This function evaluates the arc hyperbolic sine.
Function Return Value
ASINH — Function value. (Output)
Required Arguments
X — Argument for which the arc hyperbolic sine is desired. (Input)
FORTRAN 90 Interface
Generic: ASINH (X)
Specific: The specific interface names are ASINH, DASINH, CASINH, and ZASINH.
FORTRAN 77 Interface
Single: ASINH (X)
Double: The double precision function name is DASINH.
Complex: The complex name is CASINH.
Double Complex: The double complex name is ZASINH.
Description
The function ASINH(X) computes the inverse hyperbolic sine of x, sinh−1x.
For complex arguments, almost all arguments are legal. Only when |z| > b/2 can an overflow occur, where b = AMACH(2) is the largest floating point number. This error is not detected by ASINH.
Example 1
In this example, sinh−1(2.0) is computed and printed.
USE ASINH_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL VALUE, X
! Compute
X = 2.0
VALUE = ASINH(X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) X, VALUE
99999 FORMAT (' ASINH(', F6.3, ') = ', F6.3)
END
Output
ASINH( 2.000) = 1.444
Additional Example
Example 2
In this example, sinh−1(−1 + i) is computed and printed.
USE ASINH_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX VALUE, Z
! Compute
Z = (-1.0, 1.0)
VALUE = ASINH(Z)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Z, VALUE
99999 FORMAT (' ASINH((', F6.3, ',', F6.3, ')) = (', &
F6.3, ',', F6.3, ')')
END
Output
ASINH((-1.000, 1.000)) = (-1.061, 0.666)
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