clean-ups.

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

/* 
* Copyright (c) 1985 Regents of the University of California.
* 
* Use and reproduction of this software are granted  in  accordance  with
* the terms and conditions specified in  the  Berkeley  Software  License
* Agreement (in particular, this entails acknowledgement of the programs'
* source, and inclusion of this notice) with the additional understanding
* that  all  recipients  should regard themselves as participants  in  an
* ongoing  research  project and hence should  feel  obligated  to report
* their  experiences (good or bad) with these elementary function  codes,
* using "sendbug 4bsd-bugs@BERKELEY", to the authors.
*/

#ifndef lint
static char sccsid[] =
"@(#)cabs.c     1.2 (Berkeley) 8/21/85; 1.6 (ucb.elefunt) %G%";
#endif  /* not lint */

/* 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;
{
       double hypot();
       return(hypot(z.x,z.y));
}


/* 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.
*/

#if defined(vax)||defined(tahoe)        /* VAX D format */
#ifdef vax
#define _0x(A,B)        0x/**/A/**/B
#else   /* vax */
#define _0x(A,B)        0x/**/B/**/A
#endif  /* vax */
/* static double */
/* r2p1hi =  2.4142135623730950345E0     , Hex  2^  2   *  .9A827999FCEF32 */
/* r2p1lo =  1.4349369327986523769E-17   , Hex  2^-55   *  .84597D89B3754B */
/* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
static long    r2p1hix[] = { _0x(8279,411a), _0x(ef32,99fc)};
static long    r2p1lox[] = { _0x(597d,2484), _0x(754b,89b3)};
static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
#define   r2p1hi    (*(double*)r2p1hix)
#define   r2p1lo    (*(double*)r2p1lox)
#define    sqrt2    (*(double*)sqrt2x)
#else   /* defined(vax)||defined(tahoe) */
static double
r2p1hi =  2.4142135623730949234E0     , /*Hex  2^1     *  1.3504F333F9DE6 */
r2p1lo =  1.2537167179050217666E-16   , /*Hex  2^-53   *  1.21165F626CDD5 */
sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
#endif  /* defined(vax)||defined(tahoe) */

double hypot(x,y)
double x, y;
{
       static double zero=0, one=1, 
                     small=1.0E-18;    /* fl(1+small)==1 */
       static ibig=30; /* fl(1+2**(2*ibig))==1 */
       double copysign(),scalb(),logb(),sqrt(),t,r;
       int finite(), 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 */
}

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