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numbers.jl
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# basic booleans
@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
# the bool operator
@test bool(false) == false
@test bool(true) == true
@test bool(0) == false
@test bool(1) == true
@test bool(-1) == true
@test bool(0.0) == false
@test bool(1.0) == true
@test bool(0.1) == true
@test bool(-1.0) == true
@test bool(Complex(0,0)) == false
@test bool(Complex(1,0)) == true
@test_throws bool(Complex(0,1)) == true
@test bool(0//1) == false
@test bool(1//1) == true
@test bool(1//2) == true
# basic arithmetic
@test 2+3 == 5
@test 2.+3. == 5.
@test 2*3 == 6
@test 2.*3 == 6
@test 2. * 3. == 6.
@test min(1.0,1) == 1
@test minmax(5, 3) == (3, 5)
@test minmax(3., 5.) == (3., 5.)
@test minmax(5., 3.) == (3., 5.)
@test minmax(3., NaN) == (3., 3.)
@test minmax(NaN, 3.) == (3., 3.)
@test isequal(minmax(NaN, NaN), (NaN, NaN))
# 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)
# 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
# definition and printing of extreme integers
@test bin(typemin(Uint8)) == "0"
@test bin(typemax(Uint8)) == "1"^8
@test oct(typemin(Uint8)) == "0"
@test oct(typemax(Uint8)) == "377"
@test dec(typemin(Uint8)) == "0"
@test dec(typemax(Uint8)) == "255"
@test hex(typemin(Uint8)) == "0"
@test hex(typemax(Uint8)) == "ff"
@test repr(typemin(Uint8)) == "0x00"
@test string(typemin(Uint8)) == "0"
@test repr(typemax(Uint8)) == "0xff"
@test string(typemax(Uint8)) == "255"
@test base(3,typemin(Uint8)) == "0"
@test base(3,typemax(Uint8)) == "100110"
@test base(12,typemin(Uint8)) == "0"
@test base(12,typemax(Uint8)) == "193"
@test bin(typemin(Uint16)) == "0"
@test bin(typemax(Uint16)) == "1"^16
@test oct(typemin(Uint16)) == "0"
@test oct(typemax(Uint16)) == "177777"
@test dec(typemin(Uint16)) == "0"
@test dec(typemax(Uint16)) == "65535"
@test hex(typemin(Uint16)) == "0"
@test hex(typemax(Uint16)) == "ffff"
@test repr(typemin(Uint16)) == "0x0000"
@test string(typemin(Uint16)) == "0"
@test repr(typemax(Uint16)) == "0xffff"
@test string(typemax(Uint16)) == "65535"
@test base(3,typemin(Uint16)) == "0"
@test base(3,typemax(Uint16)) == "10022220020"
@test base(12,typemin(Uint16)) == "0"
@test base(12,typemax(Uint16)) == "31b13"
@test bin(typemin(Uint32)) == "0"
@test bin(typemax(Uint32)) == "1"^32
@test oct(typemin(Uint32)) == "0"
@test oct(typemax(Uint32)) == "37777777777"
@test dec(typemin(Uint32)) == "0"
@test dec(typemax(Uint32)) == "4294967295"
@test hex(typemin(Uint32)) == "0"
@test hex(typemax(Uint32)) == "ffffffff"
@test repr(typemin(Uint32)) == "0x00000000"
@test string(typemin(Uint32)) == "0"
@test repr(typemax(Uint32)) == "0xffffffff"
@test string(typemax(Uint32)) == "4294967295"
@test base(3,typemin(Uint32)) == "0"
@test base(3,typemax(Uint32)) == "102002022201221111210"
@test base(12,typemin(Uint32)) == "0"
@test base(12,typemax(Uint32)) == "9ba461593"
@test bin(typemin(Uint64)) == "0"
@test bin(typemax(Uint64)) == "1"^64
@test oct(typemin(Uint64)) == "0"
@test oct(typemax(Uint64)) == "1777777777777777777777"
@test dec(typemin(Uint64)) == "0"
@test dec(typemax(Uint64)) == "18446744073709551615"
@test hex(typemin(Uint64)) == "0"
@test hex(typemax(Uint64)) == "ffffffffffffffff"
@test repr(typemin(Uint64)) == "0x0000000000000000"
@test string(typemin(Uint64)) == "0"
@test repr(typemax(Uint64)) == "0xffffffffffffffff"
@test string(typemax(Uint64)) == "18446744073709551615"
@test base(3,typemin(Uint64)) == "0"
@test base(3,typemax(Uint64)) == "11112220022122120101211020120210210211220"
@test base(12,typemin(Uint64)) == "0"
@test base(12,typemax(Uint64)) == "839365134a2a240713"
@test bin(typemin(Uint128)) == "0"
@test bin(typemax(Uint128)) == "1"^128
@test oct(typemin(Uint128)) == "0"
@test oct(typemax(Uint128)) == "3777777777777777777777777777777777777777777"
@test hex(typemin(Uint128)) == "0"
@test hex(typemax(Uint128)) == "ffffffffffffffffffffffffffffffff"
@test repr(typemin(Uint128)) == "0x00000000000000000000000000000000"
@test string(typemin(Uint128)) == "0"
@test repr(typemax(Uint128)) == "0xffffffffffffffffffffffffffffffff"
@test string(typemax(Uint128)) == "340282366920938463463374607431768211455"
@test dec(typemin(Uint128)) == "0"
@test dec(typemax(Uint128)) == "340282366920938463463374607431768211455"
@test base(3,typemin(Uint128)) == "0"
@test base(3,typemax(Uint128)) ==
"202201102121002021012000211012011021221022212021111001022110211020010021100121010"
@test base(12,typemin(Uint128)) == "0"
@test base(12,typemax(Uint128)) == "5916b64b41143526a777873841863a6a6993"
@test bin(typemin(Int8)) == "-1"*"0"^7
@test bin(typemax(Int8)) == "1"^7
@test oct(typemin(Int8)) == "-200"
@test oct(typemax(Int8)) == "177"
@test dec(typemin(Int8)) == "-128"
@test dec(typemax(Int8)) == "127"
@test hex(typemin(Int8)) == "-80"
@test hex(typemax(Int8)) == "7f"
@test string(typemin(Int8)) == "-128"
@test string(typemax(Int8)) == "127"
@test base(3,typemin(Int8)) == "-11202"
@test base(3,typemax(Int8)) == "11201"
@test base(12,typemin(Int8)) == "-a8"
@test base(12,typemax(Int8)) == "a7"
@test bin(typemin(Int16)) == "-1"*"0"^15
@test bin(typemax(Int16)) == "1"^15
@test oct(typemin(Int16)) == "-100000"
@test oct(typemax(Int16)) == "77777"
@test dec(typemin(Int16)) == "-32768"
@test dec(typemax(Int16)) == "32767"
@test hex(typemin(Int16)) == "-8000"
@test hex(typemax(Int16)) == "7fff"
@test string(typemin(Int16)) == "-32768"
@test string(typemax(Int16)) == "32767"
@test base(3,typemin(Int16)) == "-1122221122"
@test base(3,typemax(Int16)) == "1122221121"
@test base(12,typemin(Int16)) == "-16b68"
@test base(12,typemax(Int16)) == "16b67"
@test bin(typemin(Int32)) == "-1"*"0"^31
@test bin(typemax(Int32)) == "1"^31
@test oct(typemin(Int32)) == "-20000000000"
@test oct(typemax(Int32)) == "17777777777"
@test dec(typemin(Int32)) == "-2147483648"
@test dec(typemax(Int32)) == "2147483647"
@test hex(typemin(Int32)) == "-80000000"
@test hex(typemax(Int32)) == "7fffffff"
@test string(typemin(Int32)) == "-2147483648"
@test string(typemax(Int32)) == "2147483647"
@test base(3,typemin(Int32)) == "-12112122212110202102"
@test base(3,typemax(Int32)) == "12112122212110202101"
@test base(12,typemin(Int32)) == "-4bb2308a8"
@test base(12,typemax(Int32)) == "4bb2308a7"
@test bin(typemin(Int64)) == "-1"*"0"^63
@test bin(typemax(Int64)) == "1"^63
@test oct(typemin(Int64)) == "-1000000000000000000000"
@test oct(typemax(Int64)) == "777777777777777777777"
@test dec(typemin(Int64)) == "-9223372036854775808"
@test dec(typemax(Int64)) == "9223372036854775807"
@test hex(typemin(Int64)) == "-8000000000000000"
@test hex(typemax(Int64)) == "7fffffffffffffff"
@test string(typemin(Int64)) == "-9223372036854775808"
@test string(typemax(Int64)) == "9223372036854775807"
@test base(3,typemin(Int64)) == "-2021110011022210012102010021220101220222"
@test base(3,typemax(Int64)) == "2021110011022210012102010021220101220221"
@test base(12,typemin(Int64)) == "-41a792678515120368"
@test base(12,typemax(Int64)) == "41a792678515120367"
@test bin(typemin(Int128)) == "-1"*"0"^127
@test bin(typemax(Int128)) == "1"^127
@test oct(typemin(Int128)) == "-2000000000000000000000000000000000000000000"
@test oct(typemax(Int128)) == "1777777777777777777777777777777777777777777"
@test hex(typemin(Int128)) == "-80000000000000000000000000000000"
@test hex(typemax(Int128)) == "7fffffffffffffffffffffffffffffff"
@test dec(typemin(Int128)) == "-170141183460469231731687303715884105728"
@test dec(typemax(Int128)) == "170141183460469231731687303715884105727"
@test string(typemin(Int128)) == "-170141183460469231731687303715884105728"
@test string(typemax(Int128)) == "170141183460469231731687303715884105727"
@test base(3,typemin(Int128)) ==
"-101100201022001010121000102002120122110122221010202000122201220121120010200022002"
@test base(3,typemax(Int128)) ==
"101100201022001010121000102002120122110122221010202000122201220121120010200022001"
@test base(12,typemin(Int128)) == "-2a695925806818735399a37a20a31b3534a8"
@test base(12,typemax(Int128)) == "2a695925806818735399a37a20a31b3534a7"
# floating-point printing
@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"
@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"
# signs
@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 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
@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 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 !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 lexcmp(-0.0, 0.0f0) == -1
@test lexcmp(0.0, -0.0f0) == 1
@test lexcmp(NaN, 1) == 1
@test lexcmp(1, NaN) == -1
@test lexcmp(NaN, NaN) == 0
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)
if WORD_SIZE == 64
@test y == float64(itrunc(y))
else
@test y == float64(int64(trunc(y)))
end
@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
@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
@test int128(-2.0^127) == typemin(Int128)
@test float64(uint128(3.7e19)) == 3.7e19
@test float64(uint128(3.7e30)) == 3.7e30
@test !(NaN <= 1)
@test !(NaN >= 1)
@test !(NaN < 1)
@test !(NaN > 1)
@test !(1 <= NaN)
@test !(1 >= NaN)
@test !(1 < NaN)
@test !(1 > NaN)
@test 1//1 == 1
@test 2//2 == 1
@test 1//1 == 1//1
@test 2//2 == 1//1
@test 2//4 == 3//6
@test 1//2 + 1//2 == 1
@test (-1)//3 == -(1//3)
@test 1//2 + 3//4 == 5//4
@test 1//3 * 3//4 == 1//4
@test 1//2 / 3//4 == 2//3
@test 1//0 == 1//0
@test 5//0 == 1//0
@test -1//0 == -1//0
@test -7//0 == -1//0
for a = -5:5, b = -5:5
if a == b == 0; continue; end
if ispow2(b)
@test a//b == a/b
@test convert(Rational,a/b) == a//b
end
@test rationalize(a/b) == a//b
@test a//b == a//b
if b == 0
@test_throws integer(a//b) == integer(a/b)
else
@test integer(a//b) == integer(a/b)
end
for c = -5:5
@test (a//b == c) == (a/b == c)
@test (a//b != c) == (a/b != c)
@test (a//b <= c) == (a/b <= c)
@test (a//b < c) == (a/b < c)
@test (a//b >= c) == (a/b >= c)
@test (a//b > c) == (a/b > c)
for d = -5:5
if c == d == 0; continue; end
@test (a//b == c//d) == (a/b == c/d)
@test (a//b != c//d) == (a/b != c/d)
@test (a//b <= c//d) == (a/b <= c/d)
@test (a//b < c//d) == (a/b < c/d)
@test (a//b >= c//d) == (a/b >= c/d)
@test (a//b > c//d) == (a/b > c/d)
end
end
end
@test 0.5 == 1//2
@test 0.1 != 1//10
@test 0.1 == 3602879701896397//36028797018963968
@test realmin() != 1//(BigInt(2)^1022+1)
@test realmin() == 1//(BigInt(2)^1022)
@test realmin() != 1//(BigInt(2)^1022-1)
@test realmin()/2 != 1//(BigInt(2)^1023+1)
@test realmin()/2 == 1//(BigInt(2)^1023)
@test realmin()/2 != 1//(BigInt(2)^1023-1)
@test nextfloat(0.0) != 1//(BigInt(2)^1074+1)
@test nextfloat(0.0) == 1//(BigInt(2)^1074)
@test nextfloat(0.0) != 1//(BigInt(2)^1074-1)
@test sqrt(2) == 1.4142135623730951
@test 1+1.5 == 2.5
@test 1.5+1 == 2.5
@test 1+1.5+2 == 4.5
@test is(typeof(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
for T in {Int8,Int16,Int32,Int64,Int128}
@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 = {Int8, Int16, Int32, Int64},
U = {Uint8, Uint16, Uint32, Uint64}
@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 rationals
int_types = {Int8, Uint8, Int16, Uint16, Int32, Uint32, Int64, Uint64}
for N = int_types, D = int_types
T = promote_type(N,D)
@test typeof(convert(N,2)//convert(D,3)) <: Rational{T}
end
# check type of constructed complexes
real_types = {Int8, Uint8, Int16, Uint16, Int32, Uint32, Int64, Uint64, Float32, Float64,
Rational{Int8}, Rational{Uint8}, Rational{Int16}, Rational{Uint16},
Rational{Int32}, Rational{Uint32}, Rational{Int64}, Rational{Uint64}}
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 complex(1,2) > 0
@test_throws complex(1,2) > complex(0,0)
# div, fld, rem, mod
for yr = {
1:6,
0.25:0.25:6.0,
1//4:1//4:6//1
}, xr = {
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 everything else in terms of div & fld
d = div(x,y)
f = fld(x,y)
r = rem(x,y)
m = mod(x,y)
t1 = isa(x,Rational) && isa(y,Rational) ?
promote_type(typeof(num(x)),typeof(num(y))) :
isa(x,Rational) ? promote_type(typeof(num(x)),typeof(y)) :
isa(y,Rational) ? promote_type(typeof(x),typeof(num(y))) :
promote_type(typeof(x),typeof(y))
t2 = promote_type(typeof(x),typeof(y))
@test typeof(d) <: t1
@test typeof(f) <: t1
@test typeof(r) <: t2
@test typeof(m) <: t2
@test d == f
@test r == m
@test 0 <= r < y
@test x == y*d + r
for X=[-1,1], Y=[-1,1]
sx = X*x
sy = Y*y
sd = div(sx,sy)
sf = fld(sx,sy)
sr = rem(sx,sy)
sm = mod(sx,sy)
@test typeof(sd) <: t1
@test typeof(sf) <: 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
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) ,-1) == -9223372036854775807-1 # FIXME!
@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