InfinityInts.jl

Copyright © 2020-2023 by Jeffrey Sarnoff.

This work is released under The MIT License.

---

Arithmetic with the InfInt type saturates ±Infinty, so there is no overflow or underflow.

Supports Unified Algebra constants Top (⊤ \top) and Bottom (⊥ \bot) (or Bot)

• Unified Algebra
• From Boolean Algebra To Unified Algebra

---

Exports

The exported type is InfInt32 (Infinity and Int32).

Also exported

• PosInf (prints as +∞)
• NegInf (prints as -∞)
• Indet (prints as ±∞) indeterminate or undefined

This type works as if it were defined

# `ZerInf` is the result of e.g. `PosInf * 0` or `div(0, 0)`.
@enum KindOfNum SignedInt PosInfinity NegInfinity Indeterminate

struct InfInt <: Signed
    kind::KindOfNum
    value::Int32     # only accessed when kind === SignedInt
end

While the actual implementation uses a different approach, it is useful to think of this as described.

• Internally, each Inf+Int32 value is a struct with supertype Signed.
• The actual values are stored as Float64s
  • this simplifies the development of the code from the design
  • performance is improved by limiting finite numbers to the Int32s.
  • arithmetic with Float64(::Int32) values is representationally safe
  • ^ requires work to determine the sign for saturating magnitudes

Supported operations

• ArithOps: +, -, *, div, rem fld, mod, cld, ^, factorial

• Numerics: signbit, sign, abs, abs2, copysign, flipsign

• Comparison: ==, !=, <, <=, >=, >, isless, `isequal

• Predicates: iseven, isodd, isinf, isnan, isfinite, iszero, isone

• Bit Operations: ~, |, &, ⊻, <<, >>, >>>, count_zeros, count_ones

• Binary Layouts: leading_zeros, trailing_zeros, leading_ones, trailing_ones

• Low Level Operations: hash, show

Type Coverage

• Provides all Int32 values and signed infinity:PosInf, NegInf.
• May generate the indeterminate value Indet
  • z = zero(InfInt); div(z,z) # prints ¿?
• Interoperates with Int8, Int16, Int64, Int128 (using Int32(x))

---