TheAlgorithms/Python · error · ValueError

Undefined for non-natural numbers

Error message

Undefined for non-natural numbers

What it means

Raised by pi() in maths/chudnovsky_algorithm.py when precision is an int but less than 1. The Chudnovsky series is summed for ceil(precision/14) iterations to produce exactly `precision` significant digits; zero or negative precision has no mathematical meaning, so it is rejected with ValueError (undefined for non-natural numbers).

Source

Thrown at maths/chudnovsky_algorithm.py:42

    >>> pi(10)
    '3.14159265'
    >>> pi(100)
    '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706'
    >>> pi('hello')
    Traceback (most recent call last):
        ...
    TypeError: Undefined for non-integers
    >>> pi(-1)
    Traceback (most recent call last):
        ...
    ValueError: Undefined for non-natural numbers
    """

    if not isinstance(precision, int):
        raise TypeError("Undefined for non-integers")
    elif precision < 1:
        raise ValueError("Undefined for non-natural numbers")

    getcontext().prec = precision
    num_iterations = ceil(precision / 14)
    constant_term = 426880 * Decimal(10005).sqrt()
    exponential_term = 1
    linear_term = 13591409
    partial_sum = Decimal(linear_term)
    for k in range(1, num_iterations):
        multinomial_term = factorial(6 * k) // (factorial(3 * k) * factorial(k) ** 3)
        linear_term += 545140134
        exponential_term *= -262537412640768000
        partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
    return str(constant_term / partial_sum)[:-1]


if __name__ == "__main__":
    n = 50
    print(f"The first {n} digits of pi is: {pi(n)}")

View on GitHub (pinned to f5988cc097)

Solutions

1. Clamp or validate precision >= 1 before calling: precision = max(precision, 1) if a fallback is acceptable, else raise your own error.
2. Fix the upstream computation that produced a non-positive precision.
3. Treat 0/negative precision as invalid input at your API boundary with a clear message.

Example fix

# before
pi(-1)  # ValueError: Undefined for non-natural numbers

# after
precision = 50
if precision < 1:
    raise ValueError('precision must be >= 1')
result = pi(precision)

if precision < 1:
    raise ValueError(f'precision must be >= 1, got {precision}')
digits = pi(precision)

try:
    digits = pi(precision)
except ValueError as e:
    if 'non-natural' in str(e):
        digits = pi(1)  # deliberate fallback to minimum precision
    else:
        raise

When it happens

Trigger: Calling pi(0) or pi(-1) — any integer precision < 1. Note pi(-1.5) hits the earlier TypeError instead, since the isinstance check runs first.

Common situations: Precision derived from a formula that can reach 0 (e.g. len(str) - 20 for short inputs); inverted conditionals that pass -1 as an error sentinel; user-facing parameters left at 0 by default.

Related errors

• Undefined for non-integers
• Both points must have the same dimension.
• Monogons and Digons are not polygons in the Euclidean space
• All values must be greater than 0
• Please enter positive integers for n and k where n >= k

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/bd1a3b25a79ed960. Report an issue: GitHub.