zenilib  0.5.3.0
e_atan2.c
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1 /*
2  * ====================================================
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11
12 /* __ieee754_atan2(y,x)
13  * Method :
14  * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
15  * 2. Reduce x to positive by (if x and y are unexceptional):
16  * ARG (x+iy) = arctan(y/x) ... if x > 0,
17  * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
18  *
19  * Special cases:
20  *
21  * ATAN2((anything), NaN ) is NaN;
22  * ATAN2(NAN , (anything) ) is NaN;
23  * ATAN2(+-0, +(anything but NaN)) is +-0 ;
24  * ATAN2(+-0, -(anything but NaN)) is +-pi ;
25  * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
26  * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
27  * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
28  * ATAN2(+-INF,+INF ) is +-pi/4 ;
29  * ATAN2(+-INF,-INF ) is +-3pi/4;
30  * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
31  *
32  * Constants:
33  * The hexadecimal values are the intended ones for the following
34  * constants. The decimal values may be used, provided that the
35  * compiler will convert from decimal to binary accurately enough
36  * to produce the hexadecimal values shown.
37  */
38
39 #include "math_libm.h"
40 #include "math_private.h"
41
42 static const double
43 tiny = 1.0e-300,
44 zero = 0.0,
45 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
46 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
47 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
48 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
49
50 double attribute_hidden __ieee754_atan2(double y, double x)
51 {
52  double z;
53  int32_t k,m,hx,hy,ix,iy;
54  u_int32_t lx,ly;
55
56  EXTRACT_WORDS(hx,lx,x);
57  ix = hx&0x7fffffff;
58  EXTRACT_WORDS(hy,ly,y);
59  iy = hy&0x7fffffff;
60  if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
61  ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */
62  return x+y;
63  if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
64  m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
65
66  /* when y = 0 */
67  if((iy|ly)==0) {
68  switch(m) {
69  case 0:
70  case 1: return y; /* atan(+-0,+anything)=+-0 */
71  case 2: return pi+tiny;/* atan(+0,-anything) = pi */
72  case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
73  }
74  }
75  /* when x = 0 */
76  if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
77
78  /* when x is INF */
79  if(ix==0x7ff00000) {
80  if(iy==0x7ff00000) {
81  switch(m) {
82  case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
83  case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
84  case 2: return 3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
85  case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
86  }
87  } else {
88  switch(m) {
89  case 0: return zero ; /* atan(+...,+INF) */
90  case 1: return -zero ; /* atan(-...,+INF) */
91  case 2: return pi+tiny ; /* atan(+...,-INF) */
92  case 3: return -pi-tiny ; /* atan(-...,-INF) */
93  }
94  }
95  }
96  /* when y is INF */
97  if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
98
99  /* compute y/x */
100  k = (iy-ix)>>20;
101  if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
102  else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
103  else z=atan(fabs(y/x)); /* safe to do y/x */
104  switch (m) {
105  case 0: return z ; /* atan(+,+) */
106  case 1: {
107  u_int32_t zh;
108  GET_HIGH_WORD(zh,z);
109  SET_HIGH_WORD(z,zh ^ 0x80000000);
110  }
111  return z ; /* atan(-,+) */
112  case 2: return pi-(z-pi_lo);/* atan(+,-) */
113  default: /* case 3 */
114  return (z-pi_lo)-pi;/* atan(-,-) */
115  }
116 }
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:102
static const double pi
Definition: e_atan2.c:47
static const double tiny
Definition: e_atan2.c:43
int32_t k
Definition: e_log.c:102
EGLSurface EGLint x
Definition: eglext.h:293
static const double pi_o_4
Definition: e_atan2.c:45
long int32_t
Definition: types.h:9
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:130
static const double pi_lo
Definition: e_atan2.c:48
static const double zero
Definition: e_atan2.c:44
unsigned int u_int32_t
Definition: math_private.h:29
#define EXTRACT_WORDS(ix0, ix1, d)
Definition: math_private.h:92
static const double pi_o_2
Definition: e_atan2.c:46
#define __ieee754_atan2
Definition: math_private.h:33
EGLSurface EGLint EGLint y
Definition: eglext.h:293
int32_t hx
Definition: e_log.c:102
double attribute_hidden
int32_t ix
Definition: e_rem_pio2.c:100
u_int32_t lx
Definition: e_log.c:105
GLint GLint GLint GLint z
Definition: gl2ext.h:1214
int iy
Definition: k_sin.c:69
double atan(double x)
Definition: s_atan.c:67
double fabs(double x)
Definition: s_fabs.c:29
#define m(i, j)