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path: root/libm/e_atan2.c
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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 ``` ``````/* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* __ieee754_atan2(y,x) * Method : * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). * 2. Reduce x to positive by (if x and y are unexceptional): * ARG (x+iy) = arctan(y/x) ... if x > 0, * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, * * Special cases: * * ATAN2((anything), NaN ) is NaN; * ATAN2(NAN , (anything) ) is NaN; * ATAN2(+-0, +(anything but NaN)) is +-0 ; * ATAN2(+-0, -(anything but NaN)) is +-pi ; * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; * ATAN2(+-INF,+INF ) is +-pi/4 ; * ATAN2(+-INF,-INF ) is +-3pi/4; * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; * * Constants: * The hexadecimal values are the intended ones for the following * constants. The decimal values may be used, provided that the * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ #include "math.h" #include "math_private.h" static const double tiny = 1.0e-300, zero = 0.0, pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ double attribute_hidden __ieee754_atan2(double y, double x) { double z; int32_t k,m,hx,hy,ix,iy; u_int32_t lx,ly; EXTRACT_WORDS(hx,lx,x); ix = hx&0x7fffffff; EXTRACT_WORDS(hy,ly,y); iy = hy&0x7fffffff; if(((ix|((lx|-lx)>>31))>0x7ff00000)|| ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ return x+y; if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ /* when y = 0 */ if((iy|ly)==0) { switch(m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi+tiny;/* atan(+0,-anything) = pi */ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* when x is INF */ if(ix==0x7ff00000) { if(iy==0x7ff00000) { switch(m) { case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ } } else { switch(m) { case 0: return zero ; /* atan(+...,+INF) */ case 1: return -zero ; /* atan(-...,+INF) */ case 2: return pi+tiny ; /* atan(+...,-INF) */ case 3: return -pi-tiny ; /* atan(-...,-INF) */ } } } /* when y is INF */ if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* compute y/x */ k = (iy-ix)>>20; if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ else z=atan(fabs(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* atan(+,+) */ case 1: { u_int32_t zh; GET_HIGH_WORD(zh,z); SET_HIGH_WORD(z,zh ^ 0x80000000); } return z ; /* atan(-,+) */ case 2: return pi-(z-pi_lo);/* atan(+,-) */ default: /* case 3 */ return (z-pi_lo)-pi;/* atan(-,-) */ } } /* * wrapper atan2(y,x) */ #ifndef _IEEE_LIBM double atan2(double y, double x) { double z = __ieee754_atan2(y, x); if (_LIB_VERSION == _IEEE_ || isnan(x) || isnan(y)) return z; if (x == 0.0 && y == 0.0) return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ return z; } #else strong_alias(__ieee754_atan2, atan2) #endif libm_hidden_def(atan2) ``````