BSD 4_3 release

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

diff --git a/usr/src/usr.lib/libm/pow.c b/usr/src/usr.lib/libm/pow.c
index 96319bf..516e4ef 100644 (file)
--- a/usr/src/usr.lib/libm/pow.c
+++ b/usr/src/usr.lib/libm/pow.c
@@ -1,41 +1,226 @@
-/*     @(#)pow.c       4.2     6/30/83 */
+/* 
+ * 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.
+ */

 
 

-/*
-       computes a^b.
-       uses log and exp
-*/
+#ifndef lint
+static char sccsid[] = "@(#)pow.c      4.5 (Berkeley) 8/21/85";
+#endif not lint

 
 

-#include       <errno.h>
-int errno;
-double log(), exp();
+/* 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.
+ */

 
 

-double
-pow(arg1,arg2)
-double arg1, arg2;
+#ifdef VAX     /* VAX D format */
+#include <errno.h>
+extern double infnan();
+
+/* double static */
+/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
+/* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
+/* invln2 =  1.4426950408889634148E0     , Hex  2^  1   *  .B8AA3B295C17F1 */
+/* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
+static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
+static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
+static long    invln2x[] = { 0xaa3b40b8, 0x17f1295c};
+static long     sqrt2x[] = { 0x04f340b5, 0xde6533f9};
+#define    ln2hi    (*(double*)ln2hix)
+#define    ln2lo    (*(double*)ln2lox)
+#define   invln2    (*(double*)invln2x)
+#define    sqrt2    (*(double*)sqrt2x)
+#else  /* IEEE double */
+double static
+ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
+ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
+invln2 =  1.4426950408889633870E0     , /*Hex  2^  0   *  1.71547652B82FE */
+sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
+#endif
+
+double static zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;
+
+double pow(x,y)        
+double x,y;

 {
 {

-       double temp;
-       long l;
+       double drem(),pow_p(),copysign(),t;
+       int finite();
+
+       if     (y==zero)      return(one);
+       else if(y==one
+#ifndef VAX
+               ||x!=x
+#endif
+               ) return( x );      /* if x is NaN or y=1 */
+#ifndef VAX
+       else if(y!=y)         return( y );      /* if y is NaN */
+#endif
+       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) );

 
 

-#ifdef vax
-       asm("   bispsw  $0xe0");
+       /* 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 */
+#ifdef VAX
+           return (infnan(EDOM));      /* NaN */
+#else  /* IEEE double */
+           return(zero/zero);

 #endif
 #endif

-       if(arg1 <= 0.) {
-               if(arg1 == 0.) {
-                       if(arg2 <= 0.)
-                               goto domain;
-                       return(0.);
-               }
-               l = arg2;
-               if(l != arg2)
-                       goto domain;
-               temp = exp(arg2 * log(-arg1));
-               if(l & 1)
-                       temp = -temp;
-               return(temp);

        }
        }

-       return(exp(arg2 * log(arg1)));
+}
+
+/* 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 logb(),scalb(),copysign(),log__L(),exp__E();
+        double c,s,t,z,tx,ty;
+        float sx,sy;
+       long k=0;
+        int n,m;
+
+       if(x==zero||!finite(x)) {           /* if x is +INF or +0 */
+#ifdef VAX
+            return((y>zero)?x:infnan(ERANGE)); /* if y<zero, return +INF */
+#else
+            return((y>zero)?x:one/x);
+#endif
+       }
+       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)));  
+#ifndef VAX    /* IEEE double */       /* subnormal number */
+        if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);} 
+#endif
+        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 */
+               s=(double)sx*sy-k*ln2hi;        /* (sy+ty)*(sx+tx)-kln2 */
+               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)); 

 
 

-domain:
-       errno = EDOM;
-       return(0.);

 }
 }