4.3BSD - /usr/src/usr.lib/libm/sinh.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[] = "@(#)sinh.c	4.3 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* SINH(X)
  19:  * RETURN THE HYPERBOLIC SINE OF X
  20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  21:  * CODED IN C BY K.C. NG, 1/8/85;
  22:  * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
  23:  *
  24:  * Required system supported functions :
  25:  *	copysign(x,y)
  26:  *	scalb(x,N)
  27:  *
  28:  * Required kernel functions:
  29:  *	expm1(x)	...return exp(x)-1
  30:  *
  31:  * Method :
  32:  *	1. reduce x to non-negative by sinh(-x) = - sinh(x).
  33:  *	2.
  34:  *
  35:  *	                                      expm1(x) + expm1(x)/(expm1(x)+1)
  36:  *	    0 <= x <= lnovfl     : sinh(x) := --------------------------------
  37:  *			       		                      2
  38:  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
  39:  * lnovfl+ln2 <  x <  INF        :  overflow to INF
  40:  *
  41:  *
  42:  * Special cases:
  43:  *	sinh(x) is x if x is +INF, -INF, or NaN.
  44:  *	only sinh(0)=0 is exact for finite argument.
  45:  *
  46:  * Accuracy:
  47:  *	sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
  48:  *	a test run with 1,024,000 random arguments on a VAX, the maximum
  49:  *	observed error was 1.93 ulps (units in the last place).
  50:  *
  51:  * Constants:
  52:  * The hexadecimal values are the intended ones for the following constants.
  53:  * The decimal values may be used, provided that the compiler will convert
  54:  * from decimal to binary accurately enough to produce the hexadecimal values
  55:  * shown.
  56:  */
  57: #ifdef VAX
  58: /* double static */
  59: /* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
  60: /* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
  61: /* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
  62: static long    mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2};
  63: static long    mln2lox[] = { 0x1b60a70f, 0x582a279e};
  64: static long    lnovflx[] = { 0x0f3343b0, 0x2bdac7e2};
  65: #define   mln2hi    (*(double*)mln2hix)
  66: #define   mln2lo    (*(double*)mln2lox)
  67: #define   lnovfl    (*(double*)lnovflx)
  68: #else   /* IEEE double */
  69: double static
  70: mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
  71: mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
  72: lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
  73: #endif
  74: 
  75: #ifdef VAX
  76: static max = 126                      ;
  77: #else   /* IEEE double */
  78: static max = 1023                     ;
  79: #endif
  80: 
  81: 
  82: double sinh(x)
  83: double x;
  84: {
  85:     static double  one=1.0, half=1.0/2.0 ;
  86:     double expm1(), t, scalb(), copysign(), sign;
  87: #ifndef VAX
  88:     if(x!=x) return(x); /* x is NaN */
  89: #endif
  90:     sign=copysign(one,x);
  91:     x=copysign(x,one);
  92:     if(x<lnovfl)
  93:         {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
  94: 
  95:     else if(x <= lnovfl+0.7)
  96:         /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
  97: 	    		to avoid unnecessary overflow */
  98:         return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
  99: 
 100:     else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
 101:         return( expm1(x)*sign );
 102: }

Defined functions

Defined variables

Defined macros