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#ifndef lint
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static const char RCSid[] = "$Id: tcos.c,v 3.9 2013/02/08 16:39:01 greg Exp $";
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#endif
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/*
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* Table-based cosine approximation.
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*
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* Use doubles in table even though we're not nearly that accurate just
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* to avoid conversion and guarantee that tsin(x)^2 + tcos(x)^2 == 1.
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*
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* No interpolation in this version.
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*
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* External symbols declared in rtmath.h
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*/
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#include "copyright.h"
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#include <math.h>
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#include "rtmath.h"
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#ifndef __FAST_MATH__
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#ifndef NCOSENTRY
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#define NCOSENTRY 1024
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#endif
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double
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tcos(double x) /* approximate cosine */
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{
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static double costab[NCOSENTRY+1];
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register int i;
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if (costab[0] < 0.5) /* initialize table */
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for (i = 0; i <= NCOSENTRY; i++)
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costab[i] = cos((PI/2./NCOSENTRY)*i);
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/* normalize angle */
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if (x < 0.)
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x = -x;
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i = (NCOSENTRY*2./PI) * x + 0.5;
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while (i >= 4*NCOSENTRY)
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i -= 4*NCOSENTRY;
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switch (i / NCOSENTRY) {
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case 0:
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return(costab[i]);
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case 1:
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return(-costab[(2*NCOSENTRY)-i]);
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case 2:
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return(-costab[i-(2*NCOSENTRY)]);
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case 3:
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return(costab[(4*NCOSENTRY)-i]);
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}
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return(0.); /* should never be reached */
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}
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#endif
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/* Fast arctangent approximation due to Rajan et al. 2006 */
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double
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atan2a(double y, double x)
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{
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double ratio, aratio, val;
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if (x == 0)
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return (y > 0) ? PI/2. : 3./2.*PI;
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aratio = (ratio = y/x) >= 0 ? ratio : -ratio;
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if (aratio > 1.01)
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return PI/2. - atan2a(x, y);
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val = PI/4.*ratio - ratio*(aratio - 1.)*(0.2447 + 0.0663*aratio);
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return val + PI*(x < 0);
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}
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