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Introduce flintify helper for "optimal" dispatch on integer and rational inputs #1867

Merged
merged 3 commits into from
Sep 26, 2024
Merged

Introduce flintify helper for "optimal" dispatch on integer and rational inputs #1867

merged 3 commits into from
Sep 26, 2024

Commits on Sep 26, 2024

  1. Introduce FlintInt and FlintRat helpers 

    There are a bunch of FLINT function that come in multiple varieties.
E.g. fmpz_add, fmpz_add_ui, fmpz_add_si all take one fmpz and one
additional argument of type fmpz / UInt / Int, respectively.

So naturally we define different `+` and `add!` methods in Julia using
them. But which method to invoke when adding a `ZZRingElem` and a Julia
integer of a type different from `UInt` and `Int`, such as e.g. `UInt32`
? In that case we currently always convert that into a `ZZRingElem`. But
that's inefficient, it would be be better to convert that value to a
`UInt` or `Int` value and then use the optimized `fmpz_add_ui/_si`
method.

Of course this can be done, but getting it right is tedious, repetitive
and it is easy to overlook a case.

This is where `FlintInt` comes in: this is defined as `Union{Int,
ZZRingElem}`. We then provide constructors which convert any `Integer`
to a `FlintInt` in an optimal way (at least for a bunch of built-in
integer types).

This then can be used to write optimal dispatch for Integer types
like this:

    add!(x::ZRingElem, y::ZRingElem) = ...
    add!(x::ZRingElem, y::Int) = ...
    add!(x::ZRingElem, y::UInt) = ...
    # fallback code
    add!(x::ZRingElem, y::Integer) = add!(x, FlintInt(y))

It also works for types that accept ZZRingElem and Int, but not UInt:

    add!(x::ZPolyRingElem, y::ZPolyRingElem) = ...
    add!(x::ZPolyRingElem, y::ZRingElem) = ...
    add!(x::ZPolyRingElem, y::Int) = ...
    # fallback code
    add!(x::ZPolyRingElem, y::Integer) = add!(x, FlintInt(y))

Of course I might have missed optimal conversion for some `Integer`
subtype. But then we can fix this by simply adding another `FlintInt`
constructor in a single central place.

Finally, the new type `FlintRat` plays a similar role for FLINT
functions which also take a `QQFieldElem`. While `RationalUnion` is a
counterpart to `IntegerUnion`.
    @fingolfin
    fingolfin committed Sep 26, 2024
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  2. Update src/flint/FlintTypes.jl 

    Co-authored-by: Lars Göttgens <[email protected]>
    @fingolfin @lgoettgens
    fingolfin and lgoettgens authored Sep 26, 2024
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  3. Rewrite to use flintify

    @fingolfin
    fingolfin committed Sep 26, 2024
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