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/* exp2f.c
*
* Base 2 exponential function
*
*
*
* SYNOPSIS:
*
* float x, y, exp2f();
*
* y = exp2f( 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 polynomial approximates 2**x in the basic range [-0.5, 0.5].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -127,+127 100000 1.7e-7 2.8e-8
*
*
* See exp.c for comments on error amplification.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp underflow x < -MAXL2 0.0
* exp overflow x > MAXL2 MAXNUMF
*
* For IEEE arithmetic, MAXL2 = 127.
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
static char fname[] = {"exp2f"};
static float P[] = {
1.535336188319500E-004,
1.339887440266574E-003,
9.618437357674640E-003,
5.550332471162809E-002,
2.402264791363012E-001,
6.931472028550421E-001
};
#define MAXL2 127.0
#define MINL2 -127.0
extern float MAXNUMF;
float polevlf(float, float *, int), floorf(float), ldexpf(float, int);
float exp2f( float xx )
{
float x, px;
int i0;
x = xx;
if( x > MAXL2)
{
mtherr( fname, OVERFLOW );
return( MAXNUMF );
}
if( x < MINL2 )
{
mtherr( fname, UNDERFLOW );
return(0.0);
}
/* The following is necessary because range reduction blows up: */
if( x == 0 )
return(1.0);
/* separate into integer and fractional parts */
px = floorf(x);
i0 = px;
x = x - px;
if( x > 0.5 )
{
i0 += 1;
x -= 1.0;
}
/* rational approximation
* exp2(x) = 1.0 + xP(x)
*/
px = 1.0 + x * polevlf( x, P, 5 );
/* scale by power of 2 */
px = ldexpf( px, i0 );
return(px);
}
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