Hello all, This is a (re)proposal for a divmod kernel for the compute function. This proposes the following two combinations of quotient and remainder for 'divmod'.
- [floor-quotient, modulo] - [trunc-quotient, remainder] The first proposal for divmod was made in ARROW-12755 [1] and has been discussed in GH-11116 [2], but has not yet been completed. On the other hand, the following relationships hold for the dividend, quotient, divisor, and modulo, quotient ∈ Ｚ dividend = quotient * divisor + modulo, |modulo| < |divisor| Since the sign of modulo is undefined in this expression, each language has a different behavior regarding the sign of the remainder when a negative number is involved. For example, in C, C++, Go, Java, Rust, etc., the remainder will match the sign of the divisor. This is equivalent to performing a "truncation division to zero: trunc" when finding the quotient. On the other hand, R yields a remainder that matches the sign of the divisor, which is equivalent to performing "truncated division to infinity: floor" when finding the quotient. In addition, some languages provide both of these, such as Julia and Ruby. The following table lists the signs and operators for integer remainders. Table: Language, operator and operands which sign is corresponding to the sign of remainder |Language |dividend |divisor | |:--------|:-----------|:--------------| | C | %, div | | | C++ | %, div | | | C# | % | | | Go | % | | | Java | % | Math.floorMod | | Julia | rem | mod | | MATLAB | rem | mod | | Python | math.fmod | % | | R | | %% | | Ruby | remainder | %, modulo | | Rust | % | | | Scala | % | | | Scheme | remainder | modulo | | SQL | mod | | （The remainder of floating point numbers is omitted.） Since both styles exist, it is necessary to name and implement compute functions in a way avoiding confusion that may be used by many languages. So I propose to create two different divmods sets of quotient rounding (trunc or floor) and remainders. - trunc_divmod ≡ [trunc_quotient, remainder] - floor_divmod ≡ [floor_quotient, modulo] It is inconvenient without the kernel, at least for positive number. So I put this proposal here to step the work forward. I am not an expert in this field and there may be some misunderstandings. I would appreciate it if you could point out any mistakes. [1] https://issues.apache.org/jira/browse/ARROW-12755) [2] https://github.com/apache/arrow/pull/11116) Best regards, Hirokazu SUZUKI
