BSD 4_3 release

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

diff --git a/usr/src/usr.lib/libm/exp.c b/usr/src/usr.lib/libm/exp.c
index e236251..701b2b5 100644 (file)
--- a/usr/src/usr.lib/libm/exp.c
+++ b/usr/src/usr.lib/libm/exp.c
@@ -1,47 +1,126 @@
-/*     @(#)exp.c       4.1     12/25/82        */
-
-/*
-       exp returns the exponential function of its
-       floating-point argument.
-
-       The coefficients are #1069 from Hart and Cheney. (22.35D)
-*/
-
-#include <errno.h>
-#include <math.h>
-
-int    errno;
-static double  p0      = .2080384346694663001443843411e7;
-static double  p1      = .3028697169744036299076048876e5;
-static double  p2      = .6061485330061080841615584556e2;
-static double  q0      = .6002720360238832528230907598e7;
-static double  q1      = .3277251518082914423057964422e6;
-static double  q2      = .1749287689093076403844945335e4;
-static double  log2e   = 1.4426950408889634073599247;
-static double  sqrt2   = 1.4142135623730950488016887;
-static double  maxf    = 10000;
-
-double
-exp(arg)
-double arg;
+/* 
+ * 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.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)exp.c      4.3 (Berkeley) 8/21/85";
+#endif not lint
+
+/* EXP(X)
+ * RETURN THE EXPONENTIAL OF X
+ * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
+ * CODED IN C BY K.C. NG, 1/19/85; 
+ * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85.
+ *
+ * Required system supported functions:
+ *     scalb(x,n)      
+ *     copysign(x,y)   
+ *     finite(x)
+ *
+ * Kernel function:
+ *     exp__E(x,c)
+ *
+ * Method:
+ *     1. Argument Reduction: given the input x, find r and integer k such 
+ *        that
+ *                        x = k*ln2 + r,  |r| <= 0.5*ln2 .  
+ *        r will be represented as r := z+c for better accuracy.
+ *
+ *     2. Compute expm1(r)=exp(r)-1 by 
+ *
+ *                     expm1(r=z+c) := z + exp__E(z,r)
+ *
+ *     3. exp(x) = 2^k * ( expm1(r) + 1 ).
+ *
+ * Special cases:
+ *     exp(INF) is INF, exp(NaN) is NaN;
+ *     exp(-INF)=  0;
+ *     for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ *     exp(x) returns the exponential of x nearly rounded. In a test run
+ *     with 1,156,000 random arguments on a VAX, the maximum observed
+ *     error was .768 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.
+ */
+
+#ifdef VAX     /* VAX D format */
+/* double static */
+/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
+/* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
+/* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 */
+/* lntiny = -9.5654310917272452386E1     , Hex  2^  7   * -.BF4F01D72E33AF */
+/* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */
+static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
+static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
+static long    lnhugex[] = { 0xec1d43bd, 0x9010a73e};
+static long    lntinyx[] = { 0x4f01c3bf, 0x33afd72e};
+static long    invln2x[] = { 0xaa3b40b8, 0x17f1295c};
+#define    ln2hi    (*(double*)ln2hix)
+#define    ln2lo    (*(double*)ln2lox)
+#define   lnhuge    (*(double*)lnhugex)
+#define   lntiny    (*(double*)lntinyx)
+#define   invln2    (*(double*)invln2x)
+#else  /* IEEE double */
+double static
+ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
+ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
+lnhuge =  7.1602103751842355450E2     , /*Hex  2^  9   *  1.6602B15B7ECF2 */
+lntiny = -7.5137154372698068983E2     , /*Hex  2^  9   * -1.77AF8EBEAE354 */
+invln2 =  1.4426950408889633870E0     ; /*Hex  2^  0   *  1.71547652B82FE */
+#endif
+
+double exp(x)
+double x;

 {
 {

-       double fract;
-       double temp1, temp2, xsq;
-       int ent;
-
-       if(arg == 0.)
-               return(1.);
-       if(arg < -maxf)
-               return(0.);
-       if(arg > maxf) {
-               errno = ERANGE;
-               return(HUGE);
+       double scalb(), copysign(), exp__E(), z,hi,lo,c;
+       int k,finite();
+
+#ifndef VAX
+       if(x!=x) return(x);     /* x is NaN */
+#endif
+       if( x <= lnhuge ) {
+               if( x >= lntiny ) {
+
+                   /* argument reduction : x --> x - k*ln2 */
+
+                       k=invln2*x+copysign(0.5,x);     /* k=NINT(x/ln2) */
+
+                       /* express x-k*ln2 as z+c */
+                       hi=x-k*ln2hi;
+                       z=hi-(lo=k*ln2lo);
+                       c=(hi-z)-lo;
+
+                   /* return 2^k*[expm1(x) + 1]  */
+                       z += exp__E(z,c);
+                       return (scalb(z+1.0,k));  
+               }
+               /* end of x > lntiny */
+
+               else 
+                    /* exp(-big#) underflows to zero */
+                    if(finite(x))  return(scalb(1.0,-5000));
+
+                    /* exp(-INF) is zero */
+                    else return(0.0);

        }
        }

-       arg *= log2e;
-       ent = floor(arg);
-       fract = (arg-ent) - 0.5;
-       xsq = fract*fract;
-       temp1 = ((p2*xsq+p1)*xsq+p0)*fract;
-       temp2 = ((1.0*xsq+q2)*xsq+q1)*xsq + q0;
-       return(ldexp(sqrt2*(temp2+temp1)/(temp2-temp1), ent));
+       /* end of x < lnhuge */
+
+       else 
+       /* exp(INF) is INF, exp(+big#) overflows to INF */
+           return( finite(x) ?  scalb(1.0,5000)  : x);

 }
 }