A clever homebrew modulus implementation

Question

I'm programming a PLC with some legacy software (RSLogix 500, don't ask) and it does not natively support a modulus operation, but I need one. I do not have access to: modulus, integer division, local variables, a truncate operation (though I can hack it with rounding). Furthermore, all variables available to me are laid out in tables sorted by data type. Finally, it should work for floating point decimals, for example 12345.678 MOD 10000 = 2345.678.

If we make our equation:

dividend / divisor = integer quotient, remainder

There are two obvious implementations.

Implementation 1: Perform floating point division: dividend / divisor = decimal quotient. Then hack together a truncation operation so you find the integer quotient. Multiply it by the divisor and find the difference between the dividend and that, which results in the remainder.

I don't like this because it involves a bunch of variables of different types. I can't 'pass' variables to a subroutine, so I just have to allocate some of the global variables located in multiple different variable tables, and it's difficult to follow. Unfortunately, 'difficult to follow' counts, because it needs to be simple enough for a maintenance worker to mess with.

Implementation 2: Create a loop such that while dividend > divisor divisor = dividend - divisor. This is very clean, but it violates one of the big rules of PLC programming, which is to never use loops, since if someone inadvertently modifies an index counter you could get stuck in an infinite loop and machinery would go crazy or irrecoverably fault. Plus loops are hard for maintenance to troubleshoot. Plus, I don't even have looping instructions, I have to use labels and jumps. Eww.

So I'm wondering if anyone has any clever math hacks or smarter implementations of modulus than either of these. I have access to + - * /, exponents, sqrt, trig functions, log, abs value, and AND/OR/NOT/XOR.

Answer 1

How many bits are you dealing with? You could do something like:

if dividend > 32 * divisor  dividend -= 32 * divisor
if dividend > 16 * divisor  dividend -= 16 * divisor
if dividend > 8 * divisor  dividend -= 8 * divisor
if dividend > 4 * divisor  dividend -= 4 * divisor
if dividend > 2 * divisor  dividend -= 2 * divisor
if dividend > 1 * divisor  dividend -= 1 * divisor
quotient = dividend

Just unroll as many times as there are bits in dividend. Make sure to be careful about those multiplies overflowing. This is just like your #2 except it takes log(n) instead of n iterations, so it is feasible to unroll completely.