exp10.c

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/*                                                     exp10.c
 *
 *     Base 10 exponential function
 *      (Common antilogarithm)
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, exp10();
 *
 * y = exp10( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns 10 raised to the x power.
 *
 * Range reduction is accomplished by expressing the argument
 * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
 * The Pade' form
 *
 *    1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
 *
 * is used to approximate 10**f.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE     -307,+307    30000       2.2e-16     5.5e-17
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * exp10 underflow    x < -MAXL10        0.0
 * exp10 overflow     x > MAXL10       INFINITY
 *
 * IEEE arithmetic: MAXL10 = 308.2547155599167.
 *
 */

/*
 * Cephes Math Library Release 2.2:  January, 1991
 * Copyright 1984, 1991 by Stephen L. Moshier
 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
 */
 
 
#include "mconf.h"
 
static double P[] = {
    4.09962519798587023075E-2,
    1.17452732554344059015E1,
    4.06717289936872725516E2,
    2.39423741207388267439E3,
};
 
static double Q[] = {
    /* 1.00000000000000000000E0, */
    8.50936160849306532625E1,
    1.27209271178345121210E3,
    2.07960819286001865907E3,
};
 
/* static double LOG102 = 3.01029995663981195214e-1; */
static double LOG210 = 3.32192809488736234787e0;
static double LG102A = 3.01025390625000000000E-1;
static double LG102B = 4.60503898119521373889E-6;
 
/* static double MAXL10 = 38.230809449325611792; */
static double MAXL10 = 308.2547155599167;
 
double exp10(double x)
{
    double px, xx;
    short n;
 
    if (cephes_isnan(x))
        return (x);
    if (x > MAXL10) {
        return (INFINITY);
    }
 
    if (x < -MAXL10) {          /* Would like to use MINLOG but can't */
        sf_error("exp10", SF_ERROR_UNDERFLOW, NULL);
        return (0.0);
    }
 
    /* Express 10**x = 10**g 2**n
     *   = 10**g 10**( n log10(2) )
     *   = 10**( g + n log10(2) )
     */
    px = floor(LOG210 * x + 0.5);
    n = px;
    x -= px * LG102A;
    x -= px * LG102B;
 
    /* rational approximation for exponential
     * of the fractional part:
     * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
     */
    xx = x * x;
    px = x * polevl(xx, P, 3);
    x = px / (p1evl(xx, Q, 3) - px);
    x = 1.0 + ldexp(x, 1);
 
    /* multiply by power of 2 */
    x = ldexp(x, n);
 
    return (x);
}