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/* 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 NPY_INFINITY on overflow, zero on underflow.
*
*/
/* powi.c */
/*
* Cephes Math Library Release 2.3: March, 1995
* Copyright 1984, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
extern double 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 (NPY_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 = NPY_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 = NPY_NZERO;
else
y = -y;
}
return (y);
}
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