Net2/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 */