180 lines
3.1 KiB
C
180 lines
3.1 KiB
C
/* __powil.c
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*
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* Real raised to integer power, long double precision
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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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* long double x, y, __powil();
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* int n;
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*
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* y = __powil( 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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* IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
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* IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
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* IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
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*
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* Returns INFINITY on overflow, zero on underflow.
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*
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*/
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/* __powil.c */
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/*
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Cephes Math Library Release 2.2: December, 1990
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Copyright 1984, 1990 by Stephen L. Moshier
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Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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/*
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Modified for mingw
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2002-07-22 Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifdef __MINGW32__
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#include "cephes_mconf.h"
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#else
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#include "mconf.h"
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extern long double MAXNUML, MAXLOGL, MINLOGL;
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extern long double LOGE2L;
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#ifdef ANSIPROT
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extern long double frexpl ( long double, int * );
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#else
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long double frexpl();
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#endif
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#endif /* __MINGW32__ */
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#ifndef _SET_ERRNO
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#define _SET_ERRNO(x)
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#endif
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long double __powil( x, nn )
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long double x;
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int nn;
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{
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long double w, y;
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long double s;
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int n, e, sign, asign, lx;
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if( x == 0.0L )
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{
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if( nn == 0 )
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return( 1.0L );
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else if( nn < 0 )
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return( INFINITYL );
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else
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return( 0.0L );
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}
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if( nn == 0 )
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return( 1.0L );
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if( x < 0.0L )
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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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/* Overflow detection */
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/* Calculate approximate logarithm of answer */
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s = x;
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s = frexpl( s, &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-1L) / (s + 7.0710678118654752e-1L);
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s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L;
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}
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else
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{
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s = LOGE2L * e;
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}
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if( s > MAXLOGL )
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{
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mtherr( "__powil", OVERFLOW );
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_SET_ERRNO(ERANGE);
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y = INFINITYL;
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goto done;
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}
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if( s < MINLOGL )
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{
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mtherr( "__powil", UNDERFLOW );
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_SET_ERRNO(ERANGE);
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return(0.0L);
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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 < (-MAXLOGL+2.0L) )
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{
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x = 1.0L/x;
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sign = -sign;
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}
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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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{
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y = 1.0L;
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asign = 0;
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}
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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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done:
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if( asign )
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y = -y; /* odd power of negative number */
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if( sign < 0 )
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y = 1.0L/y;
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return(y);
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}
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