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
53static const double
54tiny  = 1.0e-300,
55zero  = 0.0,
56pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
57pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
58pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
59pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
60
61double
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