source: trunk/sys/libm/e_atan2.c @ 297

Last change on this file since 297 was 1, checked in by alain, 8 years ago

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1
2/* @(#)e_atan2.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15/* __ieee754_atan2(y,x)
16 * Method :
17 *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
18 *      2. Reduce x to positive by (if x and y are unexceptional):
19 *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
20 *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
21 *
22 * Special cases:
23 *
24 *      ATAN2((anything), NaN ) is NaN;
25 *      ATAN2(NAN , (anything) ) is NaN;
26 *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
27 *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
28 *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
29 *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
30 *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
31 *      ATAN2(+-INF,+INF ) is +-pi/4 ;
32 *      ATAN2(+-INF,-INF ) is +-3pi/4;
33 *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
34 *
35 * Constants:
36 * The hexadecimal values are the intended ones for the following
37 * constants. The decimal values may be used, provided that the
38 * compiler will convert from decimal to binary accurately enough
39 * to produce the hexadecimal values shown.
40 */
41
42#include <libm/fdlibm.h>
43
44#ifdef __STDC__
45static const double 
46#else
47static double 
48#endif
49tiny  = 1.0e-300,
50zero  = 0.0,
51one   = 1.0,
52pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
53pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
54pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
55pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
56
57#ifdef __STDC__
58        double __ieee754_atan2(double y, double x)
59#else
60        double __ieee754_atan2(y,x)
61        double  y,x;
62#endif
63{ 
64        double z;
65        int k,m,hx,hy,ix,iy,n0;
66        unsigned lx,ly;
67
68        n0 = ((*(int*)&one)>>29)^1;     /* high word index */
69        hx = *(n0+(int*)&x); ix = hx&0x7fffffff;
70        lx = *(1-n0+(int*)&x);
71        hy = *(n0+(int*)&y); iy = hy&0x7fffffff;
72        ly = *(1-n0+(int*)&y);
73        if(((ix|((lx|-lx)>>31))>0x7ff00000)||
74           ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
75           return x+y;
76        if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
77        m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
78
79    /* when y = 0 */
80        if((iy|ly)==0) {
81            switch(m) {
82                case 0: 
83                case 1: return y;       /* atan(+-0,+anything)=+-0 */
84                case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
85                case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
86            }
87        }
88    /* when x = 0 */
89        if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
90           
91    /* when x is INF */
92        if(ix==0x7ff00000) {
93            if(iy==0x7ff00000) {
94                switch(m) {
95                    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
96                    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
97                    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
98                    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
99                }
100            } else {
101                switch(m) {
102                    case 0: return  zero  ;     /* atan(+...,+INF) */
103                    case 1: return -zero  ;     /* atan(-...,+INF) */
104                    case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
105                    case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
106                }
107            }
108        }
109    /* when y is INF */
110        if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
111
112    /* compute y/x */
113        k = (iy-ix)>>20;
114        if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
115        else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
116        else z=atan(fabs(y/x));         /* safe to do y/x */
117        switch (m) {
118            case 0: return       z  ;   /* atan(+,+) */
119            case 1: *(n0+(int*)&z) ^= 0x80000000;
120                    return       z  ;   /* atan(-,+) */
121            case 2: return  pi-(z-pi_lo);/* atan(+,-) */
122            default: /* case 3 */
123                    return  (z-pi_lo)-pi;/* atan(-,-) */
124        }
125}
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