Manual Reference Pages  - acospi (3fortran)

NAME

ACOSPI(3) - [MATHEMATICS:TRIGONOMETRIC] Circular Arccosine (inverse circular cosine) function

SYNOPSIS

result = acospi(x) 

         elemental real(kind=KIND) function acospi(x)


          real(kind=KIND),intent(in) :: x

CHARACTERISTICS

o KIND may be any real kind
o The returned value will be of the same type and kind as the argument.

DESCRIPTION

ACOSPI(3) computes the circular arccosine of X (inverse of COSPI(X)). The result is expressed in half-revolutions (ie. PI’s) and lies in the range

0 <= ACOSPI (X) <= 1.

OPTIONS

o X : The value to compute the circular arctangent of. The value must satisfy |X| <= 1.

RESULT

The result has a value equal to a processor-dependent approximation to the arc cosine of X.

The return value is of the same type and kind as X.

It is expressed in half-revolutions and lies in the range 0 <= ACOSPI (X) <= 1.

EXAMPLES

Sample program: 

    program demo_acospi
    use, intrinsic :: iso_fortran_env, only : real32,real64,real128
    implicit none
    character(len=*),parameter :: all=’(*(g0,1x))’
    real(kind=real64) :: x , d2r
    real(kind=real64),parameter :: &
    & PI = 3.14159265358979323846264338327950288419716939937510_real64


       ! basics
        x = PI/4.0_real64
        print all,’acospi(’,x,’) is ’, acospi(x)


       ! acospi(-1) should be PI
        write(*,*) acospi(-1.0_real64)
        d2r=acospi(-1.0_real64)/180.0_real64
        print all,’90 degrees is ’, d2r*90.0_real64, ’ radians’
       ! elemental
        print all,’elemental’,acospi([-1.0,-0.5,0.0,0.50,1.0])
       !
        print *,’-1.0’,acospi( -1.0 )
        print *,’ 0.0’,acospi(  0.0 )
        print *,’ 1.0’,acospi(  1.0 )


    end program demo_acospi
Results: 

     > acospi( 0.78539816339744828 ) is  0.21245823046654463
     >    1.0000000000000000    
     > 90 degrees is  0.50000000000000000  radians
     > elemental 1.00000000 0.666666687 0.500000000 0.333333343 0.00000000
     >  -1.0   1.00000000   
     >   0.0  0.500000000   
     >   1.0   0.00000000

STANDARD

Fortran 2023

SEE ALSO

o arc cosine in radians: ACOS(3)
o arc cosine in degrees: ACOSD(3)
o Inverse function: COS(3)

RESOURCES

o wikipedia: inverse trigonometric functions
Fortran intrinsic descriptions (license: MIT) @urbanjost

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