contrib/openbsd_libm/src/e_atan2l.c

   1 /*      $OpenBSD: e_atan2l.c,v 1.1 2008/12/09 20:00:35 martynas 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 /*
  17  * See comments in e_atan2.c.
  18  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
  19  * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
  20  */
  21
  22 #include <float.h>
  23 #include <math.h>
  24
  25 #include "invtrig.h"
  26 #include "math.h"
  27 #include "math_private.h"
  28
  29 #ifdef EXT_IMPLICIT_NBIT
  30 #define LDBL_NBIT       0
  31 #else /* EXT_IMPLICIT_NBIT */
  32 #define LDBL_NBIT       0x80000000
  33 #endif /* EXT_IMPLICIT_NBIT */
  34
  35 static volatile long double
  36 tiny  = 1.0e-300;
  37 static const long double
  38 zero  = 0.0;
  39
  40 #if defined(__amd64__) || defined(__i386__)
  41 /* XXX Work around the fact that gcc truncates long double constants on i386 */
  42 static volatile double
  43 pi1 =  3.14159265358979311600e+00,      /*  0x1.921fb54442d18p+1  */
  44 pi2 =  1.22514845490862001043e-16;      /*  0x1.1a80000000000p-53 */
  45 #define pi      ((long double)pi1 + pi2)
  46 #else
  47 static const long double
  48 pi =  3.14159265358979323846264338327950280e+00L;
  49 #endif
  50
  51 long double
  52 atan2l(long double y, long double x)
  53 {
  54         union {
  55                 long double e;
  56                 struct ieee_ext bits;
  57         } ux, uy;
  58         long double z;
  59         int32_t k,m;
  60         int16_t exptx, expsignx, expty, expsigny;
  61
  62         uy.e = y;
  63         expsigny = (uy.bits.ext_sign << 15) | uy.bits.ext_exp;
  64         expty = expsigny & 0x7fff;
  65         ux.e = x;
  66         expsignx = (ux.bits.ext_sign << 15) | ux.bits.ext_exp;
  67         exptx = expsignx & 0x7fff;
  68
  69         if ((exptx==BIAS+LDBL_MAX_EXP &&
  70              ((ux.bits.ext_frach&~LDBL_NBIT)
  71 #ifdef EXT_FRACHMBITS
  72                 | ux.bits.ext_frachm
  73 #endif /* EXT_FRACHMBITS */
  74 #ifdef EXT_FRACLMBITS
  75                 | ux.bits.ext_fraclm
  76 #endif /* EXT_FRACLMBITS */
  77                 | ux.bits.ext_fracl)!=0) ||     /* x is NaN */
  78             (expty==BIAS+LDBL_MAX_EXP &&
  79              ((uy.bits.ext_frach&~LDBL_NBIT)
  80 #ifdef EXT_FRACHMBITS
  81                 | uy.bits.ext_frachm
  82 #endif /* EXT_FRACHMBITS */
  83 #ifdef EXT_FRACLMBITS
  84                 | uy.bits.ext_fraclm
  85 #endif /* EXT_FRACLMBITS */
  86                 | uy.bits.ext_fracl)!=0))       /* y is NaN */
  87             return x+y;
  88         if (expsignx==BIAS && ((ux.bits.ext_frach&~LDBL_NBIT)
  89 #ifdef EXT_FRACHMBITS
  90                 | ux.bits.ext_frachm
  91 #endif /* EXT_FRACHMBITS */
  92 #ifdef EXT_FRACLMBITS
  93                 | ux.bits.ext_fraclm
  94 #endif /* EXT_FRACLMBITS */
  95                 | ux.bits.ext_fracl)==0)
  96             return atanl(y);                                    /* x=1.0 */
  97         m = ((expsigny>>15)&1)|((expsignx>>14)&2);      /* 2*sign(x)+sign(y) */
  98
  99     /* when y = 0 */
 100         if(expty==0 && ((uy.bits.ext_frach&~LDBL_NBIT)
 101 #ifdef EXT_FRACHMBITS
 102                 | uy.bits.ext_frachm
 103 #endif /* EXT_FRACHMBITS */
 104 #ifdef EXT_FRACLMBITS
 105                 | uy.bits.ext_fraclm
 106 #endif /* EXT_FRACLMBITS */
 107                 | uy.bits.ext_fracl)==0) {
 108             switch(m) {
 109                 case 0:
 110                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
 111                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
 112                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
 113             }
 114         }
 115     /* when x = 0 */
 116         if(exptx==0 && ((ux.bits.ext_frach&~LDBL_NBIT)
 117 #ifdef EXT_FRACHMBITS
 118                 | ux.bits.ext_frachm
 119 #endif /* EXT_FRACHMBITS */
 120 #ifdef EXT_FRACLMBITS
 121                 | ux.bits.ext_fraclm
 122 #endif /* EXT_FRACLMBITS */
 123                 | ux.bits.ext_fracl)==0)
 124             return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
 125
 126     /* when x is INF */
 127         if(exptx==BIAS+LDBL_MAX_EXP) {
 128             if(expty==BIAS+LDBL_MAX_EXP) {
 129                 switch(m) {
 130                     case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
 131                     case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
 132                     case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
 133                     case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
 134                 }
 135             } else {
 136                 switch(m) {
 137                     case 0: return  zero  ;     /* atan(+...,+INF) */
 138                     case 1: return -zero  ;     /* atan(-...,+INF) */
 139                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 140                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 141                 }
 142             }
 143         }
 144     /* when y is INF */
 145         if(expty==BIAS+LDBL_MAX_EXP)
 146             return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
 147
 148     /* compute y/x */
 149         k = expty-exptx;
 150         if(k > LDBL_MANT_DIG+2) {                       /* |y/x| huge */
 151             z=pio2_hi+pio2_lo;
 152             m&=1;
 153         }
 154         else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0;  /* |y/x| tiny, x<0 */
 155         else z=atanl(fabsl(y/x));               /* safe to do y/x */
 156         switch (m) {
 157             case 0: return       z  ;   /* atan(+,+) */
 158             case 1: return      -z  ;   /* atan(-,+) */
 159             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 160             default: /* case 3 */
 161                     return  (z-pi_lo)-pi;/* atan(-,-) */
 162         }
 163 }