Manual Reference Pages  - sinh (3fortran)

NAME

SINH(3) - [MATHEMATICS:TRIGONOMETRIC] Hyperbolic sine function

SYNOPSIS

result = sinh(x) 

         elemental TYPE(kind=KIND) function sinh(x)


          TYPE(kind=KIND) :: x

CHARACTERISTICS

o TYPE may be real or complex
o KIND may be any kind supported by the associated type.
o The returned value will be of the same type and kind as the argument.

DESCRIPTION

SINH(3) computes the hyperbolic sine of X.

The hyperbolic sine of x is defined mathematically as: 

         sinh(x) = (exp(x) - exp(-x)) / 2.0

OPTIONS

o X : The value to calculate the hyperbolic sine of

RESULT

The result has a value equal to a processor-dependent approximation to sinh(X). If X is of type complex its imaginary part is regarded as a value in radians.

EXAMPLES

Sample program: 

    program demo_sinh
    use, intrinsic :: iso_fortran_env, only : real32, real64, real128
    implicit none
    real(kind=real64) :: x = - 1.0_real64
    real(kind=real64) :: nan, inf
    character(len=20) :: line


      ! basics
       print *, sinh(x)
       print *, (exp(x)-exp(-x))/2.0


      ! sinh(3) is elemental and can handle an array
       print *, sinh([x,2.0*x,x/3.0])


       ! a NaN input returns NaN
       line=’NAN’
       read(line,*) nan
       print *, sinh(nan)


       ! a Inf input returns Inf
       line=’Infinity’
       read(line,*) inf
       print *, sinh(inf)


       ! an overflow returns Inf
       x=huge(0.0d0)
       print *, sinh(x)


    end program demo_sinh
Results: 

     > -1.1752011936438014
     > -1.1752011936438014
     > -1.1752011936438014       -3.6268604078470190      -0.33954055725615012
     >                      NaN
     >                 Infinity
     >                 Infinity

STANDARD

Fortran 95 , for a complex argument Fortran 2008

SEE ALSO

ASINH(3)

RESOURCES

o Wikipedia:hyperbolic functions
Fortran intrinsic descriptions (license: MIT) @urbanjost

Nemo Release 3.1 sinh (3fortran) November 02, 2024
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