1 2 /* @(#)e_atan2.c 1.3 95/01/18 */ 3 /* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 * 14 */ 15 16 #include <sys/cdefs.h> 17 /* 18 * See comments in e_atan2.c. 19 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 20 */ 21 22 #include <float.h> 23 24 #include "invtrig.h" 25 #include "math.h" 26 #include "math_private.h" 27 28 static volatile long double 29 tiny = 1.0e-300; 30 static const long double 31 zero = 0.0; 32 33 #ifdef __i386__ 34 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 35 static volatile double 36 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 37 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 38 #define pi ((long double)pi1 + pi2) 39 #else 40 static const long double 41 pi = 3.14159265358979323846264338327950280e+00L; 42 #endif 43 44 long double 45 atan2l(long double y, long double x) 46 { 47 union IEEEl2bits ux, uy; 48 long double z; 49 int32_t k,m; 50 int16_t exptx, expsignx, expty, expsigny; 51 52 uy.e = y; 53 expsigny = uy.xbits.expsign; 54 expty = expsigny & 0x7fff; 55 ux.e = x; 56 expsignx = ux.xbits.expsign; 57 exptx = expsignx & 0x7fff; 58 59 if ((exptx==BIAS+LDBL_MAX_EXP && 60 ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */ 61 (expty==BIAS+LDBL_MAX_EXP && 62 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */ 63 return nan_mix(x, y); 64 if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 65 return atanl(y); /* x=1.0 */ 66 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */ 67 68 /* when y = 0 */ 69 if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) { 70 switch(m) { 71 case 0: 72 case 1: return y; /* atan(+-0,+anything)=+-0 */ 73 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 74 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 75 } 76 } 77 /* when x = 0 */ 78 if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 79 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 80 81 /* when x is INF */ 82 if(exptx==BIAS+LDBL_MAX_EXP) { 83 if(expty==BIAS+LDBL_MAX_EXP) { 84 switch(m) { 85 case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */ 86 case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */ 87 case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/ 88 case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/ 89 } 90 } else { 91 switch(m) { 92 case 0: return zero ; /* atan(+...,+INF) */ 93 case 1: return -zero ; /* atan(-...,+INF) */ 94 case 2: return pi+tiny ; /* atan(+...,-INF) */ 95 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 96 } 97 } 98 } 99 /* when y is INF */ 100 if(expty==BIAS+LDBL_MAX_EXP) 101 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 102 103 /* compute y/x */ 104 k = expty-exptx; 105 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */ 106 z=pio2_hi+pio2_lo; 107 m&=1; 108 } 109 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */ 110 else z=atanl(fabsl(y/x)); /* safe to do y/x */ 111 switch (m) { 112 case 0: return z ; /* atan(+,+) */ 113 case 1: return -z ; /* atan(-,+) */ 114 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 115 default: /* case 3 */ 116 return (z-pi_lo)-pi;/* atan(-,-) */ 117 } 118 } 119