####CORE####
############
##NOTE : ####
#
#The Core Calculates the probability the Attacker wins. 
#Unless flag is defined. In which case the defender probability is calculated.
#

#Core :: Does the Core Probability Computation	
sub core {
	my ($D, $A, $T, $HD, $HA, $flag) = @_;			#Def. Attack. Terrain. HitDef. HitAtt.
	($HD, $HA) = ($HA, $HD) if $flag;			#For Defender [$flag] Switch HP in neg_bin;

	 				#E[P]		P = DT/A * Uniform(0,1) or flipped otherwise.
	my $p = (($A > $D*$T) ? $D*$T/($A*2) : $A/ ($D*$T* 2));
	$p = 1 - $p if ((!$flag && $A>$D*$T) || ($flag && $A<=$D*$T));	#If Attacker, and A>DT. Or Defender and DT>A

	print "Probability of individual hp conflict being won by ".(($flag) ? "Defender" : "Attacker")." is $p\n";
	return &neg_bin($p, $HD, $HD + $HA - 1);
}

#Core::Neg_Binomial -- The Neg. Bin. distribution at the very core of the calc.
#Neg Binomial of X (r,p) [Frequency Function] = Sum { [x-1 C r- 1] * p^r * (1-p) ^ (x-r) }
#
sub neg_bin {
	my ($p, $r, $limit)=@_;			
	my $float = 6;my $freq=0;
	my (@Sum,$chr);			
	for (my $x=$r; $x<=$limit;$x++) {
		$freq = &choose($x-1, $r-1) * ($p ** ($r)) * ((1- $p)**($x - $r))*100;	#Freq function
		$freq = sprintf( "%.".$float."g" , $freq);				#g rounds to maximum # of $float #'s in $freq
		push (@Sum, $freq);	
	}
	return (&add(@Sum), \@Sum);
}

#Core::Choose -- Combination. Nothing Special.
sub choose {
	return &pi($_[0]-$_[1]+1, $_[0])/(&pi(1, $_[1]));		#Product (k-n+1  to  n)  / (k!)
}

#Core::Pi (Product Counter)
sub pi {				### NOTE #### The counting inclues the term specified  ####		
	my $pi=1;
	for ($_[0]..$_[1]) {$pi*=$_;}		#Normal factorial would be factorial(1,n);
	return $pi;
}

#Core::Add --- ????
sub add {
	my $sum;
	$sum+=$_  foreach (@_);
	return $sum;
}
1;