mirror of
https://github.com/autc04/Retro68.git
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214 lines
4.7 KiB
C
214 lines
4.7 KiB
C
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/* @(#)z_atangent.c 1.0 98/08/13 */
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/******************************************************************
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* The following routines are coded directly from the algorithms
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* and coefficients given in "Software Manual for the Elementary
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Hall, 1980.
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******************************************************************/
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/*
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FUNCTION
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<<atan>>, <<atanf>>, <<atan2>>, <<atan2f>>, <<atangent>>, <<atangentf>>---arc tangent
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INDEX
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atan2
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INDEX
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atan2f
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INDEX
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atan
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INDEX
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atanf
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ANSI_SYNOPSIS
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#include <math.h>
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double atan(double <[x]>);
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float atan(float <[x]>);
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double atan2(double <[y]>,double <[x]>);
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float atan2f(float <[y]>,float <[x]>);
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TRAD_SYNOPSIS
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#include <math.h>
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double atan2(<[y]>,<[x]>);
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double <[y]>;
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double <[x]>;
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float atan2f(<[y]>,<[x]>);
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float <[y]>;
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float <[x]>;
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#include <math.h>
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double atan(<[x]>);
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double <[x]>;
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float atanf(<[x]>);
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float <[x]>;
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DESCRIPTION
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<<atan2>> computes the inverse tangent (arc tangent) of y / x.
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<<atan2f>> is identical to <<atan2>>, save that it operates on <<floats>>.
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<<atan>> computes the inverse tangent (arc tangent) of the input value.
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<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
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RETURNS
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@ifnottex
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<<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
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<<atan2>> returns a value in radians, in the range of -pi/2 to pi/2.
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@end ifnottex
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@tex
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<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
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<<atan2>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
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@end tex
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PORTABILITY
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<<atan>> is ANSI C. <<atanf>> is an extension.
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<<atan2>> is ANSI C. <<atan2f>> is an extension.
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*/
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/******************************************************************
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* Arctangent
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*
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* Input:
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* x - floating point value
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*
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* Output:
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* arctangent of x
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*
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* Description:
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* This routine calculates arctangents.
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*
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*****************************************************************/
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#include <float.h>
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#include "fdlibm.h"
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#include "zmath.h"
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#ifndef _DOUBLE_IS_32BITS
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static const double ROOT3 = 1.73205080756887729353;
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static const double a[] = { 0.0, 0.52359877559829887308, 1.57079632679489661923,
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1.04719755119659774615 };
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static const double q[] = { 0.41066306682575781263e+2,
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0.86157349597130242515e+2,
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0.59578436142597344465e+2,
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0.15024001160028576121e+2 };
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static const double p[] = { -0.13688768894191926929e+2,
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-0.20505855195861651981e+2,
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-0.84946240351320683534e+1,
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-0.83758299368150059274 };
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double
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_DEFUN (atangent, (double, double, double, int),
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double x _AND
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double v _AND
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double u _AND
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int arctan2)
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{
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double f, g, R, P, Q, A, res;
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int N;
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int branch = 0;
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int expv, expu;
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/* Preparation for calculating arctan2. */
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if (arctan2)
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{
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if (u == 0.0)
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if (v == 0.0)
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{
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errno = ERANGE;
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return (z_notanum.d);
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}
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else
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{
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branch = 1;
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res = __PI_OVER_TWO;
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}
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if (!branch)
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{
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int e;
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/* Get the exponent values of the inputs. */
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g = frexp (v, &expv);
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g = frexp (u, &expu);
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/* See if a divide will overflow. */
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e = expv - expu;
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if (e > DBL_MAX_EXP)
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{
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branch = 1;
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res = __PI_OVER_TWO;
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}
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/* Also check for underflow. */
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else if (e < DBL_MIN_EXP)
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{
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branch = 2;
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res = 0.0;
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}
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}
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}
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if (!branch)
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{
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if (arctan2)
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f = fabs (v / u);
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else
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f = fabs (x);
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if (f > 1.0)
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{
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f = 1.0 / f;
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N = 2;
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}
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else
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N = 0;
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if (f > (2.0 - ROOT3))
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{
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A = ROOT3 - 1.0;
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f = (((A * f - 0.5) - 0.5) + f) / (ROOT3 + f);
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N++;
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}
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/* Check for values that are too small. */
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if (-z_rooteps < f && f < z_rooteps)
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res = f;
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/* Calculate the Taylor series. */
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else
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{
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g = f * f;
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P = (((p[3] * g + p[2]) * g + p[1]) * g + p[0]) * g;
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Q = (((g + q[3]) * g + q[2]) * g + q[1]) * g + q[0];
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R = P / Q;
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res = f + f * R;
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}
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if (N > 1)
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res = -res;
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res += a[N];
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}
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if (arctan2)
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{
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if (u < 0.0)
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res = __PI - res;
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if (v < 0.0)
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res = -res;
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}
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else if (x < 0.0)
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{
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res = -res;
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}
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return (res);
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}
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#endif /* _DOUBLE_IS_32BITS */
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