Calculate difference between multiples of two different numbers

Question

This is an algorithmic problem. To keep it simple, say I have two doubles, A and B. I want to construct a function that will give me the difference until the next multiple of A or the next multiple of B, if that makes sense.

For instance, say A is 3 and B is 5.

Consider the multiples: (3,6,9,12,15) and (5,10,15).

I'd want the function to output: (3, 2, 1, 3, 1, 2, 3), since it takes 3 units to get to 3, then 2 more to get to 5, then 1 to 6, then 3 to 9, etc...

I hope this makes sense. Ideally it's a Python-esque generator (although I'm writing this in Arduino ~ C++). I need it to be fast - really fast.

Any help would really be appreciated. My pseudocode is below, but it's not that great.

a = 3
b = 5

current = 0
distToA = a
distToB = b
for i in xrange(100):
  if distToA > distToB: #B comes first
    print "Adding {0}".format(distToB)
    current += distToB
    distToA -= distToBb
    distToB = b
  elif distToB > distToA: #A comes first
    print "Adding {0}".format(distToA)
    current += distToA
    distToB -= distToA
    distToA = a
  else: #Equal
    print "Adding {0}".format(distToA)
    current += distToA #Arbitrarily, could be distToB
    distToA = a
    distToB = b

EDIT: How would this look with multiple values? Not just a and b, but also c, d, e, etc.. I'd imagine I'd just do some more if statements, but the cost is higher (more operations per branch).

Answer 1

Unclear why you're unhappy with the code you have. If it's because there are "so many " if tests, it's easy enough to do it with none:

def diffgen(a, b):
    from itertools import cycle
    diffs = []
    current = 0
    ab = a*b
    while current < ab:
        nextone = min((current // a + 1) * a,
                      (current // b + 1) * b)
        diffs.append(nextone - current)
        yield nextone - current
        current = nextone
    for d in cycle(diffs):
        yield d

Note that once you reach a*b, the sequence of diffs repeats, so no more calculations are needed then.