1181074Sdas 2181074Sdas/* @(#)e_atan2.c 1.3 95/01/18 */ 3181074Sdas/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */ 4181074Sdas/* 5181074Sdas * ==================================================== 6181074Sdas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7181074Sdas * 8181074Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 9181074Sdas * Permission to use, copy, modify, and distribute this 10181074Sdas * software is freely granted, provided that this notice 11181074Sdas * is preserved. 12181074Sdas * ==================================================== 13181074Sdas * 14181074Sdas */ 15181074Sdas 16181074Sdas#include <sys/cdefs.h> 17181074Sdas__FBSDID("$FreeBSD$"); 18181074Sdas 19181074Sdas/* 20181074Sdas * See comments in e_atan2.c. 21181074Sdas * Converted to long double by David Schultz <das@FreeBSD.ORG>. 22181074Sdas */ 23181074Sdas 24181074Sdas#include <float.h> 25181074Sdas 26181074Sdas#include "invtrig.h" 27181074Sdas#include "math.h" 28181074Sdas#include "math_private.h" 29181074Sdas 30181074Sdasstatic volatile long double 31181074Sdastiny = 1.0e-300; 32181074Sdasstatic const long double 33181152Sdaszero = 0.0; 34181074Sdas 35181152Sdas#ifdef __i386__ 36181152Sdas/* XXX Work around the fact that gcc truncates long double constants on i386 */ 37181152Sdasstatic volatile double 38181152Sdaspi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 39181152Sdaspi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 40181152Sdas#define pi ((long double)pi1 + pi2) 41181152Sdas#else 42181152Sdasstatic const long double 43181152Sdaspi = 3.14159265358979323846264338327950280e+00L; 44181152Sdas#endif 45181152Sdas 46181074Sdaslong double 47181074Sdasatan2l(long double y, long double x) 48181074Sdas{ 49181074Sdas union IEEEl2bits ux, uy; 50181074Sdas long double z; 51181074Sdas int32_t k,m; 52181074Sdas int16_t exptx, expsignx, expty, expsigny; 53181074Sdas 54181074Sdas uy.e = y; 55181074Sdas expsigny = uy.xbits.expsign; 56181074Sdas expty = expsigny & 0x7fff; 57181074Sdas ux.e = x; 58181074Sdas expsignx = ux.xbits.expsign; 59181074Sdas exptx = expsignx & 0x7fff; 60181074Sdas 61181074Sdas if ((exptx==BIAS+LDBL_MAX_EXP && 62181074Sdas ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */ 63181074Sdas (expty==BIAS+LDBL_MAX_EXP && 64181074Sdas ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */ 65181074Sdas return x+y; 66181074Sdas if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 67181074Sdas return atanl(y); /* x=1.0 */ 68181074Sdas m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */ 69181074Sdas 70181074Sdas /* when y = 0 */ 71181074Sdas if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) { 72181074Sdas switch(m) { 73181074Sdas case 0: 74181074Sdas case 1: return y; /* atan(+-0,+anything)=+-0 */ 75181074Sdas case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 76181074Sdas case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 77181074Sdas } 78181074Sdas } 79181074Sdas /* when x = 0 */ 80181074Sdas if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 81181074Sdas return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 82181074Sdas 83181074Sdas /* when x is INF */ 84181074Sdas if(exptx==BIAS+LDBL_MAX_EXP) { 85181074Sdas if(expty==BIAS+LDBL_MAX_EXP) { 86181074Sdas switch(m) { 87181074Sdas case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */ 88181074Sdas case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */ 89181074Sdas case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/ 90181074Sdas case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/ 91181074Sdas } 92181074Sdas } else { 93181074Sdas switch(m) { 94181074Sdas case 0: return zero ; /* atan(+...,+INF) */ 95181074Sdas case 1: return -zero ; /* atan(-...,+INF) */ 96181074Sdas case 2: return pi+tiny ; /* atan(+...,-INF) */ 97181074Sdas case 3: return -pi-tiny ; /* atan(-...,-INF) */ 98181074Sdas } 99181074Sdas } 100181074Sdas } 101181074Sdas /* when y is INF */ 102181074Sdas if(expty==BIAS+LDBL_MAX_EXP) 103181074Sdas return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 104181074Sdas 105181074Sdas /* compute y/x */ 106181074Sdas k = expty-exptx; 107181204Sdas if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */ 108181204Sdas z=pio2_hi+pio2_lo; 109181204Sdas m&=1; 110181204Sdas } 111181074Sdas else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */ 112181074Sdas else z=atanl(fabsl(y/x)); /* safe to do y/x */ 113181074Sdas switch (m) { 114181074Sdas case 0: return z ; /* atan(+,+) */ 115181074Sdas case 1: return -z ; /* atan(-,+) */ 116181074Sdas case 2: return pi-(z-pi_lo);/* atan(+,-) */ 117181074Sdas default: /* case 3 */ 118181074Sdas return (z-pi_lo)-pi;/* atan(-,-) */ 119181074Sdas } 120181074Sdas} 121