FLOOR is defined as "the largest integer number smaller than the parameter", thus:
- positive numbers: FLOOR(X)=integer part of X;
- negative numbers: FLOOR(X)=integer part of X minus 1 (because it must be SMALLER than the parameter, i.e. more negative!)
REMAINDER is defined as the "left over" of a division (Euclidean arithmetic). When the dividend is not an integer, the quotient is usually also not an integer, i.e. there is no remainder, but if the quotient is forced to be an integer (and that's what happens when someone tries to get the remainder or modulus of a floating-point number), there will be a non-integer "left over", obviously.
divisor) will be -1 smaller than the times a number (divisor) "goes into" another (dividend). In other words, FLOOR will return the correct answer for an integer division of a negative number, but Yarin didn't ask that!
gammax answered correctly, that code works as asked by Yarin. On the other hand, Samuel is wrong, he didn't do the maths, I guess, or he would have seen that it does work (also, he didn't say what was the divisor of his example, but I hope it was 3):
Remainder = X % Y = -100 % 3 = -1
GoesInto = (X - Remainder) / Y = (-100 - -1) / 3 = -99 / 3 = -33
By the way, I tested the code on Firefox 27.0.1, it worked as expected, with positive and negative numbers and also with non-integer values, both for dividend and divisor. Example:
-100.34 / 3.57: GoesInto = -28, Remainder = -0.3800000000000079
Yes, I noticed, there is a precision problem there, but I didn't had time to check it (I don't know if it's a problem with Firefox, Windows 7 or with my CPU's FPU). For Yarin's question, though, which only involves integers, the gammax's code works perfectly.