mirror of
https://github.com/autc04/Retro68.git
synced 2024-09-08 20:55:01 +00:00
182 lines
5.0 KiB
C
182 lines
5.0 KiB
C
|
|
/* @(#)s_atan.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*
|
|
*/
|
|
|
|
/*
|
|
FUNCTION
|
|
<<atan>>, <<atanf>>---arc tangent
|
|
|
|
INDEX
|
|
atan
|
|
INDEX
|
|
atanf
|
|
|
|
ANSI_SYNOPSIS
|
|
#include <math.h>
|
|
double atan(double <[x]>);
|
|
float atanf(float <[x]>);
|
|
|
|
TRAD_SYNOPSIS
|
|
#include <math.h>
|
|
double atan(<[x]>);
|
|
double <[x]>;
|
|
|
|
float atanf(<[x]>);
|
|
float <[x]>;
|
|
|
|
DESCRIPTION
|
|
|
|
<<atan>> computes the inverse tangent (arc tangent) of the input value.
|
|
|
|
<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
|
|
|
|
RETURNS
|
|
@ifnottex
|
|
<<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
|
|
@end ifnottex
|
|
@tex
|
|
<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
|
|
@end tex
|
|
|
|
PORTABILITY
|
|
<<atan>> is ANSI C. <<atanf>> is an extension.
|
|
|
|
*/
|
|
|
|
/* atan(x)
|
|
* Method
|
|
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
|
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
|
* is further reduced to one of the following intervals and the
|
|
* arctangent of t is evaluated by the corresponding formula:
|
|
*
|
|
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
|
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
|
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
|
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
|
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
|
*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following
|
|
* constants. The decimal values may be used, provided that the
|
|
* compiler will convert from decimal to binary accurately enough
|
|
* to produce the hexadecimal values shown.
|
|
*/
|
|
|
|
#include "fdlibm.h"
|
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
|
#ifdef __STDC__
|
|
static const double atanhi[] = {
|
|
#else
|
|
static double atanhi[] = {
|
|
#endif
|
|
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
|
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
|
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
|
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
|
};
|
|
|
|
#ifdef __STDC__
|
|
static const double atanlo[] = {
|
|
#else
|
|
static double atanlo[] = {
|
|
#endif
|
|
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
|
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
|
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
|
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
|
};
|
|
|
|
#ifdef __STDC__
|
|
static const double aT[] = {
|
|
#else
|
|
static double aT[] = {
|
|
#endif
|
|
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
|
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
|
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
|
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
|
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
|
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
|
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
|
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
|
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
|
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
|
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
|
};
|
|
|
|
#ifdef __STDC__
|
|
static const double
|
|
#else
|
|
static double
|
|
#endif
|
|
one = 1.0,
|
|
huge = 1.0e300;
|
|
|
|
#ifdef __STDC__
|
|
double atan(double x)
|
|
#else
|
|
double atan(x)
|
|
double x;
|
|
#endif
|
|
{
|
|
double w,s1,s2,z;
|
|
__int32_t ix,hx,id;
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
ix = hx&0x7fffffff;
|
|
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
|
__uint32_t low;
|
|
GET_LOW_WORD(low,x);
|
|
if(ix>0x7ff00000||
|
|
(ix==0x7ff00000&&(low!=0)))
|
|
return x+x; /* NaN */
|
|
if(hx>0) return atanhi[3]+atanlo[3];
|
|
else return -atanhi[3]-atanlo[3];
|
|
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
|
if (ix < 0x3e200000) { /* |x| < 2^-29 */
|
|
if(huge+x>one) return x; /* raise inexact */
|
|
}
|
|
id = -1;
|
|
} else {
|
|
x = fabs(x);
|
|
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
|
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
|
|
id = 0; x = (2.0*x-one)/(2.0+x);
|
|
} else { /* 11/16<=|x|< 19/16 */
|
|
id = 1; x = (x-one)/(x+one);
|
|
}
|
|
} else {
|
|
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
|
id = 2; x = (x-1.5)/(one+1.5*x);
|
|
} else { /* 2.4375 <= |x| < 2^66 */
|
|
id = 3; x = -1.0/x;
|
|
}
|
|
}}
|
|
/* end of argument reduction */
|
|
z = x*x;
|
|
w = z*z;
|
|
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
|
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
|
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
|
if (id<0) return x - x*(s1+s2);
|
|
else {
|
|
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
|
return (hx<0)? -z:z;
|
|
}
|
|
}
|
|
|
|
#endif /* _DOUBLE_IS_32BITS */
|