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Added tests for gcd and lcm for other integer datatypes. (#35451)
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@ravibitsgoa
ravibitsgoa authored Apr 19, 2020
1 parent c2f0953 commit dd738f9
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39 changes: 35 additions & 4 deletions base/intfuncs.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -18,6 +18,21 @@ julia> gcd(6,9)
julia> gcd(6,-9)
3
julia> gcd(6,0)
6
julia> gcd(0,0)
0
julia> gcd(1//3,2//3)
1//3
julia> gcd(1//3,-2//3)
1//3
julia> gcd(1//3,2)
1//3
```
"""
function gcd(a::T, b::T) where T<:Integer
Expand All @@ -32,8 +47,8 @@ end
# binary GCD (aka Stein's) algorithm
# about 1.7x (2.1x) faster for random Int64s (Int128s)
function gcd(a::T, b::T) where T<:Union{Int8,UInt8,Int16,UInt16,Int32,UInt32,Int64,UInt64,Int128,UInt128}
a == 0 && return abs(b)
b == 0 && return abs(a)
a == 0 && return checked_abs(b)
b == 0 && return checked_abs(a)
za = trailing_zeros(a)
zb = trailing_zeros(b)
k = min(za, zb)
Expand Down Expand Up @@ -69,12 +84,28 @@ julia> lcm(2,3)
julia> lcm(-2,3)
6
julia> lcm(0,3)
0
julia> lcm(0,0)
0
julia> lcm(1//3,2//3)
2//3
julia> lcm(1//3,-2//3)
2//3
julia> lcm(1//3,2)
2//1
```
"""
function lcm(a::T, b::T) where T<:Integer
# explicit a==0 test is to handle case of lcm(0,0) correctly
if a == 0
return a
# explicit b==0 test is to handle case of lcm(typemin(T),0) correctly
if a == 0 || b == 0
return zero(a)
else
return checked_abs(checked_mul(a, div(b, gcd(b,a))))
end
Expand Down
167 changes: 147 additions & 20 deletions test/intfuncs.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -3,51 +3,158 @@
using Random

@testset "gcd/lcm" begin
# Int32 and Int64 take different code paths -- test both
for T in (Int32, Int64)
# 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(3), T(-15)) === T(3)
@test gcd(T(-3), T(-15)) === T(3)
@test gcd(T(15), T(0)) === T(15)
if T <: Signed
@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(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)
end

@test gcd(typemax(T), T(1)) === T(1)
@test gcd(-typemax(T), T(1)) === T(1)
@test gcd(typemin(T), T(1)) === T(1)
@test_throws OverflowError gcd(typemin(T), typemin(T))
@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 <: Signed
@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)) === typemax(T)
@test gcd(-typemax(T), typemax(T)) === typemax(T)

@test gcd(typemin(T), T(1)) === T(1)
@test gcd(T(1), typemin(T)) === T(1)
@test gcd(typemin(T), typemin(T)+T(1)) === T(1) # gcd(n, n+1) = 1. n and n+1 are always coprime.
@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
# For Unsigned Integer types, -typemax(T) == 1.
@test gcd(-typemax(T), T(1)) === T(1)
@test gcd(T(1), -typemax(T)) === T(1)
@test gcd(-typemax(T), T(0)) === T(1)
@test gcd(T(0), -typemax(T)) === T(1)
@test gcd(-typemax(T), -typemax(T)) === T(1)
@test gcd(-typemax(T), typemax(T)) === T(1)
@test gcd(typemax(T), -typemax(T)) === T(1)

# For Unsigned Integer types, typemin(T) == 0.
@test gcd(typemin(T), T(1)) === T(1)
@test gcd(T(1), typemin(T)) === T(1)
@test gcd(typemin(T), typemin(T)+T(1)) === T(1) # gcd(n, n+1) = 1. n and n+1 are always coprime.
@test gcd(typemin(T), typemin(T)) === T(0)
@test gcd(typemin(T), T(0)) === T(0)
@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(4), T(-6)) === T(12)
@test lcm(T(-4), T(-6)) === T(12)
if T <: Signed
@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)
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(-typemax(T), T(1)) === typemax(T)
@test_throws OverflowError lcm(typemin(T), T(1))
@test_throws OverflowError lcm(typemin(T), typemin(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

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
@test lcm(0x5, 3) == 15
@test gcd(0xf, 20) == 5
end

@testset "gcd/lcm for arrays" begin
for T in (Int32, Int64)
# 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)
@test gcd(T[3,-15]) === T(3)
@test gcd(T[-3,-15]) === T(3)
if T <: Signed
@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[2, 4, 6]) === T(2)
Expand All @@ -59,17 +166,26 @@ end
@test lcm(T[4, 6]) === T(12)
@test lcm(T[3, 0]) === T(0)
@test lcm(T[0, 0]) === T(0)
@test lcm(T[4, -6]) === T(12)
@test lcm(T[-4, -6]) === T(12)
if T <: Signed
@test lcm(T[4, -6]) === T(12)
@test lcm(T[-4, -6]) === T(12)
end

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

@testset "gcdx" begin
@test gcdx(5, 12) == (1, 5, -2)
@test gcdx(5, -12) == (1, 5, 2)
@test gcdx(-25, -4) == (1, -1, 6)
# 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))
end
end

@testset "gcd/lcm/gcdx for custom types" begin
struct MyRational <: Real
val::Rational{Int}
Expand All @@ -81,6 +197,7 @@ end
@test lcm(MyRational(2//3), 3) == lcm(2//3, 3) == lcm(Real[MyRational(2//3), 3])
@test gcdx(MyRational(2//3), 3) == gcdx(2//3, 3)
end

@testset "invmod" begin
@test invmod(6, 31) === 26
@test invmod(-1, 3) === 2
Expand All @@ -90,6 +207,7 @@ end
@test invmod(2, 0x3) === 2
@test_throws DomainError invmod(0, 3)
end

@testset "powermod" begin
@test powermod(2, 3, 5) == 3
@test powermod(2, 3, -5) == -2
Expand All @@ -102,6 +220,7 @@ end
@test powermod(2, -1, -5) == -2
@test powermod(2, -2, -5) == -1
end

@testset "nextpow/prevpow" begin
@test nextpow(2, 3) == 4
@test nextpow(2, 4) == 4
Expand All @@ -115,6 +234,7 @@ end
@test_throws DomainError prevpow(0, 3)
@test_throws DomainError prevpow(0, 3)
end

@testset "ndigits/ndigits0z" begin
@testset "issue #8266" begin
@test ndigits(-15, base=10) == 2
Expand Down Expand Up @@ -171,6 +291,7 @@ end
end

end

@testset "bin/oct/dec/hex/bits" begin
@test string(UInt32('3'), base = 2) == "110011"
@test string(UInt32('3'), pad = 7, base = 2) == "0110011"
Expand Down Expand Up @@ -202,6 +323,7 @@ end
"0000000000000000000000000000000000000000000000000000010000001011")
@test bitstring(Int128(3)) == "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011"
end

@testset "digits/base" begin
@test digits(5, base = 3) == [2, 1]
@test digits(5, pad = 3) == [5, 0, 0]
Expand Down Expand Up @@ -261,6 +383,7 @@ end
"44642116066", "19000000000", "1xIpcEe"]
end
end

@testset "leading_ones and count_zeros" begin
@test leading_ones(UInt32(Int64(2) ^ 32 - 2)) == 31
@test leading_ones(1) == 0
Expand All @@ -269,18 +392,21 @@ end

@test count_zeros(Int64(1)) == 63
end

@testset "factorial" begin
@test factorial(3) == 6
@test factorial(Int8(3)) === 6
@test_throws DomainError factorial(-3)
@test_throws DomainError factorial(Int8(-3))
end

@testset "isqrt" begin
@test isqrt(4) == 2
@test isqrt(5) == 2
@test isqrt(Int8(4)) === Int8(2)
@test isqrt(Int8(5)) === Int8(2)
end

@testset "issue #4884" begin
@test isqrt(9223372030926249000) == 3037000498
@test isqrt(typemax(Int128)) == parse(Int128,"13043817825332782212")
Expand All @@ -297,6 +423,7 @@ end
@test (s+1)*(s+1) > n
end
end

# issue #9786
let ptr = Ptr{Cvoid}(typemax(UInt))
for T in (Int, Cssize_t)
Expand Down

4 comments on commit dd738f9

@nanosoldier
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Executing the daily package evaluation, I will reply here when finished:

@nanosoldier runtests(ALL, isdaily = true)

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Executing the daily benchmark build, I will reply here when finished:

@nanosoldier runbenchmarks(ALL, isdaily = true)

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Your package evaluation job has completed - possible new issues were detected. A full report can be found here. cc @maleadt

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Your benchmark job has completed - possible performance regressions were detected. A full report can be found here. cc @ararslan

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