sysdeps/ieee754/cabs.c

   1 /*
   2  * Copyright (c) 1985 Regents of the University of California.
   3  * All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  * 3. All advertising materials mentioning features or use of this software
  14  *    must display the following acknowledgement:
  15  *      This product includes software developed by the University of
  16  *      California, Berkeley and its contributors.
  17  * 4. Neither the name of the University nor the names of its contributors
  18  *    may be used to endorse or promote products derived from this software
  19  *    without specific prior written permission.
  20  *
  21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  31  * SUCH DAMAGE.
  32  */
  33
  34 #ifndef lint
  35 static char sccsid[] = "@(#)cabs.c      5.6 (Berkeley) 10/9/90";
  36 #endif /* not lint */
  37
  38 /* HYPOT(X,Y)
  39  * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
  40  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  41  * CODED IN C BY K.C. NG, 11/28/84;
  42  * REVISED BY K.C. NG, 7/12/85.
  43  *
  44  * Required system supported functions :
  45  *      copysign(x,y)
  46  *      finite(x)
  47  *      scalb(x,N)
  48  *      sqrt(x)
  49  *
  50  * Method :
  51  *      1. replace x by |x| and y by |y|, and swap x and
  52  *         y if y > x (hence x is never smaller than y).
  53  *      2. Hypot(x,y) is computed by:
  54  *         Case I, x/y > 2
  55  *
  56  *                                     y
  57  *              hypot = x + -----------------------------
  58  *                                          2
  59  *                          sqrt ( 1 + [x/y]  )  +  x/y
  60  *
  61  *         Case II, x/y <= 2
  62  *                                                 y
  63  *              hypot = x + --------------------------------------------------
  64  *                                                           2
  65  *                                                      [x/y]   -  2
  66  *                         (sqrt(2)+1) + (x-y)/y + -----------------------------
  67  *                                                                2
  68  *                                                sqrt ( 1 + [x/y]  )  + sqrt(2)
  69  *
  70  *
  71  *
  72  * Special cases:
  73  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  74  *      hypot(x,y) is NAN if x or y is NAN.
  75  *
  76  * Accuracy:
  77  *      hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
  78  *      in the last place). See Kahan's "Interval Arithmetic Options in the
  79  *      Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
  80  *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
  81  *      code follows in comments.) In a test run with 500,000 random arguments
  82  *      on a VAX, the maximum observed error was .959 ulps.
  83  *
  84  * Constants:
  85  * The hexadecimal values are the intended ones for the following constants.
  86  * The decimal values may be used, provided that the compiler will convert
  87  * from decimal to binary accurately enough to produce the hexadecimal values
  88  * shown.
  89  */
  90 #include "mathimpl.h"
  91
  92 vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
  93 vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
  94 vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
  95
  96 ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
  97 ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
  98 ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)
  99
 100 #ifdef vccast
 101 #define r2p1hi  vccast(r2p1hi)
 102 #define r2p1lo  vccast(r2p1lo)
 103 #define sqrt2   vccast(sqrt2)
 104 #endif
 105
 106 double
 107 hypot(x,y)
 108 double x, y;
 109 {
 110         static const double zero=0, one=1,
 111                       small=1.0E-18;    /* fl(1+small)==1 */
 112         static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
 113         double t,r;
 114         int exp;
 115
 116         if(finite(x))
 117             if(finite(y))
 118             {
 119                 x=copysign(x,one);
 120                 y=copysign(y,one);
 121                 if(y > x)
 122                     { t=x; x=y; y=t; }
 123                 if(x == zero) return(zero);
 124                 if(y == zero) return(x);
 125                 exp= logb(x);
 126                 if(exp-(int)logb(y) > ibig )
 127                         /* raise inexact flag and return |x| */
 128                    { one+small; return(x); }
 129
 130             /* start computing sqrt(x^2 + y^2) */
 131                 r=x-y;
 132                 if(r>y) {       /* x/y > 2 */
 133                     r=x/y;
 134                     r=r+sqrt(one+r*r); }
 135                 else {          /* 1 <= x/y <= 2 */
 136                     r/=y; t=r*(r+2.0);
 137                     r+=t/(sqrt2+sqrt(2.0+t));
 138                     r+=r2p1lo; r+=r2p1hi; }
 139
 140                 r=y/r;
 141                 return(x+r);
 142
 143             }
 144
 145             else if(y==y)          /* y is +-INF */
 146                      return(copysign(y,one));
 147             else
 148                      return(y);    /* y is NaN and x is finite */
 149
 150         else if(x==x)              /* x is +-INF */
 151                  return (copysign(x,one));
 152         else if(finite(y))
 153                  return(x);                /* x is NaN, y is finite */
 154 #if !defined(vax)&&!defined(tahoe)
 155         else if(y!=y) return(y);  /* x and y is NaN */
 156 #endif  /* !defined(vax)&&!defined(tahoe) */
 157         else return(copysign(y,one));   /* y is INF */
 158 }
 159
 160 /* CABS(Z)
 161  * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
 162  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 163  * CODED IN C BY K.C. NG, 11/28/84.
 164  * REVISED BY K.C. NG, 7/12/85.
 165  *
 166  * Required kernel function :
 167  *      hypot(x,y)
 168  *
 169  * Method :
 170  *      cabs(z) = hypot(x,y) .
 171  */
 172
 173 double
 174 cabs(z)
 175 struct __cabs_complex z;
 176 {
 177         return hypot(z.__x,z.__y);
 178 }
 179
 180 double
 181 z_abs(z)
 182 struct __cabs_complex *z;
 183 {
 184         return hypot(z->__x,z->__y);
 185 }
 186
 187 /* A faster but less accurate version of cabs(x,y) */
 188 #if 0
 189 double hypot(x,y)
 190 double x, y;
 191 {
 192         static const double zero=0, one=1;
 193                       small=1.0E-18;    /* fl(1+small)==1 */
 194         static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
 195         double temp;
 196         int exp;
 197
 198         if(finite(x))
 199             if(finite(y))
 200             {
 201                 x=copysign(x,one);
 202                 y=copysign(y,one);
 203                 if(y > x)
 204                     { temp=x; x=y; y=temp; }
 205                 if(x == zero) return(zero);
 206                 if(y == zero) return(x);
 207                 exp= logb(x);
 208                 x=scalb(x,-exp);
 209                 if(exp-(int)logb(y) > ibig )
 210                         /* raise inexact flag and return |x| */
 211                    { one+small; return(scalb(x,exp)); }
 212                 else y=scalb(y,-exp);
 213                 return(scalb(sqrt(x*x+y*y),exp));
 214             }
 215
 216             else if(y==y)          /* y is +-INF */
 217                      return(copysign(y,one));
 218             else
 219                      return(y);    /* y is NaN and x is finite */
 220
 221         else if(x==x)              /* x is +-INF */
 222                  return (copysign(x,one));
 223         else if(finite(y))
 224                  return(x);                /* x is NaN, y is finite */
 225         else if(y!=y) return(y);        /* x and y is NaN */
 226         else return(copysign(y,one));   /* y is INF */
 227 }
 228 #endif