187 lines
2.9 KiB
C
187 lines
2.9 KiB
C
/* powi.c
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*
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* Real raised to integer power
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, powi();
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* int n;
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*
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* y = powi( x, n );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns argument x raised to the nth power.
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* The routine efficiently decomposes n as a sum of powers of
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* two. The desired power is a product of two-to-the-kth
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* powers of x. Thus to compute the 32767 power of x requires
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* 28 multiplications instead of 32767 multiplications.
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*
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*
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*
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* ACCURACY:
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*
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*
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* Relative error:
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* arithmetic x domain n domain # trials peak rms
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* DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
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* IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
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* IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
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*
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* Returns MAXNUM on overflow, zero on underflow.
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*
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*/
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/* powi.c */
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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*/
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#include "mconf.h"
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#ifdef ANSIPROT
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extern double log ( double );
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extern double frexp ( double, int * );
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extern int signbit ( double );
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#else
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double log(), frexp();
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int signbit();
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#endif
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extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;
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double powi( x, nn )
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double x;
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int nn;
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{
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int n, e, sign, asign, lx;
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double w, y, s;
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/* See pow.c for these tests. */
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if( x == 0.0 )
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{
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if( nn == 0 )
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return( 1.0 );
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else if( nn < 0 )
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return( INFINITY );
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else
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{
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if( nn & 1 )
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return( x );
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else
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return( 0.0 );
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}
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}
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if( nn == 0 )
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return( 1.0 );
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if( nn == -1 )
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return( 1.0/x );
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if( x < 0.0 )
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{
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asign = -1;
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x = -x;
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}
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else
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asign = 0;
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if( nn < 0 )
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{
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sign = -1;
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n = -nn;
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}
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else
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{
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sign = 1;
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n = nn;
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}
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/* Even power will be positive. */
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if( (n & 1) == 0 )
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asign = 0;
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/* Overflow detection */
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/* Calculate approximate logarithm of answer */
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s = frexp( x, &lx );
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e = (lx - 1)*n;
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if( (e == 0) || (e > 64) || (e < -64) )
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{
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s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
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s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
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}
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else
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{
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s = LOGE2 * e;
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}
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if( s > MAXLOG )
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{
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mtherr( "powi", OVERFLOW );
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y = INFINITY;
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goto done;
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}
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#if DENORMAL
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if( s < MINLOG )
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{
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y = 0.0;
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goto done;
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}
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/* Handle tiny denormal answer, but with less accuracy
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* since roundoff error in 1.0/x will be amplified.
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* The precise demarcation should be the gradual underflow threshold.
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*/
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if( (s < (-MAXLOG+2.0)) && (sign < 0) )
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{
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x = 1.0/x;
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sign = -sign;
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}
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#else
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/* do not produce denormal answer */
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if( s < -MAXLOG )
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return(0.0);
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#endif
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/* First bit of the power */
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if( n & 1 )
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y = x;
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else
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y = 1.0;
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w = x;
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n >>= 1;
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while( n )
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{
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w = w * w; /* arg to the 2-to-the-kth power */
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if( n & 1 ) /* if that bit is set, then include in product */
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y *= w;
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n >>= 1;
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}
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if( sign < 0 )
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y = 1.0/y;
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done:
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if( asign )
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{
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/* odd power of negative number */
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if( y == 0.0 )
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y = NEGZERO;
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else
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y = -y;
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}
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return(y);
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}
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