require 'test/unit' class TestBignum < Test::Unit::TestCase def setup @verbose = $VERBOSE $VERBOSE = nil @fmax = Float::MAX.to_i @fmax2 = @fmax * 2 @big = (1 << 63) - 1 end def teardown $VERBOSE = @verbose end def fact(n) return 1 if n == 0 f = 1 while n>0 f *= n n -= 1 end return f end def test_bignum $x = fact(40) assert_equal($x, $x) assert_equal($x, fact(40)) assert_operator($x, :<, $x+2) assert_operator($x, :>, $x-2) assert_equal(815915283247897734345611269596115894272000000000, $x) assert_not_equal(815915283247897734345611269596115894272000000001, $x) assert_equal(815915283247897734345611269596115894272000000001, $x+1) assert_equal(335367096786357081410764800000, $x/fact(20)) $x = -$x assert_equal(-815915283247897734345611269596115894272000000000, $x) assert_equal(2-(2**32), -(2**32-2)) assert_equal(2**32 - 5, (2**32-3)-2) for i in 1000..1014 assert_equal(2 ** i, 1 << i) end n1 = 1 << 1000 for i in 1000..1014 assert_equal(n1, 1 << i) n1 *= 2 end n2=n1 for i in 1..10 n1 = n1 / 2 n2 = n2 >> 1 assert_equal(n1, n2) end for i in 4000..4096 n1 = 1 << i; assert_equal(n1-1, (n1**2-1) / (n1+1)) end end def test_calc b = 10**80 a = b * 9 + 7 assert_equal(7, a.modulo(b)) assert_equal(-b + 7, a.modulo(-b)) assert_equal(b + -7, (-a).modulo(b)) assert_equal(-7, (-a).modulo(-b)) assert_equal(7, a.remainder(b)) assert_equal(7, a.remainder(-b)) assert_equal(-7, (-a).remainder(b)) assert_equal(-7, (-a).remainder(-b)) assert_equal(10000000000000000000100000000000000000000, 10**40+10**20) assert_equal(100000000000000000000, 10**40/10**20) a = 677330545177305025495135714080 b = 14269972710765292560 assert_equal(0, a % b) assert_equal(0, -a % b) end def shift_test(a) b = a / (2 ** 32) c = a >> 32 assert_equal(b, c) b = a * (2 ** 32) c = a << 32 assert_equal(b, c) end def test_shift shift_test(-4518325415524767873) shift_test(-0xfffffffffffffffff) end def test_to_s assert_equal("fvvvvvvvvvvvv" ,18446744073709551615.to_s(32), "[ruby-core:10686]") assert_equal("g000000000000" ,18446744073709551616.to_s(32), "[ruby-core:10686]") assert_equal("3w5e11264sgsf" ,18446744073709551615.to_s(36), "[ruby-core:10686]") assert_equal("3w5e11264sgsg" ,18446744073709551616.to_s(36), "[ruby-core:10686]") assert_equal("nd075ib45k86f" ,18446744073709551615.to_s(31), "[ruby-core:10686]") assert_equal("nd075ib45k86g" ,18446744073709551616.to_s(31), "[ruby-core:10686]") assert_equal("1777777777777777777777" ,18446744073709551615.to_s(8)) assert_equal("-1777777777777777777777" ,-18446744073709551615.to_s(8)) assert_match(/\A10{99}1\z/, (10**100+1).to_s) assert_match(/\A10{900}9{100}\z/, (10**1000+(10**100-1)).to_s) end b = 2**64 b *= b until Bignum === b T_ZERO = b.coerce(0).first T_ONE = b.coerce(1).first T_MONE = b.coerce(-1).first T31 = b.coerce(2**31).first # 2147483648 T31P = b.coerce(T31 - 1).first # 2147483647 T32 = b.coerce(2**32).first # 4294967296 T32P = b.coerce(T32 - 1).first # 4294967295 T64 = b.coerce(2**64).first # 18446744073709551616 T64P = b.coerce(T64 - 1).first # 18446744073709551615 T1024 = b.coerce(2**1024).first T1024P = b.coerce(T1024 - 1).first f = b while Bignum === f-1 f = f >> 1 end FIXNUM_MAX = f-1 def test_prepare assert_instance_of(Bignum, T_ZERO) assert_instance_of(Bignum, T_ONE) assert_instance_of(Bignum, T_MONE) assert_instance_of(Bignum, T31) assert_instance_of(Bignum, T31P) assert_instance_of(Bignum, T32) assert_instance_of(Bignum, T32P) assert_instance_of(Bignum, T64) assert_instance_of(Bignum, T64P) assert_instance_of(Bignum, T1024) assert_instance_of(Bignum, T1024P) end def test_big_2comp assert_equal("-4294967296", (~T32P).to_s) assert_equal("..f00000000", "%x" % -T32) end def test_int2inum assert_equal([T31P], [T31P].pack("I").unpack("I")) assert_equal([T31P], [T31P].pack("i").unpack("i")) end def test_quad_pack assert_equal([ 1], [ 1].pack("q").unpack("q")) assert_equal([- 1], [- 1].pack("q").unpack("q")) assert_equal([ T31P], [ T31P].pack("q").unpack("q")) assert_equal([-T31P], [-T31P].pack("q").unpack("q")) assert_equal([ T64P], [ T64P].pack("Q").unpack("Q")) assert_equal([ 0], [ T64 ].pack("Q").unpack("Q")) end def test_str_to_inum assert_equal(1, " +1".to_i) assert_equal(-1, " -1".to_i) assert_equal(0, "++1".to_i) assert_equal(73, "111".oct) assert_equal(273, "0x111".oct) assert_equal(7, "0b111".oct) assert_equal(73, "0o111".oct) assert_equal(111, "0d111".oct) assert_equal(73, "0111".oct) assert_equal(111, Integer("111")) assert_equal(13, "111".to_i(3)) assert_raise(ArgumentError) { "111".to_i(37) } assert_equal(1333, "111".to_i(36)) assert_equal(1057, "111".to_i(32)) assert_equal(0, "00a".to_i) assert_equal(1, Integer("1 ")) assert_raise(ArgumentError) { Integer("1_") } assert_raise(ArgumentError) { Integer("1__") } assert_raise(ArgumentError) { Integer("1_0 x") } assert_equal(T31P, "1111111111111111111111111111111".to_i(2)) assert_equal(0_2, '0_2'.to_i) assert_equal(00_2, '00_2'.to_i) assert_equal(00_02, '00_02'.to_i) end def test_to_s2 assert_raise(ArgumentError) { T31P.to_s(37) } assert_equal("9" * 32768, (10**32768-1).to_s) assert_raise(RangeError) { Process.wait(1, T64P) } assert_equal("0", T_ZERO.to_s) assert_equal("1", T_ONE.to_s) end def test_to_f assert_nothing_raised { T31P.to_f.to_i } assert_raise(FloatDomainError) { (1024**1024).to_f.to_i } assert_equal(1, (2**50000).to_f.infinite?) assert_equal(-1, (-(2**50000)).to_f.infinite?) end def test_cmp assert_operator(T31P, :>, 1) assert_operator(T31P, :<, 2147483648.0) assert_operator(T31P, :<, T64P) assert_operator(T64P, :>, T31P) assert_raise(ArgumentError) { T31P < "foo" } assert_operator(T64, :<, (1.0/0.0)) assert_not_operator(T64, :>, (1.0/0.0)) end def test_eq assert_not_equal(T31P, 1) assert_equal(T31P, 2147483647.0) assert_not_equal(T31P, "foo") assert_not_equal(2**77889, (1.0/0.0), '[ruby-core:31603]') end def test_eql assert_send([T31P, :eql?, T31P]) end def test_convert assert_equal([255], [T_MONE].pack("C").unpack("C")) assert_equal([0], [T32].pack("C").unpack("C")) assert_raise(RangeError) { 0.to_s(T32) } end def test_sub assert_equal(-T31, T32 - (T32 + T31)) x = 2**100 assert_equal(1, (x+2) - (x+1)) assert_equal(-1, (x+1) - (x+2)) assert_equal(0, (2**100) - (2.0**100)) o = Object.new def o.coerce(x); [x, 2**100+2]; end assert_equal(-1, (2**100+1) - o) assert_equal(-1, T_ONE - 2) end def test_plus assert_equal(T32.to_f, T32P + 1.0) assert_raise(TypeError) { T32 + "foo" } assert_equal(1267651809154049016125877911552, (2**100) + (2**80)) assert_equal(1267651809154049016125877911552, (2**80) + (2**100)) assert_equal(2**101, (2**100) + (2.0**100)) o = Object.new def o.coerce(x); [x, 2**80]; end assert_equal(1267651809154049016125877911552, (2**100) + o) end def test_minus assert_equal(T32P.to_f, T32 - 1.0) assert_raise(TypeError) { T32 - "foo" } end def test_mul assert_equal(T32.to_f, T32 * 1.0) assert_raise(TypeError) { T32 * "foo" } o = Object.new def o.coerce(x); [x, 2**100]; end assert_equal(2**180, (2**80) * o) end def test_positive_p assert_predicate(T_ONE, :positive?) assert_not_predicate(T_MONE, :positive?) assert_not_predicate(T_ZERO, :positive?) end def test_negative_p assert_not_predicate(T_ONE, :negative?) assert_predicate(T_MONE, :negative?) assert_not_predicate(T_ZERO, :negative?) end def test_mul_balance assert_equal(3**7000, (3**5000) * (3**2000)) end def test_mul_large_numbers a = %w[ 32580286268570032115047167942578356789222410206194227403993117616454027392 62501901985861926098797067562795526004375784403965882943322008991129440928 33855888840298794008677656280486901895499985197580043127115026675632969396 55040226415022070581995493731570435346323030715226718346725312551631168110 83966158581772380474470605428802018934282425947323171408377505151988776271 85865548747366001752375899635539662017095652855537225416899242508164949615 96848508410008685252121247181772953744297349638273854170932226446528911938 03430429031094465344063914822790537339912760237589085026016396616506014081 53557719631183538265614091691713138728177917059624255801026099255450058876 97412698978242128457751836011774504753020608663272925708049430557191193188 23212591809241860763625985763438355314593186083254640117460724730431447842 15432124830037389073162094304199742919767272162759192882136828372588787906 96027938532441670018954643423581446981760344524184231299785949158765352788 38452309862972527623669323263424418781899966895996672291193305401609553502 63893514163147729201340204483973131948541009975283778189609285614445485714 63843850089417416331356938086609682943037801440660232801570877143192251897 63026816485314923378023904237699794122181407920355722922555234540701118607 37971417665315821995516986204709574657462370947443531049033704997194647442 13711787319587466437795542850136751816475182349380345341647976135081955799 56787050815348701001765730577514591032367920292271016649813170789854524395 72571698998841196411826453893352760318867994518757872432266374568779920489 55597104558927387008506485038236352630863481679853742412042588244086070827 43705456833283086410967648483312972903432798923897357373793064381177468258 69131640408147806442422254638590386673344704147156793990832671592488742473 31524606724894164324227362735271650556732855509929890983919463699819116427 ].join.to_i b = %w[ 31519454770031243652776765515030872050264386564379909299874378289835540661 99756262835346828114038365624177182230027040172583473561802565238817167503 85144159132462819032164726177606533272071955542237648482852154879445654746 25061253606344846225905712926863168413666058602449408307586532461776530803 56810626880722653177544008166119272373179841889454920521993413902672848145 77974951972342194855267960390195830413354782136431833731467699250684103370 98571305167189174270854698169136844578685346745340041520068176478277580590 43810457765638903028049263788987034217272442328962400931269515791911786205 15357047519615932249418012945178659435259428163356223753159488306813844040 93609959555018799309373542926110109744437994067754004273450659607204900586 28878103661124568217617766580438460505513654179249613168352070584906185237 34829991855182473813233425492094534396541544295119674419522772382981982574 64708442087451070125274285088681225122475041996116377707892328889948526913 82239084041628877737628853240361038273348062246951097300286513836140601495 63604611754185656404194406869925540477185577643853560887894081047256701731 66884554460428760857958761948461476977864005799494946578017758268987123749 85937011490156431231903167442071541493304390639100774497107347884381581049 85451663323551635322518839895028929788021096587229364219084708576998525298 39594168681411529110089531428721005176467479027585291807482375043729783455 35827667428080449919778142400266842990117940984804919512360370451936835708 76338722049621773169385978521438867493162717866679193103745711403152099047 27294943901673885707639094215339506973982546487889199083181789561917985023 82368442718514694400160954955539704757794969665555505203532944598698824542 00599461848630034847211204029842422678421808487300084850702007663003230882 16645745324467830796203354080471008809087072562876681588151822072260738003 ].join.to_i c = %w[ 10269128594368631269792194698469828812223242061960065022209211719149714886 03494742299892841188636314745174778237781513956755034582435818316155459882 71422025990633195596790290038198841087091600598192959108790192789550336119 13849937951116346796903163312950010689963716629093190601532313463306463573 64436438673379454947908896258675634478867189655764364639888427350090856831 84369949421175534994092429682748078316130135651006102162888937624830856951 64818150356583421988135211585954838926347035741143424980258821170351244310 33072045488402539147707418016613224788469923473310249137422855065567940804 75231970365923936034328561426062696074717204901606475826224235014948198414 19979210494282212322919438926816203585575357874850252052656098969732107129 30639419804565653489687198910271702181183420960744232756057631336661646896 48734093497394719644969417287962767186599484579769717220518657324467736902 16947995288312851432262922140679347615046098863974141226499783975470926697 95970415188661518504275964397022973192968233221707696639386238428211541334 69925631385166494600401675904803418143232703594169525858261988389529181035 06048776134746377586210180203524132714354779486439559392942733781343640971 02430607931736785273011780813863748280091795277451796799961887248262211653 38966967509803488282644299584920109534552889962877144862747797551711984992 00726518175235286668236031649728858774545087668286506201943248842967749907 05345423019480534625965140632428736051632750698608916592720742728646191514 86268964807395494825321744802493138032936406889713953832376411900451422777 06372983421062172556566901346288286168790235741528630664513209619789835729 36999522461733403414326366959273556098219489572448083984779946889707480205 42459898495081687425132939473146331452400120169525968892769310016015870148 66821361032541586130017904207971120217385522074967066199941112154460026348 07223950375610474071278649031647998546085807777970592429037128484222394216 33776560239741740193444702279919018283324070210090106960567819910943036248 16660475627526085805165023447934326510232828674828006752369603151390527384 16810180735871644266726954590262010744712519045524839388305761859432443670 05188791334908140831469790180096209292338569623252372975043915954675335333 66614002146554533771788633057869340167604765688639181655208751680821446276 75871494160208888666798836473728725968253820774671626436794492530356258709 62318715778035246655925307167306434486713879511272648637608703497794724929 54912261106702913491290913962825303534484477936036071463820553314826894581 36951927032835690160443252405644718368516656317176848748544135126122940034 68454782581240953957381976073459570718038035358630417744490242611126043987 89191812971310096496208294948623403471433467614886863238916702384858514703 24327715474804343531844042107910755966152655912676456945146277848606406879 49724219295823540160221752189725460676360350860849986313532861445465771187 86822806696323658053947125253562001971534265078959827450518368635828010637 91977444206363529864361796188661941906329947840521598310396004328950804758 79728679236044038853668859284513594307352133390781441610395116807369310560 35193762565748328526426224069629084264376146174383444988110993194030351064 29660536743256949099972314033972121470913480844652490838985461134989129492 75577567064571716731774820127381261057956083604361635892088585967074514802 51958582645785905276289980534832170529946494815794770854644518463332458915 77572397432680871220602513555535017751714443325264019171753694163676670792 04353584782364068773777058727187323211012094819929720407636607815292764459 21851731257845562153822058534043916834839514338448582518847879059020959697 90538105704766415685100946308842788321400392381169436435078204622400475281 ].join.to_i assert_equal(c, a*b, '[ruby-core:48552]') end def test_divrem assert_equal(0, T32 / T64) end def test_divide bug5490 = '[ruby-core:40429]' assert_raise(ZeroDivisionError, bug5490) {T1024./(0)} assert_equal(Float::INFINITY, T1024./(0.0), bug5490) end def test_div assert_equal(T32.to_f, T32 / 1.0) assert_raise(TypeError) { T32 / "foo" } assert_equal(0x20000000, 0x40000001.div(2.0), "[ruby-dev:34553]") bug5490 = '[ruby-core:40429]' assert_raise(ZeroDivisionError, bug5490) {T1024.div(0)} assert_raise(ZeroDivisionError, bug5490) {T1024.div(0.0)} end def test_idiv assert_equal(715827882, 1073741824.div(Rational(3,2)), ' [ruby-dev:34066]') end def test_modulo assert_raise(TypeError) { T32 % "foo" } end def test_remainder assert_equal(0, T32.remainder(1)) assert_raise(TypeError) { T32.remainder("foo") } end def test_divmod assert_equal([T32, 0], T32.divmod(1)) assert_equal([2, 0], T32.divmod(T31)) assert_raise(TypeError) { T32.divmod("foo") } end def test_quo assert_kind_of(Float, T32.quo(1.0)) assert_equal(T32.to_f, T32.quo(1)) assert_equal(T32.to_f, T32.quo(1.0)) assert_equal(T32.to_f, T32.quo(T_ONE)) assert_raise(TypeError) { T32.quo("foo") } assert_equal(1024**1024, (1024**1024).quo(1)) assert_equal(Float::INFINITY, (1024**1024).quo(1.0)) assert_equal(1024**1024*2, (1024**1024*2).quo(1)) inf = 1 / 0.0; nan = inf / inf assert_send([(1024**1024*2).quo(nan), :nan?]) end def test_pow assert_equal(1.0, T32 ** 0.0) assert_equal(1.0 / T32, T32 ** -1) assert_equal(1, (T32 ** T32).infinite?) assert_equal(1, (T32 ** (2**30-1)).infinite?) ### rational changes the behavior of Bignum#** #assert_raise(TypeError) { T32**"foo" } assert_raise(TypeError, ArgumentError) { T32**"foo" } feature3429 = '[ruby-core:30735]' assert_instance_of(Bignum, (2 ** 7830457), feature3429) end def test_and assert_equal(0, T32 & 1) assert_equal(-T32, (-T32) & (-T31)) assert_equal(0, T32 & T64) end def test_or assert_equal(T32 + 1, T32 | 1) assert_equal(T32 + T31, T32 | T31) assert_equal(-T31, (-T32) | (-T31)) assert_equal(T64 + T32, T32 | T64) assert_equal(FIXNUM_MAX, T_ZERO | FIXNUM_MAX) end def test_xor assert_equal(T32 + 1, T32 ^ 1) assert_equal(T32 + T31, T32 ^ T31) assert_equal(T31, (-T32) ^ (-T31)) assert_equal(T64 + T32, T32 ^ T64) end class DummyNumeric < Numeric def to_int 1 end end def test_and_with_float assert_raise(TypeError) { T1024 & 1.5 } end def test_and_with_rational assert_raise(TypeError, "#1792") { T1024 & Rational(3, 2) } end def test_and_with_nonintegral_numeric assert_raise(TypeError, "#1792") { T1024 & DummyNumeric.new } end def test_or_with_float assert_raise(TypeError) { T1024 | 1.5 } end def test_or_with_rational assert_raise(TypeError, "#1792") { T1024 | Rational(3, 2) } end def test_or_with_nonintegral_numeric assert_raise(TypeError, "#1792") { T1024 | DummyNumeric.new } end def test_xor_with_float assert_raise(TypeError) { T1024 ^ 1.5 } end def test_xor_with_rational assert_raise(TypeError, "#1792") { T1024 ^ Rational(3, 2) } end def test_xor_with_nonintegral_numeric assert_raise(TypeError, "#1792") { T1024 ^ DummyNumeric.new } end def test_shift2 assert_equal(2**33, (2**32) << 1) assert_equal(2**31, (2**32) << -1) assert_equal(2**33, (2**32) << 1.0) assert_equal(2**31, (2**32) << -1.0) assert_equal(2**33, (2**32) << T_ONE) assert_equal(2**31, (2**32) << T_MONE) assert_equal(2**31, (2**32) >> 1) assert_equal(2**33, (2**32) >> -1) assert_equal(2**31, (2**32) >> 1.0) assert_equal(2**33, (2**32) >> -1.0) assert_equal(2**31, (2**32) >> T_ONE) assert_equal(2**33, (2**32) >> T_MONE) assert_equal( 0, (2**32) >> (2**32)) assert_equal(-1, -(2**32) >> (2**32)) assert_equal( 0, (2**32) >> 128) assert_equal(-1, -(2**32) >> 128) assert_equal( 0, (2**31) >> 32) assert_equal(-1, -(2**31) >> 32) end def test_shift_bigshift big = 2**300 assert_equal(2**65538 / (2**65537), 2**65538 >> big.coerce(65537).first) end def test_aref assert_equal(0, (2**32)[0]) assert_equal(0, (2**32)[2**32]) assert_equal(0, (2**32)[-(2**32)]) assert_equal(0, (2**32)[T_ZERO]) assert_equal(0, (-(2**64))[0]) assert_equal(1, (-2**256)[256]) end def test_hash assert_nothing_raised { T31P.hash } end def test_coerce assert_equal([T64P, T31P], T31P.coerce(T64P)) assert_raise(TypeError) { T31P.coerce(nil) } end def test_abs assert_equal(T31P, (-T31P).abs) end def test_size assert_kind_of(Integer, T31P.size) end def test_odd assert_equal(true, (2**32+1).odd?) assert_equal(false, (2**32).odd?) end def test_even assert_equal(false, (2**32+1).even?) assert_equal(true, (2**32).even?) end def test_interrupt_during_to_s if defined?(Bignum::GMP_VERSION) return # GMP doesn't support interrupt during an operation. end time = Time.now start_flag = false end_flag = false num = (65536 ** 65536) thread = Thread.new do start_flag = true num.to_s end_flag = true end sleep 0.001 until start_flag thread.raise thread.join rescue nil time = Time.now - time skip "too fast cpu" if end_flag assert_operator(time, :<, 10) end def test_interrupt_during_bigdivrem if defined?(Bignum::GMP_VERSION) return # GMP doesn't support interrupt during an operation. end return unless Process.respond_to?(:kill) begin trace = [] oldtrap = Signal.trap(:INT) {|sig| trace << :int } a = 456 ** 100 b = 123 ** 100 c = nil 100.times do |n| a **= 3 b **= 3 trace.clear th = Thread.new do sleep 0.1; Process.kill :INT, $$ sleep 0.1; Process.kill :INT, $$ end c = a / b trace << :end th.join if trace == [:int, :int, :end] assert_equal(a / b, c) return end end skip "cannot create suitable test case" ensure Signal.trap(:INT, oldtrap) if oldtrap end end def test_too_big_to_s if (big = 2**31-1).is_a?(Fixnum) return end assert_raise_with_message(RangeError, /too big to convert/) {(1 << big).to_s} end def test_fix_fdiv assert_not_equal(0, 1.fdiv(@fmax2)) assert_in_delta(0.5, 1.fdiv(@fmax2) * @fmax, 0.01) end def test_big_fdiv assert_equal(1, @big.fdiv(@big)) assert_not_equal(0, @big.fdiv(@fmax2)) assert_not_equal(0, @fmax2.fdiv(@big)) assert_not_equal(0, @fmax2.fdiv(@fmax2)) assert_in_delta(0.5, @fmax.fdiv(@fmax2), 0.01) assert_in_delta(1.0, @fmax2.fdiv(@fmax2), 0.01) end def test_float_fdiv b = 1E+300.to_i assert_equal(b, (b ** 2).fdiv(b)) assert_send([@big.fdiv(0.0 / 0.0), :nan?]) assert_in_delta(1E+300, (10**500).fdiv(1E+200), 1E+285) end def test_obj_fdiv o = Object.new def o.coerce(x); [x, 2**100]; end assert_equal((2**200).to_f, (2**300).fdiv(o)) end def test_singleton_method # this test assumes 32bit/64bit platform assert_raise(TypeError) { a = 1 << 64; def a.foo; end } end def test_frozen assert_equal(true, (2**100).frozen?) end def test_bitwise_and_with_integer_mimic_object def (obj = Object.new).to_int 10 end assert_raise(TypeError, '[ruby-core:39491]') { T1024 & obj } def obj.coerce(other) [other, 10] end assert_equal(T1024 & 10, T1024 & obj) end def test_bitwise_or_with_integer_mimic_object def (obj = Object.new).to_int 10 end assert_raise(TypeError, '[ruby-core:39491]') { T1024 | obj } def obj.coerce(other) [other, 10] end assert_equal(T1024 | 10, T1024 | obj) end def test_bitwise_xor_with_integer_mimic_object def (obj = Object.new).to_int 10 end assert_raise(TypeError, '[ruby-core:39491]') { T1024 ^ obj } def obj.coerce(other) [other, 10] end assert_equal(T1024 ^ 10, T1024 ^ obj) end end