e_atan2.c revision 176451
12311Sjkh 22311Sjkh/* @(#)e_atan2.c 1.3 95/01/18 */ 32311Sjkh/* 42311Sjkh * ==================================================== 52311Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62311Sjkh * 72311Sjkh * Developed at SunSoft, a Sun Microsystems, Inc. business. 82311Sjkh * Permission to use, copy, modify, and distribute this 92311Sjkh * software is freely granted, provided that this notice 102311Sjkh * is preserved. 112311Sjkh * ==================================================== 122311Sjkh * 132311Sjkh */ 142311Sjkh 152311Sjkh#include <sys/cdefs.h> 162311Sjkh__FBSDID("$FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das $"); 172311Sjkh 182311Sjkh/* __ieee754_atan2(y,x) 1929452Scharnier * Method : 2050479Speter * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 212311Sjkh * 2. Reduce x to positive by (if x and y are unexceptional): 222311Sjkh * ARG (x+iy) = arctan(y/x) ... if x > 0, 232311Sjkh * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 242311Sjkh * 252311Sjkh * Special cases: 262311Sjkh * 272311Sjkh * ATAN2((anything), NaN ) is NaN; 282311Sjkh * ATAN2(NAN , (anything) ) is NaN; 292311Sjkh * ATAN2(+-0, +(anything but NaN)) is +-0 ; 302311Sjkh * ATAN2(+-0, -(anything but NaN)) is +-pi ; 312311Sjkh * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 3221895Sdavidn * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 3321895Sdavidn * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 3421895Sdavidn * ATAN2(+-INF,+INF ) is +-pi/4 ; 35170890Syar * ATAN2(+-INF,-INF ) is +-3pi/4; 36170890Syar * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 37170890Syar * 38170890Syar * Constants: 392311Sjkh * The hexadecimal values are the intended ones for the following 402311Sjkh * constants. The decimal values may be used, provided that the 41173412Skevlo * compiler will convert from decimal to binary accurately enough 42173412Skevlo * to produce the hexadecimal values shown. 432311Sjkh */ 442311Sjkh 452311Sjkh#include "math.h" 462311Sjkh#include "math_private.h" 472311Sjkh 482311Sjkhstatic const double 492311Sjkhtiny = 1.0e-300, 502311Sjkhzero = 0.0, 512311Sjkhpi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 522311Sjkhpi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 532311Sjkhpi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 542311Sjkhpi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 552311Sjkh 562311Sjkhdouble 572311Sjkh__ieee754_atan2(double y, double x) 582311Sjkh{ 592311Sjkh double z; 602311Sjkh int32_t k,m,hx,hy,ix,iy; 612311Sjkh u_int32_t lx,ly; 622311Sjkh 632311Sjkh EXTRACT_WORDS(hx,lx,x); 642311Sjkh ix = hx&0x7fffffff; 652311Sjkh EXTRACT_WORDS(hy,ly,y); 66149430Spjd iy = hy&0x7fffffff; 672311Sjkh if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 682311Sjkh ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 692311Sjkh return x+y; 702311Sjkh if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 712311Sjkh m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 722311Sjkh 732311Sjkh /* when y = 0 */ 742311Sjkh if((iy|ly)==0) { 752311Sjkh switch(m) { 762311Sjkh case 0: 772311Sjkh case 1: return y; /* atan(+-0,+anything)=+-0 */ 782311Sjkh case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 792311Sjkh case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 802311Sjkh } 812311Sjkh } 822311Sjkh /* when x = 0 */ 832311Sjkh if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 842311Sjkh 852311Sjkh /* when x is INF */ 862311Sjkh if(ix==0x7ff00000) { 872311Sjkh if(iy==0x7ff00000) { 8821895Sdavidn switch(m) { 8923884Speter case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 9030895Sache case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 9121895Sdavidn case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 922311Sjkh case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 932311Sjkh } 942311Sjkh } else { 952311Sjkh switch(m) { 962311Sjkh case 0: return zero ; /* atan(+...,+INF) */ 972311Sjkh case 1: return -zero ; /* atan(-...,+INF) */ 9874375Speter case 2: return pi+tiny ; /* atan(+...,-INF) */ 992311Sjkh case 3: return -pi-tiny ; /* atan(-...,-INF) */ 1002311Sjkh } 1012311Sjkh } 1022311Sjkh } 1032311Sjkh /* when y is INF */ 1047809Sache if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 105170890Syar 106170890Syar /* compute y/x */ 107170890Syar k = (iy-ix)>>20; 108170890Syar if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 109170890Syar else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 110170890Syar else z=atan(fabs(y/x)); /* safe to do y/x */ 111170890Syar switch (m) { 112170890Syar case 0: return z ; /* atan(+,+) */ 113170890Syar case 1: { 114170890Syar u_int32_t zh; 115170890Syar GET_HIGH_WORD(zh,z); 116170890Syar SET_HIGH_WORD(z,zh ^ 0x80000000); 117170890Syar } 118170890Syar return z ; /* atan(-,+) */ 119170890Syar case 2: return pi-(z-pi_lo);/* atan(+,-) */ 120170890Syar default: /* case 3 */ 121170890Syar return (z-pi_lo)-pi;/* atan(-,-) */ 122170890Syar } 123170890Syar} 124170890Syar