aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/libm-ieee754/e_atan2l.c
blob: 72d3eac17264be8952eaa14805b51aae8d4a13f2 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
/* e_atan2l.c -- long double version of e_atan2.c.
 * Conversion to long double by Ulrich Drepper,
 * Cygnus Support, drepper@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif

/* __ieee754_atan2l(y,x)
 * Method :
 *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
 *	2. Reduce x to positive by (if x and y are unexceptional):
 *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
 *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
 *
 * Special cases:
 *
 *	ATAN2((anything), NaN ) is NaN;
 *	ATAN2(NAN , (anything) ) is NaN;
 *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
 *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
 *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
 *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
 *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
 *	ATAN2(+-INF,+INF ) is +-pi/4 ;
 *	ATAN2(+-INF,-INF ) is +-3pi/4;
 *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const long double
#else
static long double
#endif
tiny  = 1.0e-4900L,
zero  = 0.0,
pi_o_4  = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */
pi_o_2  = 1.5707963267948966192564E+00L,  /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */
pi      = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */
pi_lo   = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */

#ifdef __STDC__
	long double __ieee754_atan2l(long double y, long double x)
#else
	long double __ieee754_atan2l(y,x)
	long double  y,x;
#endif
{
	long double z;
	int32_t k,m,hx,hy,ix,iy;
	u_int32_t sx,sy,lx,ly;

	EXTRACT_LDOUBLE_WORDS(sx,hx,lx,x);
	ix = sx&0x7fff;
	lx |= hx & 0x7fffffff;
	EXTRACT_LDOUBLE_WORDS(sy,hy,ly,y);
	iy = sy&0x7fff;
	ly |= hy & 0x7fffffff;
	if(((2*ix|((lx|-lx)>>31))>0xfffe)||
	   ((2*iy|((ly|-ly)>>31))>0xfffe))	/* x or y is NaN */
	   return x+y;
	if((sx-0x3fff|lx)==0) return __atanl(y);   /* x=1.0 */
	m = ((sy>>15)&1)|((sx>>14)&2);	/* 2*sign(x)+sign(y) */

    /* when y = 0 */
	if((iy|ly)==0) {
	    switch(m) {
		case 0:
		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
	    }
	}
    /* when x = 0 */
	if((ix|lx)==0) return (sy>=0x8000)?  -pi_o_2-tiny: pi_o_2+tiny;

    /* when x is INF */
	if(ix==0x7fff) {
	    if(iy==0x7fff) {
		switch(m) {
		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
		}
	    } else {
		switch(m) {
		    case 0: return  zero  ;	/* atan(+...,+INF) */
		    case 1: return -zero  ;	/* atan(-...,+INF) */
		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
		}
	    }
	}
    /* when y is INF */
	if(iy==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;

    /* compute y/x */
	k = sy-sx;
	if(k > 70) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**70 */
	else if(sx>=0x8000&&k<-70) z=0.0; 	/* |y|/x < -2**70 */
	else z=__atanl(fabsl(y/x));	/* safe to do y/x */
	switch (m) {
	    case 0: return       z  ;	/* atan(+,+) */
	    case 1: {
	    	      u_int32_t sz;
		      GET_LDOUBLE_EXP(sz,z);
		      SET_LDOUBLE_EXP(z,sz ^ 0x8000);
		    }
		    return       z  ;	/* atan(-,+) */
	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
	    default: /* case 3 */
	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
	}
}