lib/libm/noieee_src/n_cabs.c

   1 /*      $NetBSD: n_cabs.c,v 1.5 2003/08/07 16:44:50 agc Exp $ */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 static char sccsid[] = "@(#)cabs.c      8.1 (Berkeley) 6/4/93";
  33 #endif /* not lint */
  34
  35 /* HYPOT(X,Y)
  36  * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
  37  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  38  * CODED IN C BY K.C. NG, 11/28/84;
  39  * REVISED BY K.C. NG, 7/12/85.
  40  *
  41  * Required system supported functions :
  42  *      copysign(x,y)
  43  *      finite(x)
  44  *      scalb(x,N)
  45  *      sqrt(x)
  46  *
  47  * Method :
  48  *      1. replace x by |x| and y by |y|, and swap x and
  49  *         y if y > x (hence x is never smaller than y).
  50  *      2. Hypot(x,y) is computed by:
  51  *         Case I, x/y > 2
  52  *
  53  *                                     y
  54  *              hypot = x + -----------------------------
  55  *                                          2
  56  *                          sqrt ( 1 + [x/y]  )  +  x/y
  57  *
  58  *         Case II, x/y <= 2
  59  *                                                 y
  60  *              hypot = x + --------------------------------------------------
  61  *                                                           2
  62  *                                                      [x/y]   -  2
  63  *                         (sqrt(2)+1) + (x-y)/y + -----------------------------
  64  *                                                                2
  65  *                                                sqrt ( 1 + [x/y]  )  + sqrt(2)
  66  *
  67  *
  68  *
  69  * Special cases:
  70  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  71  *      hypot(x,y) is NAN if x or y is NAN.
  72  *
  73  * Accuracy:
  74  *      hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
  75  *      in the last place). See Kahan's "Interval Arithmetic Options in the
  76  *      Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
  77  *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
  78  *      code follows in comments.) In a test run with 500,000 random arguments
  79  *      on a VAX, the maximum observed error was .959 ulps.
  80  *
  81  * Constants:
  82  * The hexadecimal values are the intended ones for the following constants.
  83  * The decimal values may be used, provided that the compiler will convert
  84  * from decimal to binary accurately enough to produce the hexadecimal values
  85  * shown.
  86  */
  87 #define _LIBM_STATIC
  88 #include "mathimpl.h"
  89
  90 vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
  91 vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
  92 vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
  93
  94 ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
  95 ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
  96 ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)
  97
  98 #ifdef vccast
  99 #define r2p1hi  vccast(r2p1hi)
 100 #define r2p1lo  vccast(r2p1lo)
 101 #define sqrt2   vccast(sqrt2)
 102 #endif
 103
 104 double
 105 hypot(double x, double y)
 106 {
 107         static const double zero=0, one=1,
 108                       small=1.0E-18;    /* fl(1+small)==1 */
 109         static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
 110         double t,r;
 111         int exp;
 112
 113         if(finite(x))
 114             if(finite(y))
 115             {
 116                 x=copysign(x,one);
 117                 y=copysign(y,one);
 118                 if(y > x)
 119                     { t=x; x=y; y=t; }
 120                 if(x == zero) return(zero);
 121                 if(y == zero) return(x);
 122                 exp= logb(x);
 123                 if(exp-(int)logb(y) > ibig )
 124                         /* raise inexact flag and return |x| */
 125                    { one+small; return(x); }
 126
 127             /* start computing sqrt(x^2 + y^2) */
 128                 r=x-y;
 129                 if(r>y) {       /* x/y > 2 */
 130                     r=x/y;
 131                     r=r+sqrt(one+r*r); }
 132                 else {          /* 1 <= x/y <= 2 */
 133                     r/=y; t=r*(r+2.0);
 134                     r+=t/(sqrt2+sqrt(2.0+t));
 135                     r+=r2p1lo; r+=r2p1hi; }
 136
 137                 r=y/r;
 138                 return(x+r);
 139
 140             }
 141
 142             else if(y==y)          /* y is +-INF */
 143                      return(copysign(y,one));
 144             else
 145                      return(y);    /* y is NaN and x is finite */
 146
 147         else if(x==x)              /* x is +-INF */
 148                  return (copysign(x,one));
 149         else if(finite(y))
 150                  return(x);                /* x is NaN, y is finite */
 151 #if !defined(__vax__)&&!defined(tahoe)
 152         else if(y!=y) return(y);  /* x and y is NaN */
 153 #endif  /* !defined(__vax__)&&!defined(tahoe) */
 154         else return(copysign(y,one));   /* y is INF */
 155 }
 156
 157 /* CABS(Z)
 158  * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
 159  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 160  * CODED IN C BY K.C. NG, 11/28/84.
 161  * REVISED BY K.C. NG, 7/12/85.
 162  *
 163  * Required kernel function :
 164  *      hypot(x,y)
 165  *
 166  * Method :
 167  *      cabs(z) = hypot(x,y) .
 168  */
 169
 170 struct complex { double x, y; };
 171
 172 double
 173 cabs(z)
 174 struct complex z;
 175 {
 176         return hypot(z.x,z.y);
 177 }
 178
 179 double
 180 z_abs(z)
 181 struct complex *z;
 182 {
 183         return hypot(z->x,z->y);
 184 }
 185
 186 /* A faster but less accurate version of cabs(x,y) */
 187 #if 0
 188 double hypot(x,y)
 189 double x, y;
 190 {
 191         static const double zero=0, one=1;
 192                       small=1.0E-18;    /* fl(1+small)==1 */
 193         static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
 194         double temp;
 195         int exp;
 196
 197         if(finite(x))
 198             if(finite(y))
 199             {
 200                 x=copysign(x,one);
 201                 y=copysign(y,one);
 202                 if(y > x)
 203                     { temp=x; x=y; y=temp; }
 204                 if(x == zero) return(zero);
 205                 if(y == zero) return(x);
 206                 exp= logb(x);
 207                 x=scalb(x,-exp);
 208                 if(exp-(int)logb(y) > ibig )
 209                         /* raise inexact flag and return |x| */
 210                    { one+small; return(scalb(x,exp)); }
 211                 else y=scalb(y,-exp);
 212                 return(scalb(sqrt(x*x+y*y),exp));
 213             }
 214
 215             else if(y==y)          /* y is +-INF */
 216                      return(copysign(y,one));
 217             else
 218                      return(y);    /* y is NaN and x is finite */
 219
 220         else if(x==x)              /* x is +-INF */
 221                  return (copysign(x,one));
 222         else if(finite(y))
 223                  return(x);                /* x is NaN, y is finite */
 224         else if(y!=y) return(y);        /* x and y is NaN */
 225         else return(copysign(y,one));   /* y is INF */
 226 }
 227 #endif