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Conform tests to gcdx(0, 0) = (0, 0, 0)
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Also test gcd, gcdx and lcm for BigInt, and add some additional
canonical tests for gcdx.
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@albinahlback
albinahlback committed Apr 25, 2024
1 parent 9b1609f commit ad6d8d6
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244 changes: 126 additions & 118 deletions test/intfuncs.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,40 +4,44 @@ using Random

is_effect_free(args...) = Core.Compiler.is_effect_free(Base.infer_effects(args...))

⟷(a::T, b::T) where T <: {Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b
⟷(a::T, b::T) where T <: {BigInt} = a == b

@testset "gcd/lcm" begin
# All Integer data types take different code paths -- test all
# TODO: Test gcd and lcm for BigInt.
for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128)
@test gcd(T(3)) === T(3)
@test gcd(T(3), T(5)) === T(1)
@test gcd(T(3), T(15)) === T(3)
@test gcd(T(0), T(15)) === T(15)
@test gcd(T(15), T(0)) === T(15)
for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128, BigInt)
@test gcd(T(3)) ⟷ T(3)
@test gcd(T(3), T(5)) ⟷ T(1)
@test gcd(T(3), T(15)) ⟷ T(3)
@test gcd(T(0), T(15)) ⟷ T(15)
@test gcd(T(15), T(0)) ⟷ T(15)
if T <: Signed
@test gcd(T(-12)) === T(12)
@test gcd(T(0), T(-15)) === T(15)
@test gcd(T(-15), T(0)) === T(15)
@test gcd(T(3), T(-15)) === T(3)
@test gcd(T(-3), T(-15)) === T(3)
@test gcd(T(-12)) ⟷ T(12)
@test gcd(T(0), T(-15)) ⟷ T(15)
@test gcd(T(-15), T(0)) ⟷ T(15)
@test gcd(T(3), T(-15)) ⟷ T(3)
@test gcd(T(-3), T(-15)) ⟷ T(3)
end
@test gcd(T(0), T(0)) === T(0)
@test gcd(T(0), T(0)) ⟷ T(0)

@test gcd(T(2), T(4), T(6)) === T(2)
@test gcd(T(2), T(4), T(6)) ⟷ T(2)
if T <: Signed
@test gcd(T(2), T(4), T(-6)) === T(2)
@test gcd(T(2), T(-4), T(-6)) === T(2)
@test gcd(T(-2), T(4), T(-6)) === T(2)
@test gcd(T(-2), T(-4), T(-6)) === T(2)
@test gcd(T(2), T(4), T(-6)) ⟷ T(2)
@test gcd(T(2), T(-4), T(-6)) ⟷ T(2)
@test gcd(T(-2), T(4), T(-6)) ⟷ T(2)
@test gcd(T(-2), T(-4), T(-6)) ⟷ T(2)
end

@test gcd(typemax(T), T(1)) === T(1)
@test gcd(T(1), typemax(T)) === T(1)
@test gcd(typemax(T), T(0)) === typemax(T)
@test gcd(T(0), typemax(T)) === typemax(T)
@test gcd(typemax(T), typemax(T)) === typemax(T)
@test gcd(typemax(T), typemax(T)-T(1)) === T(1) # gcd(n, n-1) = 1. n and n-1 are always coprime.
if T != BigInt
@test gcd(typemax(T), T(1)) === T(1)
@test gcd(T(1), typemax(T)) === T(1)
@test gcd(typemax(T), T(0)) === typemax(T)
@test gcd(T(0), typemax(T)) === typemax(T)
@test gcd(typemax(T), typemax(T)) === typemax(T)
@test gcd(typemax(T), typemax(T)-T(1)) === T(1) # gcd(n, n-1) = 1. n and n-1 are always coprime.
end

if T <: Signed
if T <: Signed && T != BigInt
@test gcd(-typemax(T), T(1)) === T(1)
@test gcd(T(1), -typemax(T)) === T(1)
@test gcd(-typemax(T), T(0)) === typemax(T)
Expand All @@ -52,7 +56,7 @@ is_effect_free(args...) = Core.Compiler.is_effect_free(Base.infer_effects(args..
@test_throws OverflowError gcd(typemin(T), typemin(T))
@test_throws OverflowError gcd(typemin(T), T(0))
@test_throws OverflowError gcd(T(0), typemin(T))
else
elseif T != BigInt
# For Unsigned Integer types, -typemax(T) == 1.
@test gcd(-typemax(T), T(1)) === T(1)
@test gcd(T(1), -typemax(T)) === T(1)
Expand All @@ -71,83 +75,86 @@ is_effect_free(args...) = Core.Compiler.is_effect_free(Base.infer_effects(args..
@test gcd(T(0), typemin(T)) === T(0)
end

@test lcm(T(0)) === T(0)
@test lcm(T(2)) === T(2)
@test lcm(T(2), T(3)) === T(6)
@test lcm(T(3), T(2)) === T(6)
@test lcm(T(4), T(6)) === T(12)
@test lcm(T(6), T(4)) === T(12)
@test lcm(T(3), T(0)) === T(0)
@test lcm(T(0), T(3)) === T(0)
@test lcm(T(0), T(0)) === T(0)
@test lcm(T(0)) ⟷ T(0)
@test lcm(T(2)) ⟷ T(2)
@test lcm(T(2), T(3)) ⟷ T(6)
@test lcm(T(3), T(2)) ⟷ T(6)
@test lcm(T(4), T(6)) ⟷ T(12)
@test lcm(T(6), T(4)) ⟷ T(12)
@test lcm(T(3), T(0)) ⟷ T(0)
@test lcm(T(0), T(3)) ⟷ T(0)
@test lcm(T(0), T(0)) ⟷ T(0)
if T <: Signed
@test lcm(T(-12)) === T(12)
@test lcm(T(0), T(-4)) === T(0)
@test lcm(T(-4), T(0)) === T(0)
@test lcm(T(4), T(-6)) === T(12)
@test lcm(T(-4), T(-6)) === T(12)
@test lcm(T(-12)) ⟷ T(12)
@test lcm(T(0), T(-4)) ⟷ T(0)
@test lcm(T(-4), T(0)) ⟷ T(0)
@test lcm(T(4), T(-6)) ⟷ T(12)
@test lcm(T(-4), T(-6)) ⟷ T(12)
end

@test lcm(T(2), T(4), T(6)) === T(12)
@test lcm(T(2), T(4), T(0)) === T(0)
@test lcm(T(2), T(4), T(6)) ⟷ T(12)
@test lcm(T(2), T(4), T(0)) ⟷ T(0)
if T <: Signed
@test lcm(T(2), T(4), T(-6)) === T(12)
@test lcm(T(2), T(-4), T(-6)) === T(12)
@test lcm(T(-2), T(-4), T(-6)) === T(12)
@test lcm(T(-2), T(0), T(-6)) === T(0)
end

@test lcm(typemax(T), T(1)) === typemax(T)
@test lcm(T(1), typemax(T)) === typemax(T)
@test lcm(typemax(T), T(0)) === T(0)
@test lcm(T(0), typemax(T)) === T(0)
@test lcm(typemax(T), typemax(T)) === typemax(T)
@test_throws OverflowError lcm(typemax(T), typemax(T)-T(1)) # lcm(n, n-1) = n*(n-1). Since n and n-1 are always coprime.
@test_throws OverflowError lcm(typemax(T), T(2))

let x = isqrt(typemax(T))+T(1) # smallest number x such that x^2 > typemax(T)
@test lcm(x, x) === x
@test_throws OverflowError lcm(x, x+T(1)) # lcm(n, n+1) = n*(n+1). Since n and n+1 are always coprime.
@test lcm(T(2), T(4), T(-6)) ⟷ T(12)
@test lcm(T(2), T(-4), T(-6)) ⟷ T(12)
@test lcm(T(-2), T(-4), T(-6)) ⟷ T(12)
@test lcm(T(-2), T(0), T(-6)) ⟷ T(0)
end

if T <: Signed
@test lcm(-typemax(T), T(1)) === typemax(T)
@test lcm(T(1), -typemax(T)) === typemax(T)
@test lcm(-typemax(T), T(0)) === T(0)
@test lcm(T(0), -typemax(T)) === T(0)
@test lcm(-typemax(T), -typemax(T)) === typemax(T)
@test lcm(typemax(T), -typemax(T)) === typemax(T)
@test lcm(-typemax(T), typemax(T)) === typemax(T)

@test_throws OverflowError lcm(typemin(T), T(1))
@test_throws OverflowError lcm(T(1), typemin(T))
@test lcm(typemin(T), T(0)) === T(0)
@test lcm(T(0), typemin(T)) === T(0)
@test_throws OverflowError lcm(typemin(T), typemin(T)+T(1)) # lcm(n, n+1) = n*(n+1).
@test_throws OverflowError lcm(typemin(T), typemin(T))
else
# For Unsigned Integer types, -typemax(T) == 1.
@test lcm(-typemax(T), T(1)) === T(1)
@test lcm(T(1), -typemax(T)) === T(1)
@test lcm(-typemax(T), T(0)) === T(0)
@test lcm(T(0), -typemax(T)) === T(0)
@test lcm(-typemax(T), -typemax(T)) === T(1)
@test lcm(-typemax(T), typemax(T)) === typemax(T)
@test lcm(typemax(T), -typemax(T)) === typemax(T)
if T != BigInt
@test lcm(typemax(T), T(1)) === typemax(T)
@test lcm(T(1), typemax(T)) === typemax(T)
@test lcm(typemax(T), T(0)) === T(0)
@test lcm(T(0), typemax(T)) === T(0)
@test lcm(typemax(T), typemax(T)) === typemax(T)
@test_throws OverflowError lcm(typemax(T), typemax(T)-T(1)) # lcm(n, n-1) = n*(n-1). Since n and n-1 are always coprime.
@test_throws OverflowError lcm(typemax(T), T(2))

let x = isqrt(typemax(T))+T(1) # smallest number x such that x^2 > typemax(T)
@test lcm(x, x) === x
@test_throws OverflowError lcm(x, x+T(1)) # lcm(n, n+1) = n*(n+1). Since n and n+1 are always coprime.
end

# For Unsigned Integer types, typemin(T) == 0.
@test lcm(typemin(T), T(1)) === lcm(T(0), T(1)) === T(0)
@test lcm(T(1), typemin(T)) === T(0)
@test lcm(typemin(T), T(0)) === T(0)
@test lcm(T(0), typemin(T)) === T(0)
@test lcm(typemin(T), typemin(T)) === T(0)
@test lcm(typemin(T), typemin(T)+T(1)) === T(0)
if T <: Signed
@test lcm(-typemax(T), T(1)) === typemax(T)
@test lcm(T(1), -typemax(T)) === typemax(T)
@test lcm(-typemax(T), T(0)) === T(0)
@test lcm(T(0), -typemax(T)) === T(0)
@test lcm(-typemax(T), -typemax(T)) === typemax(T)
@test lcm(typemax(T), -typemax(T)) === typemax(T)
@test lcm(-typemax(T), typemax(T)) === typemax(T)

@test_throws OverflowError lcm(typemin(T), T(1))
@test_throws OverflowError lcm(T(1), typemin(T))
@test lcm(typemin(T), T(0)) === T(0)
@test lcm(T(0), typemin(T)) === T(0)
@test_throws OverflowError lcm(typemin(T), typemin(T)+T(1)) # lcm(n, n+1) = n*(n+1).
@test_throws OverflowError lcm(typemin(T), typemin(T))
else
# For Unsigned Integer types, -typemax(T) == 1.
@test lcm(-typemax(T), T(1)) === T(1)
@test lcm(T(1), -typemax(T)) === T(1)
@test lcm(-typemax(T), T(0)) === T(0)
@test lcm(T(0), -typemax(T)) === T(0)
@test lcm(-typemax(T), -typemax(T)) === T(1)
@test lcm(-typemax(T), typemax(T)) === typemax(T)
@test lcm(typemax(T), -typemax(T)) === typemax(T)

# For Unsigned Integer types, typemin(T) == 0.
@test lcm(typemin(T), T(1)) === lcm(T(0), T(1)) === T(0)
@test lcm(T(1), typemin(T)) === T(0)
@test lcm(typemin(T), T(0)) === T(0)
@test lcm(T(0), typemin(T)) === T(0)
@test lcm(typemin(T), typemin(T)) === T(0)
@test lcm(typemin(T), typemin(T)+T(1)) === T(0)
end
end
end
@test lcm(0x5, 3) == 15
@test gcd(0xf, 20) == 5
@test gcd(UInt32(6), Int8(-50)) == 2
@test gcd(typemax(UInt), -16) == 1
@test gcd(typemax(UInt), BigInt(1236189723689716298376189726398761298361892)) == 1

@testset "effects" begin
@test is_effect_free(gcd, Tuple{Int,Int})
Expand All @@ -156,45 +163,46 @@ is_effect_free(args...) = Core.Compiler.is_effect_free(Base.infer_effects(args..
end

@testset "gcd/lcm for arrays" begin
# TODO: Test gcd and lcm for BigInt arrays.
for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128)
@test gcd(T[]) === T(0)
@test gcd(T[3, 5]) === T(1)
@test gcd(T[3, 15]) === T(3)
@test gcd(T[0, 15]) === T(15)
for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128, BigInt)
@test gcd(T[]) ⟷ T(0)
@test gcd(T[3, 5]) ⟷ T(1)
@test gcd(T[3, 15]) ⟷ T(3)
@test gcd(T[0, 15]) ⟷ T(15)
if T <: Signed
@test gcd(T[-12]) === T(12)
@test gcd(T[3,-15]) === T(3)
@test gcd(T[-3,-15]) === T(3)
@test gcd(T[-12]) ⟷ T(12)
@test gcd(T[3,-15]) ⟷ T(3)
@test gcd(T[-3,-15]) ⟷ T(3)
end
@test gcd(T[0, 0]) === T(0)
@test gcd(T[0, 0]) ⟷ T(0)

@test gcd(T[2, 4, 6]) === T(2)
@test gcd(T[2, 4, 3, 5]) === T(1)
@test gcd(T[2, 4, 6]) ⟷ T(2)
@test gcd(T[2, 4, 3, 5]) ⟷ T(1)

@test lcm(T[]) === T(1)
@test lcm(T[2, 3]) === T(6)
@test lcm(T[4, 6]) === T(12)
@test lcm(T[3, 0]) === T(0)
@test lcm(T[0, 0]) === T(0)
@test lcm(T[]) ⟷ T(1)
@test lcm(T[2, 3]) ⟷ T(6)
@test lcm(T[4, 6]) ⟷ T(12)
@test lcm(T[3, 0]) ⟷ T(0)
@test lcm(T[0, 0]) ⟷ T(0)
if T <: Signed
@test lcm(T[-2]) === T(2)
@test lcm(T[4, -6]) === T(12)
@test lcm(T[-4, -6]) === T(12)
@test lcm(T[-2]) ⟷ T(2)
@test lcm(T[4, -6]) ⟷ T(12)
@test lcm(T[-4, -6]) ⟷ T(12)
end

@test lcm(T[2, 4, 6]) === T(12)
@test lcm(T[2, 4, 6]) ⟷ T(12)
end
end

@testset "gcdx" begin
# TODO: Test gcdx for BigInt.
for T in (Int8, Int16, Int32, Int64, Int128)
@test gcdx(T(5), T(12)) === (T(1), T(5), T(-2))
@test gcdx(T(5), T(-12)) === (T(1), T(5), T(2))
@test gcdx(T(-5), T(12)) === (T(1), T(-5), T(-2))
@test gcdx(T(-5), T(-12)) === (T(1), T(-5), T(2))
@test gcdx(T(-25), T(-4)) === (T(1), T(-1), T(6))
for T in (Int8, Int16, Int32, Int64, Int128, BigInt)
@test gcdx(T(5), T(12)) ⟷ (T(1), T(5), T(-2))
@test gcdx(T(5), T(-12)) ⟷ (T(1), T(5), T(2))
@test gcdx(T(-5), T(12)) ⟷ (T(1), T(-5), T(-2))
@test gcdx(T(-5), T(-12)) ⟷ (T(1), T(-5), T(2))
@test gcdx(T(-25), T(-4)) ⟷ (T(1), T(-1), T(6))
@test gcdx(T(0), T(0)) ⟷ (T(0), T(0), T(0))
@test gcdx(T(8), T(0)) ⟷ (T(8), T(1), T(0))
@test gcdx(T(0), T(-8)) ⟷ (T(8), T(0), T(-1))
end
x, y = Int8(-12), UInt(100)
d, u, v = gcdx(x, y)
Expand Down
2 changes: 1 addition & 1 deletion test/rational.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -655,7 +655,7 @@ end
@test gcdx(T(1)//T(1), T(1)//T(0)) === (T(1)//T(0), T(0), T(1))
@test gcdx(T(1)//T(0), T(1)//T(0)) === (T(1)//T(0), T(1), T(1))
@test gcdx(T(1)//T(0), T(0)//T(1)) === (T(1)//T(0), T(1), T(0))
@test gcdx(T(0)//T(1), T(0)//T(1)) === (T(0)//T(1), T(1), T(0))
@test gcdx(T(0)//T(1), T(0)//T(1)) === (T(0)//T(1), T(0), T(0))

if T <: Signed
@test gcdx(T(-1)//T(0), T(1)//T(2)) === (T(1)//T(0), T(1), T(0))
Expand Down

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