While loop

unit CollatzConjecture;

{$mode ObjFPC}{$H+}

interface

function steps(const number: integer): integer;

implementation

uses SysUtils;

function steps(const number: integer): integer;
var
  temp, count: integer;
begin
  if number < 1 then
    raise Exception.Create('Only positive integers are allowed');

  temp := number;
  count := 0;
  while temp > 1 do
  begin
    inc(count);
    if temp mod 2 = 0 then
      temp := temp div 2
    else
      temp := temp * 3 + 1;
  end;
  result := count;
end;

end.

This approach uses a while...do loop to repeatedly apply the Collatz algorithm until the value reaches 1.

Local variables

The var block declares local variables before the function body begins. In Free Pascal, all local variables must be declared in a var section that appears between the function header and its begin keyword.

var
  temp, count: integer;

Here, temp tracks the current value in the sequence and count tracks the number of steps taken.

Input validation with exceptions

The function checks for non-positive input and raises an Exception using Exception.Create:

if number < 1 then
  raise Exception.Create('Only positive integers are allowed');

The raise keyword in Free Pascal throws an exception object. Exception.Create is a constructor that accepts a string message. The SysUtils unit must be included in the uses clause for Exception to be available.

The while...do loop

The while...do loop is a pre-condition loop: it tests the condition before each iteration. If the condition is false from the start, the loop body never executes.

while temp > 1 do
begin
  ...
end;

Because the loop body contains multiple statements, it must be enclosed in a begin...end compound statement.

Arithmetic operators: mod and div

Free Pascal uses the keyword mod for the integer remainder operator and div for integer division:

if temp mod 2 = 0 then
  temp := temp div 2

These are built-in operators for the integer type. Note that = is the equality comparison operator in Pascal (not == as in C-family languages), and := is the assignment operator.

The inc procedure

inc is a built-in procedure that increments an integer variable by 1:

inc(count);

This is equivalent to count := count + 1, but inc is idiomatic in Pascal code.

The result variable

Each function has an implicit local variable called result whose type matches the function's return type. Assigning to result sets the function's return value:

result := count;

This is an alternative to the traditional Pascal syntax steps := count (assigning to the function name).