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/* exp2l.c
*
* Base 2 exponential function, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, exp2l();
*
* y = exp2l( x );
*
*
*
* DESCRIPTION:
*
* Returns 2 raised to the x power.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
* x k f
* 2 = 2 2.
*
* A Pade' form
*
* 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
*
* approximates 2**x in the basic range [-0.5, 0.5].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-16300 300000 9.1e-20 2.6e-20
*
*
* See exp.c for comments on error amplification.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp2l underflow x < -16382 0.0
* exp2l overflow x >= 16384 MAXNUM
*
*/
/*
Cephes Math Library Release 2.7: May, 1998
Copyright 1984, 1991, 1998 by Stephen L. Moshier
*/
#include <math.h>
#ifdef UNK
static long double P[] = {
6.0614853552242266094567E1L,
3.0286971917562792508623E4L,
2.0803843631901852422887E6L,
};
static long double Q[] = {
/* 1.0000000000000000000000E0,*/
1.7492876999891839021063E3L,
3.2772515434906797273099E5L,
6.0027204078348487957118E6L,
};
#endif
#ifdef IBMPC
static short P[] = {
0xffd8,0x6ad6,0x9c2b,0xf275,0x4004, XPD
0x3426,0x2dc5,0xf19f,0xec9d,0x400d, XPD
0x7ec0,0xd041,0x02e7,0xfdf4,0x4013, XPD
};
static short Q[] = {
/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
0x575b,0x9b93,0x34d6,0xdaa9,0x4009, XPD
0xe38d,0x6d74,0xa4f0,0xa005,0x4011, XPD
0xb37e,0xcfba,0x40d0,0xb730,0x4015, XPD
};
#endif
#ifdef MIEEE
static long P[] = {
0x40040000,0xf2759c2b,0x6ad6ffd8,
0x400d0000,0xec9df19f,0x2dc53426,
0x40130000,0xfdf402e7,0xd0417ec0,
};
static long Q[] = {
/*0x3fff0000,0x80000000,0x00000000,*/
0x40090000,0xdaa934d6,0x9b93575b,
0x40110000,0xa005a4f0,0x6d74e38d,
0x40150000,0xb73040d0,0xcfbab37e,
};
#endif
#define MAXL2L 16384.0L
#define MINL2L -16382.0L
extern long double MAXNUML;
#ifdef ANSIPROT
extern long double polevll ( long double, void *, int );
extern long double p1evll ( long double, void *, int );
extern long double floorl ( long double );
extern long double ldexpl ( long double, int );
extern int isnanl ( long double );
#else
long double polevll(), p1evll(), floorl(), ldexpl(), isnanl();
#endif
#ifdef INFINITIES
extern long double INFINITYL;
#endif
long double exp2l(x)
long double x;
{
long double px, xx;
int n;
#ifdef NANS
if( isnanl(x) )
return(x);
#endif
if( x > MAXL2L)
{
#ifdef INFINITIES
return( INFINITYL );
#else
mtherr( "exp2l", OVERFLOW );
return( MAXNUML );
#endif
}
if( x < MINL2L )
{
#ifndef INFINITIES
mtherr( "exp2l", UNDERFLOW );
#endif
return(0.0L);
}
xx = x; /* save x */
/* separate into integer and fractional parts */
px = floorl(x+0.5L);
n = px;
x = x - px;
/* rational approximation
* exp2(x) = 1.0 + 2xP(xx)/(Q(xx) - P(xx))
* where xx = x**2
*/
xx = x * x;
px = x * polevll( xx, P, 2 );
x = px / ( p1evll( xx, Q, 3 ) - px );
x = 1.0L + ldexpl( x, 1 );
/* scale by power of 2 */
x = ldexpl( x, n );
return(x);
}
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