Fix conversion from floats

Numbers such as `0.3` or `1.1` cannot be represented exactly using `Float32` or `Float64`. We can all digits by converting them to `BigFloat`: ```julia julia> big(0.3) 0.299999999999999988897769753748434595763683319091796875 julia> big(1.1) 1.100000000000000088817841970012523233890533447265625 ``` This PR updates the `Decimal` constructors so that floating point numbers are converted to `Decimal`s exactly in the sense that ```julia julia> hash(1.1) == hash(Decimal(1.1)) true ``` Fixes #85
JuliaMath · Nov 6, 2024 · 87e206d · 87e206d
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diff --git a/src/arithmetic.jl b/src/arithmetic.jl
@@ -212,10 +212,6 @@ function Base.:(/)(x::Decimal, y::Decimal)
     return fix(Decimal(s, c, q))
 end
 
-function Base.inv(x::Decimal)
-    return Decimal(false, BigOne, 0) / x
-end
-
 Base.abs(x::Decimal) = fix(Decimal(false, x.c, x.q))
 
 # TODO exponentiation
diff --git a/src/decimal.jl b/src/decimal.jl
@@ -1,16 +1,42 @@
 Decimal(x::Decimal) = x
+Decimal(n::Integer) = Decimal(signbit(n), abs(n), 0)
+function Decimal(x::AbstractFloat)
+    if !isfinite(x)
+        throw(ArgumentError("$x cannot be represented as a Decimal"))
+    end
+
+    # Express `x` as a rational `u = n / 2^k`, where `k ≥ 0`
+    u = Rational(abs(x))
+
+    # u.den = 2^k
+    k = ndigits(u.den, base=2) - 1
+
+    # We can write
+    #
+    #   x = n / 2^k
+    #     = n / 2^k * 10^k * 10^-k
+    #     = (n * 10^k / 2^k) * 10^-k
+    #     = (n * 5^k) * 10^-k
+
+    s = signbit(x)
+    c = u.num * BigInt(5)^k
+    q = -k
+    return Decimal(s, c, q)
+end
 
-# From real numbers to Decimal
-Decimal(x::Real) = parse(Decimal, string(x))
 Base.convert(::Type{Decimal}, x::Real) = Decimal(x)
 
-function BigInt(x::Decimal)
-    coef = BigInt(x.c * BigTen ^ x.q)
-    return x.s ? -coef : coef
+function Base.BigFloat(x::Decimal)
+    y = BigFloat(x.c)
+    if x.q ≥ 0
+        y *= BigTen^x.q
+    else
+        y /= BigTen^(-x.q)
+    end
+    return x.s ? -y : y
 end
 
-# From Decimal to numbers
-(::Type{T})(x::Decimal) where {T<:Number} = parse(T, string(x))
+(::Type{T})(x::Decimal) where {T<:Number} = T(BigFloat(x))
 
 # String representation of Decimal
 function Base.string(x::Decimal)
@@ -19,15 +45,11 @@ function Base.string(x::Decimal)
     return String(take!(io))
 end
 
-# Zero/one value
+Base.signbit(x::Decimal) = x.s
+
 Base.zero(::Type{Decimal}) = Decimal(false, 0, 0)
 Base.one(::Type{Decimal}) = Decimal(false, 1, 0)
 
 Base.iszero(x::Decimal) = iszero(x.c)
-
-# As long as we do not support Inf/NaN
 Base.isfinite(x::Decimal) = true
 Base.isnan(x::Decimal) = false
-
-# sign
-Base.signbit(x::Decimal) = x.s
diff --git a/test/test_arithmetic.jl b/test/test_arithmetic.jl
@@ -4,41 +4,6 @@ using Test
 
 @testset "Arithmetic" begin
 
-@testset "Addition" begin
-    @test Decimal(0.1) + 0.2 == 0.1 + Decimal(0.2) == Decimal(0.1) + Decimal(0.2) == Decimal(0.3)
-    @test Decimal.([0.1 0.2]) .+ [0.3 0.1] == Decimal.([0.4 0.3])
-    @test Decimal(2147483646) + Decimal(1) == Decimal(2147483647)
-    @test Decimal(1,3,-2) + parse(Decimal, "0.2523410412138103") == Decimal(false,2223410412138103,-16)
-    @test Decimal(0, 10000000000000000001, -19) + Decimal(0, 1, 0) == Decimal(0, 20000000000000000001, -19)
-end
-
-@testset "Subtraction" begin
-    @test Decimal(0.3) - 0.1 == 0.3 - Decimal(0.1)
-    @test 0.3 - Decimal(0.1) == Decimal(0.3) - Decimal(0.1)
-    @test Decimal(0.3) - Decimal(0.1) == Decimal(0.2)
-    @test Decimal.([0.3 0.1]) .- [0.1 0.5] == Decimal.([0.2 -0.4])
-end
-
-@testset "Negation" begin
-    @test -Decimal.([0.3 0.2]) == [-Decimal(0.3) -Decimal(0.2)]
-    @test -Decimal(0.3) == zero(Decimal) - Decimal(0.3)
-    @test iszero(Decimal(12.1) - Decimal(12.1))
-end
-
-@testset "Multiplication" begin
-    @test Decimal(12.21) * Decimal(2.12) == Decimal(0,258852,-4)
-    @test Decimal(12.2112543) * Decimal(2.121352) == Decimal(0,259043687318136,-13)
-    @test Decimal(0.2) * 0.1 == 0.2 * Decimal(0.1)
-    @test 0.2 * Decimal(0.1) == Decimal(0.02)
-    @test Decimal(12.34) * 0.1234 == 12.34 * Decimal(0.1234)
-    @test 12.34 * Decimal(0.1234) == Decimal(1.522756)
-    @test Decimal(0.21084210) * -2 == -2 * Decimal(0.21084210)
-    @test -2 * Decimal(0.21084210) == Decimal(-0.4216842)
-    @test Decimal(0, 2, -1) * 0.0 == zero(Decimal)
-    @test Decimal.([0.3, 0.6]) .* 5 == [Decimal(0.3)*5, Decimal(0.6)*5]
-    @test one(Decimal) * 1 == Decimal(0, 1, 0)
-end
-
 @testset "Inversion" begin
     @with_context (Emax=384, Emin=-383, precision=9, rounding=RoundNearestTiesAway) @test inv(dec"1") == dec"1"
     @with_context (Emax=384, Emin=-383, precision=9, rounding=RoundNearestTiesAway) @test inv(dec"2") == dec"0.5"
@@ -108,11 +73,4 @@ end
     @with_context (Emax=999, Emin=-999, precision=9, rounding=RoundNearestTiesAway) @test inv(dec"2") == dec"0.5"
 end
 
-@testset "Division" begin
-    @test Decimal(0.2) / Decimal(0.1) == Decimal(2)
-    @test Decimal(0.3) / Decimal(0.1) == Decimal(0,3,0)
-    @test [Decimal(0.3) / Decimal(0.1), Decimal(0.6) / Decimal(0.1)] == [Decimal(0.3), Decimal(0.6)] ./ Decimal(0.1)
-    @test [Decimal(0.3) / 0.1, Decimal(0.6) / 0.1] == [Decimal(0.3), Decimal(0.6)] ./ 0.1
-end
-
 end
diff --git a/test/test_decimal.jl b/test/test_decimal.jl
@@ -2,33 +2,18 @@ using Decimals
 using Test
 
 @testset "Conversions" begin
-
-@testset "String/Number to Decimal" begin
-    @testset "Direct" begin
-        @test Decimal(0.01) == Decimal(false, 1, -2)
-        @test Decimal(.001) == Decimal(false, 1, -3)
-        @test Decimal(15.23) == Decimal(false, 1523, -2)
-        @test Decimal(543) == Decimal(false, 543, 0)
-        @test Decimal(-345) == Decimal(true, 345, 0)
-        @test Decimal(000123) == Decimal(false, 123, 0)
-        @test Decimal(-00032) == Decimal(true, 32, 0)
-        @test Decimal(200100) == Decimal(false, 2001, 2)
-        @test Decimal(-.123) == Decimal(true, 123, -3)
-        @test Decimal(1.23000) == Decimal(false, 123, -2)
-        @test Decimal(4734.612) == Decimal(false, 4734612, -3)
-        @test Decimal(541724.2) == Decimal(false,5417242,-1)
-        @test Decimal(2.5e6) == Decimal(false, 25, 5)
-        @test Decimal(2.385350e8) == Decimal(false, 238535, 3)
-        @test Decimal(12.3e-4) == Decimal(false, 123, -5)
-        @test Decimal(-12.3e4) == Decimal(true, 123, 3)
-        @test Decimal(-12.3e-4) == Decimal(true, 123, -5)
-        @test Decimal(0.1234567891) == Decimal(false,1234567891, -10)
-        @test Decimal(0.12345678912) == Decimal(false,12345678912, -11)
+    @testset "$T" for T in [Float32, Float64, BigFloat]
+        @test T(Decimal(T(0.0))) == T(0.0)
+        @test T(Decimal(T(-0.0))) == T(-0.0)
+        @test T(Decimal(T(1.1))) == T(1.1)
+        @test T(Decimal(T(-1.1))) == T(-1.1)
     end
-end
 
-@testset "Array{<:Number} to Array{Decimal}" begin
-    @test Decimal.([0.1 0.2 0.3]) == [Decimal(0.1) Decimal(0.2) Decimal(0.3)]
+    @testset "$T" for T in [Int32, Int64, BigInt]
+        @test T(Decimal(T(0))) == T(0)
+        @test T(Decimal(T(1))) == T(1)
+        @test T(Decimal(T(-1))) == T(-1)
+    end
 end
 
 @testset "Decimal to String" begin
@@ -44,22 +29,18 @@ end
     @test string(Decimal(false, 123, -2)) == "1.23"
 end
 
-@testset "Decimal to Number" begin
-    @test Float32(Decimal(false, 1, -2)) == 0.01f0
-    @test Float64(Decimal(false, 1, -3)) == 0.001
-    @test Float64(Decimal(false, 1523, -2)) == 15.23
-    @test UInt(Decimal(false, 543, 0)) == 543
-    @test Int(Decimal(true, 345, 0)) == -345
-    @test Int32(Decimal(false, 123, 0)) == 123
-    @test Int8(Decimal(true, 32, 0)) == -32
-    @test BigInt(Decimal(false, 2001, 2)) == 200100
-    @test BigFloat(Decimal(true, 123, -3)) == big"-0.123"
-    @test Float64(Decimal(false, 123, -2)) == 1.23
-end
-
 @testset "Number functions" begin
+    @test signbit(Decimal(0, 0, 1)) == false
+    @test signbit(Decimal(1, 0, 1)) == true
+
+    @test iszero(zero(Decimal))
+    @test iszero(Decimal(0, 0, 1))
+    @test !iszero(Decimal(0, 1, 1))
+
+    @test isone(one(Decimal))
+    @test isone(Decimal(0, 1, 0))
+    @test !isone(Decimal(0, 0, 1))
+
     @test isfinite(Decimal(0, 1, 1))
     @test !isnan(Decimal(0, 1, 1))
 end
-
-end
diff --git a/test/test_equals.jl b/test/test_equals.jl
@@ -6,7 +6,6 @@ using Test
 @testset "isequal" begin
     @test isequal(Decimal(false, 2, -3), Decimal(false, 2, -3))
     @test !isequal(Decimal(false, 2, -3), Decimal(false, 2, 3))
-    @test isequal(Decimal(false, 2, -3), 0.002)
     @test isequal(Decimal(true, 2, 0), -2)
     @test !isequal(Decimal(true, 2, 0), 2)
     @test !isequal(Decimal(true, 0, -1), Decimal(false, 0, 0))
@@ -15,7 +14,6 @@ end
 @testset "==" begin
     @test Decimal(false, 2, -3) == Decimal(false, 2, -3)
     @test Decimal(false, 2, -3) != Decimal(false, 2, 3)
-    @test Decimal(false, 2, -3) == 0.002
 
     @test -2 == Decimal(true, 2, 0)
     @test 2 != Decimal(true, 2, 0)

diff --git a/test/test_hash.jl b/test/test_hash.jl
@@ -9,6 +9,7 @@ using Test
         @test hash(Decimal(0.09375)) == hash(0.09375)
         @test hash(Decimal(-3)) == hash(-3)
         @test hash(Decimal(-0.09375)) == hash(-0.09375)
+        @test hash(Decimal(1.1)) == hash(1.1)
 
         # Equality implies same hash
         @test hash(Decimal(0, 100, 0)) == hash(Decimal(0, 10, 1))

diff --git a/test/test_round.jl b/test/test_round.jl
@@ -3,14 +3,11 @@ using Test
 
 @testset "Rounding" begin
 
-@test round(Decimal(7.123456), digits=0) == Decimal(7)
-@test round(Decimal(7.123456), digits=2) == Decimal(7.12)
-@test round(Decimal(7.123456), digits=3) == Decimal(7.123)
-@test round(Decimal(7.123456), digits=5) == Decimal(7.12346)
-@test round(Decimal(7.123456), digits=6) == Decimal(7.123456)
-
-@test round.(Decimal.([0.1111, 0.2222, 0.8888]), digits=2) == Decimal.([0.11, 0.22, 0.89])
-
-@test trunc(Decimal(7.123456), digits=5) == Decimal(7.12345)
+@test round(Decimal(7.123456), digits=0) == dec"7"
+@test round(Decimal(7.123456), digits=2) == dec"7.12"
+@test round(Decimal(7.123456), digits=3) == dec"7.123"
+@test round(Decimal(7.123456), digits=5) == dec"7.12346"
+@test round(Decimal(7.123456), digits=6) == dec"7.123456"
+@test trunc(Decimal(7.123456), digits=5) == dec"7.12345"
 
 end