From 5cd301dcf5365f4fbe84eec0357b23326605af87 Mon Sep 17 00:00:00 2001 From: lane Y Date: Tue, 8 Sep 2026 11:39:36 -0400 Subject: [PATCH] Y: correct the divisor-defect numbers -- 6 of 25 corpus records, and the rate rises with magnitude --- docs/Y-standalone-rng-and-tail.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/docs/Y-standalone-rng-and-tail.md b/docs/Y-standalone-rng-and-tail.md index 23b525c..6f060e1 100644 --- a/docs/Y-standalone-rng-and-tail.md +++ b/docs/Y-standalone-rng-and-tail.md @@ -183,9 +183,13 @@ entirely. of the first 3000 integers, smallest `m = 3` giving -20 against -19. It is not precision loss at scale. `m / 0.15` is an exact integer whenever 3 divides m, and the two constants straddle it. -Measured on the corpus by inverting the stored limit: **5 of 25 player-records would get a different +And the multiples of 3 are only the floor: the disagreement rate is 33.3% up to about 1.2 million, +66.7% by 1.36 million and 100% at and above 3 million. + +Measured on the corpus by inverting the stored limit: **6 of 25 player-records would get a different stored value from the engine's current constant than the game wrote.** The defect is live, it is a -whole unit rather than an ulp, and it is one third of all inputs rather than a tail. +whole unit rather than an ulp, and it is a third of all inputs at small values and all of them at +large ones -- the opposite shape from "one ulp on large empires", which would have been harmless. The file belongs to another lane in flight, so it is reported and not fixed here.