e_atan2.c revision 181062
1141296Sdas 2141296Sdas/* @(#)e_atan2.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 12141296Sdas * 132116Sjkh */ 142116Sjkh 15176451Sdas#include <sys/cdefs.h> 16176451Sdas__FBSDID("$FreeBSD: head/lib/msun/src/e_atan2.c 181062 2008-07-31 19:57:50Z das $"); 172116Sjkh 182116Sjkh/* __ieee754_atan2(y,x) 192116Sjkh * Method : 202116Sjkh * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 21141296Sdas * 2. Reduce x to positive by (if x and y are unexceptional): 222116Sjkh * ARG (x+iy) = arctan(y/x) ... if x > 0, 232116Sjkh * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 242116Sjkh * 252116Sjkh * Special cases: 262116Sjkh * 272116Sjkh * ATAN2((anything), NaN ) is NaN; 282116Sjkh * ATAN2(NAN , (anything) ) is NaN; 292116Sjkh * ATAN2(+-0, +(anything but NaN)) is +-0 ; 302116Sjkh * ATAN2(+-0, -(anything but NaN)) is +-pi ; 312116Sjkh * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 322116Sjkh * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 332116Sjkh * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 342116Sjkh * ATAN2(+-INF,+INF ) is +-pi/4 ; 352116Sjkh * ATAN2(+-INF,-INF ) is +-3pi/4; 362116Sjkh * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 372116Sjkh * 382116Sjkh * Constants: 39141296Sdas * The hexadecimal values are the intended ones for the following 40141296Sdas * constants. The decimal values may be used, provided that the 41141296Sdas * compiler will convert from decimal to binary accurately enough 422116Sjkh * to produce the hexadecimal values shown. 432116Sjkh */ 442116Sjkh 452116Sjkh#include "math.h" 462116Sjkh#include "math_private.h" 472116Sjkh 48181062Sdasstatic volatile double 49181062Sdastiny = 1.0e-300; 508870Srgrimesstatic const double 512116Sjkhzero = 0.0, 522116Sjkhpi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 532116Sjkhpi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 54181062Sdaspi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ 55181062Sdasstatic volatile double 562116Sjkhpi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 572116Sjkh 5897407Salfreddouble 59117912Speter__ieee754_atan2(double y, double x) 608870Srgrimes{ 612116Sjkh double z; 622116Sjkh int32_t k,m,hx,hy,ix,iy; 632116Sjkh u_int32_t lx,ly; 642116Sjkh 652116Sjkh EXTRACT_WORDS(hx,lx,x); 662116Sjkh ix = hx&0x7fffffff; 672116Sjkh EXTRACT_WORDS(hy,ly,y); 682116Sjkh iy = hy&0x7fffffff; 692116Sjkh if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 702116Sjkh ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 712116Sjkh return x+y; 72141296Sdas if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 732116Sjkh m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 742116Sjkh 752116Sjkh /* when y = 0 */ 762116Sjkh if((iy|ly)==0) { 772116Sjkh switch(m) { 78141296Sdas case 0: 792116Sjkh case 1: return y; /* atan(+-0,+anything)=+-0 */ 802116Sjkh case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 812116Sjkh case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 822116Sjkh } 832116Sjkh } 842116Sjkh /* when x = 0 */ 852116Sjkh if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 86141296Sdas 872116Sjkh /* when x is INF */ 882116Sjkh if(ix==0x7ff00000) { 892116Sjkh if(iy==0x7ff00000) { 902116Sjkh switch(m) { 912116Sjkh case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 922116Sjkh case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 932116Sjkh case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 942116Sjkh case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 952116Sjkh } 962116Sjkh } else { 972116Sjkh switch(m) { 982116Sjkh case 0: return zero ; /* atan(+...,+INF) */ 992116Sjkh case 1: return -zero ; /* atan(-...,+INF) */ 1002116Sjkh case 2: return pi+tiny ; /* atan(+...,-INF) */ 1012116Sjkh case 3: return -pi-tiny ; /* atan(-...,-INF) */ 1022116Sjkh } 1032116Sjkh } 1042116Sjkh } 1052116Sjkh /* when y is INF */ 1062116Sjkh if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 1072116Sjkh 1082116Sjkh /* compute y/x */ 1092116Sjkh k = (iy-ix)>>20; 1102116Sjkh if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 1112116Sjkh else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 1122116Sjkh else z=atan(fabs(y/x)); /* safe to do y/x */ 1132116Sjkh switch (m) { 1142116Sjkh case 0: return z ; /* atan(+,+) */ 1152116Sjkh case 1: { 1162116Sjkh u_int32_t zh; 1172116Sjkh GET_HIGH_WORD(zh,z); 1182116Sjkh SET_HIGH_WORD(z,zh ^ 0x80000000); 1192116Sjkh } 1202116Sjkh return z ; /* atan(-,+) */ 1212116Sjkh case 2: return pi-(z-pi_lo);/* atan(+,-) */ 1222116Sjkh default: /* case 3 */ 1232116Sjkh return (z-pi_lo)-pi;/* atan(-,-) */ 1242116Sjkh } 1252116Sjkh} 126