The Float Precision Trap

Medium ⏱ 12 min 62% acceptance ★★★★★ 4.7

Classic gotcha: 0.1 + 0.2 == 0.3 is False in Python due to binary floating-point representation. Write a function nearly_equal(a, b, tolerance=1e-9) that returns True if two floats a and b are equal within tolerance, and False otherwise. This is the correct way to compare floats.

Examples

Example 1

Input

nearly_equal(0.1 + 0.2, 0.3)

Output

True

Explanation

The tiny representational error is within tolerance.

Example 2

Input

nearly_equal(1.0, 1.5)

Output

False

Explanation

Difference of 0.5 exceeds tolerance.

Constraints

`a`, `b` are floats.
`tolerance` defaults to 1e-9 but callers may override it.

Topics

Variables & Data Typesfloating point

Companies

Deutsche BankGoldman Sachs

Hints

Hint 1

Compare `abs(a - b)` against tolerance.

Hint 2

Do not use `==` directly on the floats.

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