/*
- * Copyright (c) 1985 Regents of the University of California.
- * All rights reserved.
+ * Copyright (c) 1985, 1993
+ * The Regents of the University of California. All rights reserved.
*
- * Redistribution and use in source and binary forms are permitted
- * provided that: (1) source distributions retain this entire copyright
- * notice and comment, and (2) distributions including binaries display
- * the following acknowledgement: ``This product includes software
- * developed by the University of California, Berkeley and its contributors''
- * in the documentation or other materials provided with the distribution
- * and in all advertising materials mentioning features or use of this
- * software. 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 ``AS IS'' AND WITHOUT ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
- * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+ * 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.
*
- * 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
- * the sendbug(8) program, to the authors.
+ * 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 5.6 (Berkeley) 6/1/90";
+static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */
/* POW(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.
- *
+ * KERNEL pow_P() REPLACED BY P. McILROY 7/22/92.
* Required system supported functions:
* scalb(x,n)
* logb(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)
+ * exp__D(a,c) exp(a + c) for |a| << |c|
+ * struct d_double dlog(x) r.a + r.b, |r.b| < |r.a|
*
* Method
* 1. Compute and return log(x) in three pieces:
* (anything) ** 1 is itself;
* (anything) ** NaN is NaN;
* NaN ** (anything except 0) is NaN;
- * +-(anything > 1) ** +INF is +INF;
+ * +(anything > 1) ** +INF is +INF;
+ * -(anything > 1) ** +INF is NaN;
* +-(anything > 1) ** -INF is +0;
* +-(anything < 1) ** +INF is +0;
- * +-(anything < 1) ** -INF is +INF;
+ * +(anything < 1) ** -INF is +INF;
+ * -(anything < 1) ** -INF is NaN;
* +-1 ** +-INF is NaN and signal INVALID;
* +0 ** +(anything except 0, NaN) is +0;
* -0 ** +(anything except 0, NaN, odd integer) is +0;
*/
#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)
+#include <math.h>
-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)
+#include "mathimpl.h"
-#ifdef vccast
-#define ln2hi vccast(ln2hi)
-#define ln2lo vccast(ln2lo)
-#define invln2 vccast(invln2)
-#define sqrt2 vccast(sqrt2)
-#endif
+#if (defined(vax) || defined(tahoe))
+#define TRUNC(x) x = (double) (float) x
+#define _IEEE 0
+#else
+#define _IEEE 1
+#define endian (((*(int *) &one)) ? 1 : 0)
+#define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000
+#define infnan(x) 0.0
+#endif /* vax or tahoe */
-const static double zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;
+const static double zero=0.0, one=1.0, two=2.0, negone= -1.0;
-static double pow_p();
+static double pow_P __P((double, double));
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));
+ if (y==zero)
+ return (one);
+ else if (y==one || (_IEEE && x != x))
+ return (x); /* if x is NaN or y=1 */
+ else if (_IEEE && y!=y) /* if y is NaN */
+ return (y);
+ else if (!finite(y)) /* if y is INF */
+ if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */
+ return (y - y);
+ else if (t>one)
+ return ((y<0)? zero : ((x<zero)? y-y : y));
+ else
+ return ((y>0)? zero : ((x<0)? y-y : -y));
+ else if (y==two)
+ return (x*x);
+ else if (y==negone)
+ return (one/x);
+ /* x > 0, x == +0 */
+ 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) );
+ 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) );
+ 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) */
- }
+ else if (x==zero) /* x is -0 */
+ return ((y>zero)? -x : one/(-x));
+ else if (_IEEE)
+ return (zero/zero);
+ else
+ return (infnan(EDOM));
}
-
-#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;
+/* kernel function for x >= 0 */
+static double
+#ifdef _ANSI_SOURCE
+pow_P(double x, double y)
+#else
+pow_P(x, y) double x, y;
+#endif
{
- 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));
-
+ struct Double s, t, __log__D();
+ double __exp__D(), huge = 1e300, tiny = 1e-300;
+
+ if (x == zero)
+ if (y > zero)
+ return (zero);
+ else if (_IEEE)
+ return (huge*huge);
+ else
+ return (infnan(ERANGE));
+ if (x == one)
+ return (one);
+ if (!finite(x))
+ if (y < zero)
+ return (zero);
+ else if (_IEEE)
+ return (huge*huge);
+ else
+ return (infnan(ERANGE));
+ if (y >= 7e18) /* infinity */
+ if (x < 1)
+ return(tiny*tiny);
+ else if (_IEEE)
+ return (huge*huge);
+ else
+ return (infnan(ERANGE));
+
+ /* Return exp(y*log(x)), using simulated extended */
+ /* precision for the log and the multiply. */
+
+ s = __log__D(x);
+ t.a = y;
+ TRUNC(t.a);
+ t.b = y - t.a;
+ t.b = s.b*y + t.b*s.a;
+ t.a *= s.a;
+ s.a = t.a + t.b;
+ s.b = (t.a - s.a) + t.b;
+ return (__exp__D(s.a, s.b));
}
-#endif /* mc68881 */