Revision 4954af9c5ee5bb1b5b9172ddbcbac03ca6e151ea authored by Keno Fischer on 01 September 2023, 19:52:14 UTC, committed by GitHub on 01 September 2023, 19:52:14 UTC
The change in #50429 moves around some dispatch boundaries and pushes the allocations in the offsetarrays `maximum!` test over the limit. The implementation of that code is massively type unstable. Somewhat, ironically, the whole original point of that test was to test that the implementation was not type-unstable (#28941), so actually opt our OffsetArrays implementation into the interface that's supposed to guarantee that. If this PR is fine here, I'll submit the same upstream to avoid diverging the implementations too much. Co-authored-by: Jameson Nash <vtjnash@gmail.com>
1 parent a173010
numbers.jl
# 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<y)==(x<=y)&(x!=y)
@test (x<=y)==(x<y)|(x==y)
@test (x==y)==(x<=y)&!(x<y)
@test -x != x
@test -y != y
@test -x != y
@test -y != x
@test -x < x
@test -y < y
@test -x < y
@test -y < x
@test -x <= x
@test -y <= y
@test -x <= y
@test -y <= x
@test -y != u
@test -y < u
@test -y <= u
c = _cmp_(x,y)
if c < 0
@test !(x == y)
@test (x < y)
@test !(y < x)
@test (x <= y)
@test !(y <= x)
@test !(u == y)
@test (u < y)
@test !(y < u)
@test (u <= y)
@test !(y <= u)
@test !(-x == -y)
@test !(-x < -y)
@test (-y < -x)
@test !(-x <= -y)
@test (-y <= -x)
elseif c > 0
@test !(x == y)
@test !(x < y)
@test (y < x)
@test !(x <= y)
@test (y <= x)
@test !(u == y)
@test !(u < y)
@test (y < u)
@test !(u <= y)
@test (y <= u)
@test !(-x == -y)
@test (-x < -y)
@test !(-y < -x)
@test (-x <= -y)
@test !(-y <= -x)
else
@test (x == y)
@test !(x < y)
@test !(y < x)
@test (x <= y)
@test (y <= x)
@test (u == y)
@test !(u < y)
@test !(y < u)
@test (u <= y)
@test (y <= u)
@test (-x == -y)
@test !(-x < -y)
@test !(-y < -x)
@test (-x <= -y)
@test (-y <= -x)
end
end
@test Int64(2)^62-1 != 2.0^62
@test Int64(2)^62 == 2.0^62
@test Int64(2)^62+1 != 2.0^62
@test 2.0^62 != Int64(2)^62-1
@test 2.0^62 == Int64(2)^62
@test 2.0^62 != Int64(2)^62+1
@test typemax(Int64) != +2.0^63
@test typemin(Int64) == -2.0^63
@test typemin(Int64)+1 != -2.0^63
@test UInt64(2)^60-1 != 2.0^60
@test UInt64(2)^60 == 2.0^60
@test UInt64(2)^60+1 != 2.0^60
@test 2.0^60 != UInt64(2)^60-1
@test 2.0^60 == UInt64(2)^60
@test 2.0^60 != UInt64(2)^60+1
@test UInt64(2)^63-1 != 2.0^63
@test UInt64(2)^63 == 2.0^63
@test UInt64(2)^63+1 != 2.0^63
@test 2.0^63 != UInt64(2)^63-1
@test 2.0^63 == UInt64(2)^63
@test 2.0^63 != UInt64(2)^63+1
@test typemax(UInt64) != 2.0^64
# issue #9085
f9085() = typemax(UInt64) != 2.0^64
@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(i<j, Float64(i)<Float64(j))
@test isequal(i>j, 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<m<=3), -5:+5)
@test all(x -> 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)
@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)
@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
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