BSD 4_3_Net_2 release

[unix-history] / usr / src / lib / libm / ieee / cabs.c

/*
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
*    notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
*    notice, this list of conditions and the following disclaimer in the
*    documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
*    must display the following acknowledgement:
*      This product includes software developed by the University of
*      California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
*    may be used to endorse or promote products derived from this software
*    without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/

#ifndef lint
static char sccsid[] = "@(#)cabs.c      5.6 (Berkeley) 10/9/90";
#endif /* not lint */

/* HYPOT(X,Y)
* RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 11/28/84; 
* REVISED BY K.C. NG, 7/12/85.
*
* Required system supported functions :
*      copysign(x,y)
*      finite(x)
*      scalb(x,N)
*      sqrt(x)
*
* Method :
*      1. replace x by |x| and y by |y|, and swap x and
*         y if y > x (hence x is never smaller than y).
*      2. Hypot(x,y) is computed by:
*         Case I, x/y > 2
*              
*                                     y
*              hypot = x + -----------------------------
*                                          2
*                          sqrt ( 1 + [x/y]  )  +  x/y
*
*         Case II, x/y <= 2 
*                                                 y
*              hypot = x + --------------------------------------------------
*                                                           2 
*                                                      [x/y]   -  2
*                         (sqrt(2)+1) + (x-y)/y + -----------------------------
*                                                                2
*                                                sqrt ( 1 + [x/y]  )  + sqrt(2)
*
*
*
* Special cases:
*      hypot(x,y) is INF if x or y is +INF or -INF; else
*      hypot(x,y) is NAN if x or y is NAN.
*
* Accuracy:
*      hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
*      in the last place). See Kahan's "Interval Arithmetic Options in the
*      Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
*      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
*      code follows in comments.) In a test run with 500,000 random arguments
*      on a VAX, the maximum observed error was .959 ulps.
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#include "mathimpl.h"

vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)

ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)

#ifdef vccast
#define r2p1hi  vccast(r2p1hi)
#define r2p1lo  vccast(r2p1lo)
#define sqrt2   vccast(sqrt2)
#endif

double
hypot(x,y)
double x, y;
{
       static const double zero=0, one=1, 
                     small=1.0E-18;    /* fl(1+small)==1 */
       static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
       double t,r;
       int exp;

       if(finite(x))
           if(finite(y))
           {   
               x=copysign(x,one);
               y=copysign(y,one);
               if(y > x) 
                   { t=x; x=y; y=t; }
               if(x == zero) return(zero);
               if(y == zero) return(x);
               exp= logb(x);
               if(exp-(int)logb(y) > ibig )    
                       /* raise inexact flag and return |x| */
                  { one+small; return(x); }

           /* start computing sqrt(x^2 + y^2) */
               r=x-y;
               if(r>y) {       /* x/y > 2 */
                   r=x/y;
                   r=r+sqrt(one+r*r); }
               else {          /* 1 <= x/y <= 2 */
                   r/=y; t=r*(r+2.0);
                   r+=t/(sqrt2+sqrt(2.0+t));
                   r+=r2p1lo; r+=r2p1hi; }

               r=y/r;
               return(x+r);

           }

           else if(y==y)          /* y is +-INF */
                    return(copysign(y,one));
           else 
                    return(y);    /* y is NaN and x is finite */

       else if(x==x)              /* x is +-INF */
                return (copysign(x,one));
       else if(finite(y))
                return(x);                /* x is NaN, y is finite */
#if !defined(vax)&&!defined(tahoe)
       else if(y!=y) return(y);  /* x and y is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */
       else return(copysign(y,one));   /* y is INF */
}

/* CABS(Z)
* RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 11/28/84.
* REVISED BY K.C. NG, 7/12/85.
*
* Required kernel function :
*      hypot(x,y)
*
* Method :
*      cabs(z) = hypot(x,y) .
*/

double
cabs(z)
struct { double x, y;} z;
{
       return hypot(z.x,z.y);
}

double
z_abs(z)
struct { double x,y;} *z;
{
       return hypot(z->x,z->y);
}

/* A faster but less accurate version of cabs(x,y) */
#if 0
double hypot(x,y)
double x, y;
{
       static const double zero=0, one=1;
                     small=1.0E-18;    /* fl(1+small)==1 */
       static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
       double temp;
       int exp;

       if(finite(x))
           if(finite(y))
           {   
               x=copysign(x,one);
               y=copysign(y,one);
               if(y > x) 
                   { temp=x; x=y; y=temp; }
               if(x == zero) return(zero);
               if(y == zero) return(x);
               exp= logb(x);
               x=scalb(x,-exp);
               if(exp-(int)logb(y) > ibig ) 
                       /* raise inexact flag and return |x| */
                  { one+small; return(scalb(x,exp)); }
               else y=scalb(y,-exp);
               return(scalb(sqrt(x*x+y*y),exp));
           }

           else if(y==y)          /* y is +-INF */
                    return(copysign(y,one));
           else 
                    return(y);    /* y is NaN and x is finite */

       else if(x==x)              /* x is +-INF */
                return (copysign(x,one));
       else if(finite(y))
                return(x);                /* x is NaN, y is finite */
       else if(y!=y) return(y);        /* x and y is NaN */
       else return(copysign(y,one));   /* y is INF */
}
#endif