lib/libm/src/s_atanl.c

   1 /*      $OpenBSD: s_atanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $    */
   2 /* @(#)s_atan.c 5.1 93/09/24 */
   3 /* FreeBSD: head/lib/msun/src/s_atan.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 SunPro, 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  * See comments in s_atan.c.
  17  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
  18  * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
  19  */
  20
  21 #include <float.h>
  22 #include <math.h>
  23
  24 #include "invtrig.h"
  25 #include "math_private.h"
  26
  27 #ifdef EXT_IMPLICIT_NBIT
  28 #define LDBL_NBIT       0
  29 #else /* EXT_IMPLICIT_NBIT */
  30 #define LDBL_NBIT       0x80000000
  31 #endif /* EXT_IMPLICIT_NBIT */
  32
  33 static const long double
  34 one   = 1.0,
  35 huge   = 1.0e300;
  36
  37 long double
  38 atanl(long double x)
  39 {
  40         union {
  41                 long double e;
  42                 struct ieee_ext bits;
  43         } u;
  44         long double w,s1,s2,z;
  45         int id;
  46         int16_t expsign, expt;
  47         int32_t expman;
  48
  49         u.e = x;
  50         expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
  51         expt = expsign & 0x7fff;
  52         if(expt >= ATAN_CONST) {        /* if |x| is large, atan(x)~=pi/2 */
  53             if(expt == BIAS + LDBL_MAX_EXP &&
  54                ((u.bits.ext_frach&~LDBL_NBIT)
  55 #ifdef EXT_FRACHMBITS
  56                 | u.bits.ext_frachm
  57 #endif /* EXT_FRACHMBITS */
  58 #ifdef EXT_FRACLMBITS
  59                 | u.bits.ext_fraclm
  60 #endif /* EXT_FRACLMBITS */
  61                 | u.bits.ext_fracl)!=0)
  62                 return x+x;             /* NaN */
  63             if(expsign>0) return  atanhi[3]+atanlo[3];
  64             else     return -atanhi[3]-atanlo[3];
  65         }
  66         /* Extract the exponent and the first few bits of the mantissa. */
  67         /* XXX There should be a more convenient way to do this. */
  68         expman = (expt << 8) |
  69                 ((u.bits.ext_frach >> (EXT_FRACHBITS - 9)) & 0xff);
  70         if (expman < ((BIAS - 2) << 8) + 0xc0) {        /* |x| < 0.4375 */
  71             if (expt < ATAN_LINEAR) {   /* if |x| is small, atanl(x)~=x */
  72                 if(huge+x>one) return x;        /* raise inexact */
  73             }
  74             id = -1;
  75         } else {
  76         x = fabsl(x);
  77         if (expman < (BIAS << 8) + 0x30) {              /* |x| < 1.1875 */
  78             if (expman < ((BIAS - 1) << 8) + 0x60) {    /* 7/16 <=|x|<11/16 */
  79                 id = 0; x = (2.0*x-one)/(2.0+x);
  80             } else {                    /* 11/16<=|x|< 19/16 */
  81                 id = 1; x  = (x-one)/(x+one);
  82             }
  83         } else {
  84             if (expman < ((BIAS + 1) << 8) + 0x38) {    /* |x| < 2.4375 */
  85                 id = 2; x  = (x-1.5)/(one+1.5*x);
  86             } else {                    /* 2.4375 <= |x| < 2^ATAN_CONST */
  87                 id = 3; x  = -1.0/x;
  88             }
  89         }}
  90     /* end of argument reduction */
  91         z = x*x;
  92         w = z*z;
  93     /* break sum aT[i]z**(i+1) into odd and even poly */
  94         s1 = z*T_even(w);
  95         s2 = w*T_odd(w);
  96         if (id<0) return x - x*(s1+s2);
  97         else {
  98             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  99             return (expsign<0)? -z:z;
 100         }
 101 }