CodeQL documentation

Pythagorean calculation with sub-optimal numerics

ID: py/pythagorean
Kind: problem
Severity: warning
Precision: medium
   - accuracy
Query suites:
   - python-security-and-quality.qls

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Calculating the length of the hypotenuse using the standard formula c = sqrt(a**2 + b**2) may lead to overflow if the two other sides are both very large. Even though c will not be much bigger than max(a, b), either a**2 or b**2 (or both) will. Thus, the calculation could overflow, even though the result is well within representable range.


Rather than sqrt(a**2 + b**2), use the built-in function hypot(a,b) from the math library.


The following code shows two different ways of computing the hypotenuse. The first is a direct rewrite of the Pythagorean theorem, the second uses the built-in function.

# We know that a^2 + b^2 = c^2, and wish to use this to compute c
from math import sqrt, hypot

a = 3e154 # a^2 > 1e308
b = 4e154 # b^2 > 1e308
# with these, c = 5e154 which is less that 1e308

def longSideDirect():
    return sqrt(a**2 + b**2) # this will overflow

def longSideBuiltin():
    return hypot(a, b) # better to use built-in function