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expx2.c

/*                                        expx2.c
 *
 *    Exponential of squared argument
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, expx2();
 * int sign;
 *
 * y = expx2( x, sign );
 *
 *
 *
 * DESCRIPTION:
 *
 * Computes y = exp(x*x) while suppressing error amplification
 * that would ordinarily arise from the inexactness of the
 * exponential argument x*x.
 *
 * If sign < 0, the result is inverted; i.e., y = exp(-x*x) .
 * 
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic    domain     # trials      peak         rms
 *   IEEE      -26.6, 26.6    10^7       3.9e-16     8.9e-17
 *
 */

/*
Cephes Math Library Release 2.9:  June, 2000
Copyright 2000 by Stephen L. Moshier
*/

#include "mconf.h"

#define M 128.0
#define MINV .0078125

double expx2 (double x, int sign)
{
    double u, u1, m, f;

    x = fabs(x);

    if (sign < 0) {
      x = -x;
    }

    /* Represent x as an exact multiple of M plus a residual.
       M is a power of 2 chosen so that exp(m * m) does not overflow
       or underflow and so that |x - m| is small.  */
    m = MINV * floor(M * x + 0.5);
    f = x - m;

    /* x^2 = m^2 + 2mf + f^2 */
    u = m * m;
    u1 = 2 * m * f + f * f;

    if (sign < 0) {
      u = -u;
      u1 = -u1;
    }

    if (u + u1 > MAXLOG) {
      return INFINITY;
    }

    /* u is exact, u1 is small.  */
    u = exp(u) * exp(u1);

    return u;
}

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