u32 modulo fix

[mizar]

#111

Fix a problem with cases like 2^31 < modulo < 2^32 due to poor implementation of ac-library's overflow/underflow check.

[mizar]

Rebased commit to current rust-lang-ja:master.

[mizar]

AtCoder Library Practice Contest F - Convolution
before: 239ms
https://atcoder.jp/contests/practice2/submissions/38240676
after: 242ms
https://atcoder.jp/contests/practice2/submissions/38240720

[TonalidadeHidrica]

@mizar Does this fix correspond to a PR in atcoder/ac-library, or is this an original improvement?

[mizar]

@TonalidadeHidrica
atcoder/ac-library#149
I have sent an issue to ac-library, but have not yet sent a pull request.

[mizar]

This proposed change has been incorporated into ACL 1.5.1 and is expected to be available in the 202301 language update for C++.

• mul_mod for 2^31 < m < 2^32 atcoder/ac-library#149
• fix #149: improve barret algorithm atcoder/ac-library#163
• https://github.com/atcoder/ac-library/releases/tag/v1.5.1
• AtCoder 2023/1 Language Update > 要確認事項

  2023/04/12 新ジャッジアップデートと共にACLのアップデートも予定しています。新バージョンは v1.5.1 です。 release はこちら https://github.com/atcoder/ac-library/releases/tag/v1.5.1

[mizar]

Regarding the proposed 2^31 <= m < 2^32 response to ModInt addition and subtraction, the response was as follows.

atcoder/ac-library#164 (comment)

Thanks for suggestion, but we don't have a plan to extend mod range to m < 2^32. As far as I know, at least 99% usage of modint is m < 2^31. TBH I don't came up any recent problems that requires 2^31 < m < 2^32. So, we prefer to prepare m < 2^31 modint rather than m < 2^32 modint with tricky technique.

[mizar]

現状のmasterブランチにrebase、および幾つかのコメントとtestを追加しました。

• internal_math における修正 (2^31以上のmodulusにおける乗算) は fix #149: improve barret algorithm atcoder/ac-library#163 にて適用されています。
• modint における修正 (2^31以上のmodulusにおける加減算) は ModInt 2^31 <= m < 2^32 for addition/subtruction atcoder/ac-library#164 にて計画外とのことでした。

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Rebase and some comments and tests have been added to the current master branch.

• Fixes in internal_math (multiplication in modulus greater than 2^31) are applied at fix #149: improve barret algorithm atcoder/ac-library#163.
• Fixes in modint (addition and subtraction in modulus greater than 2^31) were unplanned at ModInt 2^31 <= m < 2^32 for addition/subtruction atcoder/ac-library#164.