# 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) Top(T, op, x, y) = op(T.(x), T.(y)) Top(T, op) = (x, y) -> Top(T, op, x, y) _compare(x, y) = x == y for T in (Float16, Float32, Float64, BigFloat) minmax = Top(T,Base.minmax) min = Top(T,Base.min) max = Top(T,Base.max) (==) = Top(T,_compare) (===) = Top(T,Base.isequal) # we only use === to compare -0.0/0.0, `isequal` should be equivalent @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 end @testset "Base._extrema_rf for float" begin for T in (Float16, Float32, Float64, BigFloat) ordered = T[-Inf, -5, -0.0, 0.0, 3, Inf] unorded = T[NaN, -NaN] for i1 in 1:6, i2 in 1:6, j1 in 1:6, j2 in 1:6 x = ordered[i1], ordered[i2] y = ordered[j1], ordered[j2] z = ordered[min(i1,j1)], ordered[max(i2,j2)] @test Base._extrema_rf(x, y) === z end for i in 1:2, j1 in 1:6, j2 in 1:6 # unordered test (only 1 NaN) x = unorded[i] , unorded[i] y = ordered[j1], ordered[j2] @test Base._extrema_rf(x, y) === x @test Base._extrema_rf(y, x) === x end for i in 1:2, j in 1:2 # unordered test (2 NaNs) x = unorded[i], unorded[i] y = unorded[j], unorded[j] z = Base._extrema_rf(x, y) @test z === x || z === y end end 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 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 @test f9085() @test typemax(UInt64) < Float64(typemax(UInt64)) @test typemax(Int64) < Float64(typemax(Int64)) @test typemax(UInt64) <= Float64(typemax(UInt64)) @test typemax(Int64) <= Float64(typemax(Int64)) @test Float64(typemax(UInt64)) > typemax(UInt64) @test Float64(typemax(Int64)) > typemax(Int64) @test Float64(typemax(UInt64)) >= typemax(UInt64) @test Float64(typemax(Int64)) >= typemax(Int64) @test Float64(Int128(0)) == 0.0 @test Float32(Int128(0)) == 0.0f0 @test Float64(Int128(-1)) == -1.0 @test Float32(Int128(-1)) == -1.0f0 @test Float64(Int128(3)) == 3.0 @test Float32(Int128(3)) == 3.0f0 @test Float64(UInt128(10121)) == 10121.0 @test Float32(UInt128(10121)) == 10121.0f0 @test Float64(typemin(Int128)) == -2.0^127 @test Float32(typemin(Int128)) == -2.0f0^127 @test Float64(typemax(Int128)) == 2.0^127 @test Float32(typemax(Int128)) == 2.0f0^127 @test Float64(typemin(UInt128)) == 0.0 @test Float32(typemin(UInt128)) == 0.0f0 @test Float64(typemax(UInt128)) == 2.0^128 @test Float32(typemax(UInt128)) == 2.0f0^128 # leading zeros > 53 @test Float64(UInt128(Int64(2)^54)) == 1.8014398509481984e16 @test Float64(Int128(Int64(2)^54)) == 1.8014398509481984e16 @test Float32(UInt128(Int64(2)^54)) == 1.8014399f16 @test Float32(Int128(Int64(2)^54)) == 1.8014399f16 # check for double rounding in conversion @test Float64(10633823966279328163822077199654060032) == 1.0633823966279327e37 #0x1p123 @test Float64(10633823966279328163822077199654060033) == 1.063382396627933e37 #nextfloat(0x1p123) @test Float64(-10633823966279328163822077199654060032) == -1.0633823966279327e37 @test Float64(-10633823966279328163822077199654060033) == -1.063382396627933e37 # Test lsb/msb gaps of 54 (won't fit in 64 bit mantissa) @test Float64(Int128(9007199254740993)) == 9.007199254740992e15 @test Float64(UInt128(9007199254740993)) == 9.007199254740992e15 # Test 2^104-1 and 2^104 (2^104 is cutoff for which case is run in the conversion algorithm) @test Float64(Int128(20282409603651670423947251286015)) == 2.028240960365167e31 @test Float64(Int128(20282409603651670423947251286016)) == 2.028240960365167e31 @test Float64(UInt128(20282409603651670423947251286015)) == 2.028240960365167e31 @test Float64(UInt128(20282409603651670423947251286016)) == 2.028240960365167e31 end @testset "Float vs Int128 comparisons" begin @test Int128(1e30) == 1e30 @test Int128(1e30)+1 > 1e30 @test Int128(-2.0^127) == typemin(Int128) @test Float64(UInt128(3.7e19)) == 3.7e19 @test Float64(UInt128(3.7e30)) == 3.7e30 end @testset "Float16 vs Int comparisons" begin @test Inf16 != typemax(Int16) @test Inf16 != typemax(Int32) @test Inf16 != typemax(Int64) @test Inf16 != typemax(Int128) @test Inf16 != typemax(UInt16) @test Inf16 != typemax(UInt32) @test Inf16 != typemax(UInt64) @test Inf16 != typemax(UInt128) end @testset "NaN comparisons" begin @test !(NaN <= 1) @test !(NaN >= 1) @test !(NaN < 1) @test !(NaN > 1) @test !(1 <= NaN) @test !(1 >= NaN) @test !(1 < NaN) @test !(1 > NaN) end @testset "Irrational zero and one" begin @test one(pi) === true @test zero(pi) === false @test one(typeof(pi)) === true @test zero(typeof(pi)) === false end @testset "Irrationals compared with Irrationals" begin for i in (π, ℯ, γ, catalan) for j in (π, ℯ, γ, catalan) @test isequal(i==j, Float64(i)==Float64(j)) @test isequal(i!=j, Float64(i)!=Float64(j)) @test isequal(i<=j, Float64(i)<=Float64(j)) @test isequal(i>=j, Float64(i)>=Float64(j)) @test isequal(ij, Float64(i)>Float64(j)) end end end @testset "Irrational Inverses, Issue #30882" begin @test @inferred(inv(π)) ≈ 0.3183098861837907 end @testset "Irrationals compared with Rationals and Floats" begin @test Float64(pi,RoundDown) < pi @test Float64(pi,RoundUp) > pi @test !(Float64(pi,RoundDown) > pi) @test !(Float64(pi,RoundUp) < pi) @test Float64(pi,RoundDown) <= pi @test Float64(pi,RoundUp) >= pi @test Float64(pi,RoundDown) != pi @test Float64(pi,RoundUp) != pi @test Float32(pi,RoundDown) < pi @test Float32(pi,RoundUp) > pi @test !(Float32(pi,RoundDown) > pi) @test !(Float32(pi,RoundUp) < pi) @test prevfloat(big(pi)) < pi @test nextfloat(big(pi)) > pi @test !(prevfloat(big(pi)) > pi) @test !(nextfloat(big(pi)) < pi) @test 2646693125139304345//842468587426513207 < pi @test !(2646693125139304345//842468587426513207 > pi) @test 2646693125139304345//842468587426513207 != pi @test sqrt(2) == 1.4142135623730951 end Base.@irrational i46051 4863.185427757 1548big(pi) @testset "Irrational printing" begin @test sprint(show, "text/plain", π) == "π = 3.1415926535897..." @test sprint(show, "text/plain", π, context=:compact => true) == "π" @test sprint(show, π) == "π" # issue #46051 @test sprint(show, "text/plain", i46051) == "i46051 = 4863.185427757..." end @testset "Irrational round, float, ceil" begin using .MathConstants @test round(π) === 3.0 @test round(Int, ℯ) === 3 @test floor(ℯ) === 2.0 @test floor(Int, φ) === 1 @test ceil(γ) === 1.0 @test ceil(Int, catalan) === 1 end @testset "issue #6365" begin for T in (Float32, Float64) for i = 9007199254740992:9007199254740996 @test T(i) == T(BigFloat(i)) @test T(-i) == T(BigFloat(-i)) for r in (RoundNearest,RoundUp,RoundDown,RoundToZero) @test T(i,r) == T(BigFloat(i),r) @test T(-i,r) == T(BigFloat(-i),r) end end end end @testset "arithmetic with Ints and Floats" begin @test 1+1.5 == 2.5 @test 1.5+1 == 2.5 @test 1+1.5+2 == 4.5 @test isa(convert(Complex{Int16},1), Complex{Int16}) @test Complex(1,2)+1 == Complex(2,2) @test Complex(1,2)+1.5 == Complex(2.5,2.0) @test 1/Complex(2,2) == Complex(.25,-.25) @test Complex(1.5,1.0) + 1//2 == Complex(2.0,1.0) @test real(Complex(1//2,2//3)) == 1//2 @test imag(Complex(1//2,2//3)) == 2//3 @test Complex(1,2) + 1//2 == Complex(3//2,2//1) @test Complex(1,2) + 1//2 * 0.5 == Complex(1.25,2.0) @test (Complex(1,2) + 1//2) * 0.5 == Complex(0.75,1.0) @test (Complex(1,2)/Complex(2.5,3.0))*Complex(2.5,3.0) ≈ Complex(1,2) @test 0.7 < real(sqrt(Complex(0,1))) < 0.707107 end for T in Base.BitSigned_types @test abs(typemin(T)) == -typemin(T) #for x in (typemin(T),convert(T,-1),zero(T),one(T),typemax(T)) # @test signed(unsigned(x)) == x #end end #for T in (UInt8,UInt16,UInt32,UInt64,UInt128) # x in (typemin(T),one(T),typemax(T)) # @test unsigned(signed(x)) == x #end for S = Base.BitSigned64_types, U = Base.BitUnsigned64_types @test !(-one(S) == typemax(U)) @test -one(S) != typemax(U) @test -one(S) < typemax(U) @test !(typemax(U) <= -one(S)) end # check type of constructed complexes real_types = [Base.BitInteger64_types..., [Rational{T} for T in Base.BitInteger64_types]..., Float32, Float64] for A = real_types, B = real_types T = promote_type(A,B) @test typeof(Complex(convert(A,2),convert(B,3))) <: Complex{T} end # comparison should fail on complex @test_throws MethodError complex(1,2) > 0 @test_throws MethodError complex(1,2) > complex(0,0) @testset "div, fld, cld, rem, mod" begin for yr = Any[ 1:6, 0.25:0.25:6.0, 1//4:1//4:6//1 ], xr = Any[ 0:6, 0.0:0.25:6.0, 0//1:1//4:6//1 ] for y = yr, x = xr # check basic div functionality if 0 <= x < 1y @test div(+x,+y) == 0 @test div(+x,-y) == 0 @test div(-x,+y) == 0 @test div(-x,-y) == 0 end if 1y <= x < 2y @test div(+x,+y) == +1 @test div(+x,-y) == -1 @test div(-x,+y) == -1 @test div(-x,-y) == +1 end if 2y <= x < 3y @test div(+x,+y) == +2 @test div(+x,-y) == -2 @test div(-x,+y) == -2 @test div(-x,-y) == +2 end # check basic fld functionality if 0 == x @test fld(+x,+y) == 0 @test fld(+x,-y) == 0 @test fld(-x,+y) == 0 @test fld(-x,-y) == 0 end if 0 < x < 1y @test fld(+x,+y) == +0 @test fld(+x,-y) == -1 @test fld(-x,+y) == -1 @test fld(-x,-y) == +0 end if 1y == x @test fld(+x,+y) == +1 @test fld(+x,-y) == -1 @test fld(-x,+y) == -1 @test fld(-x,-y) == +1 end if 1y < x < 2y @test fld(+x,+y) == +1 @test fld(+x,-y) == -2 @test fld(-x,+y) == -2 @test fld(-x,-y) == +1 end if 2y == x @test fld(+x,+y) == +2 @test fld(+x,-y) == -2 @test fld(-x,+y) == -2 @test fld(-x,-y) == +2 end if 2y < x < 3y @test fld(+x,+y) == +2 @test fld(+x,-y) == -3 @test fld(-x,+y) == -3 @test fld(-x,-y) == +2 end # check basic cld functionality if 0 == x @test cld(+x,+y) == 0 @test cld(+x,-y) == 0 @test cld(-x,+y) == 0 @test cld(-x,-y) == 0 end if 0 < x < 1y @test cld(+x,+y) == +1 @test cld(+x,-y) == +0 @test cld(-x,+y) == +0 @test cld(-x,-y) == +1 end if 1y == x @test cld(+x,+y) == +1 @test cld(+x,-y) == -1 @test cld(-x,+y) == -1 @test cld(-x,-y) == +1 end if 1y < x < 2y @test cld(+x,+y) == +2 @test cld(+x,-y) == -1 @test cld(-x,+y) == -1 @test cld(-x,-y) == +2 end if 2y == x @test cld(+x,+y) == +2 @test cld(+x,-y) == -2 @test cld(-x,+y) == -2 @test cld(-x,-y) == +2 end if 2y < x < 3y @test cld(+x,+y) == +3 @test cld(+x,-y) == -2 @test cld(-x,+y) == -2 @test cld(-x,-y) == +3 end # check everything else in terms of div, fld, cld d = div(x,y) f = fld(x,y) c = cld(x,y) r = rem(x,y) m = mod(x,y) d2, r2 = divrem(x,y) f2, m2 = fldmod(x,y) t1 = isa(x,Rational) && isa(y,Rational) ? promote_type(typeof(numerator(x)),typeof(numerator(y))) : isa(x,Rational) ? promote_type(typeof(numerator(x)),typeof(y)) : isa(y,Rational) ? promote_type(typeof(x),typeof(numerator(y))) : promote_type(typeof(x),typeof(y)) t2 = promote_type(typeof(x),typeof(y)) @test typeof(d) <: t1 @test typeof(f) <: t1 @test typeof(c) <: t1 @test typeof(r) <: t2 @test typeof(m) <: t2 @test d == f @test c == f + (m == 0 ? 0 : 1) @test r == m @test 0 <= r < y @test x == y*d + r @test typeof(d2) == typeof(d) @test typeof(r2) == typeof(r) @test typeof(f2) == typeof(f) @test typeof(m2) == typeof(m) @test d2 == d @test r2 == r @test f2 == f @test m2 == m for X=[-1,1], Y=[-1,1] sx = X*x sy = Y*y sd = div(sx,sy) sf = fld(sx,sy) sc = cld(sx,sy) sr = rem(sx,sy) sm = mod(sx,sy) sd2, sr2 = divrem(sx,sy) sf2, sm2 = fldmod(sx,sy) @test typeof(sd) <: t1 @test typeof(sf) <: t1 @test typeof(sc) <: t1 @test typeof(sr) <: t2 @test typeof(sm) <: t2 @test sx < 0 ? -y < sr <= 0 : 0 <= sr < +y @test sy < 0 ? -y < sm <= 0 : 0 <= sm < +y @test sx == sy*sd + sr @test sx == sy*sf + sm @test typeof(sd2) == typeof(sd) @test typeof(sr2) == typeof(sr) @test typeof(sf2) == typeof(sf) @test typeof(sm2) == typeof(sm) @test sd2 == sd @test sr2 == sr @test sf2 == sf @test sm2 == sm end end end @test div(typemax(Int64) , 1) == 9223372036854775807 @test div(typemax(Int64) , 2) == 4611686018427387903 @test div(typemax(Int64) , 7) == 1317624576693539401 @test div(typemax(Int64) ,-1) == -9223372036854775807 @test div(typemax(Int64) ,-2) == -4611686018427387903 @test div(typemax(Int64) ,-7) == -1317624576693539401 @test div(typemax(Int64)-1, 1) == 9223372036854775806 @test div(typemax(Int64)-1, 2) == 4611686018427387903 @test div(typemax(Int64)-1, 7) == 1317624576693539400 @test div(typemax(Int64)-1,-1) == -9223372036854775806 @test div(typemax(Int64)-1,-2) == -4611686018427387903 @test div(typemax(Int64)-1,-7) == -1317624576693539400 @test div(typemax(Int64)-2, 1) == 9223372036854775805 @test div(typemax(Int64)-2, 2) == 4611686018427387902 @test div(typemax(Int64)-2, 7) == 1317624576693539400 @test div(typemax(Int64)-2,-1) == -9223372036854775805 @test div(typemax(Int64)-2,-2) == -4611686018427387902 @test div(typemax(Int64)-2,-7) == -1317624576693539400 @test div(typemin(Int64) , 1) == -9223372036854775807-1 @test div(typemin(Int64) , 2) == -4611686018427387904 @test div(typemin(Int64) , 7) == -1317624576693539401 @test div(typemin(Int64) ,-2) == 4611686018427387904 @test div(typemin(Int64) ,-7) == 1317624576693539401 @test div(typemin(Int64)+1, 1) == -9223372036854775807 @test div(typemin(Int64)+1, 2) == -4611686018427387903 @test div(typemin(Int64)+1, 7) == -1317624576693539401 @test div(typemin(Int64)+1,-1) == 9223372036854775807 @test div(typemin(Int64)+1,-2) == 4611686018427387903 @test div(typemin(Int64)+1,-7) == 1317624576693539401 @test div(typemin(Int64)+2, 1) == -9223372036854775806 @test div(typemin(Int64)+2, 2) == -4611686018427387903 @test div(typemin(Int64)+2, 7) == -1317624576693539400 @test div(typemin(Int64)+2,-1) == 9223372036854775806 @test div(typemin(Int64)+2,-2) == 4611686018427387903 @test div(typemin(Int64)+2,-7) == 1317624576693539400 @test div(typemin(Int64)+3, 1) == -9223372036854775805 @test div(typemin(Int64)+3, 2) == -4611686018427387902 @test div(typemin(Int64)+3, 7) == -1317624576693539400 @test div(typemin(Int64)+3,-1) == 9223372036854775805 @test div(typemin(Int64)+3,-2) == 4611686018427387902 @test div(typemin(Int64)+3,-7) == 1317624576693539400 @test fld(typemax(Int64) , 1) == 9223372036854775807 @test fld(typemax(Int64) , 2) == 4611686018427387903 @test fld(typemax(Int64) , 7) == 1317624576693539401 @test fld(typemax(Int64) ,-1) == -9223372036854775807 @test fld(typemax(Int64) ,-2) == -4611686018427387904 @test fld(typemax(Int64) ,-7) == -1317624576693539401 @test fld(typemax(Int64)-1, 1) == 9223372036854775806 @test fld(typemax(Int64)-1, 2) == 4611686018427387903 @test fld(typemax(Int64)-1, 7) == 1317624576693539400 @test fld(typemax(Int64)-1,-1) == -9223372036854775806 @test fld(typemax(Int64)-1,-2) == -4611686018427387903 @test fld(typemax(Int64)-1,-7) == -1317624576693539401 @test fld(typemax(Int64)-2, 1) == 9223372036854775805 @test fld(typemax(Int64)-2, 2) == 4611686018427387902 @test fld(typemax(Int64)-2, 7) == 1317624576693539400 @test fld(typemax(Int64)-2,-1) == -9223372036854775805 @test fld(typemax(Int64)-2,-2) == -4611686018427387903 @test fld(typemax(Int64)-2,-7) == -1317624576693539401 @test fld(typemin(Int64) , 1) == -9223372036854775807-1 @test fld(typemin(Int64) , 2) == -4611686018427387904 @test fld(typemin(Int64) , 7) == -1317624576693539402 @test fld(typemin(Int64) ,-2) == 4611686018427387904 @test fld(typemin(Int64) ,-7) == 1317624576693539401 @test fld(typemin(Int64)+1, 1) == -9223372036854775807 @test fld(typemin(Int64)+1, 2) == -4611686018427387904 @test fld(typemin(Int64)+1, 7) == -1317624576693539401 @test fld(typemin(Int64)+1,-1) == 9223372036854775807 @test fld(typemin(Int64)+1,-2) == 4611686018427387903 @test fld(typemin(Int64)+1,-7) == 1317624576693539401 @test fld(typemin(Int64)+2, 1) == -9223372036854775806 @test fld(typemin(Int64)+2, 2) == -4611686018427387903 @test fld(typemin(Int64)+2, 7) == -1317624576693539401 @test fld(typemin(Int64)+2,-1) == 9223372036854775806 @test fld(typemin(Int64)+2,-2) == 4611686018427387903 @test fld(typemin(Int64)+2,-7) == 1317624576693539400 @test fld(typemin(Int64)+3, 1) == -9223372036854775805 @test fld(typemin(Int64)+3, 2) == -4611686018427387903 @test fld(typemin(Int64)+3, 7) == -1317624576693539401 @test fld(typemin(Int64)+3,-1) == 9223372036854775805 @test fld(typemin(Int64)+3,-2) == 4611686018427387902 @test fld(typemin(Int64)+3,-7) == 1317624576693539400 @test cld(typemax(Int64) , 1) == 9223372036854775807 @test cld(typemax(Int64) , 2) == 4611686018427387904 @test cld(typemax(Int64) , 7) == 1317624576693539401 @test cld(typemax(Int64) ,-1) == -9223372036854775807 @test cld(typemax(Int64) ,-2) == -4611686018427387903 @test cld(typemax(Int64) ,-7) == -1317624576693539401 @test cld(typemax(Int64)-1, 1) == 9223372036854775806 @test cld(typemax(Int64)-1, 2) == 4611686018427387903 @test cld(typemax(Int64)-1, 7) == 1317624576693539401 @test cld(typemax(Int64)-1,-1) == -9223372036854775806 @test cld(typemax(Int64)-1,-2) == -4611686018427387903 @test cld(typemax(Int64)-1,-7) == -1317624576693539400 @test cld(typemax(Int64)-2, 1) == 9223372036854775805 @test cld(typemax(Int64)-2, 2) == 4611686018427387903 @test cld(typemax(Int64)-2, 7) == 1317624576693539401 @test cld(typemax(Int64)-2,-1) == -9223372036854775805 @test cld(typemax(Int64)-2,-2) == -4611686018427387902 @test cld(typemax(Int64)-2,-7) == -1317624576693539400 @test cld(typemin(Int64) , 1) == -9223372036854775807-1 @test cld(typemin(Int64) , 2) == -4611686018427387904 @test cld(typemin(Int64) , 7) == -1317624576693539401 @test cld(typemin(Int64) ,-2) == 4611686018427387904 @test cld(typemin(Int64) ,-7) == 1317624576693539402 @test cld(typemin(Int64)+1, 1) == -9223372036854775807 @test cld(typemin(Int64)+1, 2) == -4611686018427387903 @test cld(typemin(Int64)+1, 7) == -1317624576693539401 @test cld(typemin(Int64)+1,-1) == 9223372036854775807 @test cld(typemin(Int64)+1,-2) == 4611686018427387904 @test cld(typemin(Int64)+1,-7) == 1317624576693539401 @test cld(typemin(Int64)+2, 1) == -9223372036854775806 @test cld(typemin(Int64)+2, 2) == -4611686018427387903 @test cld(typemin(Int64)+2, 7) == -1317624576693539400 @test cld(typemin(Int64)+2,-1) == 9223372036854775806 @test cld(typemin(Int64)+2,-2) == 4611686018427387903 @test cld(typemin(Int64)+2,-7) == 1317624576693539401 @test cld(typemin(Int64)+3, 1) == -9223372036854775805 @test cld(typemin(Int64)+3, 2) == -4611686018427387902 @test cld(typemin(Int64)+3, 7) == -1317624576693539400 @test cld(typemin(Int64)+3,-1) == 9223372036854775805 @test cld(typemin(Int64)+3,-2) == 4611686018427387903 @test cld(typemin(Int64)+3,-7) == 1317624576693539401 for x=Any[typemin(Int64), -typemax(Int64), -typemax(Int64)+1, -typemax(Int64)+2, typemax(Int64)-2, typemax(Int64)-1, typemax(Int64), typemax(UInt64)-1, typemax(UInt64)-2, typemax(UInt64)], y=[-7,-2,-1,1,2,7] if x >= 0 @test div(unsigned(x),y) == unsigned(div(x,y)) @test fld(unsigned(x),y) == unsigned(fld(x,y)) @test cld(unsigned(x),y) == unsigned(cld(x,y)) end if isa(x,Signed) && y >= 0 @test div(x,unsigned(y)) == div(x,y) @test fld(x,unsigned(y)) == fld(x,y) @test cld(x,unsigned(y)) == cld(x,y) end end for x=0:5, y=1:5 @test div(UInt(x),UInt(y)) == div(x,y) @test div(UInt(x),y) == div(x,y) @test div(x,UInt(y)) == div(x,y) @test div(UInt(x),-y) == reinterpret(UInt,div(x,-y)) @test div(-x,UInt(y)) == div(-x,y) @test fld(UInt(x),UInt(y)) == fld(x,y) @test fld(UInt(x),y) == fld(x,y) @test fld(x,UInt(y)) == fld(x,y) @test fld(UInt(x),-y) == reinterpret(UInt,fld(x,-y)) @test fld(-x,UInt(y)) == fld(-x,y) @test cld(UInt(x),UInt(y)) == cld(x,y) @test cld(UInt(x),y) == cld(x,y) @test cld(x,UInt(y)) == cld(x,y) @test cld(UInt(x),-y) == reinterpret(UInt,cld(x,-y)) @test cld(-x,UInt(y)) == cld(-x,y) @test rem(UInt(x),UInt(y)) == rem(x,y) @test rem(UInt(x),y) == rem(x,y) @test rem(x,UInt(y)) == rem(x,y) @test rem(UInt(x),-y) == rem(x,-y) @test rem(-x,UInt(y)) == rem(-x,y) @test mod(UInt(x),UInt(y)) == mod(x,y) @test mod(UInt(x),y) == mod(x,y) @test mod(x,UInt(y)) == mod(x,y) @test mod(UInt(x),-y) == mod(x,-y) @test mod(-x,UInt(y)) == mod(-x,y) end @test div(typemax(UInt64) , 1) == typemax(UInt64) @test div(typemax(UInt64) ,-1) == -typemax(UInt64) @test div(typemax(UInt64)-1, 1) == typemax(UInt64)-1 @test div(typemax(UInt64)-1,-1) == -typemax(UInt64)+1 @test div(typemax(UInt64)-2, 1) == typemax(UInt64)-2 @test div(typemax(UInt64)-2,-1) == -typemax(UInt64)+2 @test signed(div(unsigned(typemax(Int64))+2, 1)) == typemax(Int64)+2 @test signed(div(unsigned(typemax(Int64))+2,-1)) == -typemax(Int64)-2 @test signed(div(unsigned(typemax(Int64))+1, 1)) == typemax(Int64)+1 @test signed(div(unsigned(typemax(Int64))+1,-1)) == -typemax(Int64)-1 @test signed(div(unsigned(typemax(Int64)) , 1)) == typemax(Int64) @test signed(div(unsigned(typemax(Int64)) ,-1)) == -typemax(Int64) @test signed(div(typemax(UInt),typemax(Int))) == 2 @test signed(div(typemax(UInt),(typemax(Int)>>1)+1)) == 3 @test signed(div(typemax(UInt),typemax(Int)>>1)) == 4 @test signed(div(typemax(UInt),typemin(Int))) == -1 @test signed(div(typemax(UInt),typemin(Int)+1)) == -2 @test signed(div(typemax(UInt),typemin(Int)>>1)) == -3 @test signed(div(typemax(UInt),(typemin(Int)>>1)+1)) == -4 @test fld(typemax(UInt64) , 1) == typemax(UInt64) @test fld(typemax(UInt64) ,-1) == -typemax(UInt64) @test fld(typemax(UInt64)-1, 1) == typemax(UInt64)-1 @test fld(typemax(UInt64)-1,-1) == -typemax(UInt64)+1 @test fld(typemax(UInt64)-2, 1) == typemax(UInt64)-2 @test fld(typemax(UInt64)-2,-1) == -typemax(UInt64)+2 @test signed(fld(unsigned(typemax(Int64))+2, 1)) == typemax(Int64)+2 @test signed(fld(unsigned(typemax(Int64))+2,-1)) == -typemax(Int64)-2 @test signed(fld(unsigned(typemax(Int64))+1, 1)) == typemax(Int64)+1 @test signed(fld(unsigned(typemax(Int64))+1,-1)) == -typemax(Int64)-1 @test signed(fld(unsigned(typemax(Int64)) , 1)) == typemax(Int64) @test signed(fld(unsigned(typemax(Int64)) ,-1)) == -typemax(Int64) @test signed(fld(typemax(UInt),typemax(Int))) == 2 @test signed(fld(typemax(UInt),(typemax(Int)>>1)+1)) == 3 @test signed(fld(typemax(UInt),typemax(Int)>>1)) == 4 @test signed(fld(typemax(UInt),typemin(Int))) == -2 @test signed(fld(typemax(UInt),typemin(Int)+1)) == -3 @test signed(fld(typemax(UInt),typemin(Int)>>1)) == -4 @test signed(fld(typemax(UInt),(typemin(Int)>>1)+1)) == -5 @test cld(typemax(UInt64) , 1) == typemax(UInt64) @test cld(typemax(UInt64) ,-1) == -typemax(UInt64) @test cld(typemax(UInt64)-1, 1) == typemax(UInt64)-1 @test cld(typemax(UInt64)-1,-1) == -typemax(UInt64)+1 @test cld(typemax(UInt64)-2, 1) == typemax(UInt64)-2 @test cld(typemax(UInt64)-2,-1) == -typemax(UInt64)+2 @test signed(cld(unsigned(typemax(Int64))+2, 1)) == typemax(Int64)+2 @test signed(cld(unsigned(typemax(Int64))+2,-1)) == -typemax(Int64)-2 @test signed(cld(unsigned(typemax(Int64))+1, 1)) == typemax(Int64)+1 @test signed(cld(unsigned(typemax(Int64))+1,-1)) == -typemax(Int64)-1 @test signed(cld(unsigned(typemax(Int64)) , 1)) == typemax(Int64) @test signed(cld(unsigned(typemax(Int64)) ,-1)) == -typemax(Int64) @test signed(cld(typemax(UInt),typemax(Int))) == 3 @test signed(cld(typemax(UInt),(typemax(Int)>>1)+1)) == 4 @test signed(cld(typemax(UInt),typemax(Int)>>1)) == 5 @test signed(cld(typemax(UInt),typemin(Int))) == -1 @test signed(cld(typemax(UInt),typemin(Int)+1)) == -2 @test signed(cld(typemax(UInt),typemin(Int)>>1)) == -3 @test signed(cld(typemax(UInt),(typemin(Int)>>1)+1)) == -4 @testset "UInt128 div/rem" begin uints = [0xadc0db298a7401251f4fa96ba429cb24, 0xd11ef418102afb1f7959b6df48d08044] for x in uints, y in uints, sx in 0:128, sy in 0:127 xs = x >> sx ys = y >> sy q, r = @inferred(divrem(xs, ys))::Tuple{UInt128,UInt128} @test xs == q*ys + r && r < ys @test q == @inferred(div(xs, ys))::UInt128 @test r == @inferred(rem(xs, ys))::UInt128 end end @testset "exceptions and special cases" begin for T in (Int8,Int16,Int32,Int64,Int128, UInt8,UInt16,UInt32,UInt64,UInt128) @test_throws DivideError div(T(1), T(0)) @test_throws DivideError fld(T(1), T(0)) @test_throws DivideError cld(T(1), T(0)) @test_throws DivideError rem(T(1), T(0)) @test_throws DivideError mod(T(1), T(0)) end for T in (Int8,Int16,Int32,Int64,Int128) @test_throws DivideError div(typemin(T), T(-1)) @test_throws DivideError fld(typemin(T), T(-1)) @test_throws DivideError cld(typemin(T), T(-1)) @test rem(typemin(T), T(-1)) === T(0) @test mod(typemin(T), T(-1)) === T(0) end end @testset "issue #4156" begin @test fld(1.4, 0.35667494393873234) == 3.0 @test div(1.4, 0.35667494393873234) == 3.0 @test fld(0.3, 0.01) == 29.0 @test div(0.3, 0.01) == 29.0 # see https://github.com/JuliaLang/julia/issues/3127 end @testset "issue #8831" begin @test rem(prevfloat(1.0),1.0) == prevfloat(1.0) @test mod(prevfloat(1.0),1.0) == prevfloat(1.0) end @test mod(Int64(2), typemax(Int64)) == 2 # issue #3046 @testset "issue #45875" begin @test cld(+1.1, 0.1) == div(+1.1, 0.1, RoundUp) == ceil(big(+1.1)/big(0.1)) == +12.0 @test fld(+1.1, 0.1) == div(+1.1, 0.1, RoundDown) == floor(big(+1.1)/big(0.1)) == +11.0 @test cld(-1.1, 0.1) == div(-1.1, 0.1, RoundUp) == ceil(big(-1.1)/big(0.1)) == -11.0 @test fld(-1.1, 0.1) == div(-1.1, 0.1, RoundDown) == floor(big(-1.1)/big(0.1)) == -12.0 end end @testset "return types" begin for T in (Int8,Int16,Int32,Int64,Int128, UInt8,UInt16,UInt32,UInt64,UInt128) z, o = T(0), T(1) @test typeof(+z) === T @test typeof(-z) === T @test typeof(abs(z)) === T @test typeof(sign(z)) === T @test typeof(copysign(z,z)) === T @test typeof(flipsign(z,z)) === T @test typeof(z+z) === T @test typeof(z-z) === T @test typeof(z*z) === T @test typeof(z÷o) === T @test typeof(z%o) === T @test typeof(fld(z,o)) === T @test typeof(mod(z,o)) === T @test typeof(cld(z,o)) === T end end # things related to floating-point epsilon @test eps() == eps(Float64) @test eps(Float64) == eps(1.0) @test eps(Float64) == eps(1.5) @test eps(Float32) == eps(1f0) @test eps(float(0)) == 5e-324 @test eps(-float(0)) == 5e-324 @test eps(nextfloat(float(0))) == 5e-324 @test eps(-nextfloat(float(0))) == 5e-324 @test eps(floatmin()) == 5e-324 @test eps(-floatmin()) == 5e-324 @test eps(floatmax()) == 2.0^(1023-52) @test eps(-floatmax()) == 2.0^(1023-52) @test isnan(eps(NaN)) @test isnan(eps(Inf)) @test isnan(eps(-Inf)) @test .1+.1+.1 != .3 @test .1+.1+.1 ≈ .3 @test .1+.1+.1-.3 ≉ 0 @test .1+.1+.1-.3 ≈ 0 atol=eps(.3) @test 1.1 ≈ 1.1f0 @test div(1e50,1) == 1e50 @test fld(1e50,1) == 1e50 @test cld(1e50,1) == 1e50 @testset "binary literals" begin @test 0b1010101 == 0x55 @test isa(0b00000000,UInt8) @test isa(0b000000000,UInt16) @test isa(0b0000000000000000,UInt16) @test isa(0b00000000000000000,UInt32) @test isa(0b00000000000000000000000000000000,UInt32) @test isa(0b000000000000000000000000000000000,UInt64) @test isa(0b0000000000000000000000000000000000000000000000000000000000000000,UInt64) @test isa(0b00000000000000000000000000000000000000000000000000000000000000000,UInt128) @test isa(0b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,UInt128) @test isa(0b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,BigInt) @test isa(0b11111111,UInt8) @test isa(0b111111111,UInt16) @test isa(0b1111111111111111,UInt16) @test isa(0b11111111111111111,UInt32) @test isa(0b11111111111111111111111111111111,UInt32) @test isa(0b111111111111111111111111111111111,UInt64) @test isa(0b1111111111111111111111111111111111111111111111111111111111111111,UInt64) @test isa(0b11111111111111111111111111111111111111111111111111111111111111111,UInt128) @test isa(0b11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111,UInt128) @test isa(0b111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111,BigInt) end @testset "octal literals" begin @test 0o10 == 0x8 @test 0o100 == 0x40 @test 0o1000 == 0x200 @test 0o724 == 0x1d4 @test isa(0o00,UInt8) @test isa(0o000,UInt8) @test isa(0o00000,UInt16) @test isa(0o000000,UInt16) @test isa(0o0000000000,UInt32) @test isa(0o00000000000,UInt32) @test isa(0o000000000000000000000,UInt64) @test isa(0o0000000000000000000000,UInt64) @test isa(0o000000000000000000000000000000000000000000,UInt128) @test isa(0o00000000000000000000000000000000000000000000,BigInt) @test isa(0o11,UInt8) @test isa(0o111,UInt8) @test isa(0o11111,UInt16) @test isa(0o111111,UInt16) @test isa(0o1111111111,UInt32) @test isa(0o11111111111,UInt32) @test isa(0o111111111111111111111,UInt64) @test isa(0o1111111111111111111111,UInt64) @test isa(0o111111111111111111111111111111111111111111,UInt128) @test isa(0o1111111111111111111111111111111111111111111,UInt128) @test isa(0o3777777777777777777777777777777777777777777,UInt128) @test isa(0o11111111111111111111111111111111111111111111,BigInt) @test 0o4000000000000000000000000000000000000000000 == 340282366920938463463374607431768211456 @test isa(0o077, UInt8) @test isa(0o377, UInt8) @test isa(0o400, UInt16) @test isa(0o077777, UInt16) @test isa(0o177777, UInt16) @test isa(0o200000, UInt32) @test isa(0o00000000000, UInt32) @test isa(0o17777777777, UInt32) @test isa(0o40000000000, UInt64) @test isa(0o0000000000000000000000, UInt64) @test isa(0o1000000000000000000000, UInt64) @test isa(0o2000000000000000000000, UInt128) @test isa(0o0000000000000000000000000000000000000000000, UInt128) @test isa(0o1000000000000000000000000000000000000000000, UInt128) @test isa(0o2000000000000000000000000000000000000000000, UInt128) @test String([0o110, 0o145, 0o154, 0o154, 0o157, 0o054, 0o040, 0o127, 0o157, 0o162, 0o154, 0o144, 0o041]) == "Hello, World!" end @testset "hexadecimal literals" begin @test isa(0x00,UInt8) @test isa(0x000,UInt16) @test isa(0x0000,UInt16) @test isa(0x00000,UInt32) @test isa(0x00000000,UInt32) @test isa(0x000000000,UInt64) @test isa(0x0000000000000000,UInt64) @test isa(0x00000000000000000,UInt128) @test isa(0x00000000000000000000000000000000,UInt128) @test isa(0x000000000000000000000000000000000,BigInt) @test isa(0x11,UInt8) @test isa(0x111,UInt16) @test isa(0x1111,UInt16) @test isa(0x11111,UInt32) @test isa(0x11111111,UInt32) @test isa(0x111111111,UInt64) @test isa(0x1111111111111111,UInt64) @test isa(0x11111111111111111,UInt128) @test isa(0x11111111111111111111111111111111,UInt128) @test isa(0x111111111111111111111111111111111,BigInt) end @testset "minus sign and unsigned literals" begin # "-" is not part of unsigned literals @test -0x10 == -(0x10) @test -0b10 == -(0b10) @test -0o10 == -(0o10) @test -0x0010 == -(0x0010) @test -0b0010 == -(0b0010) @test -0o0010 == -(0o0010) @test -0x00000000000000001 == -(0x00000000000000001) @test -0o0000000000000000000001 == -(0o0000000000000000000001) @test -0b00000000000000000000000000000000000000000000000000000000000000001 == -(0b00000000000000000000000000000000000000000000000000000000000000001) @test -0x000000000000000000000000000000001 == -(0x000000000000000000000000000000001) @test -0o0000000000000000000000000000000000000000001 == -(0o0000000000000000000000000000000000000000001) @test -0b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 == -(0b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001) @test isa(-0x00,UInt8) @test isa(-0x0000000000000000,UInt64) @test isa(-0x00000000000000000,UInt128) @test isa(-0x00000000000000000000000000000000,UInt128) @test isa(-0x000000000000000000000000000000000,BigInt) end @testset "Float32 literals" begin @test isa(1f0,Float32) @test isa(1.f0,Float32) @test isa(1.0f0,Float32) @test 1f0 == 1. @test isa(1f1,Float32) @test 1f1 == 10. end @testset "hexadecimal float literals" begin @test 0x1p0 === 1. @test 0x1p1 === 2. @test 0x.1p0 === 0.0625 @test 0x.1p1 === 0.125 @test 0xfp0 === 15. @test 0xfp1 === 30. @test 0x.fp0 === 0.9375 @test 0x.fp1 === 1.875 @test 0x1.p0 === 1. @test 0x1.p1 === 2. @test 0xf.p0 === 15. @test 0xf.p1 === 30. @test 0x1.0p0 === 1. @test 0x1.0p1 === 2. @test 0x1.1p0 === 1.0625 @test 0x1.1p1 === 2.125 @test 0x1.fp0 === 1.9375 @test 0x1.fp1 === 3.875 @test 0xf.0p0 === 15. @test 0xf.0p1 === 30. @test 0xf.1p0 === 15.0625 @test 0xf.1p1 === 30.125 @test 0xf.fp0 === 15.9375 @test 0xf.fp1 === 31.875 @test 0x1P0 === 1. @test 0x1P1 === 2. @test 0x.1P0 === 0.0625 @test 0x.1P1 === 0.125 @test 0xfP0 === 15. @test 0xfP1 === 30. @test 0x.fP0 === 0.9375 @test 0x.fP1 === 1.875 @test 0x1.P0 === 1. @test 0x1.P1 === 2. @test 0xf.P0 === 15. @test 0xf.P1 === 30. @test 0x1.0P0 === 1. @test 0x1.0P1 === 2. @test 0x1.1P0 === 1.0625 @test 0x1.1P1 === 2.125 @test 0x1.fP0 === 1.9375 @test 0x1.fP1 === 3.875 @test 0xf.0P0 === 15. @test 0xf.0P1 === 30. @test 0xf.1P0 === 15.0625 @test 0xf.1P1 === 30.125 @test 0xf.fP0 === 15.9375 @test 0xf.fP1 === 31.875 @test -0x1.0p2 === -4.0 end @testset "eps / floatmin / floatmax" begin @test 0x1p-52 == eps() @test 0x1p-52 + 1 != 1 @test 0x1p-53 + 1 == 1 @test 0x1p-1022 == floatmin() @test 0x1.fffffffffffffp1023 == floatmax() @test isinf(nextfloat(0x1.fffffffffffffp1023)) end @testset "issue #1308" begin @test string(~UInt128(0), base = 16) == "f"^32 @test (~0)%UInt128 == ~UInt128(0) @test Int128(~0) == ~Int128(0) end # no loss of precision for rational powers (issue #18114) @test BigFloat(2)^(BigFloat(1)/BigFloat(3)) == BigFloat(2)^(1//3) @testset "large shift amounts" begin @test Int32(-1)>>31 == -1 @test Int32(-1)>>32 == -1 @test Int32(-1)>>33 == -1 @test 10>>64 == 0 @test 10>>>64 == 0 @test 10<<64 == 0 end # issue #3520 - certain int literals on 32-bit systems @test -536870913 === -536870912-1 @testset "check gcd and related functions against GMP" begin for T in (Int32,Int64), ii = -20:20, jj = -20:20 i::T, j::T = ii, jj local d = gcd(i,j) @test d >= 0 @test lcm(i,j) >= 0 local ib = big(i) local jb = big(j) @test d == gcd(ib,jb) @test lcm(i,j) == lcm(ib,jb) @test gcdx(i,j) == gcdx(ib,jb) if j == 0 || d != 1 @test_throws DomainError invmod(i,j) @test_throws DomainError invmod(ib,jb) else n = invmod(i,j) @test div(n, j) == 0 @test n == invmod(ib,jb) @test mod(n*i,j) == mod(1,j) end end end @testset "powermod" begin # check powermod function against few types (in particular [U]Int128 and BigInt) for i = -10:10, p = 0:5, m = -10:10 m == 0 && continue x = powermod(i, p, m) for T in [Int32, Int64, Int128, UInt128, BigInt] T <: Unsigned && m < 0 && continue let xT = powermod(i, p, T(m)) @test x == xT @test isa(xT, T) end T <: Unsigned && i < 0 && continue @test x == mod(T(i)^p, T(m)) end end # with m==1 should give 0 @test powermod(1,0,1) == 0 @test powermod(1,0,big(1)) == 0 @test powermod(1,0,-1) == 0 @test powermod(1,0,big(-1)) == 0 # divide by zero error @test_throws DivideError powermod(1,0,0) @test_throws DivideError powermod(1,0,big(0)) # negative powers perform modular inversion before exponentiation @test powermod(1, -1, 1) == 0 @test powermod(1, -1, big(1)) == 0 end @testset "additional BigInt powermod tests" begin @test powermod(0, 1, big(6)) == 0 @test powermod(1, 0, big(6)) == 1 @test powermod(big(6), big(6), big(6)) == 0 @test powermod(10, 50, big(10)^50 - 1) == 1 @test powermod(-1, 1, big(6)) == 5 @test powermod(-1, 0, big(6)) == 1 @test powermod(-1, -1, big(6)) == 5 @test powermod(-1, 1, big(-6)) == -1 @test powermod(-1, 0, big(-6)) == -5 @test powermod(-1, -1, big(-6)) == -1 @test_throws DivideError powermod(2, -1, big(6)) @test_throws DivideError powermod(-2, -1, big(6)) end @testset "other divide-by-zero errors" begin @test_throws DivideError div(1,0) @test_throws DivideError rem(1,0) @test_throws DivideError divrem(1,0) @test_throws DivideError fld(1,0) @test_throws DivideError mod(1,0) @test_throws DivideError fldmod(1,0) @test_throws DivideError cld(1,0) @test_throws DivideError div(-1,0) @test_throws DivideError rem(-1,0) @test_throws DivideError divrem(-1,0) @test_throws DivideError fld(-1,0) @test_throws DivideError mod(-1,0) @test_throws DivideError fldmod(-1,0) @test_throws DivideError cld(-1,0) @test_throws DivideError div(UInt(1),UInt(0)) @test_throws DivideError rem(UInt(1),UInt(0)) @test_throws DivideError divrem(UInt(1),UInt(0)) @test_throws DivideError fld(UInt(1),UInt(0)) @test_throws DivideError mod(UInt(1),UInt(0)) @test_throws DivideError fldmod(UInt(1),UInt(0)) @test_throws DivideError cld(UInt(1),UInt(0)) @test_throws DivideError div(typemin(Int),-1) @test_throws DivideError fld(typemin(Int),-1) @test_throws DivideError cld(typemin(Int),-1) @test_throws DivideError divrem(typemin(Int),-1) @test_throws DivideError fldmod(typemin(Int),-1) @test rem(typemin(Int),-1) == 0 @test mod(typemin(Int),-1) == 0 end @testset "prevpow(2, _)/nextpow(2, _)" begin for i = 1:2 @test nextpow(2, i) == prevpow(2, i) == i end @test nextpow(2, 56789) == 65536 @test_throws DomainError nextpow(2, -56789) @test_throws DomainError nextpow(Int8(4), 128) @test prevpow(2, 56789) == 32768 @test_throws DomainError prevpow(2, -56789) @test_throws DomainError prevpow(Int8(4), 128) @test_throws OverflowError nextpow(Int8(4), 65) for i = 1:100 @test nextpow(2, i) == nextpow(2, big(i)) @test prevpow(2, i) == prevpow(2, big(i)) end for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64) @test nextpow(2, T(42)) === T(64) @test prevpow(2, T(42)) === T(32) end for T in (Float16, Float32, Float64) @test prevpow(2, prevfloat(T(1024.0))) == T(512.0) @test nextpow(2, nextfloat(T(1024.0))) == T(2048.0) @test prevpow(T(2.0), prevfloat(T(1024.0))) == T(512.0) @test nextpow(T(2.0), nextfloat(T(1024.0))) == T(2048.0) @test prevpow(T(2.0), prevfloat(T(Inf))) < T(Inf) @test nextpow(T(2.0), prevfloat(T(Inf))) == T(Inf) end end @testset "ispow2" begin @test ispow2(64) @test !ispow2(42) @test !ispow2(~typemax(Int)) end @testset "nextpow/prevpow" begin @test nextpow(2,1) == 1 @test prevpow(2,1) == 1 @test nextpow(3,243) == 243 @test prevpow(3,243) == 243 @test nextpow(3,241) == 243 @test prevpow(3,244) == 243 for a = -1:1 @test_throws DomainError nextpow(a, 2) @test_throws DomainError prevpow(a, 2) end @test_throws DomainError nextpow(2,0) @test_throws DomainError prevpow(2,0) end @testset "nextprod" begin @test_throws ArgumentError nextprod([2,3,5],Int128(typemax(Int))+1) @test nextprod([2,3,5],30) == nextprod((2,3,5),30) == 30 @test nextprod([2,3,5],33) == 36 @test nextprod([3,5],33) == nextprod(3:2:5,33) == 45 end @testset "nextfloat/prevfloat" begin @test nextfloat(0.0) == 5.0e-324 @test prevfloat(0.0) == -5.0e-324 @test nextfloat(-0.0) == 5.0e-324 @test prevfloat(-0.0) == -5.0e-324 @test nextfloat(-5.0e-324) === -0.0 @test prevfloat(5.0e-324) == 0.0 @test nextfloat(-1.0) > -1.0 @test prevfloat(-1.0) < -1.0 @test nextfloat(nextfloat(0.0),-2) == -5.0e-324 @test nextfloat(prevfloat(0.0), 2) == 5.0e-324 @test nextfloat(Inf) === Inf @test prevfloat(-Inf) === -Inf @test isequal(nextfloat(NaN), NaN) @test nextfloat(Inf32) === Inf32 @test prevfloat(-Inf32) === -Inf32 @test isequal(nextfloat(NaN32), NaN32) end @testset "issue #16206" begin @test prevfloat(Inf) == 1.7976931348623157e308 @test prevfloat(Inf32) == 3.4028235f38 @test nextfloat(prevfloat(Inf)) == Inf @test nextfloat(prevfloat(Inf),2) == Inf @test nextfloat(1.0,typemax(Int64)) == Inf @test nextfloat(0.0,typemin(Int64)) == -Inf @test nextfloat(1f0,typemin(Int64)) == -Inf32 @test nextfloat(1.0,typemax(UInt64)) == Inf @test nextfloat(1.0,typemax(UInt128)) == Inf @test nextfloat(1.0,big(2)^67) == Inf @test nextfloat(1.0,-big(2)^67) == -Inf end for F in (Float16,Float32,Float64) @test reinterpret(Unsigned,one(F)) === Base.exponent_one(F) @test reinterpret(Signed,one(F)) === signed(Base.exponent_one(F)) end @test eps(floatmax(Float64)) == 1.99584030953472e292 @test eps(-floatmax(Float64)) == 1.99584030953472e292 # modular multiplicative inverses of odd numbers via exponentiation for T = (UInt8,Int8,UInt16,Int16,UInt32,Int32,UInt64,Int64,UInt128,Int128) for n = 1:2:1000 @test n*(n^typemax(T)) & typemax(T) == 1 n = rand(T) | one(T) @test n*(n^typemax(T)) == 1 end end @testset "Irrational/Bool multiplication" begin @test false*pi === 0.0 @test pi*false === 0.0 @test true*pi === Float64(pi) @test pi*true === Float64(pi) end # issue #5492 @test -0.0 + false === -0.0 @testset "issue #5881" begin @test bitstring(true) == "00000001" @test bitstring(false) == "00000000" end @testset "edge cases of intrinsics" begin let g() = sqrt(-1.0) @test_throws DomainError sqrt(-1.0) end @test sqrt(NaN) === NaN let g() = sqrt(NaN) @test g() === NaN end let g(x) = sqrt(x) @test g(NaN) === NaN end end @testset "widen and widemul" begin @test widen(1.5f0) === 1.5 @test widen(Int32(42)) === Int64(42) @test widen(Int8) === Int16 @test widen(Int64) === Int128 @test widen(Float32) === Float64 @test widen(Float16) === Float32 ## Note: this should change to e.g. Float128 at some point @test widen(Float64) === BigFloat @test widen(BigInt) === BigInt @test widemul(typemax(Int64),typemax(Int64)) == 85070591730234615847396907784232501249 @test typeof(widemul(Int64(1),UInt64(1))) == Int128 @test typeof(widemul(UInt64(1),Int64(1))) == Int128 @test typeof(widemul(Int128(1),UInt128(1))) == BigInt @test typeof(widemul(UInt128(1),Int128(1))) == BigInt # Check that the widen() fallback doesn't trigger a StackOverflowError @test_throws MethodError widen(String) end @testset ".//" begin @test [1,2,3] // 4 == [1//4, 2//4, 3//4] @test [1,2,3] .// [4,5,6] == [1//4, 2//5, 3//6] @test [1+2im,3+4im] .// [5,6] == [(1+2im)//5,(3+4im)//6] @test [1//3+2im,3+4im] .// [5,6] == [(1//3+2im)//5,(3+4im)//6] end @testset "issue #7441" begin @test_throws InexactError Int32(2.0^50) @test_throws InexactError round(UInt8, 255.5) @test round(UInt8, 255.4) === 0xff @test_throws InexactError round(Int16, -32768.7) @test round(Int16, -32768.1) === Int16(-32768) end # issue #7508 @test_throws ErrorException reinterpret(Int, 0x01) @testset "issue #12832" begin @test_throws ArgumentError reinterpret(Float64, Complex{Int64}(1)) @test_throws ErrorException reinterpret(Int32, false) end # issue #41 ndigf(n) = Float64(log(Float32(n))) @test Float64(log(Float32(256))) == ndigf(256) == 5.545177459716797 # cmp on unsigned integers (see commit 24b236321e03c6d9b8cb91a450f567256a793196) @test cmp(0x77777777,0x88888888) == -1 @test cmp(0x3959dcc5d7fd177b67df4e10bc350850, 0xd63d5b1183221b0a9e38c6809b33cdec) == -1 # issue #7911 @test sum([Int128(1) Int128(2)]) == Int128(3) @testset "digits and digits!" begin @test digits(24, base = 2) == [0, 0, 0, 1, 1] @test digits(24, base = 2, pad = 3) == [0, 0, 0, 1, 1] @test digits(24, base = 2, pad = 7) == [0, 0, 0, 1, 1, 0, 0] @test digits(100) == [0, 0, 1] @test digits(BigInt(2)^128, base = 2) == [zeros(128); 1] let a = zeros(Int, 3) digits!(a, 50) @test a == [0, 5, 0] digits!(a, 9, base = 2) @test a == [1, 0, 0] digits!(a, 7, base = 2) @test a == [1, 1, 1] end end # Fill a pre allocated 2x4 matrix let a = zeros(Int,(2,4)) for i in 0:3 digits!(view(a,:,i+1),i, base = 2) end @test a == [0 1 0 1; 0 0 1 1] end @test_throws InexactError convert(UInt8, 256) @test_throws InexactError convert(UInt, -1) @test_throws InexactError convert(Int, big(2)^100) @test_throws InexactError convert(Int16, big(2)^100) @test_throws InexactError convert(Int, typemax(UInt)) @testset "infinity to integer conversion" begin for T in ( UInt8, UInt16, UInt32, UInt64, UInt128, Int8, Int16, Int32, Int64, Int128, BigInt ) for S in (Float16, Float32, Float64, BigFloat) @test_throws InexactError convert(T, typemin(S)) @test_throws InexactError convert(T, typemax(S)) end end end @testset "issue #9789" begin @test_throws InexactError convert(Int8, typemax(UInt64)) @test_throws InexactError convert(Int16, typemax(UInt64)) @test_throws InexactError convert(Int, typemax(UInt64)) end @testset "issue #14549" begin for T in (Int8, Int16, UInt8, UInt16) for F in (Float32,Float64) @test_throws InexactError convert(T, F(200000.0)) end end end let x = big(-0.0) @test signbit(x) && !signbit(abs(x)) end @testset "mod1 and fld1" begin @test all(x -> (m=mod1(x,3); 0 x == (fld1(x,3)-1)*3 + mod1(x,3), -5:+5) @test all(x -> fldmod1(x,3) == (fld1(x,3), mod1(x,3)), -5:+5) end #Issue #5570 @test map(x -> Int(mod1(UInt(x),UInt(5))), 0:15) == [5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5] @testset "Issue #9618: errors thrown by large exponentiations" begin @test_throws DomainError big(2)^-(big(typemax(UInt))+1) @test_throws OverflowError big(2)^(big(typemax(UInt))+1) @test 0==big(0)^(big(typemax(UInt))+1) end @testset "bswap (issue #9726)" begin @test bswap(0x0002) === 0x0200 @test bswap(0x01020304) === 0x04030201 @test reinterpret(Float64,bswap(0x000000000000f03f)) === 1.0 @test reinterpret(Float32,bswap(0x0000c03f)) === 1.5f0 @test reinterpret(Float16,bswap(0x003c)) === Float16(1.0) @test bswap(reinterpret(Float64,0x000000000000f03f)) === 1.0 @test bswap(reinterpret(Float32,0x0000c03f)) === 1.5f0 @test bswap(reinterpret(Float16,0x003e)) === Float16(1.5) zbuf = IOBuffer([0xbf, 0xc0, 0x00, 0x00, 0x40, 0x20, 0x00, 0x00, 0x40, 0x0c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, 0x12, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]) z1 = read(zbuf, ComplexF32) z2 = read(zbuf, ComplexF64) @test bswap(z1) === -1.5f0 + 2.5f0im @test bswap(z2) === 3.5 - 4.5im end #isreal(x::Real) = true for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat] @test isreal(x) == true end function allsubtypes!(m::Module, x::DataType, sts::Set) for s in names(m, all = true) if isdefined(m, s) && !Base.isdeprecated(m, s) t = getfield(m, s) if isa(t, Type) && t <: x && t != Union{} push!(sts, t) elseif isa(t, Module) && t !== m && nameof(t) === s && parentmodule(t) === m allsubtypes!(t, x, sts) end end end end @testset "eltype and ndims" begin let number_types = Set() allsubtypes!(Base, Number, number_types) allsubtypes!(Core, Number, number_types) @test !isempty(number_types) #eltype{T<:Number}(::Type{T}) = T for T in number_types @test eltype(T) == T end #ndims{T<:Number}(::Type{T}) = 0 for x in number_types @test ndims(x) == 0 end end end @testset "getindex(x::Number) = x" begin for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat] @test getindex(x) == x @test getindex(x, 1, 1) == x end end @testset "getindex error throwing" begin for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat] @test_throws BoundsError getindex(x,-1) @test_throws BoundsError getindex(x,0) @test_throws BoundsError getindex(x,2) @test_throws BoundsError getindex([x x],-1) @test_throws BoundsError getindex([x x],0) @test_throws BoundsError getindex([x x],length([x,x])+1) @test_throws BoundsError getindex(x, 1, 0) end end @testset "get(x::Number, ...)" begin for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat] @test get(x, 1, 99) == x @test get(x, (), 99) == x @test get(x, (1,), 99) == x @test get(x, 2, 99) == 99 @test get(x, 0, pi) == pi @test get(x, (1,2), pi) == pi c = Ref(0) @test get(() -> c[]+=1, x, 1) == x @test get(() -> c[]+=1, x, ()) == x @test get(() -> c[]+=1, x, (1,1,1)) == x @test get(() -> c[]+=1, x, 2) == 1 @test get(() -> c[]+=1, x, -1) == 2 @test get(() -> c[]+=1, x, (3,2,1)) == 3 end end @testset "copysign and flipsign" begin # copysign(x::Real, y::Real) = ifelse(signbit(x)!=signbit(y), -x, x) # flipsign(x::Real, y::Real) = ifelse(signbit(y), -x, x) for x in [1.23, 7, ℯ, 4//5] for y in [1.23, 7, ℯ, 4//5] @test copysign(x, y) == x @test copysign(x, -y) == -x @test copysign(-x, y) == x @test copysign(-x, -y) == -x @test flipsign(x, y) == x @test flipsign(x, -y) == -x @test flipsign(-x, y) == -x @test flipsign(-x, -y) == x end end end @testset "angle(z::Real) = atan(zero(z), z)" begin #function only returns two values, depending on sign @test angle(10) == 0.0 @test angle(-10) == 3.141592653589793 end @testset "in(x::Number, y::Number) = x == y" begin @test in(3,3) == true #Int @test in(2.0,2.0) == true #FP @test in(ℯ,ℯ) == true #Const @test in(4//5,4//5) == true #Rat @test in(1+2im, 1+2im) == true #Imag @test in(3, 3.0) == true #mixed end @testset "map(f::Callable, x::Number, ys::Number...) = f(x)" begin @test map(sin, 3) == sin(3) @test map(cos, 3) == cos(3) @test map(tan, 3) == tan(3) @test map(log, 3) == log(3) @test map(copysign, 1.0, -2.0) == -1.0 @test map(muladd, 2, 3, 4) == 10 end # issue #10311 let n = 1 @test n//n + n//big(n)*im == 1//1 + 1//1*im end # BigInt - (small negative) is tricky because gmp only has gmpz_sub_ui @test big(-200) - Int8(-128) == -72 @testset "n % Type" begin for T in Any[Int16, Int32, UInt32, Int64, UInt64, BigInt] if !(T <: Unsigned) @test convert(T, -200) % Int8 === Int8(56) @test convert(T, -200) % UInt8 === 0x38 @test convert(T, -300) % Int8 === Int8(-44) @test convert(T, -300) % UInt8 === 0xd4 @test convert(T, -128) % Int8 === Int8(-128) @test convert(T, -128) % UInt8 === 0x80 end @test convert(T, 127) % Int8 === Int8(127) @test convert(T, 127) % UInt8 === 0x7f @test convert(T, 128) % Int8 === Int8(-128) @test convert(T, 128) % UInt8 === 0x80 @test convert(T, 200) % Int8 === Int8(-56) @test convert(T, 300) % UInt8 === 0x2c end end @testset "InexactErrors for Ints" begin @test_throws InexactError convert(UInt8, big(300)) @test_throws InexactError UInt128(-1) for T in (Int8,Int16,Int32,Int64,Int128,UInt8,UInt16,UInt32,UInt64,UInt128) @test_throws InexactError T(big(typemax(T))+1) @test_throws InexactError T(big(typemin(T))-1) end end for (d,B) in ((4//2+1im,Rational{BigInt}),(3.0+1im,BigFloat),(2+1im,BigInt)) @test typeof(big(d)) == Complex{B} @test big(d) == d @test typeof(big.([d])) == Vector{Complex{B}} @test big.([d]) == [d] end # big fallback import Base: zero, big struct TestNumber{Inner} <: Number inner::Inner end zero(::Type{TestNumber{Inner}}) where {Inner} = TestNumber(zero(Inner)) big(test_number::TestNumber) = TestNumber(big(test_number.inner)) @test big(TestNumber{Int}) == TestNumber{BigInt} # abstract abs2 Base.:*(x::TestNumber, y::TestNumber) = TestNumber(x.inner*y.inner) Base.:(==)(x::TestNumber, y::TestNumber) = x.inner == y.inner Base.abs(x::TestNumber) = TestNumber(abs(x.inner)) @test abs2(TestNumber(3+4im)) == TestNumber(25) @testset "multiplicative inverses" begin function testmi(numrange, denrange) for d in denrange d == 0 && continue fastd = Base.multiplicativeinverse(d) for n in numrange d == -1 && n == typemin(typeof(n)) && continue @test div(n,d) == div(n,fastd) end end end testmi(-1000:1000, -100:100) @test_throws ArgumentError Base.multiplicativeinverse(0) for T in [Int8, Int16, Int32, Int64, Int128] testmi(map(T, typemin(T)+1:typemin(T)+100), map(T, -50:50)) end for T in [UInt8, UInt16, UInt32, UInt64, UInt128, Int8, Int16, Int32, Int64, Int128] testmi(map(T, typemax(T)-50:typemax(T)), map(T, 1:50)) testmi(rand(T, 50), rand(T, 50)) @test_throws ArgumentError Base.multiplicativeinverse(T(0)) end # Division overflow is not handled T = Int8 fastd = Base.multiplicativeinverse(T(-1)) @test_throws DivideError div(typemin(T), T(-1)) # does not throw: # @test_throws div(typemin(T), fastd) # test broadcasting works. @test div.(3, Base.multiplicativeinverse(3)) == 1 end @testset "ndims/indices/size/length" begin @test ndims(1) == 0 @test ndims(Integer) == 0 @test size(1,1) == 1 @test_throws BoundsError size(1,-1) @test axes(1) == () @test axes(1,1) == 1:1 @test_throws BoundsError axes(1,-1) @test isinteger(Integer(2)) == true @test !isinteger(π) @test size(1) == () @test length(1) == 1 @test firstindex(1) == 1 @test firstindex(1, 1) == 1 @test_throws BoundsError firstindex(1,0) @test lastindex(1) == 1 @test lastindex(1, 1) == 1 @test 1[end,end] == 1 @test_throws BoundsError lastindex(1,0) @test eltype(Integer) == Integer end @testset "PR #16995" begin let types = (Base.BitInteger_types..., BigInt, Bool, Rational{Int}, Rational{BigInt}, Float16, Float32, Float64, BigFloat, Complex{Int}, Complex{UInt}, ComplexF16, ComplexF32, ComplexF64) for S in types for op in (+, -) T = @inferred Base.promote_op(op, S) t = @inferred op(one(S)) @test T === typeof(t) end for R in types for op in (+, -, *, /, ^) T = @inferred Base.promote_op(op, S, R) t = @inferred op(one(S), one(R)) @test T === typeof(t) end end end @test @inferred(Base.promote_op(!, Bool)) === Bool end let types = (Base.BitInteger_types..., BigInt, Bool, Rational{Int}, Rational{BigInt}, Float16, Float32, Float64, BigFloat) for S in types, T in types for op in (<, >, <=, >=, (==)) @test @inferred(Base.promote_op(op, S, T)) === Bool end end end let types = (Base.BitInteger_types..., BigInt, Bool) for S in types T = @inferred Base.promote_op(~, S) t = @inferred ~one(S) @test T === typeof(t) for R in types for op in (&, |, <<, >>, (>>>), %, ÷) T = @inferred Base.promote_op(op, S, R) t = @inferred op(one(S), one(R)) @test T === typeof(t) end end end end end @test !isempty(complex(1,2)) @testset "rem $T rounded" for T in (Float16, Float32, Float64, BigFloat) @test rem(T(1), T(2), RoundToZero) == 1 @test rem(T(1), T(2), RoundNearest) == 1 @test rem(T(1), T(2), RoundDown) == 1 @test rem(T(1), T(2), RoundUp) == -1 @test rem(T(1), T(2), RoundFromZero) == -1 @test rem(T(1.5), T(2), RoundToZero) == 1.5 @test rem(T(1.5), T(2), RoundNearest) == -0.5 @test rem(T(1.5), T(2), RoundDown) == 1.5 @test rem(T(1.5), T(2), RoundUp) == -0.5 @test rem(T(1.5), T(2), RoundFromZero) == -0.5 @test rem(T(-1), T(2), RoundToZero) == -1 @test rem(T(-1), T(2), RoundNearest) == -1 @test rem(T(-1), T(2), RoundDown) == 1 @test rem(T(-1), T(2), RoundUp) == -1 @test rem(T(-1), T(2), RoundFromZero) == 1 @test rem(T(-1.5), T(2), RoundToZero) == -1.5 @test rem(T(-1.5), T(2), RoundNearest) == 0.5 @test rem(T(-1.5), T(2), RoundDown) == 0.5 @test rem(T(-1.5), T(2), RoundUp) == -1.5 @test rem(T(-1.5), T(2), RoundFromZero) == 0.5 for mode in [RoundToZero, RoundNearest, RoundDown, RoundUp, RoundFromZero] @test isnan(rem(T(1), T(0), mode)) @test isnan(rem(T(Inf), T(2), mode)) @test isnan(rem(T(1), T(NaN), mode)) @test rem(T(4), floatmin(T) * 2, mode) == 0 end @test isequal(rem(nextfloat(typemin(T)), T(2), RoundToZero), -0.0) @test isequal(rem(nextfloat(typemin(T)), T(2), RoundNearest), -0.0) @test isequal(rem(nextfloat(typemin(T)), T(2), RoundDown), 0.0) @test isequal(rem(nextfloat(typemin(T)), T(2), RoundUp), -0.0) @test isequal(rem(nextfloat(typemin(T)), T(2), RoundFromZero), 0.0) end @testset "rem for $T RoundNearest" for T in (Int8, Int16, Int32, Int64, Int128) for (n, r) in zip(3:7, -2:2) @test rem(T(n), T(5), RoundNearest) == rem(float(n), 5.0, RoundNearest) == r @test rem(T(n), T(-5), RoundNearest) == rem(float(n), -5.0, RoundNearest) == r @test rem(T(-n), T(-5), RoundNearest) == rem(float(-n), -5.0, RoundNearest) == -r @test rem(T(-n), T(5), RoundNearest) == rem(float(-n), 5.0, RoundNearest) == -r @test rem(T(n), T(5), RoundNearest) == rem(T(n)//T(1), T(5)//T(1), RoundNearest) @test rem(T(-n), T(5), RoundNearest) == rem(T(-n)//T(1), T(5)//T(1), RoundNearest) @test rem(T(n), T(-5), RoundNearest) == rem(T(n)//T(1), T(-5)//T(1), RoundNearest) @test rem(T(-n), T(-5), RoundNearest) == rem(T(-n)//T(1), T(-5)//T(1), RoundNearest) end end @testset "divrem rounded" begin #rounded Floats for T in (Float16, Float32, Float64, BigFloat) @test divrem(T(1.5), T(2), RoundToZero)[2] == 1.5 @test divrem(T(1.5), T(2), RoundNearest)[2] == -0.5 @test divrem(T(1.5), T(2), RoundDown)[2] == 1.5 @test divrem(T(1.5), T(2), RoundUp)[2] == -0.5 @test divrem(T(-1.5), T(2), RoundToZero)[2] == -1.5 @test divrem(T(-1.5), T(2), RoundNearest)[2] == 0.5 @test divrem(T(-1.5), T(2), RoundDown)[2] == 0.5 @test divrem(T(-1.5), T(2), RoundUp)[2] == -1.5 end #rounded Integers for (a, b) in ( (3, 2), (5, 3), (-3, 2), (5, 2), (-5, 2), (-5, 3), (5, -3)) for sign in (+1, -1) (a, b) = (a*sign, b*sign) @test divrem(a, b, RoundNearest) == (div(a, b, RoundNearest),rem(a, b, RoundNearest)) end end a = 122322388883338838388383888823233122323 b = 343443 c = 122322388883338838388383888823233122333 @test divrem(a, b) == (div(a,b), rem(a,b)) @test divrem(a, c) == (div(a,c), rem(a,c)) @test divrem(a,-(a-20), RoundDown) == (div(a,-(a-20), RoundDown), rem(a,-(a-20), RoundDown)) end @testset "rem2pi $T" for T in (Float16, Float32, Float64, BigFloat, Int8, Int16, Int32, Int64, Int128) @test rem2pi(T(1), RoundToZero) == 1 @test rem2pi(T(1), RoundNearest) == 1 @test rem2pi(T(1), RoundDown) == 1 @test rem2pi(T(1), RoundUp) ≈ 1-2pi @test rem2pi(T(2), RoundToZero) == 2 @test rem2pi(T(2), RoundNearest) == 2 @test rem2pi(T(2), RoundDown) == 2 @test rem2pi(T(2), RoundUp) ≈ 2-2pi @test rem2pi(T(4), RoundToZero) == 4 @test rem2pi(T(4), RoundNearest) ≈ 4-2pi @test rem2pi(T(4), RoundDown) == 4 @test rem2pi(T(4), RoundUp) ≈ 4-2pi @test rem2pi(T(-4), RoundToZero) == -4 @test rem2pi(T(-4), RoundNearest) ≈ 2pi-4 @test rem2pi(T(-4), RoundDown) ≈ 2pi-4 @test rem2pi(T(-4), RoundUp) == -4 @test rem2pi(T(8), RoundToZero) ≈ 8-2pi @test rem2pi(T(8), RoundNearest) ≈ 8-2pi @test rem2pi(T(8), RoundDown) ≈ 8-2pi @test rem2pi(T(8), RoundUp) ≈ 8-4pi @test rem2pi(T(-8), RoundToZero) ≈ -8+2pi @test rem2pi(T(-8), RoundNearest) ≈ -8+2pi @test rem2pi(T(-8), RoundDown) ≈ -8+4pi @test rem2pi(T(-8), RoundUp) ≈ -8+2pi # to hit n is even and n % 4 == 2 condition @test rem2pi(T(3), RoundToZero) == 3 @test rem2pi(T(3), RoundNearest) == 3 @test rem2pi(T(3), RoundDown) == 3 @test rem2pi(T(3), RoundUp) ≈ 3 - 2π @test rem2pi(T(-3), RoundToZero) == -3 @test rem2pi(T(-3), RoundNearest) == -3 @test rem2pi(T(-3), RoundDown) ≈ -3 + 2π @test rem2pi(T(-3), RoundUp) == -3 # to hit even n condition and n % 4 != 2 condition @test rem2pi(T(13), RoundToZero) ≈ 13-4π @test rem2pi(T(13), RoundNearest) ≈ 13-4π @test rem2pi(T(13), RoundDown) ≈ 13-4π @test rem2pi(T(13), RoundUp) ≈ 13-6π @test rem2pi(T(-13), RoundToZero) ≈ -13+4π @test rem2pi(T(-13), RoundNearest) ≈ -13+4π @test rem2pi(T(-13), RoundDown) ≈ -13+6π @test rem2pi(T(-13), RoundUp) ≈ -13+4π end @testset "PR #36420 $T" for T in (Float16, Float32, Float64, BigFloat) nan = reinterpret(Float64, reinterpret(UInt64, NaN) | rand(UInt64)) for r in (RoundToZero, RoundNearest, RoundDown, RoundUp) for x in (Inf, -Inf, NaN, -NaN, nan) @test isnan(rem2pi(T(x), r)) @test rem2pi(T(x), r) isa T if isnan(x) && T !== BigFloat @test rem2pi(T(x), r) === T(x) end end end end import Base.^ struct PR20530; end struct PR20889; x; end ^(::PR20530, p::Int) = 1 ^(t::PR20889, b) = t.x + b ^(t::PR20889, b::Integer) = t.x + b Base.literal_pow(::typeof(^), ::PR20530, ::Val{p}) where {p} = 2 @testset "literal powers" begin x = PR20530() p = 2 @test x^p == 1 @test x^2 == 2 @test [x, x, x].^2 == [2, 2, 2] for T in (Float16, Float32, Float64, BigFloat, Int8, Int, BigInt, Complex{Int}, ComplexF64) for p in -4:4 v = eval(:($T(2)^$p)) @test 2.0^p == v if p >= 0 || T == float(T) @test v == T(2)^p @test v isa T else @test v isa float(T) end end end @test PR20889(2)^3 == 5 @test [2,4,8].^-2 == [0.25, 0.0625, 0.015625] @test [2, 4, 8].^-2 .* 4 == [1.0, 0.25, 0.0625] # nested literal_pow @test ℯ^-2 == exp(-2) ≈ inv(ℯ^2) ≈ (ℯ^-1)^2 ≈ sqrt(ℯ^-4) end module M20889 # do we get the expected behavior without importing Base.^? using Test struct PR20889; x; end ^(t::PR20889, b) = t.x + b Test.@test PR20889(2)^3 == 5 end @testset "literal negative power accuracy" begin @test 0.7130409001548401^-2 == 0.7130409001548401^-2.0 @test 0.09496527f0^-2 == 0.09496527f0^-2.0f0 @test 0.20675883960662367^-100 == 0.20675883960662367^-100.0 @test 0.6123676f0^-100 == 0.6123676f0^-100.0f0 @test 0.004155780785470562^-1 == 0.004155780785470562^-1.0 end @testset "iszero & isone" begin # Numeric scalars for T in [Float16, Float32, Float64, BigFloat, Int8, Int16, Int32, Int64, Int128, BigInt, UInt8, UInt16, UInt32, UInt64, UInt128] @test iszero(T(0)) @test isone(T(1)) @test iszero(Complex{T}(0)) @test isone(Complex{T}(1)) if T <: Integer @test iszero(Rational{T}(0)) @test isone(Rational{T}(1)) elseif T <: AbstractFloat @test iszero(T(-0.0)) @test iszero(Complex{T}(-0.0)) end end @test !iszero(nextfloat(BigFloat(0))) @test !isone(nextfloat(BigFloat(1))) for x in (π, ℯ, γ, catalan, φ) @test !iszero(x) @test !isone(x) end # Array reduction @test !iszero([0, 1, 2, 3]) @test iszero(zeros(Int, 5)) @test !isone(tril(fill(1, 5, 5))) @test !isone(triu(fill(1, 5, 5))) @test !isone(zeros(Int, 5, 5)) @test isone(Matrix(1I, 5, 5)) @test !isone(view(rand(5,5), [1,3,4], :)) Dv = view(Diagonal([1,1, 1]), [1,2], 1:2) @test isone(Dv) @test (@allocated isone(Dv)) == 0 @test isone(Matrix(1I, 1000, 1000)) # sizeof(X) > 2M == ISONE_CUTOFF end f20065(B, i) = UInt8(B[i]) @testset "issue 20065" begin # f20065 must be called from global scope to exhibit the buggy behavior for B in (Vector{Bool}(undef, 10), Matrix{Bool}(undef, 10,10), reinterpret(Bool, rand(UInt8, 10))) @test all(x-> x <= 1, (f20065(B, i) for i in eachindex(B))) for i in 1:length(B) @test (@eval f20065($B, $i) <= 1) end end end @test inv(3//4) === 4//3 === 1 / (3//4) === 1 // (3//4) # issues #23244 & #23250 @testset "convert preserves NaN payloads" begin @testset "smallest NaNs" begin @test convert(Float32, NaN16) === NaN32 @test convert(Float32, -NaN16) === -NaN32 @test convert(Float64, NaN16) === NaN64 @test convert(Float64, -NaN16) === -NaN64 @test convert(Float16, NaN32) === NaN16 @test convert(Float16, -NaN32) === -NaN16 @test convert(Float64, NaN32) === NaN64 @test convert(Float64, -NaN32) === -NaN64 @test convert(Float32, NaN64) === NaN32 @test convert(Float32, -NaN64) === -NaN32 @test convert(Float16, NaN64) === NaN16 @test convert(Float16, -NaN64) === -NaN16 end @testset "largest NaNs" begin @test convert(Float32, reinterpret(Float16, typemax(UInt16))) === reinterpret(Float32, typemax(UInt32) >> 13 << 13) @test convert(Float64, reinterpret(Float16, typemax(UInt16))) === reinterpret(Float64, typemax(UInt64) >> 42 << 42) @test convert(Float16, reinterpret(Float32, typemax(UInt32))) === reinterpret(Float16, typemax(UInt16) >> 00 << 00) @test convert(Float64, reinterpret(Float32, typemax(UInt32))) === reinterpret(Float64, typemax(UInt64) >> 29 << 29) @test convert(Float32, reinterpret(Float64, typemax(UInt64))) === reinterpret(Float32, typemax(UInt32) >> 00 << 00) @test convert(Float16, reinterpret(Float64, typemax(UInt64))) === reinterpret(Float16, typemax(UInt16) >> 00 << 00) end @testset "random NaNs" begin nans = AbstractFloat[NaN16, NaN32, NaN64] F = [Float16, Float32, Float64] U = [UInt16, UInt32, UInt64] sig = [11, 24, 53] for i = 1:length(F), j = 1:length(F) for _ = 1:100 nan = reinterpret(F[i], rand(U[i]) | reinterpret(U[i], nans[i])) z = sig[i] - sig[j] nan′ = i <= j ? nan : reinterpret(F[i], reinterpret(U[i], nan) >> z << z) @test convert(F[i], convert(F[j], nan)) === nan′ end end end end # issue #26324 @testset "irrational promotion" begin @test π*ComplexF32(2) isa ComplexF32 @test π/ComplexF32(2) isa ComplexF32 @test log(π,ComplexF32(2)) isa ComplexF32 end @testset "printing non finite floats" begin let float_types = Set() allsubtypes!(Base, AbstractFloat, float_types) allsubtypes!(Core, AbstractFloat, float_types) filter!(!isequal(Core.BFloat16), float_types) # defined externally @test !isempty(float_types) for T in float_types for (x, sx) in [(T(NaN), "NaN"), (-T(NaN), "NaN"), (T(Inf), "Inf"), (-T(Inf), "-Inf")] @assert x isa T @test string(x) == sx @test sprint(show, x, context=:compact => true) == sx @test sprint(print, x) == sx end end end end @testset "constructor inferability for $T" for T in [AbstractFloat, #=BigFloat,=# Float16, Float32, Float64, Integer, Bool, Signed, BigInt, Int128, Int16, Int32, Int64, Int8, Unsigned, UInt128, UInt16, UInt32, UInt64, UInt8] @test all(R -> R<:T, Base.return_types(T)) end @testset "constructor inferability for BigFloat" begin T = BigFloat @test_broken all(R -> R<:T, Base.return_types(T)) @test all(m -> m.file === Symbol("deprecated.jl"), collect(methods(T))[findall(R -> !(R<:T), Base.return_types(T))]) end @testset "generic isfinite" begin @test invoke(isfinite, Tuple{Number}, 0.0) == true @test invoke(isfinite, Tuple{Number}, NaN) == false @test invoke(isfinite, Tuple{Number}, Inf) == false end struct MyRealFld <: Real x::Real end @testset "fallback error throwing for fld/cld" begin a = MyRealFld(2.0) b = MyRealFld(3.0) @test_throws MethodError fld(a, b) @test_throws MethodError cld(a, b) end @testset "Bool rounding (#25074)" begin @testset "round Bool" begin @test_throws InexactError round(Bool, -4.1) @test_throws InexactError round(Bool, 1.5) @test true == round(Bool, 1.0) @test false == round(Bool, 0.0) @test true == round(Bool, 0.6) @test false == round(Bool, 0.4) @test false == round(Bool, 0.5) @test false == round(Bool, -0.5) end @testset "trunc Bool" begin @test_throws InexactError trunc(Bool, -4.1) @test_throws InexactError trunc(Bool, 2.5) @test true == trunc(Bool, 1.0) @test false == trunc(Bool, 0.0) @test false == trunc(Bool, 0.6) @test false == trunc(Bool, 0.4) @test true == trunc(Bool, 1.8) @test false == trunc(Bool, -0.5) end @testset "floor Bool" begin @test_throws InexactError floor(Bool, -0.1) @test_throws InexactError floor(Bool, 2.5) @test true == floor(Bool, 1.0) @test false == floor(Bool, 0.0) @test false == floor(Bool, 0.6) @test true == floor(Bool, 1.8) end @testset "ceil Bool" begin @test_throws InexactError ceil(Bool, -1.4) @test_throws InexactError ceil(Bool, 1.5) @test true == ceil(Bool, 1.0) @test false == ceil(Bool, 0.0) @test true == ceil(Bool, 0.6) @test false == ceil(Bool, -0.7) end end Base.@irrational irrational_1548_pi 4863.185427757 1548big(pi) Base.@irrational irrational_inv_1548_pi 1/big(irrational_1548_pi) @testset "@irrational" begin @test irrational_1548_pi ≈ 1548big(pi) @test Float64(irrational_1548_pi) == 1548π @test irrational_1548_pi ≈ 1548pi @test irrational_1548_pi != 1548pi @test irrational_inv_1548_pi ≈ inv(1548big(pi)) @test Float64(irrational_inv_1548_pi) == 1/(1548π) @test irrational_inv_1548_pi ≈ inv(1548pi) @test irrational_inv_1548_pi != inv(1548pi) end @testset "modf" begin @testset "remd" begin denorm_min = nextfloat(0.0) minfloat = floatmin(Float64) maxfloat = floatmax(Float64) values = [3.0,denorm_min,-denorm_min, minfloat, -minfloat, maxfloat, -maxfloat] # rem (0, y) == 0 for y != 0. for val in values @test isequal(rem(0.0, val), 0.0) end # rem (-0, y) == -0 for y != 0. for val in values @test isequal(rem(-0.0, val), -0.0) end # rem (+Inf, y) == NaN values2 = [3.0,-1.1,0.0,-0.0,denorm_min,minfloat, maxfloat,Inf,-Inf] for val in values2 @test isequal(rem(Inf, val), NaN) end # rem (-Inf, y) == NaN for val in values2 @test isequal(rem(-Inf, val), NaN) end # rem (x, +0) == NaN values3 = values2[begin:end-2] for val in values3 @test isequal(rem(val, 0.0), NaN) end # rem (x, -0) == NaN for val in values3 @test isequal(rem(val, -0.0), NaN) end # rem (x, +Inf) == x for x not infinite. @test isequal(rem(0.0, Inf), 0.0) @test isequal(rem(-0.0, Inf), -0.0) @test isequal(rem(denorm_min, Inf), denorm_min) @test isequal(rem(minfloat, Inf), minfloat) @test isequal(rem(maxfloat, Inf), maxfloat) @test isequal(rem(3.0, Inf), 3.0) # rem (x, -Inf) == x for x not infinite. @test isequal(rem(0.0, -Inf), 0.0) @test isequal(rem(-0.0, -Inf), -0.0) @test isequal(rem(denorm_min, -Inf), denorm_min) @test isequal(rem(minfloat, -Inf), minfloat) @test isequal(rem(maxfloat, -Inf), maxfloat) @test isequal(rem(3.0, -Inf), 3.0) #NaN tests @test isequal(rem(0.0, NaN), NaN) @test isequal(rem(1.0, NaN), NaN) @test isequal(rem(Inf, NaN), NaN) @test isequal(rem(NaN, 0.0), NaN) @test isequal(rem(NaN, 1.0), NaN) @test isequal(rem(NaN, Inf), NaN) @test isequal(rem(NaN, NaN), NaN) #Sign tests @test isequal(rem(6.5, 2.25), 2.0) @test isequal(rem(-6.5, 2.25), -2.0) @test isequal(rem(6.5, -2.25), 2.0) @test isequal(rem(-6.5, -2.25), -2.0) values4 = [maxfloat,-maxfloat,minfloat,-minfloat, denorm_min, -denorm_min] for val in values4 @test isequal(rem(maxfloat,val), 0.0) end for val in values4 @test isequal(rem(-maxfloat,val), -0.0) end @test isequal(rem(minfloat, maxfloat), minfloat) @test isequal(rem(minfloat, -maxfloat), minfloat) values5 = values4[begin+2:end] for val in values5 @test isequal(rem(minfloat,val), 0.0) end @test isequal(rem(-minfloat, maxfloat), -minfloat) @test isequal(rem(-minfloat, -maxfloat), -minfloat) for val in values5 @test isequal(rem(-minfloat,val), -0.0) end values6 = values4[begin:end-2] for val in values6 @test isequal(rem(denorm_min,val), denorm_min) end @test isequal(rem(denorm_min, denorm_min), 0.0) @test isequal(rem(denorm_min, -denorm_min), 0.0) for val in values6 @test isequal(rem(-denorm_min,val), -denorm_min) end @test isequal(rem(-denorm_min, denorm_min), -0.0) @test isequal(rem(-denorm_min, -denorm_min), -0.0) #Max value tests values7 = [0x3p-1074,-0x3p-1074,0x3p-1073,-0x3p-1073] for val in values7 @test isequal(rem(0x1p1023,val), 0x1p-1073) end @test isequal(rem(0x1p1023, 0x3p-1022), 0x1p-1021) @test isequal(rem(0x1p1023, -0x3p-1022), 0x1p-1021) for val in values7 @test isequal(rem(-0x1p1023,val), -0x1p-1073) end @test isequal(rem(-0x1p1023, 0x3p-1022), -0x1p-1021) @test isequal(rem(-0x1p1023, -0x3p-1022), -0x1p-1021) end @testset "remf" begin @test isequal(rem(Float32(0x1p127), Float32(0x3p-149)), Float32(0x1p-149)) @test isequal(rem(Float32(0x1p127), -Float32(0x3p-149)), Float32(0x1p-149)) @test isequal(rem(Float32(0x1p127), Float32(0x3p-148)), Float32(0x1p-147)) @test isequal(rem(Float32(0x1p127), -Float32(0x3p-148)), Float32(0x1p-147)) @test isequal(rem(Float32(0x1p127), Float32(0x3p-126)), Float32(0x1p-125)) @test isequal(rem(Float32(0x1p127), -Float32(0x3p-126)), Float32(0x1p-125)) @test isequal(rem(-Float32(0x1p127), Float32(0x3p-149)), -Float32(0x1p-149)) @test isequal(rem(-Float32(0x1p127), -Float32(0x3p-149)), -Float32(0x1p-149)) @test isequal(rem(-Float32(0x1p127), Float32(0x3p-148)), -Float32(0x1p-147)) @test isequal(rem(-Float32(0x1p127), -Float32(0x3p-148)), -Float32(0x1p-147)) @test isequal(rem(-Float32(0x1p127), Float32(0x3p-126)), -Float32(0x1p-125)) @test isequal(rem(-Float32(0x1p127), -Float32(0x3p-126)), -Float32(0x1p-125)) end end @testset "FP(inf) == inf" begin # Iterate through all pairs of FP types fp_types = (Float16, Float32, Float64, BigFloat) for F ∈ fp_types, G ∈ fp_types, f ∈ (typemin, typemax) i = f(F) @test i == G(i) end end @testset "small int FP conversion" begin fp_types = (Float16, Float32, Float64, BigFloat) m = Int(maxintfloat(Float16)) for F ∈ fp_types, G ∈ fp_types, n ∈ (-m):m @test n == G(F(n)) == F(G(n)) end end @testset "`precision`" begin Fs = (Float16, Float32, Float64, BigFloat) @testset "type vs instance" begin @testset "F: $F" for F ∈ Fs @test precision(F) == precision(one(F)) @test precision(F, base = 2) == precision(one(F), base = 2) @test precision(F, base = 3) == precision(one(F), base = 3) end end @testset "`precision` of `Union` shouldn't recur infinitely, #52909" begin @testset "i: $i" for i ∈ eachindex(Fs) @testset "j: $j" for j ∈ (i + 1):lastindex(Fs) S = Fs[i] T = Fs[j] @test_throws MethodError precision(Union{S,T}) @test_throws MethodError precision(Union{S,T}, base = 3) end end end end @testset "irrational special values" begin for v ∈ (π, ℯ, γ, catalan, φ) @test v === typemin(v) === typemax(v) end end