CocoRoboDesktop/pdf.js/node_modules/cephes/cephes/powi.c

/*							powi.c
 *
 *	Real raised to integer power
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, powi();
 * int n;
 *
 * y = powi( x, n );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns argument x raised to the nth power.
 * The routine efficiently decomposes n as a sum of powers of
 * two. The desired power is a product of two-to-the-kth
 * powers of x.  Thus to compute the 32767 power of x requires
 * 28 multiplications instead of 32767 multiplications.
 *
 *
 *
 * ACCURACY:
 *
 *
 *                      Relative error:
 * arithmetic   x domain   n domain  # trials      peak         rms
 *    DEC       .04,26     -26,26    100000       2.7e-16     4.3e-17
 *    IEEE      .04,26     -26,26     50000       2.0e-15     3.8e-16
 *    IEEE        1,2    -1022,1023   50000       8.6e-14     1.6e-14
 *
 * Returns MAXNUM on overflow, zero on underflow.
 *
 */

/*							powi.c	*/

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/

#include "mconf.h"
#ifdef ANSIPROT
extern double log(double);
extern double frexp(double, int *);
extern int signbit(double);
#else
double log(), frexp();
int signbit();
#endif
extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;

double powi(x, nn) double x;
int nn;
{
  int n, e, sign, asign, lx;
  double w, y, s;

  /* See pow.c for these tests.  */
  if (x == 0.0) {
    if (nn == 0)
      return (1.0);
    else if (nn < 0)
      return (INFINITY);
    else {
      if (nn & 1)
        return (x);
      else
        return (0.0);
    }
  }

  if (nn == 0)
    return (1.0);

  if (nn == -1)
    return (1.0 / x);

  if (x < 0.0) {
    asign = -1;
    x = -x;
  } else
    asign = 0;

  if (nn < 0) {
    sign = -1;
    n = -nn;
  } else {
    sign = 1;
    n = nn;
  }

  /* Even power will be positive. */
  if ((n & 1) == 0)
    asign = 0;

  /* Overflow detection */

  /* Calculate approximate logarithm of answer */
  s = frexp(x, &lx);
  e = (lx - 1) * n;
  if ((e == 0) || (e > 64) || (e < -64)) {
    s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
    s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
  } else {
    s = LOGE2 * e;
  }

  if (s > MAXLOG) {
    mtherr("powi", OVERFLOW);
    y = INFINITY;
    goto done;
  }

#if DENORMAL
  if (s < MINLOG) {
    y = 0.0;
    goto done;
  }

  /* Handle tiny denormal answer, but with less accuracy
   * since roundoff error in 1.0/x will be amplified.
   * The precise demarcation should be the gradual underflow threshold.
   */
  if ((s < (-MAXLOG + 2.0)) && (sign < 0)) {
    x = 1.0 / x;
    sign = -sign;
  }
#else
  /* do not produce denormal answer */
  if (s < -MAXLOG)
    return (0.0);
#endif

  /* First bit of the power */
  if (n & 1)
    y = x;

  else
    y = 1.0;

  w = x;
  n >>= 1;
  while (n) {
    w = w * w; /* arg to the 2-to-the-kth power */
    if (n & 1) /* if that bit is set, then include in product */
      y *= w;
    n >>= 1;
  }

  if (sign < 0)
    y = 1.0 / y;

done:

  if (asign) {
    /* odd power of negative number */
    if (y == 0.0)
      y = NEGZERO;
    else
      y = -y;
  }
  return (y);
}