0 ** 0.5 HUNG — PyMathLn never terminates for a non-positive argument

• Type: bug (NilPy, infinite loop) — Track N
• Found: 2026-08-09 by a differential sweep of numeric semantics against CPython. Not reported by anyone; it produces no output to report.
• Status: done

Measured

Cause — one loop, read not guessed

PyMathLn normalises its argument with

while m < 1.0 do begin m := m * 2.0; Dec(e); end;

For any x <= 0 that condition can never become false: 0.0 * 2.0 is 0.0 forever, and a negative doubles away from 1. Every fractional-exponent power routes through it, so 0 ** 0.5 spun with no output, no diagnostic and no progress.

Why it rates 55 rather than the 30 its siblings got

It is an infinite loop in an utterly ordinary expression. x ** 0.5 where x happens to be 0 is not an edge case anyone writes a guard for, and the failure gives a caller nothing at all to go on — no wrong value to notice, no exception to catch, no partial output. A hang is the one failure mode worse than a silent wrong answer for a batch job.

Fix

• PyMathLn raises ValueError('math domain error') for x <= 0, CPython's own message for math.log of a non-positive. That protects every caller, not just **.
• pypow_v answers 0.0 for a zero base with a positive exponent BEFORE the logarithm path — CPython's answer, and the case that has to be settled early rather than diagnosed.
• A negative base with a fractional exponent raises a named ValueError. CPython returns a COMPLEX there and NilPy has no complex type, so a real number would be a wrong answer; see [[bug-nilpy-no-complex-number-type]].

Integer exponents are untouched: (-2) ** 3 stays on the repeated-squaring path, which is where every ordinary negative-base power lands.

Gate

test/test_nilpy_pow_domain.{npy,expected} (.expected from CPython), driven through a function so the operands are variants at run time rather than constants a folder might settle: the four hangs, integer exponents both signs, negative bases with integer exponents, 0 ** 0, 0 ** -1 (ZeroDivisionError), and positive fractional powers.

Log

• 2026-08-09 — resolved, commit ebcdfe1dc.