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: releng/11.0/lib/msun/src/e_atan2.c 181204 2008-08-02 19:17:00Z 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 45181074Sdas#include <float.h> 46181074Sdas 472116Sjkh#include "math.h" 482116Sjkh#include "math_private.h" 492116Sjkh 50181062Sdasstatic volatile double 51181062Sdastiny = 1.0e-300; 528870Srgrimesstatic const double 532116Sjkhzero = 0.0, 542116Sjkhpi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 552116Sjkhpi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 56181062Sdaspi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ 57181062Sdasstatic volatile double 582116Sjkhpi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 592116Sjkh 6097407Salfreddouble 61117912Speter__ieee754_atan2(double y, double x) 628870Srgrimes{ 632116Sjkh double z; 642116Sjkh int32_t k,m,hx,hy,ix,iy; 652116Sjkh u_int32_t lx,ly; 662116Sjkh 672116Sjkh EXTRACT_WORDS(hx,lx,x); 682116Sjkh ix = hx&0x7fffffff; 692116Sjkh EXTRACT_WORDS(hy,ly,y); 702116Sjkh iy = hy&0x7fffffff; 712116Sjkh if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 722116Sjkh ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 732116Sjkh return x+y; 74141296Sdas if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 752116Sjkh m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 762116Sjkh 772116Sjkh /* when y = 0 */ 782116Sjkh if((iy|ly)==0) { 792116Sjkh switch(m) { 80141296Sdas case 0: 812116Sjkh case 1: return y; /* atan(+-0,+anything)=+-0 */ 822116Sjkh case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 832116Sjkh case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 842116Sjkh } 852116Sjkh } 862116Sjkh /* when x = 0 */ 872116Sjkh if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 88141296Sdas 892116Sjkh /* when x is INF */ 902116Sjkh if(ix==0x7ff00000) { 912116Sjkh if(iy==0x7ff00000) { 922116Sjkh switch(m) { 932116Sjkh case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 942116Sjkh case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 952116Sjkh case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 962116Sjkh case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 972116Sjkh } 982116Sjkh } else { 992116Sjkh switch(m) { 1002116Sjkh case 0: return zero ; /* atan(+...,+INF) */ 1012116Sjkh case 1: return -zero ; /* atan(-...,+INF) */ 1022116Sjkh case 2: return pi+tiny ; /* atan(+...,-INF) */ 1032116Sjkh case 3: return -pi-tiny ; /* atan(-...,-INF) */ 1042116Sjkh } 1052116Sjkh } 1062116Sjkh } 1072116Sjkh /* when y is INF */ 1082116Sjkh if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 1092116Sjkh 1102116Sjkh /* compute y/x */ 1112116Sjkh k = (iy-ix)>>20; 112181204Sdas if(k > 60) { /* |y/x| > 2**60 */ 113181204Sdas z=pi_o_2+0.5*pi_lo; 114181204Sdas m&=1; 115181204Sdas } 116181204Sdas else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ 1172116Sjkh else z=atan(fabs(y/x)); /* safe to do y/x */ 1182116Sjkh switch (m) { 1192116Sjkh case 0: return z ; /* atan(+,+) */ 120181204Sdas case 1: 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} 126181074Sdas 127181074Sdas#if LDBL_MANT_DIG == 53 128181074Sdas__weak_reference(atan2, atan2l); 129181074Sdas#endif 130