Atlas - e_atan2.c
Home / ext / SDL / src / libm Lines: 1 | Size: 4093 bytes [Download] [Show on GitHub] [Search similar files] [Raw] [Raw (proxy)][FILE BEGIN]1#include "SDL_internal.h" 2/* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13/* __ieee754_atan2(y,x) 14 * Method : 15 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 16 * 2. Reduce x to positive by (if x and y are unexceptional): 17 * ARG (x+iy) = arctan(y/x) ... if x > 0, 18 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 19 * 20 * Special cases: 21 * 22 * ATAN2((anything), NaN ) is NaN; 23 * ATAN2(NAN , (anything) ) is NaN; 24 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 25 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 26 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 27 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 28 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 29 * ATAN2(+-INF,+INF ) is +-pi/4 ; 30 * ATAN2(+-INF,-INF ) is +-3pi/4; 31 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 32 * 33 * Constants: 34 * The hexadecimal values are the intended ones for the following 35 * constants. The decimal values may be used, provided that the 36 * compiler will convert from decimal to binary accurately enough 37 * to produce the hexadecimal values shown. 38 */ 39 40#include "math_libm.h" 41#include "math_private.h" 42 43static const double 44tiny = 1.0e-300, 45zero = 0.0, 46pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 47pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 48pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 49pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 50 51double attribute_hidden __ieee754_atan2(double y, double x) 52{ 53 double z; 54 int32_t k,m,hx,hy,ix,iy; 55 u_int32_t lx,ly; 56 57 EXTRACT_WORDS(hx,lx,x); 58 ix = hx&0x7fffffff; 59 EXTRACT_WORDS(hy,ly,y); 60 iy = hy&0x7fffffff; 61 if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)|| 62 ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */ 63 return x+y; 64 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 65 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 66 67 /* when y = 0 */ 68 if((iy|ly)==0) { 69 switch(m) { 70 case 0: 71 case 1: return y; /* atan(+-0,+anything)=+-0 */ 72 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 73 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 74 } 75 } 76 /* when x = 0 */ 77 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 78 79 /* when x is INF */ 80 if(ix==0x7ff00000) { 81 if(iy==0x7ff00000) { 82 switch(m) { 83 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 84 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 85 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 86 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 87 } 88 } else { 89 switch(m) { 90 case 0: return zero ; /* atan(+...,+INF) */ 91 case 1: return -zero ; /* atan(-...,+INF) */ 92 case 2: return pi+tiny ; /* atan(+...,-INF) */ 93 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 94 } 95 } 96 } 97 /* when y is INF */ 98 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 99 100 /* compute y/x */ 101 k = (iy-ix)>>20; 102 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 103 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 104 else z=atan(fabs(y/x)); /* safe to do y/x */ 105 switch (m) { 106 case 0: return z ; /* atan(+,+) */ 107 case 1: { 108 u_int32_t zh; 109 GET_HIGH_WORD(zh,z); 110 SET_HIGH_WORD(z,zh ^ 0x80000000); 111 } 112 return z ; /* atan(-,+) */ 113 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 114 default: /* case 3 */ 115 return (z-pi_lo)-pi;/* atan(-,-) */ 116 } 117} 118 119/* 120 * wrapper atan2(y,x) 121 */ 122#ifndef _IEEE_LIBM 123double atan2(double y, double x) 124{ 125 double z = __ieee754_atan2(y, x); 126 if (_LIB_VERSION == _IEEE_ || isnan(x) || isnan(y)) 127 return z; 128 if (x == 0.0 && y == 0.0) 129 return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ 130 return z; 131} 132#else 133strong_alias(__ieee754_atan2, atan2) 134#endif 135libm_hidden_def(atan2) 136[FILE END](C) 2025 0x4248 (C) 2025 4248 Media and 4248 Systems, All part of 0x4248 See LICENCE files for more information. Not all files are by 0x4248 always check Licencing.