Add types TropicalMaxMin and TropicalBitwise. (#16)

* Add types `TropicalMaxMin` and `TropicalBitwise`.

* fix CI

* Update src/tropical_bitwise.jl

* update

* fix minplus

---------

Co-authored-by: GiggleLiu <cacate0129@gmail.com>

Author: samuelsonric

.github/workflows/TagBot.yml

@@ -4,6 +4,22 @@ on:
     types:
       - created
   workflow_dispatch:
+    inputs:
+      lookback:
+        default: 3
+permissions:
+  actions: read
+  checks: read
+  contents: write
+  deployments: read
+  issues: read
+  discussions: read
+  packages: read
+  pages: read
+  pull-requests: read
+  repository-projects: read
+  security-events: read
+  statuses: read
 jobs:
   TagBot:
     if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'

.github/workflows/ci.yml

@@ -1,11 +1,24 @@
 name: CI
 on:
-  - push
-  - pull_request
+  push:
+    branches:
+      - master
+    tags: ['*']
+  pull_request:
+  workflow_dispatch:
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
 jobs:
   test:
     name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
     runs-on: ${{ matrix.os }}
+    timeout-minutes: 60
+    permissions: # needed to allow julia-actions/cache to proactively delete old caches that it has created
+      actions: write
+      contents: read
     strategy:
       fail-fast: false
       matrix:
@@ -17,24 +30,17 @@ jobs:
         arch:
           - x64
     steps:
-      - uses: actions/checkout@v2
-      - uses: julia-actions/setup-julia@v1
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
-      - uses: actions/cache@v1
-        env:
-          cache-name: cache-artifacts
-        with:
-          path: ~/.julia/artifacts
-          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
-          restore-keys: |
-            ${{ runner.os }}-test-${{ env.cache-name }}-
-            ${{ runner.os }}-test-
-            ${{ runner.os }}-
+      - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
+      - uses: codecov/codecov-action@v5
         with:
-          file: lcov.info
+          files: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          slug: TensorBFS/TropicalNumbers.jl

README.md

@@ -23,9 +23,11 @@ pkg> add TropicalNumbers
 
 A Topical algebra can be described as a tuple $(R, \oplus, \otimes, \mathbb{0}, \mathbb{1})$, where $R$ is the set, $\oplus$ and $\otimes$ are the opeartions and $\mathbb{0}$, $\mathbb{1}$ are their identity element, respectively. In this package, the following tropical algebras are implemented:
 * `TropicalAndOr`: $([T, F], \lor, \land, F, T)$;
+* `TropicalBitwise`: $(\mathbb{T}, |, \&, 0, \sim 0)$
 * `Tropical` (`TropicalMaxPlus`): $(\mathbb{R}, \max, +, -\infty, 0)$;
 * `TropicalMinPlus`: $(\mathbb{R}, \min, +, \infty, 0)$;
 * `TropicalMaxMul`: $(\mathbb{R}^+, \max, \times, 0, 1)$.
+* `TropicalMaxMin`: $(\mathbb{R}^+, \max, \min, -\infty, \infty)$.
 
 ```julia
 julia> using TropicalNumbers

src/TropicalNumbers.jl

@@ -5,9 +5,11 @@ export TropicalTypes, AbstractSemiring
 
 export TropicalAndOr
 export Tropical, TropicalF64, TropicalF32, TropicalF16, TropicalI64, TropicalI32, TropicalI16
-export TropicalMaxMul, TropicalMaxMulF64, TropicalMaxMulF32, TropicalMaxMulF16, TropicalMaxMulI64, TropicalMaxMulI32, TropicalMaxMulI16
 export TropicalMaxPlus, TropicalMaxPlusF64, TropicalMaxPlusF32, TropicalMaxPlusF16, TropicalMaxPlusI64, TropicalMaxPlusI32, TropicalMaxPlusI16
 export TropicalMinPlus, TropicalMinPlusF64, TropicalMinPlusF32, TropicalMinPlusF16, TropicalMinPlusI64, TropicalMinPlusI32, TropicalMinPlusI16
+export TropicalMaxMul, TropicalMaxMulF64, TropicalMaxMulF32, TropicalMaxMulF16, TropicalMaxMulI64, TropicalMaxMulI32, TropicalMaxMulI16
+export TropicalMaxMin, TropicalMaxMinF64, TropicalMaxMinF32, TropicalMaxMinF16, TropicalMaxMinI64, TropicalMaxMinI32, TropicalMaxMinI16
+export TropicalBitwise, TropicalBitwiseI64, TropicalBitwiseI32, TropicalBitwiseI16
 export CountingTropical, CountingTropicalF16, CountingTropicalF32, CountingTropicalF64, CountingTropicalI16, CountingTropicalI32, CountingTropicalI64
 
 
@@ -41,6 +43,8 @@ include("tropical_maxplus.jl")
 include("tropical_andor.jl")
 include("tropical_minplus.jl")
 include("tropical_maxmul.jl")
+include("tropical_maxmin.jl")
+include("tropical_bitwise.jl")
 include("counting_tropical.jl")
 
 const TropicalTypes{T} = Union{CountingTropical{T}, Tropical{T}}
@@ -53,17 +57,20 @@ for NBIT in [16, 32, 64]
     @eval const $(Symbol(:TropicalMaxPlus, :F, NBIT)) = TropicalMaxPlus{$(Symbol(:Float, NBIT))}
     @eval const $(Symbol(:TropicalMinPlus, :F, NBIT)) = TropicalMinPlus{$(Symbol(:Float, NBIT))}
     @eval const $(Symbol(:TropicalMaxMul, :F, NBIT)) = TropicalMaxMul{$(Symbol(:Float, NBIT))}
+    @eval const $(Symbol(:TropicalMaxMin, :F, NBIT)) = TropicalMaxMin{$(Symbol(:Float, NBIT))}
     @eval const $(Symbol(:CountingTropical, :F, NBIT)) = CountingTropical{$(Symbol(:Float, NBIT)),$(Symbol(:Float, NBIT))}
 
     @eval const $(Symbol(:Tropical, :I, NBIT)) = Tropical{$(Symbol(:Int, NBIT))}
     @eval const $(Symbol(:TropicalMaxPlus, :I, NBIT)) = TropicalMaxPlus{$(Symbol(:Int, NBIT))}
     @eval const $(Symbol(:TropicalMinPlus, :I, NBIT)) = TropicalMinPlus{$(Symbol(:Int, NBIT))}
     @eval const $(Symbol(:TropicalMaxMul, :I, NBIT)) = TropicalMaxMul{$(Symbol(:Int, NBIT))}
+    @eval const $(Symbol(:TropicalMaxMin, :I, NBIT)) = TropicalMaxMin{$(Symbol(:Int, NBIT))}
+    @eval const $(Symbol(:TropicalBitwise, :I, NBIT)) = TropicalBitwise{$(Symbol(:Int, NBIT))}
     @eval const $(Symbol(:CountingTropical, :I, NBIT)) = CountingTropical{$(Symbol(:Int, NBIT)),$(Symbol(:Float, NBIT))}
 end
 
 # alias
-for T in [:Tropical, :TropicalMaxMul, :TropicalMinPlus, :CountingTropical]
+for T in [:Tropical, :TropicalMaxMul, :TropicalMaxMin, :CountingTropical]
     for OP in [:>, :<, :(==), :>=, :<=, :isless]
         @eval Base.$OP(a::$T, b::$T) = $OP(a.n, b.n)
     end
@@ -76,6 +83,16 @@ for T in [:Tropical, :TropicalMaxMul, :TropicalMinPlus, :CountingTropical]
     end
 end
 
+for T in [:TropicalMinPlus, :TropicalBitwise]
+    @eval begin
+        content(x::$T) = x.n
+        content(x::Type{$T{X}}) where X = X
+        Base.isapprox(x::AbstractArray{<:$T}, y::AbstractArray{<:$T}; kwargs...) = all(isapprox.(x, y; kwargs...))
+        Base.show(io::IO, ::MIME"text/plain", t::$T) = Base.show(io, t)
+        Base.isnan(x::$T) = isnan(content(x))
+    end
+end
+
 for T in [:TropicalAndOr]
     for OP in [:>, :<, :(==), :>=, :<=, :isless]
         @eval Base.$OP(a::$T, b::$T) = $OP(a.n, b.n)
@@ -88,7 +105,7 @@ for T in [:TropicalAndOr]
     end
 end
 
-for T in [:Tropical, :TropicalMaxMul, :TropicalMinPlus, :CountingTropical]
+for T in [:Tropical, :TropicalMinPlus, :TropicalMaxMul, :CountingTropical]
     @eval begin
         # this is for CUDA matmul
         Base.:(*)(a::$T, b::Bool) = b ? a : zero(a)
@@ -100,4 +117,11 @@ for T in [:Tropical, :TropicalMaxMul, :TropicalMinPlus, :CountingTropical]
     end
 end
 
+for T in [:TropicalMaxMin, :TropicalBitwise]
+    @eval begin
+        Base.:(*)(a::$T, b::Bool) = b ? a : zero(a)
+        Base.:(*)(b::Bool, a::$T) = b ? a : zero(a)
+    end
+end
+
 end # module

src/tropical_andor.jl

@@ -12,6 +12,8 @@ It maps
 * `1` to `true` in regular algebra,
 * `0` to `false` in regular algebra.
 
+For the parallel bit-wise version, see [`TropicalBitwise`](@ref).
+
 Example
 -------------------------
 ```jldoctest; setup=:(using TropicalNumbers)

src/tropical_bitwise.jl

@@ -0,0 +1,110 @@
+"""
+    TropicalBitwise{T} <: AbstractSemiring
+
+`TropicalBitwise` is a semiring algebra that parallelizes the [`TropicalAndOr`](@ref) algebra,
+It can be described by
+* TropicalBitwise, (ℝ, |, &, 0, ~0).
+
+It maps
+* `+` to `|`
+* `*` to `&`
+* `0` to `0`
+* `1` to `~0`
+
+Example
+-------------------------
+```jldoctest; setup=:(using TropicalNumbers)
+julia> TropicalBitwise(1) + TropicalBitwise(3)
+3ₛ
+
+julia> TropicalBitwise(1) * TropicalBitwise(3)
+1ₛ
+
+julia> zero(TropicalBitwiseI64)
+0ₛ
+
+julia> one(TropicalBitwiseI64)
+-1ₛ
+```
+"""
+struct TropicalBitwise{T} <: AbstractSemiring
+    n::T
+end
+
+function TropicalBitwise(a::TropicalBitwise)
+    return TropicalBitwise(a.n)
+end
+
+function TropicalBitwise{T}(a::TropicalBitwise) where {T}
+    return TropicalBitwise{T}(a.n)
+end
+
+function Base.show(io::IO, a::TropicalBitwise)
+    print(io, "$(a.n)ₛ")
+    return
+end
+
+function Base.isapprox(a::TropicalBitwise, b::TropicalBitwise; kw...)
+    return isapprox(a.n, b.n; kw...)
+end
+
+function Base.promote_rule(::Type{TropicalBitwise{U}}, ::Type{TropicalBitwise{V}}) where {U, V}
+    W = promote_type(U, V)
+    return TropicalBitwise{W}
+end
+
+function Base.:+(a::TropicalBitwise, b::TropicalBitwise)
+    n = a.n | b.n
+    return TropicalBitwise(n)
+end
+
+function Base.:*(a::TropicalBitwise, b::TropicalBitwise)
+    n = a.n & b.n
+    return TropicalBitwise(n)
+end
+
+function Base.zero(::Type{T}) where {T <: TropicalBitwise}
+    return typemin(T)
+end
+
+function Base.zero(::T) where {T <: TropicalBitwise}
+    return zero(T)
+end
+
+function Base.one(::Type{T}) where {T <: TropicalBitwise}
+    return typemax(T)
+end
+
+function Base.one(::T) where {T <: TropicalBitwise}
+    return one(T)
+end
+
+function Base.typemin(::Type{TropicalBitwise{T}}) where {T}
+    n = zero(T)
+    return TropicalBitwise(n)
+end
+
+function Base.typemax(::Type{TropicalBitwise{T}}) where {T}
+    n = ~zero(T)
+    return TropicalBitwise(n)
+end
+
+function Base.:(==)(a::TropicalBitwise, b::TropicalBitwise)
+    return a.n == b.n
+end
+
+function Base.:>=(a::TropicalBitwise, b::TropicalBitwise)
+    return b.n <= a.n
+end
+
+function Base.:<=(a::TropicalBitwise, b::TropicalBitwise)
+    return a.n | b.n == b.n
+end
+
+function Base.:<(a::TropicalBitwise, b::TropicalBitwise)
+    return a != b && a <= b
+end
+
+function Base.:>(a::TropicalBitwise, b::TropicalBitwise)
+    return b < a
+end

src/tropical_maxmin.jl

@@ -0,0 +1,89 @@
+"""
+    TropicalMaxMin{T} <: AbstractSemiring
+
+TropicalMaxMin is a semiring algebra, can be described by
+* TropicalMaxMin, (ℝ, max, min, -Inf, Inf).
+
+It maps
+* `+` to `max` in regular algebra,
+* `*` to `min` in regular algebra,
+* `0` to `-Inf` in regular algebra (for integer content types, this is a small integer).
+* `1` to `Inf` in regular algebra, (for integer content types, this is a large integer)
+
+Example
+-------------------------
+```jldoctest; setup=:(using TropicalNumbers)
+julia> TropicalMaxMin(1.0) + TropicalMaxMin(3.0)
+3.0ₛ
+
+julia> TropicalMaxMin(1.0) * TropicalMaxMin(3.0)
+1.0ₛ
+
+julia> zero(TropicalMaxMinF64)
+-Infₛ
+
+julia> one(TropicalMaxMinF64)
+Infₛ
+```
+"""
+struct TropicalMaxMin{T} <: AbstractSemiring
+    n::T
+end
+
+function TropicalMaxMin(a::TropicalMaxMin)
+    return TropicalMaxMin(a.n)
+end
+
+function TropicalMaxMin{T}(a::TropicalMaxMin) where {T}
+    return TropicalMaxMin{T}(a.n)
+end
+
+function Base.show(io::IO, a::TropicalMaxMin)
+    print(io, "$(a.n)ₛ")
+    return
+end
+
+function Base.isapprox(a::TropicalMaxMin, b::TropicalMaxMin; kw...)
+    return isapprox(a.n, b.n; kw...)
+end
+
+function Base.promote_rule(::Type{TropicalMaxMin{U}}, ::Type{TropicalMaxMin{V}}) where {U, V}
+    W = promote_type(U, V)
+    return TropicalMaxMin{W}
+end
+
+function Base.:+(a::TropicalMaxMin, b::TropicalMaxMin)
+    n = max(a.n, b.n)
+    return TropicalMaxMin(n)
+end
+
+function Base.:*(a::TropicalMaxMin, b::TropicalMaxMin)
+    n = min(a.n, b.n)
+    return TropicalMaxMin(n)
+end
+
+function Base.zero(::Type{T}) where {T <: TropicalMaxMin}
+    return typemin(T)
+end
+
+function Base.zero(::T) where {T <: TropicalMaxMin}
+    return zero(T)
+end
+
+function Base.one(::Type{T}) where {T <: TropicalMaxMin}
+    return typemax(T)
+end
+
+function Base.one(::T) where {T <: TropicalMaxMin}
+    return one(T)
+end
+
+function Base.typemin(::Type{TropicalMaxMin{T}}) where {T}
+    n = neginf(T)
+    return TropicalMaxMin(n)
+end
+
+function Base.typemax(::Type{TropicalMaxMin{T}}) where {T}
+    n = posinf(T)
+    return TropicalMaxMin(n)
+end