Initial data commit

Task/Modular-arithmetic/Julia/modular-arithmetic.julia

@@ -0,0 +1,28 @@
+struct Modulo{T<:Integer} <: Integer
+    val::T
+    mod::T
+    Modulo(n::T, m::T) where T = new{T}(mod(n, m), m)
+end
+modulo(n::Integer, m::Integer) = Modulo(promote(n, m)...)
+
+Base.show(io::IO, md::Modulo) = print(io, md.val, " (mod $(md.mod))")
+Base.convert(::Type{T}, md::Modulo) where T<:Integer = convert(T, md.val)
+Base.copy(md::Modulo{T}) where T = Modulo{T}(md.val, md.mod)
+
+Base.:+(md::Modulo) = copy(md)
+Base.:-(md::Modulo) = Modulo(md.mod - md.val, md.mod)
+for op in (:+, :-, :*, :÷, :^)
+    @eval function Base.$op(a::Modulo, b::Integer)
+        val = $op(a.val, b)
+        return Modulo(mod(val, a.mod), a.mod)
+    end
+    @eval Base.$op(a::Integer, b::Modulo) = $op(b, a)
+    @eval function Base.$op(a::Modulo, b::Modulo)
+        if a.mod != b.mod throw(InexactError()) end
+        val = $op(a.val, b.val)
+        return Modulo(mod(val, a.mod), a.mod)
+    end
+end
+
+f(x) = x ^ 100 + x + 1
+@show f(modulo(10, 13))