鍓嶈█姣忎釜浜哄湪鍐欎唬鐮佺殑鏃跺€欓兘浼氶亣鍒版墍璋撶殑娴偣閿欒銆傚鏋滀綘娌℃湁韪╄繃娴偣鏁伴敊璇殑鍧戯紝鍙兘璇翠綘澶垢杩愪簡銆備互涓嬪浘涓殑Python涓轰緥锛?.1+0.2涓嶇瓑浜?.3锛?.7/10涓嶇瓑浜?.87锛岃€屾槸0.869999...锛岃繖鐪熺殑寰堝鎬煠斾絾杩欑粷瀵逛笉鏄湴鐙眀ug锛孭ython鐨勮璁′篃娌℃湁闂锛屼絾鏄畠鏄诞鐐规暟鍦ㄥ仛璁＄畻鏃剁殑蹇呯劧缁撴灉锛屾墍浠ュ嵆浣挎槸JavaScript鎴栬€呭叾浠栬瑷€涔熸槸涓€鏍风殑锛氳绠楁満濡備綍瀛樺偍涓€涓暣鏁帮紙Integer锛変箣鍓嶈鐨勫叧浜庝负浠€涔堜細鍑虹幇娴偣鏁伴敊璇紝涓嬮潰璇磋璁＄畻鏈哄浣曠敤0鍜?琛ㄧず鏁存暟锛屼簩杩涘埗澶у搴旇閮界煡閬擄細姣斿101琛ㄧず$2^2+2^0$涔熷氨鏄?锛?010琛ㄧず$2^3+2^1$鍗?0锛屽鏋滄槸鏃犵鍙风殑32浣嶆暣鏁帮紝鍒欒〃绀哄畠鏈?2涓綅缃彲浠ユ斁0鎴?锛屾墍浠ユ渶灏忓€间负0000...0000鍗?锛岃€屾渶澶у€?111...1111琛ㄧず$2^{31}+2^{30}+...+2^1+2^0$涓?294967295浠庢帓鍒楃粍鍚堢殑瑙掑害鏉ョ湅锛屽洜涓烘瘡涓猙it鍙互鏄?涔熷彲浠ユ槸1锛屾暣涓彉閲忕殑鍊奸兘鏄?2^{32}$閮芥槸鍙互鐨勶紝鎵€浠?鍒?2^{23}-1$涔嬮棿鐨勪换浣曞€奸兘鍙互鍑嗙‘琛ㄨ揪锛屼笉浼氭湁浠讳綍閿欒銆傝櫧鐒朵粠0鍒?2^{23}-1$鐨勬暣鏁版湁寰堝锛屼絾鏄诞鐐规暟鐨勪釜鏁版槸鏈夐檺鐨勶紝涔熷氨鏄彧鏈?2^{32}$閭ｄ箞澶氾紱浣嗘槸娴偣鏁板氨涓嶄竴鏍蜂簡锛屾垜浠彲浠ヨ繖鏍锋兂锛氫粠1鍒?0鐨勫尯闂村彧鏈夊崄涓暣鏁帮紝浣嗘槸娴偣鏁板嵈鏈夋棤绌峰涓紝姣斿5.1銆?.11銆?.111绛夛紝娓呭崟涓嶈兘绌峰敖銆備絾鏄洜涓?2浣嶇┖闂村彧鏈?鲁虏鐨勫彲鑳斤紝涓轰簡鎶婃墍鏈夌殑娴偣鏁伴兘濉炶繘杩欎釜32浣嶇┖闂达紝寰堝CPU鍘傚晢鍙戞槑浜嗗悇绉嶆诞鐐规暟鐨勮〃绀烘柟寮忥紝浣嗘槸濡傛灉姣忎竴涓殑鏍煎紡CPU涓嶄竴鏍峰緢楹荤儲锛屾墍浠ユ渶鍚庤繕鏄噰鐢ㄤ簡IEEE鍙戝竷鐨処EEE754浣滀负娴偣杩愮畻鐨勯€氱敤鏍囧噯锛岀幇鍦ㄧ殑CPU涔熸槸鎸夌収杩欎釜鏍囧噯璁捐鐨勩€侷EEE754IEEE754瀹氫箟浜嗗緢澶氫笢瑗匡紝鍖呮嫭鍗曠簿搴︼紙32浣嶏級銆佸弻绮惧害锛?4浣嶏級鍜岀壒娈婂€硷紙鏃犵┓澶с€丯aN锛夌瓑鐨勮〃绀恒€傚浜庢诞鐐规暟8.5锛屽鏋滆鏀规垚IEEE754鏍煎紡鐨勮瘽锛屽繀椤诲厛鍋氫竴浜涘綊涓€鍖栧鐞嗭細灏?.5鎷嗘垚8+0.5锛屽嵆$2^3+(\cfrac{1}{2})^1$锛岀劧鍚庡啓鎴愪簩杩涘埗鍙樻垚1000.1锛屾渶鍚庡啓鎴?1.0001\times2^3$锛屽緢鍍忓崄杩涘埗鐨勭瀛﹁鏁版硶銆傚湪IEEE754涓紝鍗曠簿搴︽诞鐐规暟鏄皢32浣嶆诞鐐规暟鎷嗗垎涓虹鍙枫€佹寚鏁板拰鍒嗘暟涓夐儴鍒嗭紝瀹冧滑鍔犺捣鏉ヤ竴鍏辨槸32浣嶇鍙凤紙sign锛夛細鏈€宸﹁竟1浣嶄唬琛ㄦ璐熷彿銆傚鏋滄暟涓烘鏁帮紝鍒欑鍙蜂负0锛屽惁鍒欎负1闃剁爜锛堟寚鏁帮級锛氫腑闂?浣嶈〃绀哄綊涓€鍖栧悗鐨勫箓锛屾寚鏁颁负鐪熷€?127鐨勬牸寮忥紝鍗?鍔犱笂127绛変簬130鐨勫熬鏁帮紙鍒嗘暟锛夛細鏈€鍙宠竟鐨?3浣嶆槸灏忔暟閮ㄥ垎锛屽湪1.0001鐨勬儏鍐典笅鍘绘帀1鍚庨潰鐨?001锛屾墍浠ュ鏋滆〃绀?.5鐨勮瘽鏄?2浣嶆牸寮忕殑璇濓紝搴旇鏄繖鏍风殑锛氫粈涔堟儏鍐典笅浼氬嚭閿欙紵鍓嶉潰8.5鐨勪緥瀛愬彲浠ヨ〃绀轰负$2^3+(\cfrac{1}{2})^1$锛屽洜涓?鍜?.5閮芥槸2鐨勫箓锛屾墍浠ュ畬鍏ㄤ笉浼氭湁绮惧害闂銆備絾鏄鏋滄槸8.9锛屽洜涓烘病鏈夊姙娉曞姞涓?鐨勬鏂癸紝鎵€浠ヤ細寮哄埗琛ㄧず涓?1.0001110011...\times2^3$锛屼細鍑虹幇$0.0000003$宸﹀彸鐨勮宸€傚鏋滄偍瀵圭粨鏋滄劅鍒板ソ濂囷紝鍙互璁块棶IEEE-754FloatingPointConverter缃戠珯骞跺皾璇曚竴涓嬨€傚弻绮惧害娴偣鏁颁笂闈㈡彁鍒扮殑鍗曠簿搴︽诞鐐规暟鍙敤32浣嶆潵琛ㄧず銆備负浜嗕娇璇樊鏇村皬锛孖EEE754杩樺畾涔変簡濡備綍浣跨敤64浣嶆潵琛ㄧず娴偣鏁般€備笌32浣嶇浉姣旓紝灏忔暟閮ㄥ垎鎵╁ぇ浜嗕袱浣嶃€傛锛屼粠23浣嶅埌52浣嶏紝閭ｄ箞鍑嗙‘鐜囪嚜鐒朵細鎻愰珮寰堝銆備互鍒氭墠鐨?.9涓轰緥锛岃櫧鐒跺鏋滅敤64浣嶈〃绀哄彲浠ユ洿鍑嗙‘锛屼絾鏄敱浜?.9涓嶈兘瀹屽叏鍐欐垚2鐨勫箓鐩稿姞锛屾墍浠ュ埌浜嗗皬鏁扮偣鍚?6浣嶈繕鏄細鍑虹幇閿欒锛屼絾鏄笌鍗曠簿搴︾殑璇樊涓?.0000003鐩告瘮锛岃灏忓緢澶氥€傜被浼肩殑鎯呭喌涓嬶紝Python涓殑1.0绛変簬0.999...999锛?23绛変簬122.999...999锛屽洜涓哄畠浠箣闂寸殑宸窛澶皬浜嗭紝涓嶈兘鏀惧湪灏忔暟閲岄潰锛屾墍浠ヤ粠浜岃繘鍒舵牸寮忕湅浼间箮鏄粬浠殑姣忎竴鐐归兘鏄竴鏍风殑銆傝В鍐虫柟妗堢敱浜庢诞鐐规暟鐨勯敊璇槸涓嶅彲閬垮厤鐨勶紝鎴戜滑涓嶅緱涓嶅繊鍙楀畠銆備笅闈㈡槸涓ょ甯歌鐨勫鐞嗘柟寮忥細璁剧疆鏈€澶у厑璁歌宸碉紙epsilon锛夋湁浜涜瑷€浼氭彁渚涙墍璋撶殑epsilon锛岀敤鏉ヨ浣犲垽鏂槸鍚﹀湪娴偣鏁拌宸厑璁歌寖鍥村唴锛孭ython涓璭psilon鐨勫€肩害涓?2.2e^{-16}$鎵€浠ュ彲浠ュ皢0.1+0.2==0.3鏀瑰啓涓?.1+0.2鈥?.3<=epsilon锛岃繖鏍峰氨鍙互閬垮厤娴偣鏁伴敊璇湪杩愮畻涓€犳垚楹荤儲锛屽苟涓斿彲浠ユ纭瘮杈?.1鍔?.2鏄惁绛変簬0.3銆傚綋鐒讹紝濡傛灉绯荤粺娌℃湁鎻愪緵锛屼綘涔熷彲浠ヨ嚜宸卞畾涔変竴涓猠psilon锛岃缃湪2鐨?15娆℃柟宸﹀彸銆傚皬鏁伴儴鍒嗗叏閮ㄥ鍏ュ熬鏁般€傜敱浜庤浆鎹㈡椂鍙兘鏈夐敊璇紝骞茶剢涓嶈浆鎹紝鐩存帴鐢ㄥ崄杩涘埗璁＄畻銆傚湪Python涓湁涓€涓悕涓篸ecimal鐨勬ā鍧楋紝鍦↗avaScript涓湁涓€涓被浼肩殑鍖呫€傚畠鍙互甯綘璁＄畻鍗佽繘鍒讹紝灏卞儚浣犲彲浠ョ敤绗斿拰绾歌绠?.1+0.2涓€鏍凤紝缁濆涓嶄細鍑洪敊锛屼笉浼氬嚭閿欍€傝櫧鐒朵娇鐢ㄥ崄杩涘埗璁＄畻鍙互瀹屽叏閬垮厤娴偣鏁伴敊璇紝浣嗘槸鐢变簬Decimal鐨勫崄杩涘埗璁＄畻鏄ā鎷熺殑锛屾墍浠ュ湪鏈€搴曞眰鐨凜PU鐢佃矾涓粛鐒朵娇鐢ㄤ簩杩涘埗璁＄畻锛屾墽琛岄€熷害浼氭瘮鍘熺敓鐨勬诞鐐硅绠楁參寰堝銆傛墍浠ヤ笉寤鸿瀵规墍鏈夋诞鐐硅繍绠楅兘浣跨敤Decimal銆?/p>
