Perl | Tail Calls in Function Recursion

Recursion in Perl is any function that does not uses the for loop or the while loop, instead calls itself during the execution of the program and the corresponding function is known as recursive function.

Tail recursive function is a special case of recursion in which the function call statement is performed as the final action of the procedure. So return loop(..); would work, but return loop() + operation; would not. Tail recursion (or tail-end recursion) is particularly useful, and often easy to handle in implementations. The implementation of tail-recursion is mainly done to avoid the space occupied by stack data structure which keeps track of the data returned from the previous recursion call statement.

Following are few examples for a better understanding of the concept:

Examples 1:

#!/usr/bin/perl

# Perl Program to calculate Factorial

# Recursion without tail call
sub recurse_fact
{
    my $x = $_[0];

    # checking if that value is 0 or 1
    if ($x == 0 || $x == 1)
    {
        return 1;
    }

    # Recursively calling function with
    # the next value which is one less
    # than current one
    else
    {
        return $x * recurse_fact($x - 1);
    }
}

# Recursion using Tail Call
sub tail_recurse_fact
{
    my ($ans, $x) = @_;

    # checking if that value is 0 or 1
    if ($x == 0 || $x == 1)
    {
        return $ans;
    }

    # Recursively calling function with
    # the next value which is one less
    # than current one
    else
    {
        return tail_recurse_fact($ans * $x, $x - 1);
    }
}

# Driver Code
$a = 5;

# Function call and printing result after return
print "Factorial of a number $a ",
          "through recursion is ", recurse_fact($a);

print "\nFactorial of a number $a ",
       "through tail-recursion is ",
           tail_recurse_fact(1, $a);

Output:

Factorial of a number 5 through recursion is 120
Factorial of a number 5 through tail-recursion is 120

In the non-tail version, the compiler needs to keep track of the number you’re going to multiply it with, whereas in the tail-call version the compiler can realize that the only work left to do is another function call and it can forget about all of the variables and states used in the current function.

Examples 2:

#!/usr/bin/perl

# Perl program to demonstrate the
# use of tail-recursion
use strict;
use warnings;

sub recurse_fib
{
    my $n = shift;

    if ($n == 1 or $n == 2)
    {
        return 1
    }

    # recursive calling
    return (recurse_fib($n - 1) +
            recurse_fib($n - 2));
}

sub tail_recurse_fib
{
    my ($n, $a, $b) = @_;

    if ($n == 1)
    {
        return $a
    }
    if ($n == 2)
    {
        return $b
    }
    else
    {
        # tail recursive calling
        return tail_recurse_fib($n - 1, $b, $a + $b)
    }
}

# Driver code
$a = 10;
print "Fibonacci upto $a through recursion is ",
                                recurse_fib($a);
print "\nFibonacci upto $a through tail-recursion is ",
                            tail_recurse_fib($a, 1, 1);

Output:

Fibonacci upto 10 through recursion is 55
Fibonacci upto 10 through tail-recursion is 55

Use of goto statement to demonstrate Tail Recursion: goto will transfer the compiler to the subroutine of the given name from the currently running subroutine. This will replace the function call and creates a recursion process in the same way.

# Perl program to demonstrate the
# use of tail-recursion
use warnings;

sub recurse
{
    my $i = shift;
    return if $i == 0;
    recurse($i - 1);
}

sub tail_recurse
{
    my $i = shift;
    return if $i == 0;
    @_ = ($i - 1);
    goto &tail_recurse;
}

# Driver Code
print "recursing\n";
recurse(200);

print "tail_recursing\n";
tail_recurse(200);

Output:

recursing
tail_recursing

In the above example the recurse function will produce a fatal error of ‘deep recursion’ while the tail_recurse will work fine.

Elimination of Tail Call

Tail recursive is better than non-tail recursive as tail-recursive can be optimized by modern compilers. What a modern compiler do to optimize the tail recursive code is known as tail call elimination. Tail call elimination saves stack space. It replaces a function call with a goto statement. This really isn’t elimination – it is an optimization.

Sometimes a deeply recursive method is the easiest solution to a problem, but if you recurse more than a couple of hundred calls you’ll hit Perl’s “deep recursion” error. That is the reason why tail-recursive is used over non-tail recursive codes in Perl.

If we take a closer look at the above-discussed function, we can remove the last call with goto. Below are examples of tail call elimination.

Examples 1: Factorial of a number

#!/usr/bin/perl

# Perl Program to calculate Factorial
sub tail_recurse_fact
{
    my $ans = shift;
    my $x = shift;

    # checking if that value is 0 or 1
    if ($x == 0 || $x == 1)
    {
        return $ans;
    }

    # Recursively calling function with
    # the next value which is one less
    # than current one
    else
    {
        @_ = ($x * $ans, $x - 1);
        goto &tail_recurse_fact;
    }
}

# Driver Code
$a = 5;

# Function call and printing result after return
print "Factorial of a number $a ",
     "through tail-recursion is ",
         tail_recurse_fact(1, $a);

Output:

Factorial of a number 5 through tail-recursion is 120

Examples 2: Fibonacci upto n

#!/usr/bin/perl

# Perl program to demonstrate the
# use of tail-recursion-elimination
use strict;
use warnings;

sub tail_recurse_fib
{
    my $n = shift;
    my $a = shift;
    my $b = shift;

    if ($n == 1)
    {
        return $a
    }
    if ($n == 2)
    {
        return $b
    }
    else
    {
        @_ = ($n - 1, $b, $a + $b);

        # tail recursive calling
        goto &tail_recurse_fib;
    }
}

# Driver code
$a = 10;
print "Fibonacci upto $a through tail-recursion is ",
                          tail_recurse_fib($a, 1, 1);

Output:

Fibonacci upto 10 through recursion is 55
Fibonacci upto 10 through tail-recursion is 55