Update.
[glibc.git] / sysdeps / libm-ieee754 / e_atan2l.c
blobaff7a3d9765c3aa3411969ff8f1845d5943c4fc0
1 /* e_atan2l.c -- long double version of e_atan2.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
4 */
6 /*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
17 #if defined(LIBM_SCCS) && !defined(lint)
18 static char rcsid[] = "$NetBSD: $";
19 #endif
21 /* __ieee754_atan2l(y,x)
22 * Method :
23 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
24 * 2. Reduce x to positive by (if x and y are unexceptional):
25 * ARG (x+iy) = arctan(y/x) ... if x > 0,
26 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
28 * Special cases:
30 * ATAN2((anything), NaN ) is NaN;
31 * ATAN2(NAN , (anything) ) is NaN;
32 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
33 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
34 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
35 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
36 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
37 * ATAN2(+-INF,+INF ) is +-pi/4 ;
38 * ATAN2(+-INF,-INF ) is +-3pi/4;
39 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
41 * Constants:
42 * The hexadecimal values are the intended ones for the following
43 * constants. The decimal values may be used, provided that the
44 * compiler will convert from decimal to binary accurately enough
45 * to produce the hexadecimal values shown.
48 #include "math.h"
49 #include "math_private.h"
51 #ifdef __STDC__
52 static const long double
53 #else
54 static long double
55 #endif
56 tiny = 1.0e-4900L,
57 zero = 0.0,
58 pi_o_4 = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */
59 pi_o_2 = 1.5707963267948966192564E+00L, /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */
60 pi = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */
61 pi_lo = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */
63 #ifdef __STDC__
64 long double __ieee754_atan2l(long double y, long double x)
65 #else
66 long double __ieee754_atan2l(y,x)
67 long double y,x;
68 #endif
70 long double z;
71 int32_t k,m,hx,hy,ix,iy;
72 u_int32_t sx,sy,lx,ly;
74 GET_LDOUBLE_WORDS(sx,hx,lx,x);
75 ix = sx&0x7fff;
76 lx |= hx & 0x7fffffff;
77 GET_LDOUBLE_WORDS(sy,hy,ly,y);
78 iy = sy&0x7fff;
79 ly |= hy & 0x7fffffff;
80 if(((2*ix|((lx|-lx)>>31))>0xfffe)||
81 ((2*iy|((ly|-ly)>>31))>0xfffe)) /* x or y is NaN */
82 return x+y;
83 if((sx-0x3fff|lx)==0) return __atanl(y); /* x=1.0 */
84 m = ((sy>>15)&1)|((sx>>14)&2); /* 2*sign(x)+sign(y) */
86 /* when y = 0 */
87 if((iy|ly)==0) {
88 switch(m) {
89 case 0:
90 case 1: return y; /* atan(+-0,+anything)=+-0 */
91 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
92 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
95 /* when x = 0 */
96 if((ix|lx)==0) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
98 /* when x is INF */
99 if(ix==0x7fff) {
100 if(iy==0x7fff) {
101 switch(m) {
102 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
103 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
104 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
105 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
107 } else {
108 switch(m) {
109 case 0: return zero ; /* atan(+...,+INF) */
110 case 1: return -zero ; /* atan(-...,+INF) */
111 case 2: return pi+tiny ; /* atan(+...,-INF) */
112 case 3: return -pi-tiny ; /* atan(-...,-INF) */
116 /* when y is INF */
117 if(iy==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
119 /* compute y/x */
120 k = sy-sx;
121 if(k > 70) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**70 */
122 else if(sx>=0x8000&&k<-70) z=0.0; /* |y|/x < -2**70 */
123 else z=__atanl(fabsl(y/x)); /* safe to do y/x */
124 switch (m) {
125 case 0: return z ; /* atan(+,+) */
126 case 1: {
127 u_int32_t sz;
128 GET_LDOUBLE_EXP(sz,z);
129 SET_LDOUBLE_EXP(z,sz ^ 0x8000);
131 return z ; /* atan(-,+) */
132 case 2: return pi-(z-pi_lo);/* atan(+,-) */
133 default: /* case 3 */
134 return (z-pi_lo)-pi;/* atan(-,-) */