projects / uclibc-ng.git / blame
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|---|---|---|
| 7ce331c0 EA |
1 | /* |
| 2 | * ==================================================== | |
| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| 4 | * | |
| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
| 6 | * Permission to use, copy, modify, and distribute this | |
| c4e44e97 | 7 | * software is freely granted, provided that this notice |
| 7ce331c0 EA |
8 | * is preserved. |
| 9 | * ==================================================== | |
| 10 | */ | |
| 11 | ||
| 7ce331c0 EA |
12 | /* __ieee754_atan2(y,x) |
| 13 | * Method : | |
| 14 | * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). | |
| c4e44e97 | 15 | * 2. Reduce x to positive by (if x and y are unexceptional): |
| 7ce331c0 EA |
16 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
| 17 | * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, | |
| 18 | * | |
| 19 | * Special cases: | |
| 20 | * | |
| 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; | |
| 31 | * | |
| 32 | * Constants: | |
| c4e44e97 EA |
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 | |
| 7ce331c0 EA |
36 | * to produce the hexadecimal values shown. |
| 37 | */ | |
| 38 | ||
| 39 | #include "math.h" | |
| 40 | #include "math_private.h" | |
| 41 | ||
| c4e44e97 | 42 | static const double |
| 7ce331c0 EA |
43 | tiny = 1.0e-300, |
| 44 | zero = 0.0, | |
| 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 */ | |
| 49 | ||
| 38b7304e | 50 | double attribute_hidden __ieee754_atan2(double y, double x) |
| c4e44e97 | 51 | { |
| 7ce331c0 EA |
52 | double z; |
| 53 | int32_t k,m,hx,hy,ix,iy; | |
| 54 | u_int32_t lx,ly; | |
| 55 | ||
| 56 | EXTRACT_WORDS(hx,lx,x); | |
| 57 | ix = hx&0x7fffffff; | |
| 58 | EXTRACT_WORDS(hy,ly,y); | |
| 59 | iy = hy&0x7fffffff; | |
| 60 | if(((ix|((lx|-lx)>>31))>0x7ff00000)|| | |
| 61 | ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ | |
| 62 | return x+y; | |
| 348d65d1 | 63 | if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ |
| 7ce331c0 EA |
64 | m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ |
| 65 | ||
| 66 | /* when y = 0 */ | |
| 67 | if((iy|ly)==0) { | |
| 68 | switch(m) { | |
| c4e44e97 | 69 | case 0: |
| 7ce331c0 EA |
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 */ | |
| 73 | } | |
| 74 | } | |
| 75 | /* when x = 0 */ | |
| 76 | if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; | |
| c4e44e97 | 77 | |
| 7ce331c0 EA |
78 | /* when x is INF */ |
| 79 | if(ix==0x7ff00000) { | |
| 80 | if(iy==0x7ff00000) { | |
| 81 | switch(m) { | |
| 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)*/ | |
| 86 | } | |
| 87 | } else { | |
| 88 | switch(m) { | |
| 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) */ | |
| 93 | } | |
| 94 | } | |
| 95 | } | |
| 96 | /* when y is INF */ | |
| 97 | if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; | |
| 98 | ||
| 99 | /* compute y/x */ | |
| 100 | k = (iy-ix)>>20; | |
| 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 */ | |
| 104 | switch (m) { | |
| 105 | case 0: return z ; /* atan(+,+) */ | |
| 106 | case 1: { | |
| 107 | u_int32_t zh; | |
| 108 | GET_HIGH_WORD(zh,z); | |
| 109 | SET_HIGH_WORD(z,zh ^ 0x80000000); | |
| 110 | } | |
| 111 | return z ; /* atan(-,+) */ | |
| 112 | case 2: return pi-(z-pi_lo);/* atan(+,-) */ | |
| 113 | default: /* case 3 */ | |
| 114 | return (z-pi_lo)-pi;/* atan(-,-) */ | |
| 115 | } | |
| 116 | } | |
| 30bd4a6c DV |
117 | |
| 118 | /* | |
| 119 | * wrapper atan2(y,x) | |
| 120 | */ | |
| 121 | #ifndef _IEEE_LIBM | |
| 122 | double atan2(double y, double x) | |
| 123 | { | |
| 90ca90c5 | 124 | double z = __ieee754_atan2(y, x); |
| 30bd4a6c DV |
125 | if (_LIB_VERSION == _IEEE_ || isnan(x) || isnan(y)) |
| 126 | return z; | |
| 127 | if (x == 0.0 && y == 0.0) | |
| 128 | return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ | |
| 129 | return z; | |
| 130 | } | |
| 131 | #else | |
| 132 | strong_alias(__ieee754_atan2, atan2) | |
| 133 | #endif | |
| 134 | libm_hidden_def(atan2) |