+/*
+ * 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 */
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