From e491c6eea9ad599a0ae766a3217bd9a16ca3a25a Mon Sep 17 00:00:00 2001 From: Katie Hockman Date: Wed, 27 Jan 2021 10:33:35 -0500 Subject: math/big: fix comment in divRecursiveStep There appears to be a typo in the description of the recursive division algorithm. Two things seem suspicious with the original comment: 1. It is talking about choosing s, but s doesn't appear anywhere in the equation. 2. The math in the equation is incorrect. Where B = len(v)/2 s = B - 1 Proof that it is incorrect: len(v) - B >= B + 1 len(v) - len(v)/2 >= len(v)/2 + 1 This doesn't hold if len(v) is even, e.g. 10: 10 - 10/2 >= 10/2 + 1 10 - 5 >= 5 + 1 5 >= 6 // this is false The new equation will be the following, which will be mathematically correct: len(v) - s >= B + 1 len(v) - (len(v)/2 - 1) >= len(v)/2 + 1 len(v) - len(v)/2 + 1 >= len(v)/2 + 1 len(v) - len(v)/2 >= len(v)/2 This holds if len(v) is even or odd. e.g. 10 10 - 10/2 >= 10/2 10 - 5 >= 5 5 >= 5 e.g. 11 11 - 11/2 >= 11/2 11 - 5 >= 5 6 >= 5 Change-Id: If77ce09286cf7038637b5dfd0fb7d4f828023f56 Reviewed-on: https://go-review.googlesource.com/c/go/+/287372 Run-TryBot: Katie Hockman Reviewed-by: Filippo Valsorda Trust: Katie Hockman --- src/math/big/nat.go | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/math/big/nat.go b/src/math/big/nat.go index 068176e1c1..bbd6c8850b 100644 --- a/src/math/big/nat.go +++ b/src/math/big/nat.go @@ -881,7 +881,7 @@ func (z nat) divRecursiveStep(u, v nat, depth int, tmp *nat, temps []*nat) { // then floor(u1/v1) >= floor(u/v) // // Moreover, the difference is at most 2 if len(v1) >= len(u/v) - // We choose s = B-1 since len(v)-B >= B+1 >= len(u/v) + // We choose s = B-1 since len(v)-s >= B+1 >= len(u/v) s := (B - 1) // Except for the first step, the top bits are always // a division remainder, so the quotient length is <= n. -- cgit v1.2.3-54-g00ecf