Question

I’m looking for a simple explanation for how Ruby’s modulo operand works and why, in Ruby

puts  4 % 3   # 1
puts -4 % 3   # 2 <--why?
puts -4 % -3  # -1 

but in PHP:

<?php

echo  4 % 3;  #  1
echo -4 % 3;  # -1
echo -4 % -3; # -1

Looks to me like -4 % 3 is actally 8 % 3 (8 being the difference between 4 and -4).

Answer 1

They can both be considered correct, depending on your definition. If a % n == r, then it should hold that:

a == q*n + r

where q == a / n.

Whether r is positive or negative is determined by the value of q. So in your example, either of:

-4 == -1*3 + (-1)   // PHP
-4 == -2*3 + 2      // Ruby

To put it another way, the definition of % depends on the definition of /.

See also the table here: http://en.wikipedia.org/wiki/Modulus_operator#Remainder_calculation_for_the_modulo_operation. You’ll see that this varies substantially between various programming languages.