Question

I’m trying to divide some large numbers in Python but i’m getting some strange results

NStr = "7D5E9B01D4DCF9A4B31D61E62F0B679C79695ACA70BACF184518" \
       "8BDF94B0B58FAF4A3E1C744C5F9BAB699ABD47BA842464EE93F4" \
       "9B151CC354B21D53DC0C7FADAC44E8F4BDF078F935D9D07A2C07" \
       "631D0DFB0B869713A9A83393CEC42D898516A28DDCDBEA13E87B" \
       "1F874BC8DC06AF03F219CE2EA4050FA996D30CE351257287" 

N = long(NStr, 16)
f2 = 476

fmin = N / float(f2)

print N - (fmin * float(f2))

This outputs as 0.0 as expected. However if I, for example, change the code to

fmin = N / float(f2)
fmin += 1

I still get an output of 0.0

I also tried using the decimal package

fmin = Decimal(N) / Decimal(f2)
print Decimal(N) - (fmin * Decimal(f2))

But that gives me an output of -1.481136900397802034028076389E+280

I assume i’m not telling python how to handle the large numbers properly, but i’m stumped on where to go from here.

I should also add that the end goal is to calculate

fmin = ceil(N / float(f2))

as a long and as accurate as possible

Answer 1

Expanding on my comment, if N and f2 are longs strictly greater than 0, then

 fmin = (N - 1) // f2 + 1

is exactly ceil(N / float(f2)) (but even more accurately than using floats).

(The use of // rather than / for integer division is for compatibility with Python 3.x for no extra effort.)

It is because N // f2 gives you (basically) floor(N / float(f2)) and so N // f2 + 1 is almost always the same as ceil. However, when N is a multiple of f2, N // f2 + 1 is too large (the +1 shouldn’t be there) but using N - 1 fixes this, and doesn’t break the other case.

(This doesn’t work for either N, f2 less than or equal to 0, but that can handled separately)