test/gmp.jl - master - githubmirror/julia

test/gmp.jl
839 строк27 KB
Lilith Orion Hafner
New `prod(::AbstractArray{BigInt})` implementation (#59456)
20 сен 2025, 20:37
20 сен 2025, 20:37191be7c
# This file is a part of Julia. License is MIT: https://julialang.org/license

using Random, Serialization

a = parse(BigInt,"123456789012345678901234567890")
b = parse(BigInt,"123456789012345678901234567891")
c = parse(BigInt,"246913578024691357802469135780")
d = parse(BigInt,"-246913578024691357802469135780")
ee = typemax(Int64)
@testset "basics" begin
    @test BigInt <: Signed
    @test big(1) isa Signed

    if sizeof(Culong) >= 8
        @test_throws OutOfMemoryError big(96608869069402268615522366320733234710)^16374500563449903721
        @test_throws OutOfMemoryError 555555555555555555555555555555555555555555555555555^55555555555555555
    end

    let x = big(1)
        @test signed(x) === x
        @test convert(Signed, x) === x
        @test Signed(x) === x
        @test_throws MethodError convert(Unsigned, x) # could change in the future
    end
    @test a+BigInt(1) == b
    @test typeof(a+1) == BigInt
    @test a+1 == b
    @test isequal(a+1, b)
    @test b == a+1
    @test !(b == a)
    @test b > a
    @test b >= a
    @test !(b < a)
    @test !(b <= a)

    @test typeof(a * 2) == BigInt
    @test a*2 == c
    @test c-a == a
    @test c == a + a
    @test c+1 == a+b


    @test typeof(d) == BigInt
    @test d == -c

    @test typeof(BigInt(ee)) == BigInt
    @test BigInt(ee)+1 == parse(BigInt,"9223372036854775808")
    @testset "printing" begin
        #Multiple calls for sanity check, since we're doing direct memory manipulation
        @test string(a) == "123456789012345678901234567890"
        @test string(b) == "123456789012345678901234567891"
        @test string(c) == "246913578024691357802469135780"
        @test string(d) == "-246913578024691357802469135780"
        @test string(a) == "123456789012345678901234567890"
    end
    @testset "constructors" begin
        @test typeof(BigInt(typemax(Int8))) == BigInt
        @test typeof(BigInt(typemax(Int16))) == BigInt
        @test typeof(BigInt(typemax(Int32))) == BigInt
        @test typeof(BigInt(typemax(Int64))) == BigInt
        @test typeof(BigInt(typemax(Int128))) == BigInt

        @test typeof(BigInt(true)) == BigInt
        @test typeof(BigInt(typemax(UInt8))) == BigInt
        @test typeof(BigInt(typemax(UInt16))) == BigInt
        @test typeof(BigInt(typemax(UInt32))) == BigInt
        @test typeof(BigInt(typemax(UInt64))) == BigInt
        @test typeof(BigInt(typemax(UInt128))) == BigInt

        @test typeof(BigInt(BigInt(1))) == BigInt

        for x in (Int16(0), 1, 3//4, big(5//6), big(9))
            @test big(typeof(x)) == typeof(big(x))
            @test big(typeof(complex(x, x))) == typeof(big(complex(x, x)))
        end
    end
    @testset "division" begin
        oz = big(1 // 0)
        zo = big(0 // 1)

        @test_throws DivideError() oz / oz
        @test oz == oz / one(oz)
        @test -oz == oz / (-one(oz))
        @test zero(oz) == one(oz) / oz
        @test_throws DivideError() zo / zo
        @test one(zo) / zo == big(1//0)
        @test -one(zo) / zo == big(-1//0)
    end
end
@testset "div, fld, mod, rem" begin
    for i = -10:10, j = [-10:-1; 1:10]
        @test div(BigInt(i), BigInt(j)) == div(i,j)
        @test fld(BigInt(i), BigInt(j)) == fld(i,j)
        @test mod(BigInt(i), BigInt(j)) == mod(i,j)
        @test rem(BigInt(i), BigInt(j)) == rem(i,j)
    end
end
@testset "copysign / sign" begin
    x = BigInt(1)
    y = BigInt(-1)
    @test copysign(x, y) == y
    @test copysign(y, x) == x

    @test sign(BigInt(-3)) == -1
    @test sign(BigInt( 0)) == 0
    @test sign(BigInt( 3)) == 1
end

@testset "Signed addition" begin
    @test a+Int8(1) == b
    @test a+Int16(1) == b
    @test a+Int32(1) == b
    @test a+Int64(1) == b
    @test a+Int128(1) == b
    @test Int8(1)+ a == b
    @test Int16(1)+a == b
    @test Int32(1)+a == b
    @test Int64(1)+a == b
    @test b+Int8(-1) == a
    @test b+Int16(-1) == a
    @test b+Int32(-1) == a
    @test b+Int64(-1) == a
    @test Int8(-1)+ b == a
    @test Int16(-1)+b == a
    @test Int32(-1)+b == a
    @test Int64(-1)+b == a
end
@testset "Unsigned addition" begin
    @test a+true == b
    @test a+UInt8(1) == b
    @test a+UInt16(1) == b
    @test a+UInt32(1) == b
    @test a+UInt64(1) == b
    @test a+UInt128(1) == b
    @test true+a == b
    @test UInt8(1)+ a == b
    @test UInt16(1)+a == b
    @test UInt32(1)+a == b
    @test UInt64(1)+a == b
end
@testset "Signed subtraction" begin
    @test b-Int8(1) == a
    @test b-Int16(1) == a
    @test b-Int32(1) == a
    @test b-Int64(1) == a
    @test Int8(1)- b == -a
    @test Int16(1)-b == -a
    @test Int32(1)-b == -a
    @test Int64(1)-b == -a
    @test a-Int8(-1) == b
    @test a-Int16(-1) == b
    @test a-Int32(-1) == b
    @test a-Int64(-1) == b
    @test Int8(-1)- a == -b
    @test Int16(-1)-a == -b
    @test Int32(-1)-a == -b
    @test Int64(-1)-a == -b
end
@testset "Unsigned subtraction" begin
    @test b-true == a
    @test b-UInt8(1) == a
    @test b-UInt16(1) == a
    @test b-UInt32(1) == a
    @test b-UInt64(1) == a
    @test true-b == -a
    @test UInt8(1)- b == -a
    @test UInt16(1)-b == -a
    @test UInt32(1)-b == -a
    @test UInt64(1)-b == -a
end
@testset "Signed multiplication" begin
    @test a*Int8(1) == a
    @test a*Int16(1) == a
    @test a*Int32(1) == a
    @test a*Int64(1) == a
    @test Int8(1)* a == a
    @test Int16(1)*a == a
    @test Int32(1)*a == a
    @test Int64(1)*a == a
    @test a*Int8(-1) == -a
    @test a*Int16(-1) == -a
    @test a*Int32(-1) == -a
    @test a*Int64(-1) == -a
    @test Int8(-1)* a == -a
    @test Int16(-1)*a == -a
    @test Int32(-1)*a == -a
    @test Int64(-1)*a == -a
end
@testset "Unsigned multiplication" begin
    @test a*true == a
    @test a*UInt8(1) == a
    @test a*UInt16(1) == a
    @test a*UInt32(1) == a
    @test a*UInt64(1) == a
    @test true*a == a
    @test UInt8(1)* a == a
    @test UInt16(1)*a == a
    @test UInt32(1)*a == a
    @test UInt64(1)*a == a
end

@testset "bitshifts" begin
    @test BigInt(5) << 3 == 40
    @test BigInt(5) >> 1 == 2
    @test BigInt(-5) << 3 == -40
    @test BigInt(-5) >> 1 == -3
    @test BigInt(5) >> -3 == 40
    @test BigInt(5) << -1 == 2
    @test BigInt(-5) >> -3 == -40
    @test BigInt(-5) << -1 == -3
end
@testset "boolean ops" begin
    @test ~BigInt(123) == -124
    @test BigInt(123) & BigInt(234) == 106
    @test BigInt(123) | BigInt(234) == 251
    @test BigInt(123) ⊻ BigInt(234) == 145

    @test gcd(BigInt(48), BigInt(180)) == 12
    @test lcm(BigInt(48), BigInt(180)) == 720
end
@testset "combinatorics" begin
    @test factorial(BigInt(40)) == parse(BigInt,"815915283247897734345611269596115894272000000000")
    @test_throws DomainError factorial(BigInt(-1))
    @test_throws DomainError factorial(BigInt(rand(-999:-2)))
    @test binomial(BigInt(1), -1) == BigInt(0)
    @test binomial(BigInt(1), 2)  == BigInt(0)
    @test binomial(BigInt(-53), 42) == parse(BigInt,"959509335087854414441273718")
    @test binomial(BigInt(113), BigInt(42)) == parse(BigInt,"18672199984318438125634054194360")
end
let a, b
    a = rand(1:100, 10000)
    b = map(BigInt, a)
    @test sum(a) == sum(b)
    @test 0 == sum(BigInt[]) isa BigInt
    @test prod(b) == foldl(*, b)
    @test 1 == prod(BigInt[]) isa BigInt
    @test prod(BigInt[0, 0, 0]) == 0 # issue #46665
    # Test prod with negative numbers
    @test prod(BigInt[-2, 3, -4]) == 24
    @test prod(BigInt[-1, -2, -3]) == -6
    @test prod(BigInt[-5]) == -5
    @test prod(BigInt[-2, -2, -2, -2]) == 16
end

@testset "Iterated arithmetic" begin
    local a, b, c, d, f, g
    a = parse(BigInt,"315135")
    b = parse(BigInt,"12412")
    c = parse(BigInt,"3426495623485904783478347")
    d = parse(BigInt,"-1398984130")
    f = parse(BigInt,"2413804710837418037418307081437315263635345357386985747464")
    g = parse(BigInt,"-1")

    @test +(a, b) == parse(BigInt,"327547")
    @test 327547 == sum((a, b)) isa BigInt
    @test +(a, b, c) == parse(BigInt,"3426495623485904783805894")
    @test 3426495623485904783805894 == sum((a, b, c)) isa BigInt
    @test +(a, b, c, d) == parse(BigInt,"3426495623485903384821764")
    @test 3426495623485903384821764 == sum((a, b, c, d)) isa BigInt
    @test +(a, b, c, d, f) == parse(BigInt,"2413804710837418037418307081437318690130968843290370569228")
    @test 2413804710837418037418307081437318690130968843290370569228 == sum((a, b, c, d, f)) isa BigInt
    @test +(a, b, c, d, f, g) == parse(BigInt,"2413804710837418037418307081437318690130968843290370569227")
    @test 2413804710837418037418307081437318690130968843290370569227 == sum((a, b, c, d, f, g)) isa BigInt

    @test *(a, b) == parse(BigInt,"3911455620")
    @test *(a, b, c) == parse(BigInt,"13402585563389346256121263521460140")
    @test *(a, b, c, d) == parse(BigInt,"-18750004504148804423388563022070650287578200")
    @test *(a, b, c, d, f) == parse(BigInt,"-45258849200337190631492857400003938881995610529251881450243326128168934937055005474972396281351684800")
    @test *(a, b, c, d, f, g) == parse(BigInt,"45258849200337190631492857400003938881995610529251881450243326128168934937055005474972396281351684800")

    @test xor(a, b) == parse(BigInt,"327299")
    @test xor(a, b, c) == parse(BigInt,"3426495623485904783798472")
    @test xor(a, b, c, d) == parse(BigInt,"-3426495623485906178489610")
    @test xor(a, b, c, d, f) == parse(BigInt,"-2413804710837418037418307081437316711364709261074607933698")
    @test xor(a, b, c, d, f, g) == parse(BigInt,"2413804710837418037418307081437316711364709261074607933697")

    @test nand(a, b) == parse(BigInt,"-125")
    @test ⊼(a, b) == parse(BigInt,"-125")

    @test nor(a, b) == parse(BigInt,"-327424")
    @test ⊽(a, b) == parse(BigInt,"-327424")

    @test (&)(a, b) == parse(BigInt,"124")
    @test (&)(a, b, c) == parse(BigInt,"72")
    @test (&)(a, b, c, d) == parse(BigInt,"8")
    @test (&)(a, b, c, d, f) == parse(BigInt,"8")
    @test (&)(a, b, c, d, f, g) == parse(BigInt,"8")

    @test (|)(a, b) == parse(BigInt,"327423")
    @test (|)(a, b, c) == parse(BigInt,"3426495623485904783802111")
    @test (|)(a, b, c, d) == parse(BigInt,"-1396834561")
    @test (|)(a, b, c, d, f) == parse(BigInt,"-1358954753")
    @test (|)(a, b, c, d, f, g) == parse(BigInt,"-1")
end

@testset "bit operations" begin
    for x in (315135, 12412, 3426495623485904783478347)
        @test trailing_ones(big(x)) == trailing_ones(x)
        @test trailing_zeros(big(x)) == trailing_zeros(x)
        @test count_ones(big(x)) == count_ones(x)
        @test count_zeros(-big(x)) == count_zeros(-x)
    end

    @test_throws DomainError trailing_zeros(big(0))
    @test_throws DomainError trailing_ones(big(-1)) # -1 is all ones

    @test_throws DomainError count_zeros(big(0))
    @test_throws DomainError count_zeros(big(rand(UInt)))
    @test_throws DomainError count_ones(big(-1))
    @test_throws DomainError count_ones(-big(rand(UInt))-1)
end

# Large Fibonacci to exercise BigInt
# from Bill Hart, https://groups.google.com/group/julia-dev/browse_frm/thread/798e2d1322daf633
function mul(a::Vector{BigInt}, b::Vector{BigInt})
   x = a[2]*b[2]
   c = Vector{BigInt}(undef, 3)
   c[1] = a[1]*b[1] + x
   c[2] = a[1]*b[2] + a[2]*b[3]
   c[3] = x + a[3]*b[3]
   return c
end

function bigfib(n)
    n == 0 && return BigInt(0)
    n -= 1
    r = [BigInt(1), BigInt(1), BigInt(0)]
    s = [BigInt(1), BigInt(0), BigInt(1)]
    while true
       (n & 1) == 1 && (s = mul(s,r))
       (n >>= 1) == 0 && return s[1]
       r = mul(r,r)
    end
end
@test [bigfib(n) for n=0:10] == [0,1,1,2,3,5,8,13,21,34,55]

let s, n = bigfib(1000001)
    @test ndigits(n) == 208988
    @test mod(n,big(10)^15) == 359244926937501
    @test div(n,big(10)^208973) == 316047687386689

    s = string(n)
    @test length(s) == 208988
    @test endswith(s, "359244926937501")
    @test startswith(s, "316047687386689")
end

@testset "digits" begin
    n = Int64(2080310129088201558)
    N = big(n)
    for base in (2,7,10,11,16,30,50,62,64,100,128), pad in (0,1,10,100)
        @test digits(n; base, pad) == digits(N; base, pad) == digits(UInt8, N; base, pad)
        @test digits(-n; base, pad) == digits(-N; base, pad)
        @test digits!(Vector{Int}(undef, pad), n; base) == digits!(Vector{Int}(undef, pad), N; base)
    end
    @test digits(UInt8, n; base=1<<8) == digits(UInt8, N; base=1<<8)
    @test digits(UInt16, n; base=1<<16) == digits(UInt16, N; base=1<<16)
end

# serialization (#5133)
let n = parse(BigInt, "359334085968622831041960188598043661065388726959079837"),
    b = IOBuffer()
    serialize(b, n)
    seek(b, 0)
    @test deserialize(b) == n
end

@testset "issue #5873" begin
    @test ndigits(big(90)) == 2
    @test ndigits(big(99)) == 2
    ndigits_mismatch(n) = ndigits(n) != ndigits(BigInt(n))
    @test !any(ndigits_mismatch, 8:9)
    @test !any(ndigits_mismatch, 64:99)
    @test !any(ndigits_mismatch, 512:999)
    @test !any(ndigits_mismatch, 8192:9999)
end
# The following should not crash (#16579)
ndigits(big(rand(Int)), base=rand(63:typemax(Int)))
ndigits(big(rand(Int)), base=big(2)^rand(2:999))

for x in big.([-20:20; rand(Int)])
    for _base in -1:1
        @test_throws DomainError ndigits(x, base=_base)
    end
end

@test Base.ndigits0zpb(big(0), big(rand(2:100))) == 0

# digits with BigInt bases (#16844)
@test digits(big(2)^256, base = big(2)^128) == [0, 0, 1]

@testset "conversion from float" begin
    @test BigInt(2.0) == BigInt(2.0f0) == BigInt(big(2.0)) == 2
    @test_throws InexactError convert(BigInt, 2.1)
    @test_throws InexactError convert(BigInt, big(2.1))
end
@testset "truncation" begin
    # cf. issue #13367
    for T = (Float16, Float32, Float64)
        @test trunc(BigInt, T(2.1)) == 2
        @test unsafe_trunc(BigInt, T(2.1)) == 2
        @test round(BigInt, T(2.1)) == 2
        @test floor(BigInt, T(2.1)) == 2
        @test ceil(BigInt, T(2.1)) == 3

        @test_throws InexactError trunc(BigInt, T(Inf))
        @test_throws InexactError round(BigInt, T(Inf))
        @test_throws InexactError floor(BigInt, T(Inf))
        @test_throws InexactError ceil(BigInt, T(Inf))
    end
end

@testset "string(::BigInt)" begin
    # cf. issue #18849"
    # bin, oct, dec, hex should not call sizeof on BigInts
    # when padding is desired
    padding = 4
    low = big(4)
    high = big(2^20)
    @test string(low, pad = padding, base = 2) == "0100"
    @test string(low, pad = padding, base = 8) == "0004"
    @test string(low, pad = padding, base = 10) == "0004"
    @test string(low, pad = padding, base = 16) == "0004"

    @test string(high, pad = padding, base = 2) == "100000000000000000000"
    @test string(high, pad = padding, base = 8) == "4000000"
    @test string(high, pad = padding, base = 10) == "1048576"
    @test string(high, pad = padding, base = 16) == "100000"

    @test string(-low, pad = padding, base = 2) == "-0100" # handle negative numbers correctly
    @test string(-low, pad = padding, base = 8) == "-0004"
    @test string(-low, pad = padding, base = 10) == "-0004"
    @test string(-low, pad = padding, base = 16) == "-0004"

    @test string(-high, pad = padding, base = 2) == "-100000000000000000000"
    @test string(-high, pad = padding, base = 8) == "-4000000"
    @test string(-high, pad = padding, base = 10) == "-1048576"
    @test string(-high, pad = padding, base = 16) == "-100000"

    # cf. issue #13367
    @test string(big(3), base = 2) == "11"
    @test string(big(9), base = 8) == "11"
    @test string(-big(9), base = 8) == "-11"
    @test string(big(12), base = 16) == "c"

    # respect 0-padding on big(0)
    for base in (2, 8, 10, 16)
        @test string(big(0), base=base, pad=0) == ""
    end
    @test string(big(0), base = rand(2:62), pad = 0) == ""
end

@testset "Base.GMP.MPZ.export!" begin

    function Base_GMP_MPZ_import!(x::BigInt, n::AbstractVector{T}; order::Integer=-1, nails::Integer=0, endian::Integer=0) where {T<:Base.BitInteger}
        ccall((:__gmpz_import, Base.GMP.MPZ.libgmp),
               Cvoid,
               (Base.GMP.MPZ.mpz_t, Csize_t, Cint, Csize_t, Cint, Csize_t, Ptr{Cvoid}),
               x, length(n), order, sizeof(T), endian, nails, n)
        return x
    end
    # test import
    bytes_to_import_from = Vector{UInt8}([1, 0])
    int_to_import_to = BigInt()
    Base_GMP_MPZ_import!(int_to_import_to, bytes_to_import_from, order=0)
    @test int_to_import_to == BigInt(256)

    # test export
    int_to_export_from = BigInt(256)
    bytes_to_export_to = Vector{UInt8}(undef, 2)
    Base.GMP.MPZ.export!(bytes_to_export_to, int_to_export_from, order=0)
    @test all(bytes_to_export_to .== bytes_to_import_from)

    # test both composed import(export) is identity
    int_to_export_from = BigInt(256)
    bytes_to_export_to = Vector{UInt8}(undef, 2)
    Base.GMP.MPZ.export!(bytes_to_export_to, int_to_export_from, order=0)
    int_to_import_to = BigInt()
    Base_GMP_MPZ_import!(int_to_import_to, bytes_to_export_to, order=0)
    @test int_to_export_from == int_to_import_to

    # test both composed export(import) is identity
    bytes_to_import_from = Vector{UInt8}([1, 0])
    int_to_import_to = BigInt()
    Base_GMP_MPZ_import!(int_to_import_to, bytes_to_import_from, order=0)
    bytes_to_export_to = Vector{UInt8}(undef, 2)
    Base.GMP.MPZ.export!(bytes_to_export_to, int_to_export_from, order=0)
    @test all(bytes_to_export_to .== bytes_to_import_from)

    # test export of 0 is T[0]
    zero_to_export = BigInt(0)
    bytes_to_export_to = Vector{UInt8}(undef, 0)
    Base.GMP.MPZ.export!(bytes_to_export_to, zero_to_export, order=0)
    @test bytes_to_export_to == UInt8[0]

    # test export on nonzero vector
    x_to_export = BigInt(6)
    bytes_to_export_to = UInt8[1, 2, 3, 4, 5]
    Base.GMP.MPZ.export!(bytes_to_export_to, x_to_export, order=0)
    @test bytes_to_export_to == UInt8[6, 0, 0, 0, 0]
end

@test isqrt(big(4)) == 2
@test isqrt(big(5)) == 2


@testset "Exponentiation operator" begin
    @test big(5)^true == big(5)
    @test big(5)^false == one(BigInt)
    testvals = Int8[-128:-126; -3:3; 125:127]
    @testset "BigInt and Int8 are consistent: $i^$j" for i in testvals, j in testvals
        int8_res = try
            i^j
        catch e
            e
        end
        if int8_res isa Int8
            @test (big(i)^big(j)) % Int8 === int8_res
        else
            # Test both have exception of the same type
            @test_throws typeof(int8_res) big(i)^big(j)
        end
    end
end

@testset "modular invert" begin
    # test invert is correct and does not mutate
    a = BigInt(3)
    b = BigInt(7)
    i = BigInt(5)
    @test Base.GMP.MPZ.invert(a, b) == i
    @test a == BigInt(3)
    @test b == BigInt(7)

    # test in place invert does mutate first argument
    a = BigInt(3)
    b = BigInt(7)
    i = BigInt(5)
    i_inplace = BigInt(3)
    Base.GMP.MPZ.invert!(i_inplace, b)
    @test i_inplace == i

    # test in place invert does mutate only first argument
    a = BigInt(3)
    b = BigInt(7)
    i = BigInt(5)
    i_inplace = BigInt(0)
    Base.GMP.MPZ.invert!(i_inplace, a, b)
    @test i_inplace == i
    @test a == BigInt(3)
    @test b == BigInt(7)
end

@testset "math ops returning BigFloat" begin
    # operations that when applied to Int64 give Float64, should give BigFloat
    @test typeof(exp(a)) == BigFloat
    @test typeof(exp2(a)) == BigFloat
    @test typeof(exp10(a)) == BigFloat
    @test typeof(expm1(a)) == BigFloat
    @test typeof(cosh(a)) == BigFloat
    @test typeof(sinh(a)) == BigFloat
    @test typeof(tanh(a)) == BigFloat
    @test typeof(sech(a)) == BigFloat
    @test typeof(csch(a)) == BigFloat
    @test typeof(coth(a)) == BigFloat
    @test typeof(cbrt(a)) == BigFloat
    @test typeof(tan(a)) == BigFloat
    @test typeof(cos(a)) == BigFloat
    @test typeof(sin(a)) == BigFloat
end

# Issue #24298
@test mod(BigInt(6), UInt(5)) == mod(6, 5)

@test iseven(zero(BigInt))
@test isodd(BigInt(typemax(UInt)))

@testset "cmp has values in [-1, 0, 1], issue #28780" begin
    # _rand produces values whose log2 is better distributed than rand
    _rand(::Type{BigInt}, n=1000) = let x = big(2)^rand(1:rand(1:n))
        rand(-x:x)
    end
    _rand(F::Type{<:AbstractFloat}) = F(_rand(BigInt, round(Int, log2(floatmax(F))))) + rand(F)
    _rand(T) = rand(T)
    for T in (Base.BitInteger_types..., BigInt, Float64, Float32, Float16)
        @test cmp(big(2)^130, one(T)) === 1
        @test cmp(-big(2)^130, one(T)) === -1
        c = cmp(_rand(BigInt), _rand(T))
        @test c ∈ (-1, 0, 1)
        @test c isa Int
        (T <: Integer && T !== BigInt) || continue
        x = rand(T)
        @test cmp(big(2)^130, x) === cmp(x, -big(2)^130) === 1
        @test cmp(-big(2)^130, x) === cmp(x, big(2)^130) === -1
        @test cmp(big(x), x) === cmp(x, big(x)) === 0
    end
    c = cmp(_rand(BigInt), _rand(BigInt))
    @test c ∈ (-1, 0, 1)
    @test c isa Int
end

@testset "generic conversion from Integer" begin
    x = rand(Int128)
    @test BigInt(x) % Int128 === x
    y = rand(UInt128)
    @test BigInt(y) % UInt128 === y
end

@testset "conversion from typemin(T)" begin
    @test big(Int8(-128)) == big"-128"
    @test big(Int16(-32768)) == big"-32768"
    @test big(Int32(-2147483648)) == big"-2147483648"
    @test big(Int64(-9223372036854775808)) == big"-9223372036854775808"
    @test big(Int128(-170141183460469231731687303715884105728)) == big"-170141183460469231731687303715884105728"
end

@testset "type conversion with Signed, Unsigned" begin
    x = BigInt(typemin(Int128)) - 1
    @test x % Signed === x
    @test_throws MethodError x % Unsigned
    y = BigInt(1)
    @test y % Signed === y
    @test_throws MethodError y % Unsigned
end

@testset "conversion to Float" begin
    x = big"2"^256 + big"2"^(256-53) + 1
    @test Float64(x) == reinterpret(Float64, 0x4ff0000000000001)
    @test Float64(-x) == -Float64(x)
    x = (x >> 1) + 1
    @test Float64(x) == reinterpret(Float64, 0x4fe0000000000001)
    @test Float64(-x) == -Float64(x)

    x = big"2"^64 + big"2"^(64-24) + 1
    @test Float32(x) == reinterpret(Float32, 0x5f800001)
    @test Float32(-x) == -Float32(x)
    x = (x >> 1) + 1
    @test Float32(x) == reinterpret(Float32, 0x5f000001)
    @test Float32(-x) == -Float32(x)

    x = big"2"^15 + big"2"^(15-11) + 1
    @test Float16(x) == reinterpret(Float16, 0x7801)
    @test Float16(-x) == -Float16(x)
    x = (x >> 1) + 1
    @test Float16(x) == reinterpret(Float16, 0x7401)
    @test Float16(-x) == -Float16(x)

    for T in (Float16, Float32, Float64)
        n = exponent(floatmax(T))
        @test T(big"2"^(n+1)) === T(Inf)
        @test T(big"2"^(n+1) - big"2"^(n-precision(T))) === T(Inf)
        @test T(big"2"^(n+1) - big"2"^(n-precision(T)) - 1) === floatmax(T)
    end
end

a = Rational{BigInt}(12345678901234567890123456789, 987654321987654320)
b = Rational{BigInt}(12345678902222222212111111109, 987654321987654320)
c = Rational{BigInt}(24691357802469135780246913578, 987654321987654320)
d = Rational{BigInt}(- 12345678901234567890123456789, 493827160993827160)
e = Rational{BigInt}(12345678901234567890123456789, 12345678902222222212111111109)
@testset "big rational basics" begin
    @test a+BigInt(1) == b
    @test typeof(a+1) == Rational{BigInt}
    @test a+1 == b
    @test isequal(a+1, b)
    @test b == a+1
    @test !(b == a)
    @test b > a
    @test b >= a
    @test !(b < a)
    @test !(b <= a)

    @test typeof(a * 2) == Rational{BigInt}
    @test a*2 == c
    @test c-a == a
    @test c == a + a
    @test c+1 == a+b

    @test typeof(d) == Rational{BigInt}
    @test d == -c


    @test e == a // b

    @testset "gmp cmp" begin
        @test Base.GMP.MPQ.cmp(b, a) ==  1
        @test Base.GMP.MPQ.cmp(a, b) == -1
        @test Base.GMP.MPQ.cmp(a, a) ==  0
    end

    @testset "division errors" begin
        oz = Rational{BigInt}(0, 1)
        zo = Rational{BigInt}(1, 0)

        @test oz + oz == 3 * oz == oz
        @test oz // zo == oz
        @test zo // oz == zo

        @test_throws DivideError() zo - zo
        @test_throws DivideError() zo + (-zo)
        @test_throws DivideError() zo * oz
        @test_throws DivideError() oz // oz
        @test_throws DivideError() zo // zo
    end

    @testset "big infinities" begin
        oz   = Rational{BigInt}(1, 0)
        zo   = Rational{BigInt}(0, 1)
        o    = Rational{BigInt}(1, 1)

        @test oz + zo    == oz
        @test zo - oz    == -oz
        @test zo + (-oz) == -oz
        @test -oz + zo   == -oz

        @test (-oz) * (-oz) == oz
        @test (-oz) * oz    == -oz

        @test o // zo       == oz
        @test (-o) // zo    == -oz

        @test Rational{BigInt}(-1, 0) == -1//0
        @test Rational{BigInt}(1, 0) == 1//0
    end
end


aa = 1//2
bb = -1//3
cc = 3//2
a = Rational{BigInt}(aa)
b = Rational{BigInt}(bb)
c = Rational{BigInt}(cc)
t = Rational{BigInt}(0, 1)
@testset "big rational inplace" begin
    @test Base.GMP.MPQ.add!(t, a, b) == 1//6
    @test t == 1//6
    @test Base.GMP.MPQ.add!(t, t) == 1//3
    @test t == 1//3

    @test iszero(Base.GMP.MPQ.sub!(t, t))
    @test iszero(t)
    @test Base.GMP.MPQ.sub!(t, b, c) == -11//6
    @test t == -11//6

    @test Base.GMP.MPQ.mul!(t, a, b) == -1//6
    @test t == -1//6
    @test Base.GMP.MPQ.mul!(t, t) == 1//36
    @test t == 1//36
    @test iszero(Base.GMP.MPQ.mul!(t, Rational{BigInt}(0)))

    @test Base.GMP.MPQ.div!(t, a, b) == -3//2
    @test t == -3//2
    @test Base.GMP.MPQ.div!(t, a) == -3//1
    @test t == -3//1

    @test aa == a && bb == b && cc == c

    @testset "set" begin
        @test Base.GMP.MPQ.set!(a, b) == b
        @test a == b == bb

        Base.GMP.MPQ.add!(a, b, c)
        @test b == bb

        @test Base.GMP.MPQ.set_z!(a, BigInt(0)) == 0
        @test iszero(a)
        @test Base.GMP.MPQ.set_z!(a, BigInt(3)) == 3
        @test a == BigInt(3)

        @test Base.GMP.MPQ.set_ui(1, 2)      == 1//2
        @test Base.GMP.MPQ.set_ui(0, 1)      == 0//1
        @test Base.GMP.MPQ.set_ui!(a, 1, 2)  == 1//2
        @test a == 1//2

        @test Base.GMP.MPQ.set_si(1, 2)      == 1//2
        @test Base.GMP.MPQ.set_si(-1, 2)     == -1//2
        @test Base.GMP.MPQ.set_si!(a, -1, 2) == -1//2
        @test a == -1//2
    end

    @testset "infinities" begin
        oz   = Rational{BigInt}(1, 0)
        zo   = Rational{BigInt}(0, 1)
        oo   = Rational{BigInt}(1, 1)

        @test Base.GMP.MPQ.add!(zo, oz) == oz
        @test zo == oz
        zo = Rational{BigInt}(0, 1)

        @test Base.GMP.MPQ.sub!(zo, oz) == -oz
        @test zo == -oz
        zo = Rational{BigInt}(0, 1)

        @test Base.GMP.MPQ.add!(zo, -oz) == -oz
        @test zo == -oz
        zo = Rational{BigInt}(0, 1)

        @test Base.GMP.MPQ.sub!(zo, -oz) == oz
        @test zo == oz
        zo = Rational{BigInt}(0, 1)

        @test Base.GMP.MPQ.mul!(-oz, -oz) == oz
        @test Base.GMP.MPQ.mul!(-oz, oz)  == -oz
        @test Base.GMP.MPQ.mul!(oz, -oz)  == -1//0
        @test oz == -1//0
        oz = Rational{BigInt}(1, 0)

        @test Base.GMP.MPQ.div!(oo, zo) == oz
        @test oo == oz
        oo = Rational{BigInt}(1, 1)

        @test Base.GMP.MPQ.div!(-oo, zo) == -oz
    end
end

@testset "hashing" begin
    for i in 1:10:100
        for shift in vcat(0:8, 9:8:81)
            for sgn in (1, -1)
                bint = sgn * (big(11)^i << shift)
                bfloat = float(bint)
                @test (hash(bint) == hash(bfloat)) == (bint == bfloat)
                @test hash(bint, Base.HASH_SEED) ==
                    @invoke(hash(bint::Real, Base.HASH_SEED))
                @test Base.hash_integer(bint, Base.HASH_SEED) ==
                    @invoke(Base.hash_integer(bint::Integer, Base.HASH_SEED))
            end
        end
    end

    bint = big(0)
    bfloat = float(bint)
    @test (hash(bint) == hash(bfloat)) == (bint == bfloat)
    @test hash(bint, Base.HASH_SEED) ==
        @invoke(hash(bint::Real, Base.HASH_SEED))
    @test Base.hash_integer(bint, Base.HASH_SEED) ==
        @invoke(Base.hash_integer(bint::Integer, Base.HASH_SEED))
end