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numbers.jl
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numbers.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
using Base.MathConstants
using Random
using LinearAlgebra
const ≣ = isequal # convenient for comparing NaNs
@testset "basic booleans" begin
@test true
@test !false
@test !!true
@test !!!false
@test true == true
@test false == false
@test true != false
@test false != true
@test ~true == false
@test ~false == true
@test false & false == false
@test true & false == false
@test false & true == false
@test true & true == true
@test false | false == false
@test true | false == true
@test false | true == true
@test true | true == true
@test false ⊻ false == false
@test true ⊻ false == true
@test false ⊻ true == true
@test true ⊻ true == false
@test xor(false, false) == false
@test xor(true, false) == true
@test xor(false, true) == true
@test xor(true, true) == false
@test false ⊼ false == true
@test true ⊼ false == true
@test false ⊼ true == true
@test true ⊼ true == false
@test nand(false, false) == true
@test nand(true, false) == true
@test nand(false, true) == true
@test nand(true, true) == false
@test false ⊽ false == true
@test true ⊽ false == false
@test false ⊽ true == false
@test true ⊽ true == false
@test nor(false, false) == true
@test nor(true, false) == false
@test nor(false, true) == false
@test nor(true, true) == false
end
@testset "bool operator" begin
@test Bool(false) == false
@test Bool(true) == true
@test Bool(0) == false
@test Bool(1) == true
@test_throws InexactError Bool(-1)
@test Bool(0.0) == false
@test Bool(1.0) == true
@test_throws InexactError Bool(0.1)
@test_throws InexactError Bool(-1.0)
@test Bool(Complex(0,0)) == false
@test Bool(Complex(1,0)) == true
@test_throws InexactError Bool(Complex(0,1))
@test Bool(0//1) == false
@test Bool(1//1) == true
@test_throws InexactError Bool(1//2)
@test iszero(false) && !iszero(true)
@test isone(true) && !isone(false)
@test typemin(Bool) == false
@test typemax(Bool) == true
@test abs(false) == false
@test abs(true) == true
end
@testset "basic arithmetic" begin
@test 2 + 3 == 5
@test 2.0 + 3.0 == 5.
@test 2 * 3 == 6
@test 2.0 * 3 == 6
@test 2.0 * 3.0 == 6.
@test min(1.0,1) == 1
end
@testset "min, max and minmax" begin
@test min(1) === 1
@test max(1) === 1
@test minmax(1) === (1, 1)
@test minmax(5, 3) == (3, 5)
@test minmax(3., 5.) == (3., 5.)
@test minmax(5., 3.) == (3., 5.)
@test minmax(3., NaN) ≣ (NaN, NaN)
@test minmax(NaN, 3) ≣ (NaN, NaN)
@test minmax(Inf, NaN) ≣ (NaN, NaN)
@test minmax(NaN, Inf) ≣ (NaN, NaN)
@test minmax(-Inf, NaN) ≣ (NaN, NaN)
@test minmax(NaN, -Inf) ≣ (NaN, NaN)
@test minmax(NaN, NaN) ≣ (NaN, NaN)
@test min(-0.0,0.0) === min(0.0,-0.0)
@test max(-0.0,0.0) === max(0.0,-0.0)
@test minmax(-0.0,0.0) === minmax(0.0,-0.0)
@test max(-3.2, 5.1) == max(5.1, -3.2) == 5.1
@test min(-3.2, 5.1) == min(5.1, -3.2) == -3.2
@test max(-3.2, Inf) == max(Inf, -3.2) == Inf
@test max(-3.2, NaN) ≣ max(NaN, -3.2) ≣ NaN
@test min(5.1, Inf) == min(Inf, 5.1) == 5.1
@test min(5.1, -Inf) == min(-Inf, 5.1) == -Inf
@test min(5.1, NaN) ≣ min(NaN, 5.1) ≣ NaN
@test min(5.1, -NaN) ≣ min(-NaN, 5.1) ≣ NaN
@test minmax(-3.2, 5.1) == (min(-3.2, 5.1), max(-3.2, 5.1))
@test minmax(-3.2, Inf) == (min(-3.2, Inf), max(-3.2, Inf))
@test minmax(-3.2, NaN) ≣ (min(-3.2, NaN), max(-3.2, NaN))
@test (max(Inf,NaN), max(-Inf,NaN), max(Inf,-NaN), max(-Inf,-NaN)) ≣ (NaN,NaN,NaN,NaN)
@test (max(NaN,Inf), max(NaN,-Inf), max(-NaN,Inf), max(-NaN,-Inf)) ≣ (NaN,NaN,NaN,NaN)
@test (min(Inf,NaN), min(-Inf,NaN), min(Inf,-NaN), min(-Inf,-NaN)) ≣ (NaN,NaN,NaN,NaN)
@test (min(NaN,Inf), min(NaN,-Inf), min(-NaN,Inf), min(-NaN,-Inf)) ≣ (NaN,NaN,NaN,NaN)
@test minmax(-Inf,NaN) ≣ (min(-Inf,NaN), max(-Inf,NaN))
end
@testset "fma" begin
let x = Int64(7)^7
@test fma(x-1, x-2, x-3) == (x-1) * (x-2) + (x-3)
@test (fma((x-1)//(x-2), (x-3)//(x-4), (x-5)//(x-6)) ==
(x-1)//(x-2) * (x-3)//(x-4) + (x-5)//(x-6))
end
let x = BigInt(7)^77
@test fma(x-1, x-2, x-3) == (x-1) * (x-2) + (x-3)
@test (fma((x-1)//(x-2), (x-3)//(x-4), (x-5)//(x-6)) ==
(x-1)//(x-2) * (x-3)//(x-4) + (x-5)//(x-6))
end
let eps = 1//BigInt(2)^30, one_eps = 1+eps,
eps64 = Float64(eps), one_eps64 = Float64(one_eps)
@test eps64 == Float64(eps)
@test rationalize(BigInt, eps64, tol=0) == eps
@test one_eps64 == Float64(one_eps)
@test rationalize(BigInt, one_eps64, tol=0) == one_eps
@test one_eps64 * one_eps64 - 1 != Float64(one_eps * one_eps - 1)
@test fma(one_eps64, one_eps64, -1) == Float64(one_eps * one_eps - 1)
end
let eps = 1//BigInt(2)^15, one_eps = 1+eps,
eps32 = Float32(eps), one_eps32 = Float32(one_eps)
@test eps32 == Float32(eps)
@test rationalize(BigInt, eps32, tol=0) == eps
@test one_eps32 == Float32(one_eps)
@test rationalize(BigInt, one_eps32, tol=0) == one_eps
@test one_eps32 * one_eps32 - 1 != Float32(one_eps * one_eps - 1)
@test fma(one_eps32, one_eps32, -1) == Float32(one_eps * one_eps - 1)
end
let eps = 1//BigInt(2)^7, one_eps = 1+eps,
eps16 = Float16(Float32(eps)), one_eps16 = Float16(Float32(one_eps))
@test eps16 == Float16(Float32(eps))
@test rationalize(BigInt, eps16, tol=0) == eps
@test one_eps16 == Float16(Float32(one_eps))
@test rationalize(BigInt, one_eps16, tol=0) == one_eps
@test one_eps16 * one_eps16 - 1 != Float16(Float32(one_eps * one_eps - 1))
@test (fma(one_eps16, one_eps16, -1) ==
Float16(Float32(one_eps * one_eps - 1)))
end
let eps = 1//BigInt(2)^200, one_eps = 1+eps,
eps256 = BigFloat(eps), one_eps256 = BigFloat(one_eps)
@test eps256 == BigFloat(eps)
@test rationalize(BigInt, eps256, tol=0) == eps
@test one_eps256 == BigFloat(one_eps)
@test rationalize(BigInt, one_eps256, tol=0) == one_eps
@test one_eps256 * one_eps256 - 1 != BigFloat(one_eps * one_eps - 1)
@test fma(one_eps256, one_eps256, -1) == BigFloat(one_eps * one_eps - 1)
end
end
@testset "muladd" begin
let eps = 1//BigInt(2)^30, one_eps = 1+eps,
eps64 = Float64(eps), one_eps64 = Float64(one_eps)
@test eps64 == Float64(eps)
@test one_eps64 == Float64(one_eps)
@test one_eps64 * one_eps64 - 1 != Float64(one_eps * one_eps - 1)
@test muladd(one_eps64, one_eps64, -1) ≈ Float64(one_eps * one_eps - 1)
end
let eps = 1//BigInt(2)^15, one_eps = 1+eps,
eps32 = Float32(eps), one_eps32 = Float32(one_eps)
@test eps32 == Float32(eps)
@test one_eps32 == Float32(one_eps)
@test one_eps32 * one_eps32 - 1 != Float32(one_eps * one_eps - 1)
@test muladd(one_eps32, one_eps32, -1) ≈ Float32(one_eps * one_eps - 1)
end
let eps = 1//BigInt(2)^7, one_eps = 1+eps,
eps16 = Float16(Float32(eps)), one_eps16 = Float16(Float32(one_eps))
@test eps16 == Float16(Float32(eps))
@test one_eps16 == Float16(Float32(one_eps))
@test one_eps16 * one_eps16 - 1 != Float16(Float32(one_eps * one_eps - 1))
@test muladd(one_eps16, one_eps16, -1) ≈ Float16(Float32(one_eps * one_eps - 1))
end
@test muladd(1,2,3) == 1*2+3
@test muladd(big(1),2,3) == big(1)*2+3
@test muladd(UInt(1),2,3) == UInt(1)*2+3
@test muladd(1//1,2,3) == (1//1)*2+3
@test muladd(big(1//1),2,3) == big(1//1)*2+3
@test muladd(1.0,2,3) == 1.0*2+3
@test muladd(big(1.0),2,3) == big(1.0)*2+3
end
# lexing typemin(Int64)
@test (-9223372036854775808)^1 == -9223372036854775808
@test [1 -1 -9223372036854775808] == [1 -1 typemin(Int64)]
# large integer literals
@test isa(-170141183460469231731687303715884105729,BigInt)
@test isa(-170141183460469231731687303715884105728,Int128)
@test isa(-9223372036854775809,Int128)
@test isa(-9223372036854775808,Int64)
@test isa(9223372036854775807,Int64)
@test isa(9223372036854775808,Int128)
@test isa(170141183460469231731687303715884105727,Int128)
@test isa(170141183460469231731687303715884105728,BigInt)
@test isa(0170141183460469231731687303715884105728,BigInt)
# GMP allocation overflow should not cause crash
if Base.GMP.ALLOC_OVERFLOW_FUNCTION[] && sizeof(Int) > 4
@test_throws OutOfMemoryError BigInt(2)^(typemax(Culong))
end
# exponentiating with a negative base
@test -3^2 == -9
@test -9223372036854775808^2 == -(9223372036854775808^2)
@test -10000000000000000000^2 == -(10000000000000000000^2)
@test -170141183460469231731687303715884105728^2 ==
-(170141183460469231731687303715884105728^2)
# numeric literal coefficients
let x = 10
@test 2x == 20
@test 9223372036854775808x == 92233720368547758080
@test 170141183460469231731687303715884105728x ==
1701411834604692317316873037158841057280
end
@test 2(10) == 20
@test 9223372036854775808(10) == 92233720368547758080
@test 170141183460469231731687303715884105728(10) ==
1701411834604692317316873037158841057280
@testset "bin/oct/dec/hex/base for extreme integers" begin
# definition and printing of extreme integers
@test string(typemin(UInt8), base = 2) == "0"
@test string(typemax(UInt8), base = 2) == "1"^8
@test string(typemin(UInt8), base = 8) == "0"
@test string(typemax(UInt8), base = 8) == "377"
@test string(typemin(UInt8), base = 10) == "0"
@test string(typemax(UInt8), base = 10) == "255"
@test string(typemin(UInt8), base = 16) == "0"
@test string(typemax(UInt8), base = 16) == "ff"
@test repr(typemin(UInt8)) == "0x00"
@test string(typemin(UInt8)) == "0"
@test repr(typemax(UInt8)) == "0xff"
@test string(typemax(UInt8)) == "255"
@test string(typemin(UInt8), base = 3) == "0"
@test string(typemax(UInt8), base = 3) == "100110"
@test string(typemin(UInt8), base = 12) == "0"
@test string(typemax(UInt8), base = 12) == "193"
@test string(typemin(UInt16), base = 2) == "0"
@test string(typemax(UInt16), base = 2) == "1"^16
@test string(typemin(UInt16), base = 8) == "0"
@test string(typemax(UInt16), base = 8) == "177777"
@test string(typemin(UInt16), base = 10) == "0"
@test string(typemax(UInt16), base = 10) == "65535"
@test string(typemin(UInt16), base = 16) == "0"
@test string(typemax(UInt16), base = 16) == "ffff"
@test repr(typemin(UInt16)) == "0x0000"
@test string(typemin(UInt16)) == "0"
@test repr(typemax(UInt16)) == "0xffff"
@test string(typemax(UInt16)) == "65535"
@test string(typemin(UInt16), base = 3) == "0"
@test string(typemax(UInt16), base = 3) == "10022220020"
@test string(typemin(UInt16), base = 12) == "0"
@test string(typemax(UInt16), base = 12) == "31b13"
@test string(typemin(UInt32), base = 2) == "0"
@test string(typemax(UInt32), base = 2) == "1"^32
@test string(typemin(UInt32), base = 8) == "0"
@test string(typemax(UInt32), base = 8) == "37777777777"
@test string(typemin(UInt32), base = 10) == "0"
@test string(typemax(UInt32), base = 10) == "4294967295"
@test string(typemin(UInt32), base = 16) == "0"
@test string(typemax(UInt32), base = 16) == "ffffffff"
@test repr(typemin(UInt32)) == "0x00000000"
@test string(typemin(UInt32)) == "0"
@test repr(typemax(UInt32)) == "0xffffffff"
@test string(typemax(UInt32)) == "4294967295"
@test string(typemin(UInt32), base = 3) == "0"
@test string(typemax(UInt32), base = 3) == "102002022201221111210"
@test string(typemin(UInt32), base = 12) == "0"
@test string(typemax(UInt32), base = 12) == "9ba461593"
@test string(typemin(UInt64), base = 2) == "0"
@test string(typemax(UInt64), base = 2) == "1"^64
@test string(typemin(UInt64), base = 8) == "0"
@test string(typemax(UInt64), base = 8) == "1777777777777777777777"
@test string(typemin(UInt64), base = 10) == "0"
@test string(typemax(UInt64), base = 10) == "18446744073709551615"
@test string(typemin(UInt64), base = 16) == "0"
@test string(typemax(UInt64), base = 16) == "ffffffffffffffff"
@test repr(typemin(UInt64)) == "0x0000000000000000"
@test string(typemin(UInt64)) == "0"
@test repr(typemax(UInt64)) == "0xffffffffffffffff"
@test string(typemax(UInt64)) == "18446744073709551615"
@test string(typemin(UInt64), base = 3) == "0"
@test string(typemax(UInt64), base = 3) == "11112220022122120101211020120210210211220"
@test string(typemin(UInt64), base = 12) == "0"
@test string(typemax(UInt64), base = 12) == "839365134a2a240713"
@test string(typemin(UInt128), base = 2) == "0"
@test string(typemax(UInt128), base = 2) == "1"^128
@test string(typemin(UInt128), base = 8) == "0"
@test string(typemax(UInt128), base = 8) == "3777777777777777777777777777777777777777777"
@test string(typemin(UInt128), base = 16) == "0"
@test string(typemax(UInt128), base = 16) == "ffffffffffffffffffffffffffffffff"
@test repr(typemin(UInt128)) == "0x00000000000000000000000000000000"
@test string(typemin(UInt128)) == "0"
@test repr(typemax(UInt128)) == "0xffffffffffffffffffffffffffffffff"
@test string(typemax(UInt128)) == "340282366920938463463374607431768211455"
@test string(typemin(UInt128), base = 10) == "0"
@test string(typemax(UInt128), base = 10) == "340282366920938463463374607431768211455"
@test string(typemin(UInt128), base = 3) == "0"
@test string(typemax(UInt128), base = 3) ==
"202201102121002021012000211012011021221022212021111001022110211020010021100121010"
@test string(typemin(UInt128), base = 12) == "0"
@test string(typemax(UInt128), base = 12) == "5916b64b41143526a777873841863a6a6993"
@test string(typemin(Int8), base = 2) == "-1"*"0"^7
@test string(typemax(Int8), base = 2) == "1"^7
@test string(typemin(Int8), base = 8) == "-200"
@test string(typemax(Int8), base = 8) == "177"
@test string(typemin(Int8), base = 10) == "-128"
@test string(typemax(Int8), base = 10) == "127"
@test string(typemin(Int8), base = 16) == "-80"
@test string(typemax(Int8), base = 16) == "7f"
@test string(typemin(Int8)) == "-128"
@test string(typemax(Int8)) == "127"
@test string(typemin(Int8), base = 3) == "-11202"
@test string(typemax(Int8), base = 3) == "11201"
@test string(typemin(Int8), base = 12) == "-a8"
@test string(typemax(Int8), base = 12) == "a7"
@test string(typemin(Int16), base = 2) == "-1"*"0"^15
@test string(typemax(Int16), base = 2) == "1"^15
@test string(typemin(Int16), base = 8) == "-100000"
@test string(typemax(Int16), base = 8) == "77777"
@test string(typemin(Int16), base = 10) == "-32768"
@test string(typemax(Int16), base = 10) == "32767"
@test string(typemin(Int16), base = 16) == "-8000"
@test string(typemax(Int16), base = 16) == "7fff"
@test string(typemin(Int16)) == "-32768"
@test string(typemax(Int16)) == "32767"
@test string(typemin(Int16), base = 3) == "-1122221122"
@test string(typemax(Int16), base = 3) == "1122221121"
@test string(typemin(Int16), base = 12) == "-16b68"
@test string(typemax(Int16), base = 12) == "16b67"
@test string(typemin(Int32), base = 2) == "-1"*"0"^31
@test string(typemax(Int32), base = 2) == "1"^31
@test string(typemin(Int32), base = 8) == "-20000000000"
@test string(typemax(Int32), base = 8) == "17777777777"
@test string(typemin(Int32), base = 10) == "-2147483648"
@test string(typemax(Int32), base = 10) == "2147483647"
@test string(typemin(Int32), base = 16) == "-80000000"
@test string(typemax(Int32), base = 16) == "7fffffff"
@test string(typemin(Int32)) == "-2147483648"
@test string(typemax(Int32)) == "2147483647"
@test string(typemin(Int32), base = 3) == "-12112122212110202102"
@test string(typemax(Int32), base = 3) == "12112122212110202101"
@test string(typemin(Int32), base = 12) == "-4bb2308a8"
@test string(typemax(Int32), base = 12) == "4bb2308a7"
@test string(typemin(Int64), base = 2) == "-1"*"0"^63
@test string(typemax(Int64), base = 2) == "1"^63
@test string(typemin(Int64), base = 8) == "-1000000000000000000000"
@test string(typemax(Int64), base = 8) == "777777777777777777777"
@test string(typemin(Int64), base = 10) == "-9223372036854775808"
@test string(typemax(Int64), base = 10) == "9223372036854775807"
@test string(typemin(Int64), base = 16) == "-8000000000000000"
@test string(typemax(Int64), base = 16) == "7fffffffffffffff"
@test string(typemin(Int64)) == "-9223372036854775808"
@test string(typemax(Int64)) == "9223372036854775807"
@test string(typemin(Int64), base = 3) == "-2021110011022210012102010021220101220222"
@test string(typemax(Int64), base = 3) == "2021110011022210012102010021220101220221"
@test string(typemin(Int64), base = 12) == "-41a792678515120368"
@test string(typemax(Int64), base = 12) == "41a792678515120367"
@test string(typemin(Int128), base = 2) == "-1"*"0"^127
@test string(typemax(Int128), base = 2) == "1"^127
@test string(typemin(Int128), base = 8) == "-2000000000000000000000000000000000000000000"
@test string(typemax(Int128), base = 8) == "1777777777777777777777777777777777777777777"
@test string(typemin(Int128), base = 16) == "-80000000000000000000000000000000"
@test string(typemax(Int128), base = 16) == "7fffffffffffffffffffffffffffffff"
@test string(typemin(Int128), base = 10) == "-170141183460469231731687303715884105728"
@test string(typemax(Int128), base = 10) == "170141183460469231731687303715884105727"
@test string(typemin(Int128)) == "-170141183460469231731687303715884105728"
@test string(typemax(Int128)) == "170141183460469231731687303715884105727"
@test string(typemin(Int128), base = 3) ==
"-101100201022001010121000102002120122110122221010202000122201220121120010200022002"
@test string(typemax(Int128), base = 3) ==
"101100201022001010121000102002120122110122221010202000122201220121120010200022001"
@test string(typemin(Int128), base = 12) == "-2a695925806818735399a37a20a31b3534a8"
@test string(typemax(Int128), base = 12) == "2a695925806818735399a37a20a31b3534a7"
end
@testset "floating-point printing" begin
@test repr(1.0) == "1.0"
@test repr(-1.0) == "-1.0"
@test repr(0.0) == "0.0"
@test repr(-0.0) == "-0.0"
@test repr(0.1) == "0.1"
@test repr(0.2) == "0.2"
@test repr(0.3) == "0.3"
@test repr(0.1+0.2) != "0.3"
@test repr(Inf) == "Inf"
@test repr(-Inf) == "-Inf"
@test repr(NaN) == "NaN"
@test repr(-NaN) == "NaN"
@test repr(Float64(pi)) == "3.141592653589793"
# issue 6608
@test sprint(show, 666666.6, context=:compact => true) == "6.66667e5"
@test sprint(show, 666666.049, context=:compact => true) == "666666.0"
@test sprint(show, 666665.951, context=:compact => true) == "666666.0"
@test sprint(show, 66.66666, context=:compact => true) == "66.6667"
@test sprint(show, -666666.6, context=:compact => true) == "-6.66667e5"
@test sprint(show, -666666.049, context=:compact => true) == "-666666.0"
@test sprint(show, -666665.951, context=:compact => true) == "-666666.0"
@test sprint(show, -66.66666, context=:compact => true) == "-66.6667"
@test sprint(show, -498796.2749933266, context=:compact => true) == "-4.98796e5"
@test sprint(show, 123456.78, context=:compact=>true) == "1.23457e5"
# issue 37941
@test sprint(show, MIME("text/plain"), Float16(0.0)) == "Float16(0.0)"
@test sprint(show, MIME("text/plain"), -Float16(0.0)) == "Float16(-0.0)"
@test sprint(show, MIME("text/plain"), Float16(5.0)) == "Float16(5.0)"
@test sprint(show, MIME("text/plain"), -Float16(5.0)) == "Float16(-5.0)"
@test sprint(show, MIME("text/plain"), Float16(Inf)) == "Inf16"
@test sprint(show, MIME("text/plain"), -Float16(Inf)) == "-Inf16"
@test sprint(show, MIME("text/plain"), Float16(NaN)) == "NaN16"
@test repr(1.0f0) == "1.0f0"
@test repr(-1.0f0) == "-1.0f0"
@test repr(0.0f0) == "0.0f0"
@test repr(-0.0f0) == "-0.0f0"
@test repr(0.1f0) == "0.1f0"
@test repr(0.2f0) == "0.2f0"
@test repr(0.3f0) == "0.3f0"
@test repr(0.1f0+0.2f0) == "0.3f0"
@test repr(Inf32) == "Inf32"
@test repr(-Inf32) == "-Inf32"
@test repr(NaN32) == "NaN32"
@test repr(-NaN32) == "NaN32"
@test repr(Float32(pi)) == "3.1415927f0"
end
@testset "signs" begin
@test sign(1) == 1
@test sign(-1) == -1
@test sign(0) == 0
@test sign(1.0) == 1
@test sign(-1.0) == -1
@test sign(0.0) == 0
@test sign(-0.0) == 0
@test sign( 1.0/0.0) == 1
@test sign(-1.0/0.0) == -1
@test sign(Inf) == 1
@test sign(-Inf) == -1
@test isequal(sign(NaN), NaN)
@test isequal(sign(-NaN), NaN)
@test sign(2//3) == 1
@test sign(-2//3) == -1
@test sign(0//1) == 0
@test sign(-0//1) == 0
@test sign(1//0) == 1
@test sign(-1//0) == -1
@test isa(sign(2//3), Rational{Int})
@test isa(2//3 + 2//3im, Complex{Rational{Int}})
@test isa(sign(2//3 + 2//3im), ComplexF64)
@test sign(pi) === 1.0
@test sign(pi) === -sign(-pi)
@test sign(one(UInt)) == 1
@test sign(zero(UInt)) == 0
isdefined(Main, :Furlongs) || @eval Main include("testhelpers/Furlongs.jl")
using .Main.Furlongs
x = Furlong(3.0)
@test sign(x) * x == x
@test sign(-x) * -x == x
@test signbit(1) == 0
@test signbit(0) == 0
@test signbit(-1) == 1
@test signbit(1.0) == 0
@test signbit(0.0) == 0
@test signbit(-0.0) == 1
@test signbit(-1.0) == 1
@test signbit(1.0/0.0) == 0
@test signbit(-1.0/0.0) == 1
@test signbit(Inf) == 0
@test signbit(-Inf) == 1
@test signbit(NaN) == 0
@test signbit(-NaN) == 1
@test signbit(2//3) == 0
@test signbit(-2//3) == 1
@test signbit(0//1) == 0
@test signbit(-0//1) == 0
@test signbit(1//0) == 0
@test signbit(-1//0) == 1
end
@testset "copysign" begin
@test copysign(big(1.0),big(-2.0)) == big(-1.0)
@test copysign(-1,1) == 1
@test copysign(1,-1) == -1
@test copysign(-1,1.0) == 1
@test copysign(1,-1.0) == -1
@test copysign(-1,1//2) == 1
@test copysign(1,-1//2) == -1
@test copysign(1.0,-1) == -1.0
@test copysign(-1.0,1) == 1.0
@test copysign(1.0,-1.0) == -1.0
@test copysign(-1.0,1.0) == 1.0
@test copysign(1.0,-1//2) == -1.0
@test copysign(-1.0,1//2) == 1.0
@test copysign(1//2,-1) == -1//2
@test copysign(-1//2,1) == 1//2
@test copysign(1//2,-1//2) == -1//2
@test copysign(-1//2,1//2) == 1//2
@test copysign(1//2,-1.0) == -1//2
@test copysign(-1//2,1.0) == 1//2
# verify type stability with integer (x is negative)
@test eltype(copysign(-1,1)) <: Integer
@test eltype(copysign(-1,BigInt(1))) <: Integer
@test eltype(copysign(-1,1.0)) <: Integer
@test eltype(copysign(-1,1//2)) <: Integer
@test eltype(copysign(-BigInt(1),1)) <: Integer
@test eltype(copysign(-BigInt(1),1.0)) <: Integer
@test eltype(copysign(-BigInt(1),1//2)) <: Integer
@test eltype(copysign(-BigInt(1),BigInt(1))) <: Integer
@test eltype(copysign(-1,-1)) <: Integer
@test eltype(copysign(-1,-BigInt(1))) <: Integer
@test eltype(copysign(-1,-1.0)) <: Integer
@test eltype(copysign(-1,-1//2)) <: Integer
@test eltype(copysign(-BigInt(1),-1)) <: Integer
@test eltype(copysign(-BigInt(1),-1.0)) <: Integer
@test eltype(copysign(-BigInt(1),-1//2)) <: Integer
@test eltype(copysign(-BigInt(1),-BigInt(1))) <: Integer
# verify type stability with integer (x is positive)
@test eltype(copysign(1,1)) <: Integer
@test eltype(copysign(1,BigInt(1))) <: Integer
@test eltype(copysign(1,1.0)) <: Integer
@test eltype(copysign(1,1//2)) <: Integer
@test eltype(copysign(BigInt(1),1)) <: Integer
@test eltype(copysign(BigInt(1),1.0)) <: Integer
@test eltype(copysign(BigInt(1),1//2)) <: Integer
@test eltype(copysign(BigInt(1),BigInt(1))) <: Integer
@test eltype(copysign(1,-1)) <: Integer
@test eltype(copysign(1,-BigInt(1))) <: Integer
@test eltype(copysign(1,-1.0)) <: Integer
@test eltype(copysign(1,-1//2)) <: Integer
@test eltype(copysign(BigInt(1),-1)) <: Integer
@test eltype(copysign(BigInt(1),-1.0)) <: Integer
@test eltype(copysign(BigInt(1),-1//2)) <: Integer
@test eltype(copysign(BigInt(1),-BigInt(1))) <: Integer
# verify type stability with real (x is negative)
@test eltype(copysign(-1.0,1)) <: Real
@test eltype(copysign(-1.0,BigInt(1))) <: Real
@test eltype(copysign(-1.0,1.0)) <: Real
@test eltype(copysign(-1.0,1//2)) <: Real
@test eltype(copysign(-1.0,-1)) <: Real
@test eltype(copysign(-1.0,-BigInt(1))) <: Real
@test eltype(copysign(-1.0,-1.0)) <: Real
@test eltype(copysign(-1.0,-1//2)) <: Real
# Verify type stability with real (x is positive)
@test eltype(copysign(1.0,1)) <: Real
@test eltype(copysign(1.0,BigInt(1))) <: Real
@test eltype(copysign(1.0,1.0)) <: Real
@test eltype(copysign(1.0,1//2)) <: Real
@test eltype(copysign(1.0,-1)) <: Real
@test eltype(copysign(1.0,-BigInt(1))) <: Real
@test eltype(copysign(1.0,-1.0)) <: Real
@test eltype(copysign(1.0,-1//2)) <: Real
# Verify type stability with rational (x is negative)
@test eltype(copysign(-1//2,1)) <: Rational
@test eltype(copysign(-1//2,BigInt(1))) <: Rational
@test eltype(copysign(-1//2,1.0)) <: Rational
@test eltype(copysign(-1//2,1//2)) <: Rational
@test eltype(copysign(-1//2,-1)) <: Rational
@test eltype(copysign(-1//2,-BigInt(1))) <: Rational
@test eltype(copysign(-1//2,-1.0)) <: Rational
@test eltype(copysign(-1//2,-1//2)) <: Rational
# Verify type stability with rational (x is positive)
@test eltype(copysign(-1//2,1)) <: Rational
@test eltype(copysign(-1//2,BigInt(1))) <: Rational
@test eltype(copysign(-1//2,1.0)) <: Rational
@test eltype(copysign(-1//2,1//2)) <: Rational
@test eltype(copysign(-1//2,-1)) <: Rational
@test eltype(copysign(-1//2,-BigInt(1))) <: Rational
@test eltype(copysign(-1//2,-1.0)) <: Rational
@test eltype(copysign(-1//2,-1//2)) <: Rational
# test x = NaN
@test isnan(copysign(0/0,1))
@test isnan(copysign(0/0,-1))
# test x = Inf
@test isinf(copysign(1/0,1))
@test isinf(copysign(1/0,-1))
# with Unsigned argument
@test copysign(Float16(-1), 0x01) === Float16(1)
@test copysign(Float16(1), 0x01) === Float16(1)
@test copysign(-1.0f0, 0x01) === 1.0f0
@test copysign(1.0f0, 0x01) === 1.0f0
@test copysign(-1.0, 0x01) === 1.0
@test copysign(-1, 0x02) === 1
@test copysign(big(-1), 0x02) == 1
@test copysign(big(-1.0), 0x02) == 1.0
@test copysign(-1//2, 0x01) == 1//2
end
@testset "isnan/isinf/isfinite" begin
@test isnan(1) == false
@test isnan(1.0) == false
@test isnan(-1.0) == false
@test isnan(Inf) == false
@test isnan(-Inf) == false
@test isnan(NaN) == true
@test isnan(1//2) == false
@test isnan(-2//3) == false
@test isnan(5//0) == false
@test isnan(-3//0) == false
@test isinf(1) == false
@test isinf(1.0) == false
@test isinf(-1.0) == false
@test isinf(Inf) == true
@test isinf(-Inf) == true
@test isinf(NaN) == false
@test isinf(1//2) == false
@test isinf(-2//3) == false
@test isinf(5//0) == true
@test isinf(-3//0) == true
@test isfinite(1) == true
@test isfinite(1.0) == true
@test isfinite(-1.0) == true
@test isfinite(Inf) == false
@test isfinite(-Inf) == false
@test isfinite(NaN) == false
@test isfinite(1//2) == true
@test isfinite(-2//3) == true
@test isfinite(5//0) == false
@test isfinite(-3//0) == false
@test isfinite(pi) == true
@test isequal(-Inf,-Inf)
@test isequal(-1.0,-1.0)
@test isequal(-0.0,-0.0)
@test isequal(+0.0,+0.0)
@test isequal(+1.0,+1.0)
@test isequal(+Inf,+Inf)
@test isequal(-NaN,-NaN)
@test isequal(-NaN,+NaN)
@test isequal(+NaN,-NaN)
@test isequal(+NaN,+NaN)
@test !isequal(-Inf,+Inf)
@test !isequal(-1.0,+1.0)
@test !isequal(-0.0,+0.0)
@test !isequal(+0.0,-0.0)
@test !isequal(+1.0,-1.0)
@test !isequal(+Inf,-Inf)
@test isequal(-0.0f0,-0.0)
@test isequal( 0.0f0, 0.0)
@test !isequal(-0.0f0, 0.0)
@test !isequal(0.0f0 ,-0.0)
@test !isless(-Inf,-Inf)
@test isless(-Inf,-1.0)
@test isless(-Inf,-0.0)
@test isless(-Inf,+0.0)
@test isless(-Inf,+1.0)
@test isless(-Inf,+Inf)
@test isless(-Inf,-NaN)
@test isless(-Inf,+NaN)
@test !isless(-1.0,-Inf)
@test !isless(-1.0,-1.0)
@test isless(-1.0,-0.0)
@test isless(-1.0,+0.0)
@test isless(-1.0,+1.0)
@test isless(-1.0,+Inf)
@test isless(-1.0,-NaN)
@test isless(-1.0,+NaN)
@test !isless(-0.0,-Inf)
@test !isless(-0.0,-1.0)
@test !isless(-0.0,-0.0)
@test isless(-0.0,+0.0)
@test isless(-0.0,+1.0)
@test isless(-0.0,+Inf)
@test isless(-0.0,-NaN)
@test isless(-0.0,+NaN)
@test !isless(+0.0,-Inf)
@test !isless(+0.0,-1.0)
@test !isless(+0.0,-0.0)
@test !isless(+0.0,+0.0)
@test isless(+0.0,+1.0)
@test isless(+0.0,+Inf)
@test isless(+0.0,-NaN)
@test isless(+0.0,+NaN)
@test !isless(+1.0,-Inf)
@test !isless(+1.0,-1.0)
@test !isless(+1.0,-0.0)
@test !isless(+1.0,+0.0)
@test !isless(+1.0,+1.0)
@test isless(+1.0,+Inf)
@test isless(+1.0,-NaN)
@test isless(+1.0,+NaN)
@test !isless(+Inf,-Inf)
@test !isless(+Inf,-1.0)
@test !isless(+Inf,-0.0)
@test !isless(+Inf,+0.0)
@test !isless(+Inf,+1.0)
@test !isless(+Inf,+Inf)
@test isless(+Inf,-NaN)
@test isless(+Inf,+NaN)
@test !isless(-NaN,-Inf)
@test !isless(-NaN,-1.0)
@test !isless(-NaN,-0.0)
@test !isless(-NaN,+0.0)
@test !isless(-NaN,+1.0)
@test !isless(-NaN,+Inf)
@test !isless(-NaN,-NaN)
@test !isless(-NaN,+NaN)
@test !isless(+NaN,-Inf)
@test !isless(+NaN,-1.0)
@test !isless(+NaN,-0.0)
@test !isless(+NaN,+0.0)
@test !isless(+NaN,+1.0)
@test !isless(+NaN,+Inf)
@test !isless(+NaN,-NaN)
@test !isless(+NaN,+NaN)
@test !isless(+NaN,1)
@test !isless(-NaN,1)
@test isequal( 0, 0.0)
@test isequal( 0.0, 0)
@test !isequal( 0,-0.0)
@test !isequal(-0.0, 0)
@test isless(-0.0, 0)
@test !isless( 0,-0.0)
@test isless(-0.0, 0.0f0)
@test cmp(isless, -0.0, 0.0f0) == -1
@test cmp(isless, 0.0, -0.0f0) == 1
@test cmp(isless, NaN, 1) == 1
@test cmp(isless, 1, NaN) == -1
@test cmp(isless, NaN, NaN) == 0
end
@testset "Float vs Integer comparison" begin
for x=-5:5, y=-5:5
@test (x==y)==(Float64(x)==Int64(y))
@test (x!=y)==(Float64(x)!=Int64(y))
@test (x< y)==(Float64(x)< Int64(y))
@test (x> y)==(Float64(x)> Int64(y))
@test (x<=y)==(Float64(x)<=Int64(y))
@test (x>=y)==(Float64(x)>=Int64(y))
@test (x==y)==(Int64(x)==Float64(y))
@test (x!=y)==(Int64(x)!=Float64(y))
@test (x< y)==(Int64(x)< Float64(y))
@test (x> y)==(Int64(x)> Float64(y))
@test (x<=y)==(Int64(x)<=Float64(y))
@test (x>=y)==(Int64(x)>=Float64(y))
if x >= 0
@test (x==y)==(UInt64(x)==Float64(y))
@test (x!=y)==(UInt64(x)!=Float64(y))
@test (x< y)==(UInt64(x)< Float64(y))
@test (x> y)==(UInt64(x)> Float64(y))
@test (x<=y)==(UInt64(x)<=Float64(y))
@test (x>=y)==(UInt64(x)>=Float64(y))
end
if y >= 0
@test (x==y)==(Float64(x)==UInt64(y))
@test (x!=y)==(Float64(x)!=UInt64(y))
@test (x< y)==(Float64(x)< UInt64(y))
@test (x> y)==(Float64(x)> UInt64(y))
@test (x<=y)==(Float64(x)<=UInt64(y))
@test (x>=y)==(Float64(x)>=UInt64(y))
end
end
function _cmp_(x::Union{Int64,UInt64}, y::Float64)
if x==Int64(2)^53-2 && y==2.0^53-2; return 0; end
if x==Int64(2)^53-2 && y==2.0^53-1; return -1; end
if x==Int64(2)^53-2 && y==2.0^53 ; return -1; end
if x==Int64(2)^53-2 && y==2.0^53+2; return -1; end
if x==Int64(2)^53-2 && y==2.0^53+3; return -1; end
if x==Int64(2)^53-2 && y==2.0^53+4; return -1; end
if x==Int64(2)^53-1 && y==2.0^53-2; return +1; end
if x==Int64(2)^53-1 && y==2.0^53-1; return 0; end
if x==Int64(2)^53-1 && y==2.0^53 ; return -1; end
if x==Int64(2)^53-1 && y==2.0^53+2; return -1; end
if x==Int64(2)^53-1 && y==2.0^53+3; return -1; end
if x==Int64(2)^53-1 && y==2.0^53+4; return -1; end
if x==Int64(2)^53 && y==2.0^53-2; return +1; end
if x==Int64(2)^53 && y==2.0^53-1; return +1; end
if x==Int64(2)^53 && y==2.0^53 ; return 0; end
if x==Int64(2)^53 && y==2.0^53+2; return -1; end
if x==Int64(2)^53 && y==2.0^53+4; return -1; end
if x==Int64(2)^53+1 && y==2.0^53-2; return +1; end
if x==Int64(2)^53+1 && y==2.0^53-1; return +1; end
if x==Int64(2)^53+1 && y==2.0^53 ; return +1; end
if x==Int64(2)^53+1 && y==2.0^53+2; return -1; end
if x==Int64(2)^53+1 && y==2.0^53+4; return -1; end
if x==Int64(2)^53+2 && y==2.0^53-2; return +1; end
if x==Int64(2)^53+2 && y==2.0^53-1; return +1; end
if x==Int64(2)^53+2 && y==2.0^53 ; return +1; end
if x==Int64(2)^53+2 && y==2.0^53+2; return 0; end
if x==Int64(2)^53+2 && y==2.0^53+4; return -1; end
if x==Int64(2)^53+3 && y==2.0^53-2; return +1; end
if x==Int64(2)^53+3 && y==2.0^53-1; return +1; end
if x==Int64(2)^53+3 && y==2.0^53 ; return +1; end
if x==Int64(2)^53+3 && y==2.0^53+2; return +1; end
if x==Int64(2)^53+3 && y==2.0^53+4; return -1; end
if x==Int64(2)^53+4 && y==2.0^53-2; return +1; end
if x==Int64(2)^53+4 && y==2.0^53-1; return +1; end
if x==Int64(2)^53+4 && y==2.0^53 ; return +1; end
if x==Int64(2)^53+4 && y==2.0^53+2; return +1; end
if x==Int64(2)^53+4 && y==2.0^53+4; return 0; end
if x==Int64(2)^53+5 && y==2.0^53-2; return +1; end
if x==Int64(2)^53+5 && y==2.0^53-1; return +1; end
if x==Int64(2)^53+5 && y==2.0^53 ; return +1; end
if x==Int64(2)^53+5 && y==2.0^53+2; return +1; end
if x==Int64(2)^53+5 && y==2.0^53+4; return +1; end
error("invalid: _cmp_($x,$y)")
end
for x = Int64(2)^53-2:Int64(2)^53+5,
y = [2.0^53-2 2.0^53-1 2.0^53 2.0^53+2 2.0^53+4]
u = UInt64(x)
@test y == Float64(trunc(Int64,y))
@test (x==y)==(y==x)
@test (x!=y)==!(x==y)
@test (-x==-y)==(-y==-x)
@test (-x!=-y)==!(-x==-y)
@test (x<y)==(x<=y)&(x!=y)
@test (x<=y)==(x<y)|(x==y)
@test (x==y)==(x<=y)&!(x<y)
@test -x != x
@test -y != y
@test -x != y
@test -y != x
@test -x < x
@test -y < y
@test -x < y
@test -y < x
@test -x <= x
@test -y <= y
@test -x <= y
@test -y <= x
@test -y != u
@test -y < u
@test -y <= u
c = _cmp_(x,y)
if c < 0
@test !(x == y)
@test (x < y)
@test !(y < x)
@test (x <= y)
@test !(y <= x)
@test !(u == y)
@test (u < y)
@test !(y < u)
@test (u <= y)
@test !(y <= u)
@test !(-x == -y)
@test !(-x < -y)
@test (-y < -x)
@test !(-x <= -y)
@test (-y <= -x)
elseif c > 0
@test !(x == y)
@test !(x < y)
@test (y < x)
@test !(x <= y)
@test (y <= x)
@test !(u == y)
@test !(u < y)
@test (y < u)
@test !(u <= y)
@test (y <= u)
@test !(-x == -y)
@test (-x < -y)
@test !(-y < -x)
@test (-x <= -y)
@test !(-y <= -x)
else
@test (x == y)
@test !(x < y)
@test !(y < x)
@test (x <= y)
@test (y <= x)
@test (u == y)
@test !(u < y)
@test !(y < u)
@test (u <= y)
@test (y <= u)
@test (-x == -y)
@test !(-x < -y)
@test !(-y < -x)
@test (-x <= -y)
@test (-y <= -x)
end
end
@test Int64(2)^62-1 != 2.0^62
@test Int64(2)^62 == 2.0^62
@test Int64(2)^62+1 != 2.0^62
@test 2.0^62 != Int64(2)^62-1
@test 2.0^62 == Int64(2)^62
@test 2.0^62 != Int64(2)^62+1
@test typemax(Int64) != +2.0^63
@test typemin(Int64) == -2.0^63
@test typemin(Int64)+1 != -2.0^63
@test UInt64(2)^60-1 != 2.0^60
@test UInt64(2)^60 == 2.0^60
@test UInt64(2)^60+1 != 2.0^60
@test 2.0^60 != UInt64(2)^60-1
@test 2.0^60 == UInt64(2)^60
@test 2.0^60 != UInt64(2)^60+1
@test UInt64(2)^63-1 != 2.0^63
@test UInt64(2)^63 == 2.0^63
@test UInt64(2)^63+1 != 2.0^63
@test 2.0^63 != UInt64(2)^63-1
@test 2.0^63 == UInt64(2)^63
@test 2.0^63 != UInt64(2)^63+1
@test typemax(UInt64) != 2.0^64
# issue #9085
f9085() = typemax(UInt64) != 2.0^64