How to process % to negative number in Visual Foxpro

Question

How to do % to negative number in VF?

MOD(10,-3) = -2

MOD(-10,3) = 2

MODE(-10,-3) = -1

Why?

Answer 1

It is a regular modulo:

The mod function is defined as the amount by which a number exceeds the largest integer multiple of the divisor that is not greater than that number.

You can think of it like this:

10 % -3:

The largest multiple of 10 that is less than -3 is -2.

So 10 % -3 is -2.

-10 % 3:

Now, why -10 % 3 is 2?

The easiest way to think about it is to add to the negative number a multiple of 2 so that the number becomes positive.

-10 + (4*3) = 2 so -10 % 3 = (-10 + 12) % 3 = 2 % 3 = 3

Answer 2

Here's what we said about this in The Hacker's Guide to Visual FoxPro:

MOD() and % are pretty straightforward when dealing with positive numbers, but they get interesting when one or both of the numbers is negative. The key to understanding the results is the following equation:

MOD(x,y) = x - (y * FLOOR(x/y))

Since the mathematical modulo operation isn't defined for negative numbers, it's a pleasure to see that the FoxPro definitions are mathematically consistent. However, they may be different from what you'd initially expect, so you may want to check for negative divisors or dividends.

A little testing (and the manuals) tells us that a positive divisor gives a positive result while a negative divisor gives a negative result.