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#ifndef lint |
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static const char RCSid[] = "$Id: tcos.c,v 3.8 2013/02/08 16:10:07 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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|
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#include "copyright.h" |
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|
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#include <math.h> |
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|
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#include "rtmath.h" |
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|
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#ifndef NCOSENTRY |
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#define NCOSENTRY 1024 |
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#endif |
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|
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|
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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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|
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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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|
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|
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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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|
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if (x == 0) |
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return (y > 0) ? PI/2. : 3./2.*PI; |
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|
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aratio = (ratio = y/x) >= 0 ? ratio : -ratio; |
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|
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if (aratio > 1.01) |
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return PI/2. - atan2a(x, y); |
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|
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val = PI/4.*ratio - ratio*(aratio - 1.)*(0.2447 + 0.0663*aratio); |
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|
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return val + PI*(x < 0); |
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} |
