184 lines
3.3 KiB
C
184 lines
3.3 KiB
C
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/* exp2.c
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*
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* Base 2 exponential function
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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, exp2();
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*
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* y = exp2( 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 2 raised to the x power.
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*
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* Range reduction is accomplished by separating the argument
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* into an integer k and fraction f such that
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* x k f
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* 2 = 2 2.
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*
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* A Pade' form
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*
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* 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
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*
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* approximates 2**x in the basic range [-0.5, 0.5].
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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 -1022,+1024 30000 1.8e-16 5.4e-17
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*
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*
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* See exp.c for comments on error amplification.
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*
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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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* exp underflow x < -MAXL2 0.0
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* exp overflow x > MAXL2 MAXNUM
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*
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* For DEC arithmetic, MAXL2 = 127.
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* For IEEE arithmetic, MAXL2 = 1024.
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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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#ifdef UNK
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const static double P[] = {
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2.30933477057345225087E-2,
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2.02020656693165307700E1,
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1.51390680115615096133E3,
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};
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const static double Q[] = {
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/* 1.00000000000000000000E0,*/
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2.33184211722314911771E2,
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4.36821166879210612817E3,
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};
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#define MAXL2 1024.0
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#define MINL2 -1024.0
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0036675,0027102,0122327,0053227,
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0041241,0116724,0115412,0157355,
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0042675,0036404,0101733,0132226,
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0042151,0027450,0077732,0160744,
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0043210,0100661,0077550,0056560,
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};
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#define MAXL2 127.0
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#define MINL2 -127.0
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0xead3,0x549a,0xa5c8,0x3f97,
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0x5bde,0x9361,0x33ba,0x4034,
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0x7693,0x907b,0xa7a0,0x4097,
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x5c3c,0x0ffb,0x25e5,0x406d,
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0x0bae,0x2fed,0x1036,0x40b1,
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};
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#define MAXL2 1024.0
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#define MINL2 -1022.0
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0x3f97,0xa5c8,0x549a,0xead3,
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0x4034,0x33ba,0x9361,0x5bde,
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0x4097,0xa7a0,0x907b,0x7693,
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};
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static unsigned short Q[] = {
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/*0x3ff0,0x0000,0x0000,0x0000,*/
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0x406d,0x25e5,0x0ffb,0x5c3c,
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0x40b1,0x1036,0x2fed,0x0bae,
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};
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#define MAXL2 1024.0
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#define MINL2 -1022.0
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#endif
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#ifdef ANSIPROT
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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 double floor ( double );
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extern double ldexp ( double, 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 polevl(), p1evl(), floor(), ldexp();
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int isnan(), isfinite();
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#endif
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#ifdef INFINITIES
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extern double INFINITY;
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#endif
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extern double MAXNUM;
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double exp2(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 > MAXL2)
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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( "exp2", OVERFLOW );
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return( MAXNUM );
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#endif
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}
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if( x < MINL2 )
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{
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#ifndef INFINITIES
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mtherr( "exp2", UNDERFLOW );
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#endif
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return(0.0);
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}
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xx = x; /* save x */
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/* separate into integer and fractional parts */
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px = floor(x+0.5);
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n = px;
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x = x - px;
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/* rational approximation
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* exp2(x) = 1 + 2xP(xx)/(Q(xx) - P(xx))
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* where xx = x**2
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*/
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xx = x * x;
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px = x * polevl( xx, P, 2 );
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x = px / ( p1evl( xx, Q, 2 ) - px );
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x = 1.0 + ldexp( x, 1 );
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/* scale 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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