How to resolve the algorithm Pi step by step in the FreeBASIC programming language

Published on 12 May 2024 09:40 PM
#Freebasic

How to resolve the algorithm Pi step by step in the FreeBASIC programming language

Table of Contents

Problem Statement

Create a program to continually calculate and output the next decimal digit of

π

{\displaystyle \pi }

(pi). The program should continue forever (until it is aborted by the user) calculating and outputting each decimal digit in succession. The output should be a decimal sequence beginning   3.14159265 ...

Note: this task is about   calculating   pi.   For information on built-in pi constants see Real constants and functions.

Related Task Arithmetic-geometric mean/Calculate Pi

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pi step by step in the FreeBASIC programming language

Source code in the freebasic programming language

' version 05-07-2018
' compile with: fbc -s console

' unbounded spigot
' Ctrl-c to end program or close console window

#Include "gmp.bi"

Dim As UInteger num, ndigit, fp = Not 0
Dim As mpz_ptr q,r,t,k,n,l,tmp1,tmp2
   q = Allocate(Len(__Mpz_struct)) : Mpz_init_set_ui(q,1)
   r = Allocate(Len(__Mpz_struct)) : Mpz_init(r)
   t = Allocate(Len(__Mpz_struct)) : Mpz_init_set_ui(t,1)
   k = Allocate(Len(__Mpz_struct)) : Mpz_init_set_ui(k,1)
   n = Allocate(Len(__Mpz_struct)) : Mpz_init_set_ui(n,3)
   l = Allocate(Len(__Mpz_struct)) : Mpz_init_set_ui(l,3)
tmp1 = Allocate(Len(__Mpz_struct)) : Mpz_init(tmp1)
tmp2 = Allocate(Len(__Mpz_struct)) : Mpz_init(tmp2)

Do
    mpz_mul_2exp(tmp1, q, 2)
    mpz_add(tmp1,tmp1,r)
    mpz_sub(tmp1,tmp1,t)
    mpz_mul(tmp2, n, t)
    If mpz_cmp(tmp1, tmp2) < 0 Then 
        Print mpz_get_ui(n); : ndigit += 1 : If ndigit Mod 50 = 0 Then Print " :";ndigit 
        If fp Then Print "."; : fp = Not fp : Print :ndigit = 0
        mpz_sub(tmp1, r, tmp2)
        mpz_mul_ui(tmp1, tmp1, 10)
        mpz_mul_ui(tmp2, q, 3)
        mpz_add(tmp2, tmp2, r)
        mpz_mul_ui(tmp2, tmp2, 10)
        mpz_set(r, tmp1)
        mpz_mul_ui(tmp1, n, 10)
        mpz_tdiv_q(tmp2, tmp2, t)
        mpz_sub(n, tmp2, tmp1)
        mpz_mul_ui(q, q, 10)
    Else
        mpz_mul(tmp2, r, l)
        mpz_mul(tmp1, q, k)
        mpz_mul_ui(tmp1, tmp1, 7)
        mpz_add(tmp1, tmp1, tmp2)
        mpz_mul_2exp(tmp2, q, 1)
        mpz_add(tmp2, tmp2, r)
        mpz_mul(tmp2, tmp2, l)
        mpz_mul(t, t, l)
        mpz_tdiv_q(tmp1, tmp1, t)
        mpz_mul(q, q, k)
        mpz_add_ui(k, k, 1)
        mpz_add_ui(l, l, 2)
        mpz_set(n, tmp1)
        mpz_set(r, tmp2)     
    End If
Loop

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