1 2 /* @(#)e_atan2.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, 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 15 /* __ieee754_atan2(y,x) 16 * Method : 17 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 18 * 2. Reduce x to positive by (if x and y are unexceptional): 19 * ARG (x+iy) = arctan(y/x) ... if x > 0, 20 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 21 * 22 * Special cases: 23 * 24 * ATAN2((anything), NaN ) is NaN; 25 * ATAN2(NAN , (anything) ) is NaN; 26 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 27 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 28 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 29 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 30 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 31 * ATAN2(+-INF,+INF ) is +-pi/4 ; 32 * ATAN2(+-INF,-INF ) is +-3pi/4; 33 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 34 * 35 * Constants: 36 * The hexadecimal values are the intended ones for the following 37 * constants. The decimal values may be used, provided that the 38 * compiler will convert from decimal to binary accurately enough 39 * to produce the hexadecimal values shown. 40 */ 41 42 #include "fdlibm.h" 43 44 #ifndef _DOUBLE_IS_32BITS 45 46 #ifdef __STDC__ 47 static const double 48 #else 49 static double 50 #endif 51 tiny = 1.0e-300, 52 zero = 0.0, 53 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 54 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 55 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 56 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 57 58 #ifdef __STDC__ __ieee754_atan2(double y,double x)59 double __ieee754_atan2(double y, double x) 60 #else 61 double __ieee754_atan2(y,x) 62 double y,x; 63 #endif 64 { 65 double z; 66 int32_t k,m,hx,hy,ix,iy; 67 uint32_t lx,ly; 68 69 EXTRACT_WORDS(hx,lx,x); 70 ix = hx&0x7fffffff; 71 EXTRACT_WORDS(hy,ly,y); 72 iy = hy&0x7fffffff; 73 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 74 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 75 return x+y; 76 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 77 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 78 79 /* when y = 0 */ 80 if((iy|ly)==0) { 81 switch(m) { 82 case 0: 83 case 1: return y; /* atan(+-0,+anything)=+-0 */ 84 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 85 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 86 } 87 } 88 /* when x = 0 */ 89 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 90 91 /* when x is INF */ 92 if(ix==0x7ff00000) { 93 if(iy==0x7ff00000) { 94 switch(m) { 95 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 96 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 97 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 98 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 99 } 100 } else { 101 switch(m) { 102 case 0: return zero ; /* atan(+...,+INF) */ 103 case 1: return -zero ; /* atan(-...,+INF) */ 104 case 2: return pi+tiny ; /* atan(+...,-INF) */ 105 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 106 } 107 } 108 } 109 /* when y is INF */ 110 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 111 112 /* compute y/x */ 113 k = (iy-ix)>>20; 114 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 115 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 116 else z=atan(fabs(y/x)); /* safe to do y/x */ 117 switch (m) { 118 case 0: return z ; /* atan(+,+) */ 119 case 1: { 120 uint32_t zh; 121 GET_HIGH_WORD(zh,z); 122 SET_HIGH_WORD(z,zh ^ 0x80000000); 123 } 124 return z ; /* atan(-,+) */ 125 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 126 default: /* case 3 */ 127 return (z-pi_lo)-pi;/* atan(-,-) */ 128 } 129 } 130 131 #endif /* defined(_DOUBLE_IS_32BITS) */ 132