Log10 is inexact for powers of ten — int(log10(n)) is off by one

import math
for n in [1, 10, 100, 1000, 10000, 100000, 1000000]:
    print(n, math.log10(n), int(math.log10(n)))

Silent, and it breaks the standard digit-count idiom. int(math.log10(n)) + 1 is how everyone counts digits; here it is wrong for almost every power of ten, and right for 100000, so a spot check can pass. Nothing raises — the value is a plausible float a hair below the integer.

Cause

lib/rtl/math.pas:

function Log10(x: Double): Double;
begin
  Result := Ln(x) / 2.30258509299404568402;
end;

Ln is a series expansion, and dividing its result by ln(10) lands just below the integer for exact powers of ten. A correctly-rounded log10 (what libm and therefore CPython give) returns the integer exactly.

Log2 and LogN are the same shape and want checking together — log2(8) happens to come out exactly 3.0 today, which is luck, not correctness.

Suggested fix

The cheap, well-founded one: compute as now, round the result to the nearest integer k, and if 10^k reproduces x exactly (integer power comparison, in the representable range) return k as an exact float. That makes every exact power of ten exact — the cases that matter and the cases that are checkable — without changing any other value. Same treatment for Log2 with 2^k, where the check is exact for the whole double range.

Improving Ln's accuracy generally would be better still but is a bigger job; the exactness fix stands on its own.

Also found, same sweep, much lower impact

math.exp(1) = 2.7182818284590446 against CPython's 2.718281828459045 — 1 ulp. Worth a note next to Exp, not worth its own ticket.

Found by

Sweeping the numeric/math surface against CPython. Everything else measured correct: //, % and divmod with negative operands, round half-to-even, int()/float() conversions, ** including negative and fractional exponents, bit operators, big-int literals, bin/oct/hex, math.pi, sqrt, sin, cos, gcd, fabs, hypot, fmod, floor, ceil, log2.

Gate

make lib-test + a test asserting math.log10 and int(math.log10(n)) for every power of ten from 1 to 1e15, log2 for every power of two in range, and a handful of non-power values against CPython.

Log

• 2026-08-09 — resolved, commit 2ae8d1509.