BitIntegers

This package implements fixed-width integer types similar to standard builtin-ones like Int or UInt128. The following types, with obvious meaning, are exported: Int256, UInt256, Int512, UInt512, Int1024, UInt1024; they come with string macros to construct them (like for Int128 and UInt128), e.g. int256"123". It's possible to instantiate a new pair of types with the exported @define_integers macro:

julia> BitIntegers.@define_integers 24

julia> UInt24(1), Int24(2)
(0x000001, 2)

julia> BitIntegers.@define_integers 8 MyInt8 MyUInt8

julia> MyUInt8(1)
0x01

julia> myint8"123" # the string macro is named like the type, in lower case
123

These custom integers work as similarly as possible to bit integers defined in Base. In particular type promotion (promote_rule), with the additional following rules: when two types have the same signedness (both <: Signed or both <: Unsigned) and bit widths:

• when both types are defined with @define_integers, promote_rule returns Union{}, which means promote_type will end up returning an abstract type (via typejoin); the user can disambiguate by defining its own promote_rule;
• when one type is defined with @define_integers and the other is defined in Base, promote_rule returns the former.

This package is implemented using primitive type and julia intrinsics, the caveat being that it might not always be legal (e.g. in some julia versions, Primes.factor(rand(UInt256)) used to make LLVM abort the program, while it was fine for Int256).

There are another couple of outstanding issues:

1. the intrinsics for division operations used to make LLVM fail for widths greater than 128 bits, so they are here implemented via conversion to BigInt first, which makes them quite slow; it got slightly better in recent julia (nightly pre-1.10), where it prints JIT session error: Symbols not found: [ __divei4 ] but at least doesn't abort.

2. prior to Julia version 1.2: for some reason, importing this code invalidates many precompiled functions from Base, so the REPL experience becomes very annoyingly slow until functions get recompiled (fixed by JuliaLang/julia#30830);

3. prior to Julia version 1.4: creating arrays of types of size not a power of two easily leads to errors and segfaults (cf. e.g. #1, fixed by JuliaLang/julia#33283).

• fix incorrect bswap for odd byte-sizes (#41)

• change and document how promote_rule is implemented (#36)
• export @define_integers
• fix performance bug in bitshift for widths <= 128 bits