4.3BSD - /usr/src/usr.lib/libm/acosh.c

   1: /*
   2:  * Copyright (c) 1985 Regents of the University of California.
   3:  *
   4:  * Use and reproduction of this software are granted  in  accordance  with
   5:  * the terms and conditions specified in  the  Berkeley  Software  License
   6:  * Agreement (in particular, this entails acknowledgement of the programs'
   7:  * source, and inclusion of this notice) with the additional understanding
   8:  * that  all  recipients  should regard themselves as participants  in  an
   9:  * ongoing  research  project and hence should  feel  obligated  to report
  10:  * their  experiences (good or bad) with these elementary function  codes,
  11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
  12:  */
  13: 
  14: #ifndef lint
  15: static char sccsid[] = "@(#)acosh.c	1.2 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* ACOSH(X)
  19:  * RETURN THE INVERSE HYPERBOLIC COSINE OF X
  20:  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
  21:  * CODED IN C BY K.C. NG, 2/16/85;
  22:  * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
  23:  *
  24:  * Required system supported functions :
  25:  *	sqrt(x)
  26:  *
  27:  * Required kernel function:
  28:  *	log1p(x) 		...return log(1+x)
  29:  *
  30:  * Method :
  31:  *	Based on
  32:  *		acosh(x) = log [ x + sqrt(x*x-1) ]
  33:  *	we have
  34:  *		acosh(x) := log1p(x)+ln2,	if (x > 1.0E20); else
  35:  *		acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
  36:  *	These formulae avoid the over/underflow complication.
  37:  *
  38:  * Special cases:
  39:  *	acosh(x) is NaN with signal if x<1.
  40:  *	acosh(NaN) is NaN without signal.
  41:  *
  42:  * Accuracy:
  43:  *	acosh(x) returns the exact inverse hyperbolic cosine of x nearly
  44:  *	rounded. In a test run with 512,000 random arguments on a VAX, the
  45:  *	maximum observed error was 3.30 ulps (units of the last place) at
  46:  *	x=1.0070493753568216 .
  47:  *
  48:  * Constants:
  49:  * The hexadecimal values are the intended ones for the following constants.
  50:  * The decimal values may be used, provided that the compiler will convert
  51:  * from decimal to binary accurately enough to produce the hexadecimal values
  52:  * shown.
  53:  */
  54: 
  55: #ifdef VAX  /* VAX D format */
  56: /* static double */
  57: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
  58: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
  59: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
  60: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
  61: #define    ln2hi    (*(double*)ln2hix)
  62: #define    ln2lo    (*(double*)ln2lox)
  63: #else   /* IEEE double */
  64: static double
  65: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
  66: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
  67: #endif
  68: 
  69: double acosh(x)
  70: double x;
  71: {
  72:     double log1p(),sqrt(),t,big=1.E20; /* big+1==big */
  73: 
  74: #ifndef VAX
  75:     if(x!=x) return(x); /* x is NaN */
  76: #endif
  77: 
  78:     /* return log1p(x) + log(2) if x is large */
  79:     if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
  80: 
  81:     t=sqrt(x-1.0);
  82:     return(log1p(t*(t+sqrt(x+1.0))));
  83: }

Defined functions

Defined variables

Defined macros