BSD 4_3_Net_2 release

[unix-history] / usr / src / lib / libm / common_source / pow.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[] = "@(#)pow.c       5.7 (Berkeley) 10/9/90";
#endif /* not lint */

/* POW(X,Y)  
* RETURN X**Y 
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/8/85; 
* REVISED BY K.C. NG on 7/10/85.
*
* Required system supported functions:
*      scalb(x,n)      
*      logb(x)         
*      copysign(x,y)   
*      finite(x)       
*      drem(x,y)
*
* Required kernel functions:
*      exp__E(a,c)     ...return  exp(a+c) - 1 - a*a/2
*      log__L(x)       ...return  (log(1+x) - 2s)/s, s=x/(2+x) 
*      pow_p(x,y)      ...return  +(anything)**(finite non zero)
*
* Method
*      1. Compute and return log(x) in three pieces:
*              log(x) = n*ln2 + hi + lo,
*         where n is an integer.
*      2. Perform y*log(x) by simulating muti-precision arithmetic and 
*         return the answer in three pieces:
*              y*log(x) = m*ln2 + hi + lo,
*         where m is an integer.
*      3. Return x**y = exp(y*log(x))
*              = 2^m * ( exp(hi+lo) ).
*
* Special cases:
*      (anything) ** 0  is 1 ;
*      (anything) ** 1  is itself;
*      (anything) ** NaN is NaN;
*      NaN ** (anything except 0) is NaN;
*      +-(anything > 1) ** +INF is +INF;
*      +-(anything > 1) ** -INF is +0;
*      +-(anything < 1) ** +INF is +0;
*      +-(anything < 1) ** -INF is +INF;
*      +-1 ** +-INF is NaN and signal INVALID;
*      +0 ** +(anything except 0, NaN)  is +0;
*      -0 ** +(anything except 0, NaN, odd integer)  is +0;
*      +0 ** -(anything except 0, NaN)  is +INF and signal DIV-BY-ZERO;
*      -0 ** -(anything except 0, NaN, odd integer)  is +INF with signal;
*      -0 ** (odd integer) = -( +0 ** (odd integer) );
*      +INF ** +(anything except 0,NaN) is +INF;
*      +INF ** -(anything except 0,NaN) is +0;
*      -INF ** (odd integer) = -( +INF ** (odd integer) );
*      -INF ** (even integer) = ( +INF ** (even integer) );
*      -INF ** -(anything except integer,NaN) is NaN with signal;
*      -(x=anything) ** (k=integer) is (-1)**k * (x ** k);
*      -(anything except 0) ** (non-integer) is NaN with signal;
*
* Accuracy:
*      pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX,
*      and a Zilog Z8000,
*                      pow(integer,integer)
*      always returns the correct integer provided it is representable.
*      In a test run with 100,000 random arguments with 0 < x, y < 20.0
*      on a VAX, the maximum observed error was 1.79 ulps (units in the 
*      last place).
*
* 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 <errno.h>
#include "mathimpl.h"

vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)
vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)

ic(ln2hi,  6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
ic(ln2lo,  1.9082149292705877000E-10, -33, 1.A39EF35793C76)
ic(invln2, 1.4426950408889633870E0,     0, 1.71547652B82FE)
ic(sqrt2,  1.4142135623730951455E0,     0, 1.6A09E667F3BCD)

#ifdef vccast
#define ln2hi   vccast(ln2hi)
#define ln2lo   vccast(ln2lo)
#define invln2  vccast(invln2)
#define sqrt2   vccast(sqrt2)
#endif

const static double zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;

static double pow_p();

double pow(x,y)         
double x,y;
{
       double t;

       if     (y==zero)      return(one);
       else if(y==one
#if !defined(vax)&&!defined(tahoe)
               ||x!=x
#endif  /* !defined(vax)&&!defined(tahoe) */
               ) return( x );      /* if x is NaN or y=1 */
#if !defined(vax)&&!defined(tahoe)
       else if(y!=y)         return( y );      /* if y is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */
       else if(!finite(y))                     /* if y is INF */
            if((t=copysign(x,one))==one) return(zero/zero);
            else if(t>one) return((y>zero)?y:zero);
            else return((y<zero)?-y:zero);
       else if(y==two)       return(x*x);
       else if(y==negone)    return(one/x);

   /* sign(x) = 1 */
       else if(copysign(one,x)==one) return(pow_p(x,y));

   /* sign(x)= -1 */
       /* if y is an even integer */
       else if ( (t=drem(y,two)) == zero)      return( pow_p(-x,y) );

       /* if y is an odd integer */
       else if (copysign(t,one) == one) return( -pow_p(-x,y) );

       /* Henceforth y is not an integer */
       else if(x==zero)        /* x is -0 */
           return((y>zero)?-x:one/(-x));
       else {                  /* return NaN */
#if defined(vax)||defined(tahoe)
           return (infnan(EDOM));      /* NaN */
#else   /* defined(vax)||defined(tahoe) */
           return(zero/zero);
#endif  /* defined(vax)||defined(tahoe) */
       }
}

#ifndef mc68881
/* pow_p(x,y) return x**y for x with sign=1 and finite y */
static double pow_p(x,y)       
double x,y;
{
       double c,s,t,z,tx,ty;
#ifdef tahoe
       double tahoe_tmp;
#endif  /* tahoe */
       float sx,sy;
       long k=0;
       int n,m;

       if(x==zero||!finite(x)) {           /* if x is +INF or +0 */
#if defined(vax)||defined(tahoe)
            return((y>zero)?x:infnan(ERANGE)); /* if y<zero, return +INF */
#else   /* defined(vax)||defined(tahoe) */
            return((y>zero)?x:one/x);
#endif  /* defined(vax)||defined(tahoe) */
       }
       if(x==1.0) return(x);   /* if x=1.0, return 1 since y is finite */

   /* reduce x to z in [sqrt(1/2)-1, sqrt(2)-1] */
       z=scalb(x,-(n=logb(x)));  
#if !defined(vax)&&!defined(tahoe)      /* IEEE double; subnormal number */
       if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);} 
#endif  /* !defined(vax)&&!defined(tahoe) */
       if(z >= sqrt2 ) {n += 1; z *= half;}  z -= one ;

   /* log(x) = nlog2+log(1+z) ~ nlog2 + t + tx */
       s=z/(two+z); c=z*z*half; tx=s*(c+log__L(s*s)); 
       t= z-(c-tx); tx += (z-t)-c;

  /* if y*log(x) is neither too big nor too small */
       if((s=logb(y)+logb(n+t)) < 12.0) 
           if(s>-60.0) {

       /* compute y*log(x) ~ mlog2 + t + c */
               s=y*(n+invln2*t);
               m=s+copysign(half,s);   /* m := nint(y*log(x)) */ 
               k=y; 
               if((double)k==y) {      /* if y is an integer */
                   k = m-k*n;
                   sx=t; tx+=(t-sx); }
               else    {               /* if y is not an integer */    
                   k =m;
                   tx+=n*ln2lo;
                   sx=(c=n*ln2hi)+t; tx+=(c-sx)+t; }
          /* end of checking whether k==y */

               sy=y; ty=y-sy;          /* y ~ sy + ty */
#ifdef tahoe
               s = (tahoe_tmp = sx)*sy-k*ln2hi;
#else   /* tahoe */
               s=(double)sx*sy-k*ln2hi;        /* (sy+ty)*(sx+tx)-kln2 */
#endif  /* tahoe */
               z=(tx*ty-k*ln2lo);
               tx=tx*sy; ty=sx*ty;
               t=ty+z; t+=tx; t+=s;
               c= -((((t-s)-tx)-ty)-z);

           /* return exp(y*log(x)) */
               t += exp__E(t,c); return(scalb(one+t,m));
            }
       /* end of if log(y*log(x)) > -60.0 */
           
           else
               /* exp(+- tiny) = 1 with inexact flag */
                       {ln2hi+ln2lo; return(one);}
           else if(copysign(one,y)*(n+invln2*t) <zero)
               /* exp(-(big#)) underflows to zero */
                       return(scalb(one,-5000)); 
           else
               /* exp(+(big#)) overflows to INF */
                       return(scalb(one, 5000)); 

}
#endif /* mc68881 */