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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