1 /* @(#)e_atan2.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
16 #endif
17
18 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
19 // unary minus operator applied to unsigned type, result still unsigned
20 #pragma warning ( disable : 4146 )
21 #endif
22
23 /* __ieee754_atan2(y,x)
24 * Method :
25 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
26 * 2. Reduce x to positive by (if x and y are unexceptional):
27 * ARG (x+iy) = arctan(y/x) ... if x > 0,
28 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
29 *
30 * Special cases:
31 *
32 * ATAN2((anything), NaN ) is NaN;
33 * ATAN2(NAN , (anything) ) is NaN;
34 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
35 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
36 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
37 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
38 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
39 * ATAN2(+-INF,+INF ) is +-pi/4 ;
40 * ATAN2(+-INF,-INF ) is +-3pi/4;
41 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
42 *
43 * Constants:
44 * The hexadecimal values are the intended ones for the following
45 * constants. The decimal values may be used, provided that the
46 * compiler will convert from decimal to binary accurately enough
47 * to produce the hexadecimal values shown.
48 */
49
50 #include "math.h"
51 #include "math_private.h"
52
53 static const double
54 tiny = 1.0e-300,
55 zero = 0.0,
56 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
57 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
58 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
59 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
60
61 double
__ieee754_atan2(double y,double x)62 __ieee754_atan2(double y, double x)
63 {
64 double z;
65 int32_t k,m,hx,hy,ix,iy;
66 u_int32_t lx,ly;
67
68 EXTRACT_WORDS(hx,lx,x);
69 ix = hx&0x7fffffff;
70 EXTRACT_WORDS(hy,ly,y);
71 iy = hy&0x7fffffff;
72 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
73 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
74 return x+y;
75 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
76 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
77
78 /* when y = 0 */
79 if((iy|ly)==0) {
80 switch(m) {
81 case 0:
82 case 1: return y; /* atan(+-0,+anything)=+-0 */
83 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
84 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
85 }
86 }
87 /* when x = 0 */
88 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
89
90 /* when x is INF */
91 if(ix==0x7ff00000) {
92 if(iy==0x7ff00000) {
93 switch(m) {
94 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
95 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
96 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
97 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
98 }
99 } else {
100 switch(m) {
101 case 0: return zero ; /* atan(+...,+INF) */
102 case 1: return -zero ; /* atan(-...,+INF) */
103 case 2: return pi+tiny ; /* atan(+...,-INF) */
104 case 3: return -pi-tiny ; /* atan(-...,-INF) */
105 }
106 }
107 }
108 /* when y is INF */
109 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
110
111 /* compute y/x */
112 k = (iy-ix)>>20;
113 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
114 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
115 else z=atan(fabs(y/x)); /* safe to do y/x */
116 switch (m) {
117 case 0: return z ; /* atan(+,+) */
118 case 1: {
119 u_int32_t zh;
120 GET_HIGH_WORD(zh,z);
121 SET_HIGH_WORD(z,zh ^ 0x80000000);
122 }
123 return z ; /* atan(-,+) */
124 case 2: return pi-(z-pi_lo);/* atan(+,-) */
125 default: /* case 3 */
126 return (z-pi_lo)-pi;/* atan(-,-) */
127 }
128 }
129