2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
12 /* __ieee754_atan2(y,x)
14 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
15 * 2. Reduce x to positive by (if x and y are unexceptional):
16 * ARG (x+iy) = arctan(y/x) ... if x > 0,
17 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
21 * ATAN2((anything), NaN ) is NaN;
22 * ATAN2(NAN , (anything) ) is NaN;
23 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
24 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
25 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
26 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
27 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
28 * ATAN2(+-INF,+INF ) is +-pi/4 ;
29 * ATAN2(+-INF,-INF ) is +-3pi/4;
30 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
33 * The hexadecimal values are the intended ones for the following
34 * constants. The decimal values may be used, provided that the
35 * compiler will convert from decimal to binary accurately enough
36 * to produce the hexadecimal values shown.
40 #include "math_private.h"
45 pi_o_4
= 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
46 pi_o_2
= 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
47 pi
= 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
48 pi_lo
= 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
50 double attribute_hidden
__ieee754_atan2(double y
, double x
)
53 int32_t k
,m
,hx
,hy
,ix
,iy
;
56 EXTRACT_WORDS(hx
,lx
,x
);
58 EXTRACT_WORDS(hy
,ly
,y
);
60 if(((ix
|((lx
|-lx
)>>31))>0x7ff00000)||
61 ((iy
|((ly
|-ly
)>>31))>0x7ff00000)) /* x or y is NaN */
63 if(((hx
-0x3ff00000)|lx
)==0) return atan(y
); /* x=1.0 */
64 m
= ((hy
>>31)&1)|((hx
>>30)&2); /* 2*sign(x)+sign(y) */
70 case 1: return y
; /* atan(+-0,+anything)=+-0 */
71 case 2: return pi
+tiny
;/* atan(+0,-anything) = pi */
72 case 3: return -pi
-tiny
;/* atan(-0,-anything) =-pi */
76 if((ix
|lx
)==0) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
82 case 0: return pi_o_4
+tiny
;/* atan(+INF,+INF) */
83 case 1: return -pi_o_4
-tiny
;/* atan(-INF,+INF) */
84 case 2: return 3.0*pi_o_4
+tiny
;/*atan(+INF,-INF)*/
85 case 3: return -3.0*pi_o_4
-tiny
;/*atan(-INF,-INF)*/
89 case 0: return zero
; /* atan(+...,+INF) */
90 case 1: return -zero
; /* atan(-...,+INF) */
91 case 2: return pi
+tiny
; /* atan(+...,-INF) */
92 case 3: return -pi
-tiny
; /* atan(-...,-INF) */
97 if(iy
==0x7ff00000) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
101 if(k
> 60) z
=pi_o_2
+0.5*pi_lo
; /* |y/x| > 2**60 */
102 else if(hx
<0&&k
<-60) z
=0.0; /* |y|/x < -2**60 */
103 else z
=atan(fabs(y
/x
)); /* safe to do y/x */
105 case 0: return z
; /* atan(+,+) */
109 SET_HIGH_WORD(z
,zh
^ 0x80000000);
111 return z
; /* atan(-,+) */
112 case 2: return pi
-(z
-pi_lo
);/* atan(+,-) */
113 default: /* case 3 */
114 return (z
-pi_lo
)-pi
;/* atan(-,-) */
122 double atan2(double y
, double x
)
124 double z
= __ieee754_atan2(y
, x
);
125 if (_LIB_VERSION
== _IEEE_
|| isnan(x
) || isnan(y
))
127 if (x
== 0.0 && y
== 0.0)
128 return __kernel_standard(y
,x
,3); /* atan2(+-0,+-0) */
132 strong_alias(__ieee754_atan2
, atan2
)
134 libm_hidden_def(atan2
)