CODESARRAY

Short note, by Codesarray, , 2 min read

Python int overflow: why 2 ** 1000 just works

Most languages keep a whole number in 64 bits and overflow past it. A Python int has no limit, and the reason also explains why floats still do.

Most languages keep a whole number in 64 bits. Go past about 9 quintillion, 9223372036854775807 to be exact, and the number overflows: in Java it wraps around to a negative value, in C the result is undefined. Python int overflow is not a thing. A Python int just keeps counting, and this note shows how far and why.

Past 64 bits, still an int

print(2 ** 63)
print(2 ** 64)
big = 2 ** 1000
print(len(str(big)))
print(type(big))
9223372036854775808
18446744073709551616
302
<class 'int'>

2 ** 63 is the first number a signed 64-bit integer cannot hold. Python prints it. 2 ** 64 goes one bit further, and Python prints that too. 2 ** 1000 has 302 digits, and type(big) shows it is still an ordinary int, the same type as 3. There is no separate "big integer" type to ask for.

Why: an int is not a fixed box

In most languages an integer is a fixed box of 64 bits, so there is a largest value it can hold. A Python int is stored in as many chunks as it needs, and Python adds more chunks as the number grows. Memory is the only limit, which in practice means none. The cost is a little speed: arithmetic on a number that spans several chunks takes longer than one machine instruction, which is why Python is slower than C at raw number crunching and why that almost never matters.

Floats are the fixed box

print(2.0 ** 1000)
print(2.0 ** 1024)
1.0715086071862673e+301
OverflowError: (34, 'Result too large')

A float is always 64 bits, so it does have a largest value: a little under 1.8e308. 2.0 ** 1000 fits. 2.0 ** 1024 does not, and because there is nowhere for it to go Python raises OverflowError rather than quietly returning something wrong. The second line is the last line of the traceback.

What to take from this

  • int has no upper limit. 2 ** 1000 is as ordinary as 2 ** 3.
  • Python stores an int in as many chunks as it needs, and the only cost is a little speed.
  • float is a fixed 64-bit box, so 2.0 ** 1024 raises OverflowError.

This is a short note on Variables and types, lesson 2 of the Python beginner track.

This article goes with the video Ints never overflow. Watch it on YouTube.