1a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 2a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project/* @(#)e_atan2.c 1.3 95/01/18 */ 3a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project/* 4a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ==================================================== 5a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 7a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 8a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Permission to use, copy, modify, and distribute this 9a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * software is freely granted, provided that this notice 10a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * is preserved. 11a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ==================================================== 12a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 13a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project */ 14a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 15a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project#ifndef lint 16a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectstatic char rcsid[] = "$FreeBSD: src/lib/msun/src/e_atan2.c,v 1.10 2005/02/04 18:26:05 das Exp $"; 17a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project#endif 18a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 19a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project/* __ieee754_atan2(y,x) 20a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Method : 21a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 22a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 2. Reduce x to positive by (if x and y are unexceptional): 23a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ARG (x+iy) = arctan(y/x) ... if x > 0, 24a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 25a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 26a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Special cases: 27a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 28a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2((anything), NaN ) is NaN; 29a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(NAN , (anything) ) is NaN; 30a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-0, +(anything but NaN)) is +-0 ; 31a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-0, -(anything but NaN)) is +-pi ; 32a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 33a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 34a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 35a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-INF,+INF ) is +-pi/4 ; 36a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-INF,-INF ) is +-3pi/4; 37a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 38a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * 39a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * Constants: 40a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * The hexadecimal values are the intended ones for the following 41a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * constants. The decimal values may be used, provided that the 42a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * compiler will convert from decimal to binary accurately enough 43a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project * to produce the hexadecimal values shown. 44a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project */ 45a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 46a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project#include "math.h" 47a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project#include "math_private.h" 48a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 49a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectstatic const double 50a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projecttiny = 1.0e-300, 51a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectzero = 0.0, 52a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectpi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 53a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectpi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 54a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectpi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 55a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectpi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 56a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 57a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Projectdouble 58a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project__ieee754_atan2(double y, double x) 59a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project{ 60a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project double z; 61a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project int32_t k,m,hx,hy,ix,iy; 62a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project u_int32_t lx,ly; 63a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 64a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project EXTRACT_WORDS(hx,lx,x); 65a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project ix = hx&0x7fffffff; 66a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project EXTRACT_WORDS(hy,ly,y); 67a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project iy = hy&0x7fffffff; 68a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 69a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 70a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project return x+y; 7172d3489612b77d4544e500a2a2a1783914ee56b7Scott Turner if(((hx-0x3ff00000) | lx)==0) return atan(y); /* x=1.0 */ 72a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 73a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 74a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project /* when y = 0 */ 75a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if((iy|ly)==0) { 76a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project switch(m) { 77a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 0: 78a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 1: return y; /* atan(+-0,+anything)=+-0 */ 79a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 80a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 81a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 82a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 83a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project /* when x = 0 */ 84a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 85a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 86a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project /* when x is INF */ 87a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if(ix==0x7ff00000) { 88a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if(iy==0x7ff00000) { 89a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project switch(m) { 90a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 91a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 92a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 93a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 94a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 95a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } else { 96a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project switch(m) { 97a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 0: return zero ; /* atan(+...,+INF) */ 98a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 1: return -zero ; /* atan(-...,+INF) */ 99a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 2: return pi+tiny ; /* atan(+...,-INF) */ 100a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 3: return -pi-tiny ; /* atan(-...,-INF) */ 101a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 102a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 103a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 104a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project /* when y is INF */ 105a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 106a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project 107a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project /* compute y/x */ 108a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project k = (iy-ix)>>20; 109a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 110a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 111a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project else z=atan(fabs(y/x)); /* safe to do y/x */ 112a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project switch (m) { 113a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 0: return z ; /* atan(+,+) */ 114a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 1: { 115a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project u_int32_t zh; 116a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project GET_HIGH_WORD(zh,z); 117a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project SET_HIGH_WORD(z,zh ^ 0x80000000); 118a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 119a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project return z ; /* atan(-,+) */ 120a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project case 2: return pi-(z-pi_lo);/* atan(+,-) */ 121a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project default: /* case 3 */ 122a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project return (z-pi_lo)-pi;/* atan(-,-) */ 123a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project } 124a27d2baa0c1a2ec70f47ea9199b1dd6762c8a34The Android Open Source Project} 125