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