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# This file is a part of Julia. License is MIT: https://julialang.org/license
using Random
@testset "gcd/lcm" begin
# Int32 and Int64 take different code paths -- test both
for T in (Int32, Int64)
@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(0), T(0)) === T(0)
@test gcd(T(2), T(4), T(6)) === T(2)
@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 lcm(T(0)) === T(0)
@test lcm(T(2)) === T(2)
@test lcm(T(2), T(3)) === T(6)
@test lcm(T(4), T(6)) === T(12)
@test lcm(T(3), T(0)) === 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)
@test lcm(T(2), T(4), T(6)) === T(12)
@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))
end
end
@testset "gcd/lcm for arrays" begin
for T in (Int32, Int64)
@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)
@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 lcm(T[]) === T(1)
@test lcm(T[2]) === T(2)
@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[4, -6]) === T(12)
@test lcm(T[-4, -6]) === T(12)
@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)
end
@testset "invmod" begin
@test invmod(6, 31) === 26
@test invmod(-1, 3) === 2
@test invmod(1, -3) === -2
@test invmod(-1, -3) === -1
@test invmod(0x2, 0x3) === 0x2
@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
@test powermod(2, 0, 5) == 1
@test powermod(2, 0, -5) == -4
@test powermod(2, -1, 5) == 3
@test powermod(2, -2, 5) == 4
@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
@test nextpow(2, 7) == 8
@test_throws DomainError nextpow(0, 3)
@test_throws DomainError nextpow(3, 0)
@test prevpow(2, 3) == 2
@test prevpow(2, 4) == 4
@test prevpow(2, 5) == 4
@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
@test ndigits(-15, base=-10) == 2
@test ndigits(-1, base=10) == 1
@test ndigits(-1, base=-10) == 2
@test ndigits(2, base=10) == 1
@test ndigits(2, base=-10) == 1
@test ndigits(10, base=10) == 2
@test ndigits(10, base=-10) == 3
@test ndigits(17, base=10) == 2
@test ndigits(17, base=-10) == 3
@test ndigits(unsigned(17), base=-10) == 3
@test ndigits(146, base=-3) == 5
end
let (n, b) = rand(Int, 2)
-1 <= b <= 1 && (b = 2) # invalid bases
@test ndigits(n) == ndigits(big(n)) == ndigits(n, base=10)
@test ndigits(n, base=b) == ndigits(big(n), base=b)
end
for b in -1:1
@test_throws DomainError ndigits(rand(Int), base=b)
end
@test ndigits(Int8(5)) == ndigits(5)
# issue #19367
@test ndigits(Int128(2)^64, base=256) == 9
# test unsigned bases
@test ndigits(9, base=0x2) == 4
@test ndigits(0x9, base=0x2) == 4
# ndigits is defined for Bool
@test iszero([Base.ndigits0z(false, b) for b in [-20:-2;2:20]])
@test all(n -> n == 1, Base.ndigits0z(true, b) for b in [-20:-2;2:20])
@test all(n -> n == 1, ndigits(x, base=b) for b in [-20:-2;2:20] for x in [true, false])
# issue #29148
@test ndigits(typemax(UInt64), base=-2) == ndigits(big(typemax(UInt64)), base=-2)
for T in Base.BitInteger_types
n = rand(T)
b = -rand(2:100)
@test ndigits(n, base=b) == ndigits(big(n), base=b)
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"
@test string(3, base = 2) == "11"
@test string(3, pad = 2, base = 2) == "11"
@test string(3, pad = 3, base = 2) == "011"
@test string(-3, base = 2) == "-11"
@test string(-3, pad = 3, base = 2) == "-011"
@test string(9, base = 8) == "11"
@test string(-9, base = 8) == "-11"
@test string(121, base = 10) == "121"
@test string(12, base = 16) == "c"
@test string(-12, pad = 3, base = 16) == "-00c"
@test string(5, pad = 7, base = 2) == "0000101"
@test bitstring(Int16(3)) == "0000000000000011"
@test bitstring('3') == "00110011000000000000000000000000"
@test bitstring(1035) == (Int == Int32 ? "00000000000000000000010000001011" :
"0000000000000000000000000000000000000000000000000000010000001011")
@test bitstring(Int128(3)) == "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011"
end
@testset "digits/base" begin
@test digits(4, base = 2) == [0, 0, 1]
@test digits(5, base = 3) == [2, 1]
@testset "digits/base with negative bases" begin
@testset "digits(n::$T, base = b)" for T in (Int, UInt, BigInt, Int32, UInt32)
@test digits(T(8163), base = -10) == [3, 4, 2, 2, 1]
if !(T<:Unsigned)
@test digits(T(-8163), base = -10) == [7, 7, 9, 9]
end
if T !== BigInt
b = rand(-32:-2)
for n = T[rand(T), typemax(T), typemin(T)]
# issue #29183
@test digits(n, base=b) == digits(signed(widen(n)), base=b)
end
end
end
@test [string(n, base = b)
for n = [-10^9, -10^5, -2^20, -2^10, -100, -83, -50, -34, -27, -16, -7, -3, -2, -1,
0, 1, 2, 3, 4, 7, 16, 27, 34, 50, 83, 100, 2^10, 2^20, 10^5, 10^9]
for b = [-2, -3, -7, -10, -60]] ==
["11000101101001010100101000000000", "11211100201202120012",
"144246601121", "1000000000", "2hANlK", "111000111010100000",
"122011122112", "615462", "100000", "1XlK", "1100000000000000000000",
"11000202101022", "25055043", "19169584", "59Hi", "110000000000",
"12102002", "3005", "1036", "Iu", "11101100", "121112", "1515",
"1900", "2K", "11111101", "120011", "1651", "97", "2b", "11010010",
"2121", "1616", "50", "1A", "100010", "2202", "51", "46", "1Q",
"100101", "1000", "41", "33", "1X", "110000", "1102", "35", "24",
"1i", "1001", "1202", "10", "13", "1r", "1101", "10", "14", "17",
"1v", "10", "11", "15", "18", "1w", "11", "12", "16", "19", "1x", "0",
"0", "0", "0", "0", "1", "1", "1", "1", "1", "110", "2", "2", "2",
"2", "111", "120", "3", "3", "3", "100", "121", "4", "4", "4",
"11011", "111", "160", "7", "7", "10000", "211", "152", "196", "G",
"1101111", "12000", "146", "187", "R", "1100110", "12111", "136",
"174", "Y", "1110110", "11022", "101", "150", "o", "1010111", "10002",
"236", "123", "1xN", "110100100", "10201", "202", "100", "1xe",
"10000000000", "2211011", "14012", "19184", "1h4",
"100000000000000000000", "2001112212121", "162132144", "1052636",
"1uqiG", "1101001101111100000", "21002022201", "1103425", "1900000",
"SEe", "1001100111011111101111000000000", "120220201100111010001",
"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
@test leading_zeros(Int32(1)) == 31
@test leading_zeros(UInt32(Int64(2) ^ 32 - 2)) == 0
@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")
@test isqrt(Int128(typemax(Int64))^2-1) == 9223372036854775806
@test isqrt(0) == 0
for i = 1:1000
n = rand(UInt128)
s = isqrt(n)
@test s*s <= n
@test (s+1)*(s+1) > n
n = rand(UInt64)
s = isqrt(n)
@test s*s <= n
@test (s+1)*(s+1) > n
end
end
# issue #9786
let ptr = Ptr{Cvoid}(typemax(UInt))
for T in (Int, Cssize_t)
@test T(ptr) == -1
@test ptr == Ptr{Cvoid}(T(ptr))
@test typeof(Ptr{Float64}(T(ptr))) == Ptr{Float64}
end
end
# issue #15911
@inferred string(1)
# issue #22837
for b in [-100:-2; 2:100;]
@test Base.ndigits0z(0, b) == 0
end
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