date and time created 85/05/23 14:06:03 by miriam

SCCS-vsn: old/libm/libm/cosh.c 1.1

diff --git a/usr/src/old/libm/libm/cosh.c b/usr/src/old/libm/libm/cosh.c
new file mode 100644 (file)
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+++ b/usr/src/old/libm/libm/cosh.c
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+From Prof. Kahan at UC at Berkeley
+/* 
+ * 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[] = "@(#)cosh.c     1.1 (Berkeley) %G%";
+#endif not lint
+
+/* COSH(X)
+ * RETURN THE HYPERBOLIC COSINE OF X
+ * 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 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
+ *
+ * Required system supported functions :
+ *     copysign(x,y)
+ *     scalb(x,N)
+ *
+ * Required kernel function:
+ *     exp(x) 
+ *     exp__E(x,c)     ...return exp(x+c)-1-x for |x|<0.3465
+ *
+ * Method :
+ *     1. Replace x by |x|. 
+ *     2. 
+ *                                                     [ exp(x) - 1 ]^2 
+ *         0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
+ *                                                        2*exp(x)
+ *
+ *                                                exp(x) +  1/exp(x)
+ *         0.3465   <= x <= 22      :  cosh(x) := -------------------
+ *                                                        2
+ *         22       <= x <= lnovfl  :  cosh(x) := exp(x)/2 
+ *         lnovfl   <= x <= lnovfl+log(2)
+ *                                  :  cosh(x) := exp(x)/2 (avoid overflow)
+ *         log(2)+lnovfl <  x <  INF:  overflow to INF
+ *
+ *     Note: .3465 is a number near one half of ln2.
+ *
+ * Special cases:
+ *     cosh(x) is x if x is +INF, -INF, or NAN.
+ *     only cosh(0)=1 is exact for finite x.
+ *
+ * Accuracy:
+ *     cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
+ *     In a test run with 768,000 random arguments on a VAX, the maximum
+ *     observed error was 1.23 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
+/* double static  */
+/* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
+/* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
+/* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
+static long    mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2};
+static long    mln2lox[] = { 0x1b60a70f, 0x582a279e};
+static long    lnovflx[] = { 0x0f3343b0, 0x2bdac7e2};
+#define   mln2hi    (*(double*)mln2hix)
+#define   mln2lo    (*(double*)mln2lox)
+#define   lnovfl    (*(double*)lnovflx)
+#else  /* IEEE double */
+double static 
+mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
+mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
+lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
+#endif
+
+#ifdef VAX
+static max = 126                      ;
+#else  /* IEEE */
+static max = 1023                     ;
+#endif
+
+double cosh(x)
+double x;
+{      
+       static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
+       double scalb(),copysign(),exp(),exp__E(),t;
+
+       if(x!=x) return(x);
+       if((x=copysign(x,one)) <= 22)
+           if(x<0.3465) 
+               if(x<small) return(one+x);
+               else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
+
+           else /* for x lies in [0.3465,22] */
+               { t=exp(x); return((t+one/t)*half); }
+
+       if( lnovfl <= x && x <= (lnovfl+0.7)) 
+        /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 
+         * and return 2^max*exp(x) to avoid unnecessary overflow 
+         */
+           return(scalb(exp((x-mln2hi)-mln2lo), max)); 
+
+       else 
+           return(exp(x)*half);        /* for large x,  cosh(x)=exp(x)/2 */
+}