224 lines
5.2 KiB
C
224 lines
5.2 KiB
C
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/* exp10.c
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*
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* Base 10 exponential function
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* (Common antilogarithm)
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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, exp10();
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*
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* y = exp10( 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 10 raised to the x power.
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*
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* Range reduction is accomplished by expressing the argument
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* as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
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* The Pade' form
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*
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* 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
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*
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* is used to approximate 10**f.
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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 -307,+307 30000 2.2e-16 5.5e-17
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* Test result from an earlier version (2.1):
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* DEC -38,+38 70000 3.1e-17 7.0e-18
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* exp10 underflow x < -MAXL10 0.0
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* exp10 overflow x > MAXL10 MAXNUM
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*
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* DEC arithmetic: MAXL10 = 38.230809449325611792.
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* IEEE arithmetic: MAXL10 = 308.2547155599167.
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*
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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, 1991, 2000 by Stephen L. Moshier
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*/
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#include "mconf.h"
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#ifdef UNK
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const static double P[] = {
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4.09962519798587023075E-2,
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1.17452732554344059015E1,
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4.06717289936872725516E2,
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2.39423741207388267439E3,
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};
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const static double Q[] = {
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/* 1.00000000000000000000E0,*/
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8.50936160849306532625E1,
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1.27209271178345121210E3,
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2.07960819286001865907E3,
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};
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/* const static double LOG102 = 3.01029995663981195214e-1; */
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const static double LOG210 = 3.32192809488736234787e0;
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const static double LG102A = 3.01025390625000000000E-1;
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const static double LG102B = 4.60503898119521373889E-6;
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/* const static double MAXL10 = 38.230809449325611792; */
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const static double MAXL10 = 308.2547155599167;
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0037047,0165657,0114061,0067234,
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0041073,0166243,0123052,0144643,
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0042313,0055720,0024032,0047443,
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0043025,0121714,0070232,0050007,
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0041652,0027756,0071216,0050075,
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0042637,0001367,0077263,0136017,
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0043001,0174673,0024157,0133416,
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};
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/*
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static unsigned short L102[] = {0037632,0020232,0102373,0147770};
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#define LOG102 *(double *)L102
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*/
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static unsigned short L210[] = {0040524,0115170,0045715,0015613};
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#define LOG210 *(double *)L210
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static unsigned short L102A[] = {0037632,0020000,0000000,0000000,};
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#define LG102A *(double *)L102A
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static unsigned short L102B[] = {0033632,0102373,0147767,0114220,};
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#define LG102B *(double *)L102B
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static unsigned short MXL[] = {0041430,0166131,0047761,0154130,};
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#define MAXL10 ( *(double *)MXL )
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0x2dd4,0xf306,0xfd75,0x3fa4,
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0x5934,0x74c5,0x7d94,0x4027,
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0x49e4,0x0503,0x6b7a,0x4079,
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0x4a01,0x8e13,0xb479,0x40a2,
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0xca08,0xce51,0x45fd,0x4055,
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0x7782,0xefd6,0xe05e,0x4093,
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0xf6e2,0x650d,0x3f37,0x40a0,
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};
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/*
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static unsigned short L102[] = {0x79ff,0x509f,0x4413,0x3fd3};
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#define LOG102 *(double *)L102
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*/
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static unsigned short L210[] = {0xa371,0x0979,0x934f,0x400a};
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#define LOG210 *(double *)L210
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static unsigned short L102A[] = {0x0000,0x0000,0x4400,0x3fd3,};
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#define LG102A *(double *)L102A
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static unsigned short L102B[] = {0xf312,0x79fe,0x509f,0x3ed3,};
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#define LG102B *(double *)L102B
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const static double MAXL10 = 308.2547155599167;
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0x3fa4,0xfd75,0xf306,0x2dd4,
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0x4027,0x7d94,0x74c5,0x5934,
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0x4079,0x6b7a,0x0503,0x49e4,
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0x40a2,0xb479,0x8e13,0x4a01,
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};
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static unsigned short Q[] = {
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/*0x3ff0,0x0000,0x0000,0x0000,*/
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0x4055,0x45fd,0xce51,0xca08,
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0x4093,0xe05e,0xefd6,0x7782,
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0x40a0,0x3f37,0x650d,0xf6e2,
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};
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/*
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static unsigned short L102[] = {0x3fd3,0x4413,0x509f,0x79ff};
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#define LOG102 *(double *)L102
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*/
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static unsigned short L210[] = {0x400a,0x934f,0x0979,0xa371};
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#define LOG210 *(double *)L210
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static unsigned short L102A[] = {0x3fd3,0x4400,0x0000,0x0000,};
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#define LG102A *(double *)L102A
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static unsigned short L102B[] = {0x3ed3,0x509f,0x79fe,0xf312,};
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#define LG102B *(double *)L102B
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const static double MAXL10 = 308.2547155599167;
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#endif
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#ifdef ANSIPROT
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extern double floor ( double );
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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 floor(), ldexp(), polevl(), p1evl();
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int isnan(), isfinite();
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#endif
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extern double MAXNUM;
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#ifdef INFINITIES
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extern double INFINITY;
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#endif
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double exp10(x)
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double x;
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{
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double px, xx;
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short n;
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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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if( x > MAXL10 )
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{
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#ifdef INFINITIES
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return( INFINITY );
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#else
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mtherr( "exp10", OVERFLOW );
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return( MAXNUM );
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#endif
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}
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if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
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{
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#ifndef INFINITIES
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mtherr( "exp10", UNDERFLOW );
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#endif
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return(0.0);
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}
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/* Express 10**x = 10**g 2**n
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* = 10**g 10**( n log10(2) )
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* = 10**( g + n log10(2) )
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*/
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px = floor( LOG210 * x + 0.5 );
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n = px;
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x -= px * LG102A;
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x -= px * LG102B;
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/* rational approximation for exponential
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* of the fractional part:
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* 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
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*/
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xx = x * x;
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px = x * polevl( xx, P, 3 );
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x = px/( p1evl( xx, Q, 3 ) - px );
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x = 1.0 + ldexp( x, 1 );
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/* multiply by power of 2 */
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x = ldexp( x, n );
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return(x);
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}
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