1 /* $NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos Exp $ */ 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 __RCSID("$NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos Exp $"); 18 19 /* 20 * See comments in e_atan2.c. 21 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 22 */ 23 24 #include "namespace.h" 25 26 #ifdef __weak_alias 27 __weak_alias(atan2l, _atan2l) 28 #endif 29 30 #include <float.h> 31 #include <machine/ieee.h> 32 33 #include "math.h" 34 #include "math_private.h" 35 36 #ifdef __HAVE_LONG_DOUBLE 37 38 #if LDBL_MANT_DIG == 64 39 #include "../ld80/invtrig.h" 40 #elif LDBL_MANT_DIG == 113 41 #include "../ld128/invtrig.h" 42 #else 43 #error "Unsupported long double format" 44 #endif 45 46 #ifdef LDBL_IMPLICIT_NBIT 47 #define LDBL_NBIT 0 48 #endif 49 50 static volatile long double 51 tiny = 1.0e-300; 52 static const long double 53 zero = 0.0; 54 55 #ifdef __i386__ 56 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 57 static volatile double 58 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 59 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 60 #define pi ((long double)pi1 + pi2) 61 #else 62 static const long double 63 pi = 3.14159265358979323846264338327950280e+00L; 64 #endif 65 66 long double 67 atan2l(long double y, long double x) 68 { 69 union ieee_ext_u ux, uy; 70 long double z; 71 int32_t k,m; 72 int16_t exptx, expsignx, expty, expsigny; 73 74 uy.extu_ld = y; 75 expsigny = GET_EXPSIGN(&uy); 76 expty = expsigny & 0x7fff; 77 ux.extu_ld = x; 78 expsignx = GET_EXPSIGN(&ux); 79 exptx = expsignx & 0x7fff; 80 81 if ((exptx==BIAS+LDBL_MAX_EXP && 82 ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)!=0) || /* x is NaN */ 83 (expty==BIAS+LDBL_MAX_EXP && 84 ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0)) /* y is NaN */ 85 return nan_mix(x, y); 86 if (expsignx==BIAS && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0) 87 return atanl(y); /* x=1.0 */ 88 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */ 89 90 /* when y = 0 */ 91 if(expty==0 && ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)==0) { 92 switch(m) { 93 case 0: 94 case 1: return y; /* atan(+-0,+anything)=+-0 */ 95 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 96 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 97 } 98 } 99 /* when x = 0 */ 100 if(exptx==0 && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0) 101 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 102 103 /* when x is INF */ 104 if(exptx==BIAS+LDBL_MAX_EXP) { 105 if(expty==BIAS+LDBL_MAX_EXP) { 106 switch(m) { 107 case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */ 108 case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */ 109 case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/ 110 case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/ 111 } 112 } else { 113 switch(m) { 114 case 0: return zero ; /* atan(+...,+INF) */ 115 case 1: return -zero ; /* atan(-...,+INF) */ 116 case 2: return pi+tiny ; /* atan(+...,-INF) */ 117 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 118 } 119 } 120 } 121 /* when y is INF */ 122 if(expty==BIAS+LDBL_MAX_EXP) 123 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; 124 125 /* compute y/x */ 126 k = expty-exptx; 127 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */ 128 z=pio2_hi+pio2_lo; 129 m&=1; 130 } 131 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */ 132 else z=atanl(fabsl(y/x)); /* safe to do y/x */ 133 switch (m) { 134 case 0: return z ; /* atan(+,+) */ 135 case 1: return -z ; /* atan(-,+) */ 136 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 137 default: /* case 3 */ 138 return (z-pi_lo)-pi;/* atan(-,-) */ 139 } 140 } 141 142 #else 143 144 long double 145 atan2l(long double y, long double x) 146 { 147 return atan2(y, x); 148 } 149 150 #endif 151