fdf,0xe7ee,0xd979,0x5a1a,
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0x401a,0x40a2,0xc66c,0x74c9,
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0x403d,0xc9a9,0x7e3d,0x411d,
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0x404e,0x4e6d,0x64eb,0xdcdc,
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0x404c,0x5e12,0x2519,0xd312,
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0x4033,0xe3a5,0x89b1,0x3130
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};
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static unsigned short Q[] = {
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0x402e,0x1016,0x0dfb,0xd0a2,
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0x4054,0xaf6d,0x47ae,0x79c7,
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0x406b,0x9542,0xa44b,0x455a,
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0x4073,0x3411,0x2983,0x10d7,
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0x406a,0xde94,0x2a8d,0x3423,
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0x404d,0xd578,0x4e89,0xc9c8
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};
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#endif
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#define SQRTH 0.70710678118654752440
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#define L102A 3.0078125E-1
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#define L102B 2.48745663981195213739E-4
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#define L10EA 4.3359375E-1
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#define L10EB 7.00731903251827651129E-4
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#ifdef ANSIPROT
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extern double frexp ( double, int * );
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extern double ldexp ( double, int );
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern int isnan ( double );
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extern int isfinite ( double );
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#else
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double frexp(), ldexp(), polevl(), p1evl();
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int isnan(), isfinite();
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#endif
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extern double LOGE2, SQRT2, INFINITY, NAN;
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double c_log10(x)
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double x;
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{
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VOLATILE double z;
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double y;
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#ifdef DEC
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short *q;
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#endif
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int e;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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#endif
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#ifdef INFINITIES
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if( x == INFINITY )
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return(x);
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#endif
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/* Test for domain */
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if( x <= 0.0 )
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{
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if( x == 0.0 )
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{
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mtherr( fname, SING );
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return( -INFINITY );
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}
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else
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{
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mtherr( fname, DOMAIN );
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return( NAN );
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}
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}
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/* separate mantissa from exponent */
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#ifdef DEC
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q = (short *)&x;
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e = *q; /* short containing exponent */
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e = ((e >> 7) & 0377) - 0200; /* the exponent */
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*q &= 0177; /* strip exponent from x */
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*q |= 040000; /* x now between 0.5 and 1 */
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#endif
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#ifdef IBMPC
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x = frexp( x, &e );
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/*
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q = (short *)&x;
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q += 3;
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e = *q;
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e = ((e >> 4) & 0x0fff) - 0x3fe;
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*q &= 0x0f;
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*q |= 0x3fe0;
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*/
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#endif
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/* Equivalent C language standard library function: */
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#ifdef UNK
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x = frexp( x, &e );
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#endif
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#ifdef MIEEE
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x = frexp( x, &e );
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#endif
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/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
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if( x < SQRTH )
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{
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e -= 1;
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x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
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}
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else
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{
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x = x - 1.0;
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}
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/* rational form */
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z = x*x;
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y = x * ( z * polevl( x, P, 6 ) / p1evl( x, Q, 6 ) );
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y = y - ldexp( z, -1 ); /* y - 0.5 * x**2 */
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/* multiply log of fraction by log10(e)
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* and base 2 exponent by log10(2)
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*/
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z = (x + y) * L10EB; /* accumulate terms in order of size */
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z += y * L10EA;
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z += x * L10EA;
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z += e * L102B;
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z += e * L102A;
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return( z );
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}
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