compiler/stdc/math/s_atanl.c

   1 /* @(#)s_atan.c 5.1 93/09/24 */
   2 /* FreeBSD: head/lib/msun/src/s_atan.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 SunPro, 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 #ifndef lint
  15 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_atanl.c,v 1.1 2008/07/31 22:41:26 das Exp $";
  16 #endif
  17
  18 /*
  19  * See comments in s_atan.c.
  20  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
  21  */
  22
  23 #include <float.h>
  24 #include "math.h"
  25
  26 #include "invtrig.h"
  27 #include "math_private.h"
  28
  29 static const long double
  30 one   = 1.0,
  31 huge   = 1.0e300;
  32
  33 long double
  34 atanl(long double x)
  35 {
  36         union IEEEl2bits u;
  37         long double w,s1,s2,z;
  38         int id;
  39         int16_t expsign, expt;
  40         int32_t expman;
  41
  42         u.e = x;
  43         expsign = u.xbits.expsign;
  44         expt = expsign & 0x7fff;
  45         if(expt >= ATAN_CONST) {        /* if |x| is large, atan(x)~=pi/2 */
  46             if(expt == BIAS + LDBL_MAX_EXP &&
  47                ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
  48                 return x+x;             /* NaN */
  49             if(expsign>0) return  atanhi[3]+atanlo[3];
  50             else     return -atanhi[3]-atanlo[3];
  51         }
  52         /* Extract the exponent and the first few bits of the mantissa. */
  53         /* XXX There should be a more convenient way to do this. */
  54         expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
  55         if (expman < ((BIAS - 2) << 8) + 0xc0) {        /* |x| < 0.4375 */
  56             if (expt < ATAN_LINEAR) {   /* if |x| is small, atanl(x)~=x */
  57                 if(huge+x>one) return x;        /* raise inexact */
  58             }
  59             id = -1;
  60         } else {
  61         x = fabsl(x);
  62         if (expman < (BIAS << 8) + 0x30) {              /* |x| < 1.1875 */
  63             if (expman < ((BIAS - 1) << 8) + 0x60) {    /* 7/16 <=|x|<11/16 */
  64                 id = 0; x = (2.0*x-one)/(2.0+x);
  65             } else {                    /* 11/16<=|x|< 19/16 */
  66                 id = 1; x  = (x-one)/(x+one);
  67             }
  68         } else {
  69             if (expman < ((BIAS + 1) << 8) + 0x38) {    /* |x| < 2.4375 */
  70                 id = 2; x  = (x-1.5)/(one+1.5*x);
  71             } else {                    /* 2.4375 <= |x| < 2^ATAN_CONST */
  72                 id = 3; x  = -1.0/x;
  73             }
  74         }}
  75     /* end of argument reduction */
  76         z = x*x;
  77         w = z*z;
  78     /* break sum aT[i]z**(i+1) into odd and even poly */
  79         s1 = z*T_even(w);
  80         s2 = w*T_odd(w);
  81         if (id<0) return x - x*(s1+s2);
  82         else {
  83             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  84             return (expsign<0)? -z:z;
  85         }
  86 }