Initial hashing support

src/Decimals.jl

@@ -20,6 +20,8 @@ struct Decimal <: AbstractFloat
     Decimal(s::Integer, c::Integer, e::Integer) = new(Bool(s), c, e)
 end
 
+include("bigint.jl")
+
 # Convert between Decimal objects, numbers, and strings
 include("decimal.jl")
 
@@ -35,4 +37,6 @@ include("equals.jl")
 # Rounding
 include("round.jl")
 
+include("hash.jl")
+
 end

src/bigint.jl

@@ -0,0 +1,55 @@
+@static if VERSION < v"1.10-"
+    const libgmp = :libgmp
+else
+    const libgmp = Base.GMP.libgmp
+end
+
+function isdivisible(x::BigInt, n::Int)
+    r = ccall((:__gmpz_divisible_ui_p, libgmp), Cint,
+              (Base.GMP.MPZ.mpz_t, Culong), x, n)
+    return r != 0
+end
+
+function exactdiv(x::BigInt, n::Int)
+    y = BigInt()
+    ccall((:__gmpz_divexact_ui, libgmp), Cvoid,
+          (Base.GMP.MPZ.mpz_t, Base.GMP.MPZ.mpz_t, Culong), y, x, n)
+    return y
+end
+
+"""
+    maxexp(n)
+
+Return maximum exponent E such that n^E is representable both as Int and
+Culong (i.e., n^(E+1) would overflow).
+"""
+function maxexp(n::Int)
+    maxval = min(typemax(Culong), typemax(Int))
+    return ceil(Int, log(n, maxval)) - 1
+end
+
+"""
+    cancelfactor(x::BigInt, ::Val{N})
+
+Remove all occurrences of the factor `N` from `x`. The result is pair `(y, E)`
+such that `x = y * N^E`.
+"""
+function cancelfactor(x::BigInt, ::Val{N}) where {N}
+    if iszero(x)
+        return x, 0
+    end
+
+    q = 0
+    while isdivisible(x, N)
+        d = N
+        q += 1
+        for e in 2:maxexp(N)
+            isdivisible(x, d * N) || break
+            d *= N
+            q += 1
+        end
+        x = exactdiv(x, d)
+    end
+
+    return x, q
+end

src/decimal.jl

@@ -82,4 +82,3 @@ end
 
 # sign
 Base.signbit(x::Decimal) = x.s
-

src/equals.jl

@@ -15,8 +15,6 @@ function Base.:(==)(x::Decimal, y::Decimal)
     a.c == b.c && a.q == b.q && a.s == b.s
 end
 
-Base.iszero(x::Decimal) = iszero(x.c)
-
 function Base.:(<)(x::Decimal, y::Decimal)
     # return early on zero
     if iszero(x) && iszero(y)

src/hash.jl

@@ -0,0 +1,16 @@
+function Base.decompose(x::Decimal)
+    if iszero(x)
+        return (big(0), 0, big((-1)^x.s))
+    end
+
+    coef = (-1)^x.s * x.c
+
+    if x.q ≥ 0
+        return (coef * big(5)^x.q, x.q, big(1))
+    else
+        coef, exp = cancelfactor(coef, Val(5))
+        q = -x.q - exp
+        return (coef, x.q, big(5) ^ q)
+    end
+end
+

test/runtests.jl

@@ -12,11 +12,13 @@ global d = [
     Decimal(true, 4, -6)
 ]
 
+include("test_arithmetic.jl")
+include("test_bigint.jl")
 include("test_constructor.jl")
 include("test_decimal.jl")
-include("test_norm.jl")
-include("test_arithmetic.jl")
 include("test_equals.jl")
+include("test_hash.jl")
+include("test_norm.jl")
 include("test_round.jl")
 
 end

test/test_bigint.jl

@@ -0,0 +1,35 @@
+@testset "BigInt" begin
+    @testset "isdivisible" begin
+        @test Decimals.isdivisible(big(12), 1)
+        @test Decimals.isdivisible(big(12), 2)
+        @test Decimals.isdivisible(big(12), 3)
+        @test Decimals.isdivisible(big(12), 4)
+        @test Decimals.isdivisible(big(12), 6)
+
+        prime = big(1709)
+        @test Decimals.isdivisible(prime, 1)
+        @test Decimals.isdivisible(prime, Int(prime))
+        @test !any(n -> Decimals.isdivisible(prime, n), 2:1708)
+    end
+
+    @testset "exactdiv" begin
+        @test Decimals.exactdiv(big(12), 2) == big(6)
+        @test Decimals.exactdiv(big(12), 3) == big(4)
+        @test Decimals.exactdiv(big(12), 4) == big(3)
+        @test Decimals.exactdiv(big(12), 6) == big(2)
+    end
+
+    @testset "maxexp" begin
+        for n in [2, 5, 10]
+            E = Decimals.maxexp(n)
+            @test n^E > n^(E + 1) # overflow
+        end
+    end
+
+    @testset "cancelfactor" begin
+        @test Decimals.cancelfactor(big(0), Val(3)) == (big(0), 0)
+        @test Decimals.cancelfactor(big(3)^8, Val(3)) == (big(1), 8)
+        @test Decimals.cancelfactor(big(3)^128, Val(3)) == (big(1), 128)
+        @test Decimals.cancelfactor(big(948659)^8, Val(948659)) == (big(1), 8)
+    end
+end

test/test_hash.jl

@@ -0,0 +1,21 @@
+using Decimals
+using Test
+
+@testset "Hashing" begin
+    @testset "hash" begin
+        @test hash(Decimal(0.)) == hash(0.)
+        @test hash(Decimal(-0.)) == hash(-0.)
+        @test hash(Decimal(3)) == hash(3)
+        @test hash(Decimal(0.09375)) == hash(0.09375)
+        @test hash(Decimal(-3)) == hash(-3)
+        @test hash(Decimal(-0.09375)) == hash(-0.09375)
+
+        # Equality implies same hash
+        @test hash(Decimal(0, 100, 0)) == hash(Decimal(0, 10, 1))
+        @test hash(Decimal(0, 100, 0)) == hash(Decimal(0, 1, 2))
+        @test hash(Decimal(1, 100, 0)) == hash(Decimal(1, 10, 1))
+        @test hash(Decimal(1, 100, 0)) == hash(Decimal(1, 1, 2))
+
+        @test hash(Decimal(0, 310, -2)) == hash(Decimal(0, 31, -1))
+    end
+end