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e_atan2.c
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1 
2 /* @(#)e_atan2.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, 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 "fdlibm.h"
43 
44 #ifdef __STDC__
45 static const double
46 #else
47 static double
48 #endif
49 tiny = 1.0e-300,
50 zero = 0.0,
51 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
52 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
53 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
54 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
55 
56 #ifdef __STDC__
57  double __ieee754_atan2(double y, double x)
58 #else
59  double __ieee754_atan2(y,x)
60  double y,x;
61 #endif
62 {
63  double z;
64  int k,m,hx,hy,ix,iy;
65  unsigned lx,ly;
66 
67  hx = __HI(x); ix = hx&0x7fffffff;
68  lx = __LO(x);
69  hy = __HI(y); iy = hy&0x7fffffff;
70  ly = __LO(y);
71  if(((ix|((lx|-lx)>>31))>0x7ff00000)||
72  ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
73  return x+y;
74  if((hx-(0x3ff00000|lx))==0) return atan(y); /* x=1.0 */
75  m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
76 
77  /* when y = 0 */
78  if((iy|ly)==0) {
79  switch(m) {
80  case 0:
81  case 1: return y; /* atan(+-0,+anything)=+-0 */
82  case 2: return pi+tiny;/* atan(+0,-anything) = pi */
83  case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
84  }
85  }
86  /* when x = 0 */
87  if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
88 
89  /* when x is INF */
90  if(ix==0x7ff00000) {
91  if(iy==0x7ff00000) {
92  switch(m) {
93  case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
94  case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
95  case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
96  case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
97  }
98  } else {
99  switch(m) {
100  case 0: return zero ; /* atan(+...,+INF) */
101  case 1: return -zero ; /* atan(-...,+INF) */
102  case 2: return pi+tiny ; /* atan(+...,-INF) */
103  case 3: return -pi-tiny ; /* atan(-...,-INF) */
104  }
105  }
106  }
107  /* when y is INF */
108  if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
109 
110  /* compute y/x */
111  k = (iy-ix)>>20;
112  if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
113  else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
114  else z=atan(fabs(y/x)); /* safe to do y/x */
115  switch (m) {
116  case 0: return z ; /* atan(+,+) */
117  case 1: __HI(z) ^= 0x80000000;
118  return z ; /* atan(-,+) */
119  case 2: return pi-(z-pi_lo);/* atan(+,-) */
120  default: /* case 3 */
121  return (z-pi_lo)-pi;/* atan(-,-) */
122  }
123 }