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 __FBSDID("$FreeBSD$"); 18 19 /* 20 * See comments in e_atan2.c. 21 * Converted to long double by David Schultz <das (at) FreeBSD.ORG>. 22 */ 23 24 #include <float.h> 25 26 #include "invtrig.h" 27 #include "math.h" 28 #include "math_private.h" 29 30 static volatile long double 31 tiny = 1.0e-300; 32 static const long double 33 zero = 0.0; 34 35 #ifdef __i386__ 36 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 37 static volatile double 38 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 39 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 40 #define pi ((long double)pi1 + pi2) 41 #else 42 static const long double 43 pi = 3.14159265358979323846264338327950280e+00L; 44 #endif 45 46 long double 47 atan2l(long double y, long double x) 48 { 49 union IEEEl2bits ux, uy; 50 long double z; 51 int32_t k,m; 52 int16_t exptx, expsignx, expty, expsigny; 53 54 uy.e = y; 55 expsigny = uy.xbits.expsign; 56 expty = expsigny & 0x7fff; 57 ux.e = x; 58 expsignx = ux.xbits.expsign; 59 exptx = expsignx & 0x7fff; 60 61 if ((exptx==BIAS+LDBL_MAX_EXP && 62 ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */ 63 (expty==BIAS+LDBL_MAX_EXP && 64 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */ 65 return x+y; 66 if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 67 return atanl(y); /* x=1.0 */ 68 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */ 69 70 /* when y = 0 */ 71 if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) { 72 switch(m) { 73 case 0: 74 case 1: return y; /* atan(+-0,+anything)=+-0 */ 75 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 76 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 77 } 78 } 79 /* when x = 0 */ 80 if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) 81 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 82 83 /* when x is INF */ 84 if(exptx==BIAS+LDBL_MAX_EXP) { 85 if(expty==BIAS+LDBL_MAX_EXP) { 86 switch(m) { 87 case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */ 88 case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */ 89 case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/ 90 case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/ 91 } 92 } else { 93 switch(m) { 94 case 0: return zero ; /* atan(+...,+INF) */ 95 case 1: return -zero ; /* atan(-...,+INF) */ 96 case 2: return pi+tiny ; /* atan(+...,-INF) */ 97 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 98 } 99 } 100 } 101 /* when y is INF */ 102 if(expty==BIAS+LDBL_MAX_EXP) 103 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 104 105 /* compute y/x */ 106 k = expty-exptx; 107 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */ 108 z=pio2_hi+pio2_lo; 109 m&=1; 110 } 111 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */ 112 else z=atanl(fabsl(y/x)); /* safe to do y/x */ 113 switch (m) { 114 case 0: return z ; /* atan(+,+) */ 115 case 1: return -z ; /* atan(-,+) */ 116 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 117 default: /* case 3 */ 118 return (z-pi_lo)-pi;/* atan(-,-) */ 119 } 120 } 121
