Task: Continued fraction




Go: package main

import "fmt"

type cfTerm struct {
    a, b int
}



type cf []cfTerm

func cfSqrt2(nTerms int) cf {
    f := make(cf, nTerms)
    for n := range f {
        f[n] = cfTerm{2, 1}
    }
    f[0].a = 1
    return f
}

func cfNap(nTerms int) cf {
    f := make(cf, nTerms)
    for n := range f {
        f[n] = cfTerm{n, n - 1}
    }
    f[0].a = 2
    f[1].b = 1
    return f
}

func cfPi(nTerms int) cf {
    f := make(cf, nTerms)
    for n := range f {
        g := 2*n - 1
        f[n] = cfTerm{6, g * g}
    }
    f[0].a = 3
    return f
}

func (f cf) real() (r float64) {
    for n := len(f) - 1; n > 0; n-- {
        r = float64(f[n].b) / (float64(f[n].a) + r)
    }
    return r + float64(f[0].a)
}

func main() {
    fmt.Println("sqrt2:", cfSqrt2(20).real())
    fmt.Println("nap:  ", cfNap(20).real())
    fmt.Println("pi:   ", cfPi(20).real())
}






COBOL:        identification division.
       program-id. show-continued-fractions.

       environment division.
       configuration section.
       repository.
           function continued-fractions
           function all intrinsic.

       procedure division.
       fractions-main.

       display "Square root 2 approximately   : "
               continued-fractions("sqrt-2-alpha", "sqrt-2-beta", 100)
       display "Napier constant approximately : "
               continued-fractions("napier-alpha", "napier-beta", 40)
       display "Pi approximately              : "
               continued-fractions("pi-alpha", "pi-beta", 10000)

       goback.
       end program show-continued-fractions.

      
       identification division.
       function-id. continued-fractions.
      
       data division.
       working-storage section.
       01 alpha-function       usage program-pointer.
       01 beta-function        usage program-pointer.
       01 alpha                usage float-long.
       01 beta                 usage float-long.
       01 running              usage float-long.
       01 i                    usage binary-long.

       linkage section.
       01 alpha-name           pic x any length.
       01 beta-name            pic x any length.
       01 iterations           pic 9 any length.
       01 approximation        usage float-long.

       procedure division using
           alpha-name beta-name iterations
           returning approximation.

       set alpha-function to entry alpha-name
       if alpha-function = null then
           display "error: no " alpha-name " function" upon syserr
           goback
       end-if
       set beta-function to entry beta-name
       if beta-function = null then
           display "error: no " beta-name " function" upon syserr
           goback
       end-if

       move 0 to alpha beta running
       perform varying i from iterations by -1 until i = 0
           call alpha-function using i returning alpha
           call beta-function using i returning beta
           compute running = beta / (alpha + running)
       end-perform
       call alpha-function using 0 returning alpha
       compute approximation = alpha + running

       goback.
       end function continued-fractions.

      
       identification division.
       program-id. sqrt-2-alpha.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       if iteration equal 0 then
           move 1.0 to result
       else
           move 2.0 to result
       end-if

       goback.
       end program sqrt-2-alpha.

      
       identification division.
       program-id. sqrt-2-beta.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       move 1.0 to result

       goback.
       end program sqrt-2-beta.

      
       identification division.
       program-id. napier-alpha.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       if iteration equal 0 then
           move 2.0 to result
       else
           move iteration to result
       end-if

       goback.
       end program napier-alpha.

      
       identification division.
       program-id. napier-beta.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       if iteration = 1 then
           move 1.0 to result
       else
           compute result = iteration - 1.0
       end-if

       goback.
       end program napier-beta.

      
       identification division.
       program-id. pi-alpha.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       if iteration equal 0 then
           move 3.0 to result
       else
           move 6.0 to result
       end-if

       goback.
       end program pi-alpha.

      
       identification division.
       program-id. pi-beta.

       data division.
       working-storage section.
       01 result               usage float-long.

       linkage section.
       01 iteration            usage binary-long unsigned.

       procedure division using iteration returning result.
       compute result = (2 * iteration - 1) ** 2

       goback.
       end program pi-beta.