4.3BSD - /usr/src/usr.lib/libm/asinh.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[] = "@(#)asinh.c	1.2 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* ASINH(X)
  19:  * RETURN THE INVERSE HYPERBOLIC SINE 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 3/7/85, 3/24/85, 4/16/85.
  23:  *
  24:  * Required system supported functions :
  25:  *	copysign(x,y)
  26:  *	sqrt(x)
  27:  *
  28:  * Required kernel function:
  29:  *	log1p(x) 		...return log(1+x)
  30:  *
  31:  * Method :
  32:  *	Based on
  33:  *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  34:  *	we have
  35:  *	asinh(x) := x  if  1+x*x=1,
  36:  *		 := sign(x)*(log1p(x)+ln2))	 if sqrt(1+x*x)=x, else
  37:  *		 := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
  38:  *
  39:  * Accuracy:
  40:  *	asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
  41:  *	In a test run with 52,000 random arguments on a VAX, the maximum
  42:  *	observed error was 1.58 ulps (units in the last place).
  43:  *
  44:  * Constants:
  45:  * The hexadecimal values are the intended ones for the following constants.
  46:  * The decimal values may be used, provided that the compiler will convert
  47:  * from decimal to binary accurately enough to produce the hexadecimal values
  48:  * shown.
  49:  */
  50: 
  51: #ifdef VAX  /* VAX D format */
  52: /* static double */
  53: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
  54: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
  55: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
  56: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
  57: #define    ln2hi    (*(double*)ln2hix)
  58: #define    ln2lo    (*(double*)ln2lox)
  59: #else   /* IEEE double */
  60: static double
  61: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
  62: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
  63: #endif
  64: 
  65: double asinh(x)
  66: double x;
  67: {
  68:     double copysign(),log1p(),sqrt(),t,s;
  69:     static double small=1.0E-10,    /* fl(1+small*small) == 1 */
  70:               big  =1.0E20, /* fl(1+big) == big */
  71:               one  =1.0   ;
  72: 
  73: #ifndef VAX
  74:     if(x!=x) return(x); /* x is NaN */
  75: #endif
  76:     if((t=copysign(x,one))>small)
  77:         if(t<big) {
  78:             s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
  79:         else    /* if |x| > big */
  80:         {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
  81:     else    /* if |x| < small */
  82:         return(x);
  83: }

Defined functions

Defined variables

Defined macros