The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 1 | |
| 2 | /* @(#)e_atan2.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | * |
| 13 | */ |
| 14 | |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 15 | #include <sys/cdefs.h> |
| 16 | __FBSDID("$FreeBSD$"); |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 17 | |
| 18 | /* __ieee754_atan2(y,x) |
| 19 | * Method : |
| 20 | * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). |
| 21 | * 2. Reduce x to positive by (if x and y are unexceptional): |
| 22 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
| 23 | * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, |
| 24 | * |
| 25 | * Special cases: |
| 26 | * |
| 27 | * ATAN2((anything), NaN ) is NaN; |
| 28 | * ATAN2(NAN , (anything) ) is NaN; |
| 29 | * ATAN2(+-0, +(anything but NaN)) is +-0 ; |
| 30 | * ATAN2(+-0, -(anything but NaN)) is +-pi ; |
| 31 | * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; |
| 32 | * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; |
| 33 | * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; |
| 34 | * ATAN2(+-INF,+INF ) is +-pi/4 ; |
| 35 | * ATAN2(+-INF,-INF ) is +-3pi/4; |
| 36 | * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; |
| 37 | * |
| 38 | * Constants: |
| 39 | * The hexadecimal values are the intended ones for the following |
| 40 | * constants. The decimal values may be used, provided that the |
| 41 | * compiler will convert from decimal to binary accurately enough |
| 42 | * to produce the hexadecimal values shown. |
| 43 | */ |
| 44 | |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 45 | #include <float.h> |
| 46 | |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 47 | #include "math.h" |
| 48 | #include "math_private.h" |
| 49 | |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 50 | static volatile double |
| 51 | tiny = 1.0e-300; |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 52 | static const double |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 53 | zero = 0.0, |
| 54 | pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ |
| 55 | pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 56 | pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ |
| 57 | static volatile double |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 58 | pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ |
| 59 | |
| 60 | double |
| 61 | __ieee754_atan2(double y, double x) |
| 62 | { |
| 63 | double z; |
| 64 | int32_t k,m,hx,hy,ix,iy; |
| 65 | u_int32_t lx,ly; |
| 66 | |
| 67 | EXTRACT_WORDS(hx,lx,x); |
| 68 | ix = hx&0x7fffffff; |
| 69 | EXTRACT_WORDS(hy,ly,y); |
| 70 | iy = hy&0x7fffffff; |
| 71 | if(((ix|((lx|-lx)>>31))>0x7ff00000)|| |
| 72 | ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ |
| 73 | return x+y; |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 74 | if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 75 | m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ |
| 76 | |
| 77 | /* when y = 0 */ |
| 78 | if((iy|ly)==0) { |
| 79 | switch(m) { |
| 80 | case 0: |
| 81 | case 1: return y; /* atan(+-0,+anything)=+-0 */ |
| 82 | case 2: return pi+tiny;/* atan(+0,-anything) = pi */ |
| 83 | case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ |
| 84 | } |
| 85 | } |
| 86 | /* when x = 0 */ |
| 87 | if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
| 88 | |
| 89 | /* when x is INF */ |
| 90 | if(ix==0x7ff00000) { |
| 91 | if(iy==0x7ff00000) { |
| 92 | switch(m) { |
| 93 | case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ |
| 94 | case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ |
| 95 | case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
| 96 | case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ |
| 97 | } |
| 98 | } else { |
| 99 | switch(m) { |
| 100 | case 0: return zero ; /* atan(+...,+INF) */ |
| 101 | case 1: return -zero ; /* atan(-...,+INF) */ |
| 102 | case 2: return pi+tiny ; /* atan(+...,-INF) */ |
| 103 | case 3: return -pi-tiny ; /* atan(-...,-INF) */ |
| 104 | } |
| 105 | } |
| 106 | } |
| 107 | /* when y is INF */ |
| 108 | if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
| 109 | |
| 110 | /* compute y/x */ |
| 111 | k = (iy-ix)>>20; |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 112 | if(k > 60) { /* |y/x| > 2**60 */ |
| 113 | z=pi_o_2+0.5*pi_lo; |
| 114 | m&=1; |
| 115 | } |
| 116 | else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 117 | else z=atan(fabs(y/x)); /* safe to do y/x */ |
| 118 | switch (m) { |
| 119 | case 0: return z ; /* atan(+,+) */ |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 120 | case 1: return -z ; /* atan(-,+) */ |
The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame] | 121 | case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
| 122 | default: /* case 3 */ |
| 123 | return (z-pi_lo)-pi;/* atan(-,-) */ |
| 124 | } |
| 125 | } |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 126 | |
| 127 | #if LDBL_MANT_DIG == 53 |
| 128 | __weak_reference(atan2, atan2l); |
| 129 | #endif |