On Mon, 14 Jul 2025 15:40:18 GMT, fabioromano1 <d...@openjdk.org> wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 1964: >> >>> 1962: final double rad = Math.nextUp(x >= 0 ? x : x + 0x1p64); >>> 1963: final double approx = n == 3 ? Math.cbrt(rad) : >>> Math.pow(rad, Math.nextUp(1.0 / n)); >>> 1964: long rLong = (long) Math.ceil(Math.nextUp(approx)); >> >> Does `rLong` need to be an overestimate of the true value, or does the >> algorithm also works for underestimates? >> I'm asking because I'm not sure that `Math.pow()` has strong guarantees >> about its error bounds, whatever the documentation states. > > @rgiulietti The convergence of the recurrence is guaranteed if the initial > estimate is larger than or equal to the exact value, AFAIK no guarantee is > given when the estimate is smaller than the exact value. This is my hunch as well. So while the use of `nextUp()` and `ceil()` certainly help to achieve an overestimate, I'm less sure that this is sufficient when using `pow()`. If the latter has some error bigger than a few ulps, then we are in trouble. ------------- PR Review Comment: https://git.openjdk.org/jdk/pull/24898#discussion_r2205251784
