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SINH

       REAL FUNCTION  SINH (X)
 C$    (Hyperbolic Sine)
 C$    Return the hyperbolic  sine of  the REAL  argument X.   The
 C$    algorithm uses  the  host exponential  function  for  large
 C$    abs(X), with care taken to prevent premature overflow.  For
 C$    small abs(x),  a  5-term  polynomial  expansion  generating
 C$    results correct to  about 16.73 digits,  which is  adequate
 C$    for single precision computation on all existing commercial
 C$    computers.
 C$
 C$    The polynomial coefficients are taken from table SINH  1985
 C$    in J.F. Hart et al, "Computer Approximations", R.E. Krieger
 C$    Publishing Co., Malabar, FL, USA (1978).  The ELEFUNT tests
 C$    of W.J. Cody, Jr.  and W. Waite,  "Software Manual for  the
 C$    Elementary Functions", Prentice-Hall, Englewood Cliffs, NJ,
 C$    USA (1980)  have  been  made on  the  DEC-20/60,  with  the
 C$    following results:
 C$
 C$    abs(x) in 0 .. 1/2   - maximum relative error: 1.00 bits lost
 C$                         - RMS relative error:     0.00 bits lost
 C$    abs(x) in 3 .. 88.03 - maximum relative error: 2.44 bits lost
 C$                         - RMS relative error:     0.67 bits lost
 C$    (04-SEP-82)