uclibc-ng/libm/float/expf.c

/*							expf.c
 *
 *	Exponential function
 *
 *
 *
 * SYNOPSIS:
 *
 * float x, y, expf();
 *
 * y = expf( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns e (2.71828...) 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
 *    e  = 2  e.
 *
 * A polynomial is used to approximate exp(f)
 * in the basic range [-0.5, 0.5].
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      +- MAXLOG   100000      1.7e-7      2.8e-8
 *
 *
 * Error amplification in the exponential function can be
 * a serious matter.  The error propagation involves
 * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
 * which shows that a 1 lsb error in representing X produces
 * a relative error of X times 1 lsb in the function.
 * While the routine gives an accurate result for arguments
 * that are exactly represented by a double precision
 * computer number, the result contains amplified roundoff
 * error for large arguments not exactly represented.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * expf underflow    x < MINLOGF         0.0
 * expf overflow     x > MAXLOGF         MAXNUMF
 *
 */

/*
Cephes Math Library Release 2.2:  June, 1992
Copyright 1984, 1987, 1989 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

/* Single precision exponential function.
 * test interval: [-0.5, +0.5]
 * trials: 80000
 * peak relative error: 7.6e-8
 * rms relative error: 2.8e-8
 */
#include <math.h>
extern float LOG2EF, MAXLOGF, MINLOGF, MAXNUMF;

static float C1 =   0.693359375;
static float C2 =  -2.12194440e-4;



float floorf( float ), ldexpf( float, int );

float expf( float xx )
{
float x, z;
int n;

x = xx;


if( x > MAXLOGF)
	{
	mtherr( "expf", OVERFLOW );
	return( MAXNUMF );
	}

if( x < MINLOGF )
	{
	mtherr( "expf", UNDERFLOW );
	return(0.0);
	}

/* Express e**x = e**g 2**n
 *   = e**g e**( n loge(2) )
 *   = e**( g + n loge(2) )
 */
z = floorf( LOG2EF * x + 0.5 ); /* floor() truncates toward -infinity. */
x -= z * C1;
x -= z * C2;
n = z;

z = x * x;
/* Theoretical peak relative error in [-0.5, +0.5] is 4.2e-9. */
z =
((((( 1.9875691500E-4  * x
   + 1.3981999507E-3) * x
   + 8.3334519073E-3) * x
   + 4.1665795894E-2) * x
   + 1.6666665459E-1) * x
   + 5.0000001201E-1) * z
   + x
   + 1.0;

/* multiply by power of 2 */
x = ldexpf( z, n );

return( x );
}