Multiply Very Large Numbers Accurately in Python

Question

I am trying to multiply very large floats by very large integers in Python and am noticing small inaccuracies. For example:

a = 45310630.0
b = 1023473145

c = int(a * b)
print(c)

The answer I am getting is 46374212988031352 but I know the answer should be 46374212988031350. When I change variable "a" to an integer, the multiplication is performed correctly. However, since "a" comes from a division (and might not be a whole number), I can't simply convert it to an integer.

Answer 1

If you use fractions.Fraction you can handle larger numbers accurately, at the cost of some efficiency:

from fractions import Fraction
a = Fraction(45310630.0)
b = Fraction(1023473145)

c = int(a * b)
print(c)

Output:

46374212988031350

Some timings:

In [2]: a = Fraction(45310630.0)
   ...: b = Fraction(1023473145)
   ...:

In [3]: %timeit int(a * b)
3.92 µs ± 21.9 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

In [4]: a = 45310630.0
   ...: b = 1023473145
   ...:

In [5]: %timeit int(a * b)
479 ns ± 13.9 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)