! / 0 0 0 0 704 ` €€€HH0 >R_ZN53_$LT$typenum..Greater$u20$as$u20$core..fmt..Debug$GT$3fmt17h0569bf8e68394ab7E_ZN50_$LT$typenum..Less$u20$as$u20$core..fmt..Debug$GT$3fmt17h7301f5e08ad45538E_ZN51_$LT$typenum..Equal$u20$as$u20$core..fmt..Debug$GT$3fmt17heda02dea1309542eE_ZN53_$LT$typenum..bit..B0$u20$as$u20$core..fmt..Debug$GT$3fmt17h083ab0f401baa62cE_ZN53_$LT$typenum..bit..B1$u20$as$u20$core..fmt..Debug$GT$3fmt17hcd19a46cc0aa6fb8E_ZN53_$LT$typenum..int..Z0$u20$as$u20$core..fmt..Debug$GT$3fmt17h818b72784f1a27e1E_ZN57_$LT$typenum..uint..UTerm$u20$as$u20$core..fmt..Debug$GT$3fmt17h06a7798c77f59db7E_ZN58_$LT$typenum..array..ATerm$u20$as$u20$core..fmt..Debug$GT$3fmt17hb876e0c83d6ad7fcE// 320 ` typenum-16e81b5c6d389767.typenum.18281aa78d2b1b01-cgu.0.rcgu.o/ typenum-16e81b5c6d389767.typenum.18281aa78d2b1b01-cgu.1.rcgu.o/ typenum-16e81b5c6d389767.typenum.18281aa78d2b1b01-cgu.2.rcgu.o/ typenum-16e81b5c6d389767.typenum.18281aa78d2b1b01-cgu.3.rcgu.o/ 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<؛<ى?ك?؛?ىC؛CïF؛FïI؛IïL؛LïO؛OcompareءQPءS؛S«U¹W؛W«Y¹[؛[«]¹`؛`minءc؛c›f؛f›i؛i›m؛mmaxءp؛pês؛sêv؛vêintءyyyyyyyyyy y yyy yyyyyyyyyyyyyyyyyyy y!y"y#y‍Uء‍«y،ة،«y¤«y¦ةy¨ةyy«ةyI8ءI16ءI32ءI64ءISIZEءto_i8ءto_i16ءto_i32ءto_i64ءto_isizeءy¸ة¸¦ ¸° ¸» ¸ئ ¸ر ¸ق ¸ë ¸ù ¸‡ ¸• y ؤةؤ¦ ؤ° ؤ» ؤئ ؤر ؤق ؤë ؤù ؤ‡ ؤ• y ذ؛ذ£yسةس؛س£y×ة×؛×£y غIءغ؛غ’yكةك؛ك’yمةم؛م’yçUlءçUrءç؛ç’yى‚ ىŒ ى؛ى’yٌ‚ ٌŒ ٌ؛ٌ’yِ‚ ِŒ ِ؛ِ’yû¨û¹û؛ûprivate_integer_addءy€¨€¹€؛€®y…¨…¹…؛…®yٹ؛ٹ‚yچةچ؛چ‚y‘ة‘؛‘‚y•ة•؛•‚y™ة™؛™‚y‌‚ ‌Œ ‌؛‌‚y¢‚ ¢Œ ¢؛¢‚y§‚ §Œ §؛§‚y¬‚ ¬Œ ¬؛¬‚y ±±؛±چy!µةµ؛µچy"¹ة¹؛¹چy#½‚ ½Œ ½؛½چy$آ‚ آŒ آ؛آچy%ا‚ اŒ ا؛اچy&ج‚ جŒ ج؛جچy'رر؛ر·yimpl_int_divءy$y%y&y(ظMءظ¨ظ؛ظpartial_divءy)ق؛ق«àIMءy*âةâ؛â«هˆy+çةç؛ç«êˆy,ىةى؛ى«ïˆy-ٌةٌ؛ٌ«ôˆy.ِ¹ِ¨ِ؛ِ«ْˆy/ü¹ü¨ü؛ü«€ˆy0‚Plء‚Prء‚؛‚«†ˆy1ˆNlءˆNrءˆ؛ˆ«Œˆy2ژژ؛ژ÷yimpl_int_remءy3“؛“powiءy4–ة–؛–•y5ڑةڑ؛ڑ•y6‍ة‍؛‍•y7¢ة¢؛¢•y8¦ة¦؛¦•y9ھةھ؛ھ•y:®ة®؛®•y;²‚ ²Œ ²؛²•y<·‚ ·Œ ·؛·•y=¼‚ ¼Œ ¼؛¼•y'y(y)y>ؤ؛y?ئةئ؛y@ةةة؛yAجةج؛yBدةد؛yCزU1ءزU2ءز؛yDض½ضاض؛yEع½عاع؛yFق½قاق؛y*y+y,y-y.yGç؛ç›yHêةê؛ê›yIîةî؛î›yJٍةٍ؛ٍ›yKِةِ؛ِ›yLْ‚ ْŒ ْ؛ْ›yMے‚ ےŒ ے؛ے›yN„‚ „Œ „؛„›yO‰‚ ‰Œ ‰؛‰›yPژ؛ژêyQ‘ة‘؛‘êyR•ة•؛•êyS™ة™؛™êyT‌ة‌؛‌êyU،‚ ،Œ ،؛،êyV¦‚ ¦Œ ¦؛¦êyW«‚ «Œ «؛«êyX°‚ °Œ °؛°êyYµto_intءµINTءyZ¸ي¸ûy[»ي»ûy\¾ي¾ûy]ءةءيءûy^إةإيإûy_ةةةيةûy`حةحيحûyaرةريرûybصةصيصûycظةظيظûydفةفيفû marker_traitsءللNonZeroءلZeroءل¶هto_orderingءلBitءçدçطç«çêçِلUnsignedءيديU16ءيU32ءيU64ءيUSIZEءي¦ ي° ي» يئ ير يêيto_u16ءيto_u32ءيto_u64ءيto_usizeءيق يë يù ي‡ ي• لIntegerء‚¦ ‚° ‚» ‚ئ ‚ر ‚ق ‚ë ‚ù ‚‡ ‚• ل TypeArrayءل PowerOfTwoءoperator_aliasesءڈڈڈڈڈڈڈڈڈڈ ڈ ڈڈڈ ڈڈڈڈڈڈڈڈڈڈAndء§Aء§BءڈOrءھ“'ھœ'ڈXorء“'œ'ڈShleftء°“'°œ'ڈShrightء³“'³œ'ڈSumء¶“'¶œ'ڈDiffء¹“'¹œ'ڈProdء¼“'¼œ'ڈQuotء؟“'؟œ'ڈModءآ“'آœ'ڈPartialQuotءإ“'إœ'ڈNegateءب“'ڈAbsValءت“'ڈExpءج“'جœ'ڈGcfءد“'دœ'ڈAdd1ءز“'ڈSub1ءش“'ڈDoubleءض“'ڈSquareءط“'ڈCubeءع“'ڈSqrtءـ“'ڈCompareءق“'قœ'ڈLengthءلهڈMinimumءم“'مœ'ڈMaximumءو“'وœ'ڈڈڈڈڈڈڈڈLeءً“'ًœ'ڈ}َ“'َœ'ڈGrءِ“'ِœ'ڈGrEqءù“'ùœ'ڈLeEqءü“'üœ'ڈNotEqءے“'ےœ'ڈLog2ء‚“'privateء„„„„„„„„„„Internalء„InternalMarkerء„„Trimء‘؛‘trimء„TrimOutء”“'„TrimTrailingZerosء–؛–trim_trailing_zerosء„TrimTrailingZerosOutء™“'„Invertء›؛›invertء„ InvertOutء‍“'„ PrivateInvertء ك ؛ private_invertء„PrivateInvertOutء¤“'¤ك„ InvertedUTermء§ „InvertedUIntء©IUء©œ'©msbء©lsbء„ PrivateAndء®ك®؛®private_andء„ PrivateAndOutء²“'²ك„ PrivateXorءµكµ؛µprivate_xorء„ PrivateXorOutء¹“'¹ك„ PrivateSubء¼ك¼؛¼private_subء„ PrivateSubOutءہ“'ہك„PrivateIntegerAddءأdأ¨أ؛أ®„PrivateIntegerAddOutءب¹بdب¨„ PrivatePowءجYءج¨ج؛جprivate_powء„ PrivatePowOutءر“'رê4ر¨„ ShiftDiffءصكص؛„ShiftDiffOutءط“'طك„BitDiffءغكغ؛„ BitDiffOutءق“'قك„InvertedUnsignedءل¶$„م¶$„ه·1هœ'ه¶$„é؛éے/„ىةىœ'ى؛ىے/„ٌ·1ٌ؛ٌث0„ُ·1ُةُœ'ُ؛ُث0„û؛ûے/„‏·1‏œ'‏؛‏ے/„ ƒةƒ؛ƒث0„ ‡ة‡·1‡œ'‡؛‡ث0„چ؛چھ/„گ·1گ؛گھ/„ ”·1”؛”ھ/„کةک؛کو.„ PrivateCmpءœكœSoFarءœ؛œprivate_cmpء„ PrivateCmpOutء،“'،ك،،:„ PrivateSetBitء¥¥œ'¥؛¥private_set_bitء„PrivateSetBitOutءھ¨ھھœ'„ PrivateDivء®¨®Dء®Qء®Rء®®Quotientء® Remainderء®private_div_quotientء®private_div_remainderء„PrivateDivQuotء¸¨¸„<¸چ<¸–<¸„ PrivateDivRemء¾¨¾„<¾چ<¾–<¾„PrivateDivIfءؤ¨ؤ„<ؤچ<ؤ–<ؤؤRcmpDءؤ§<ؤ·<ؤprivate_div_if_quotientءؤprivate_div_if_remainderء„PrivateDivIfQuotءد¨د„<دچ<د–<دد¸>„PrivateDivIfRemءض¨ض„<ضچ<ض–<ضض¸>„ PrivateDivIntءفdفDivisorءف؛فprivate_div_intء„PrivateDivIntOutءâ“'âdâ؟@„ PrivateRemءوURemءو؟@و؛وprivate_remء„ PrivateRemOutءë“'ë®Aë؟@„ PrivateMinءïكï CmpResultءï؛ïprivate_minء„ PrivateMinOutءô“'ôœ'ô¤B„ PrivateMaxءّكّ¤Bّ؛ّprivate_maxء„ PrivateMaxOutء‎“'‎œ'‎¤B„ „ „„„ „„ IsLessPrivateء‡ك‡Cmpء‡؛‡is_less_privateء„Œ“'Œœ'Œ؛ŒµD„‘“'‘œ'‘؛‘µD„–“'–œ'–؛–µD„IsEqualPrivateء›ك›¢D›؛›is_equal_privateء„ “' œ' ؛ éE„¥“'¥œ'¥؛¥éE„ھ“'ھœ'ھ؛ھéE„IsGreaterPrivateء¯ك¯¢D¯؛¯is_greater_privateء„´“'´œ'´؛´ G„¹“'¹œ'¹؛¹ G„¾“'¾œ'¾؛¾ G„IsLessOrEqualPrivateءأكأ¢Dأ؛أis_less_or_equal_privateء„ب“'بœ'ب؛بفH„ح“'حœ'ح؛حفH„ز“'زœ'ز؛زفH„IsNotEqualPrivateء×ك×¢D×؛×is_not_equal_privateء„ـ“'ـœ'ـ؛ـ‌J„ل“'لœ'ل؛ل‌J„و“'وœ'و؛و‌J„IsGreaterOrEqualPrivateءëكë¢Dë؛ëis_greater_or_equal_privateء„ً“'ًœ'ً؛ًكK„ُ“'ُœ'ُ؛ُكK„ ْ“'ْœ'ْ؛ْكK„PrivateSquareRootءے؛„PrivateLogarithm2ءپ ؛type_operatorsءƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ Sameءگ كگ ؛ƒ “ ه“ ؛ƒ Absء– ؛ƒ ک ؛ƒ ڑ ةڑ ؛ƒ ‌ ة‌ ؛ƒ Powء ً) ؛ •ƒ impl_pow_fءƒ impl_pow_iءƒ ¢D¦ ك¦ ؛¦ «© ˆƒ Lenء« ؛« «ƒ PartialDivء® ك® ؛® لƒ Minء² ك² ؛² ›ƒ Maxء¶ ك¶ ؛¶ êƒ ƒ IsLessء» ك» ؛» is_lessءƒ ƒ ہ “'ہ œ'ہ ؛ہ œQƒ IsEqualءإ كإ ؛إ is_equalءƒ ƒ ت “'ت œ'ت ؛ت ôQƒ IsGreaterءد كد ؛د is_greaterءƒ ƒ ش “'ش œ'ش ؛ش دRƒ IsLessOrEqualءظ كظ ؛ظ is_less_or_equalءƒ ƒ ق “'ق œ'ق ؛ق °Sƒ IsNotEqualءم كم ؛م is_not_equalءƒ ƒ è “'è œ'è ؛è ”Tƒ IsGreaterOrEqualءي كي ؛ي is_greater_or_equalءƒ ƒ ٍ “'ٍ œ'ٍ ؛ٍ ْTƒ ®ƒ SquareRootءّ ؛ƒ Logarithm2ءْ ؛ƒ Gcdءü كü ؛ƒ ToIntءے هے يے ûuintءƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ !ƒ "ƒ #ƒ $ƒ %ƒ &ƒ 'ƒ (ƒ )ƒ *ƒ +ƒ ,ƒ -ƒ .ƒ /ƒ 0ƒ 1ƒ 2ƒ 3ƒ 4ƒ 5ƒ 6ƒ 7ƒ 8ƒ 9ƒ :ƒ ;ƒ <ƒ =ƒ >ƒ ?ƒ @ƒ Aƒ Bƒ Cƒ Dƒ ة «ƒ ث دث ¼#ث ا#ث ز#ث ف#ث ¦ ث ° ث » ث ئ ث ر ث êث ڑ$ث ¨$ث ¶$ث ؤ$ث ق ث ë ث ù ث ‡ ث • ƒ à ةà œ'à «ƒ ن ةن œ'ن دن ¼#ن ا#ن ز#ن ف#ن ¦ ن ° ن » ن ئ ن ر ن êن ڑ$ن ¨$ن ¶$ن ؤ$ن ق ن ë ن ù ن ‡ ن • ƒ û ةû œ'ƒ ƒ ƒ €ةƒ ‚؛‚«ƒ …ة…œ'…؛…«ƒ ٹ؛ٹ’ƒ 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ح؛ح§Cƒ _ƒ ˆشةش؛شêƒ ‰طةطœ'طŒ ط؛طêƒ ٹق¨ق؛ƒ ‹ل؛ƒ Œم؛ƒ چهةهBaءهBbءه؛ƒ ژê¨ê؛ƒ ڈي؛ƒ گïةïœ'ï؛ƒ ‘َيَûƒ ’ِيِûƒ “ùيùûƒ ”üيüûƒ •ےيےûƒ –‚ي‚ûƒ —…ي…ûƒ کˆيˆûƒ ™‹ي‹ûƒ ڑژةژœ'ژيژûƒ ›“ة“œ'“ي“ûƒ œکةکœ'کيکûƒ ‌‌ة‌œ'‌ي‌ûƒ ‍¢ة¢œ'¢ي¢ûƒ ں§ة§œ'§ي§ûƒ ¬ة¬œ'¬ي¬ûƒ ،±ة±œ'±ي±ûƒ ¢¶ة¶œ'¶ي¶û¸»»»»»»»»أVءأ“'»tarrء»ا؛ا«»تڈچت“'ت؛ت«»د؛د’»زAlءزVlءزArءزVrءز؛ز’»ظ؛ظ‚»ـ‹ژـپژـںژـ•ژـ؛ـ‚»مكم؛مچ» çڈچç“'çكç؛çچ» ي؛يچ»ًةً؛ًچ»ôةô؛ôچ» ّڈچّ“'ّ؛ّچ»‎ڈچ‎“'‎ة‎؛‎چ»ƒڈچƒ“'ƒةƒ؛ƒچ»‰ك‰؛‰·»چڈچچ“'چكچ؛چ·»“ك“؛“ل»—ڈچ—“'—ك—؛—ل»»‍ك‍؛‍÷»¢ڈچ¢“'¢ك¢؛¢÷»»©؛©£»¬ڈچ¬“'¬؛¬£ ؟ق"ءق"أق"assert_type_eqءassert_typeءsealedءاااااااااا ا ااا اااSealedءااااـةـœ'ااàةاâةااا ا اèڈچè“'opء__op_internal__ءconstsءيييييييييي 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ٌ»I9iPؤ$ثإظئç°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$êإّئي×ا´ثإ´ êإء واقظئق ّئêç† يà£ؤغˆ<‡¤¢‡¤ڈ‡¤•ڈ‡¤ˆ<ؤؤ ؤ ‹ژر ر ںژؤؤئ•ج´جؤظظîî î پژْْ•ژîîئ£حآحîپپھc°0•ج´جإ£حآحإŒŒ“âً£ °0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$،خ°خ“°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$•ج£ح÷°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$´جآح‎،خؤ•جؤ ´جر °خî£حî آحْ÷† ‎ً£—کوق:‡¤ِ‡¤هٍہëه‡¤ق:ژژ ژ اھژژثاھكژ‌²² ² خھ²²ثخھڈس²ہôX°0اھڈستخھڈستثثزىأڈ°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$§ش¶شفگھتڈسذ§شژاھژ ¶ش²خھ² ت† ذأڈض ïڑ <‡¤´ éُ، ‡¤§ ، éُڑ <ƒ"َا!<‡¤ل!œشخ!‡¤ش!خ!ا!<°#÷ô"<‡¤ژ#àنû"‡¤پ#û"ô"<‘%ک%ک%خھ‘%‘%ثéُخھéُ‘%ں%ل$J°0éُéُخھتéُھ%°%اھ±%ü©$ˆ°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$éُ‏ظت$éُ°$گھ¶$‏ظ‘%خھک%°$éُ† ¶$©$ˆہ'ا' ا' اھہ'ہ'ثٍ,ٍ,†طô,ڑطث ڈµهEغأ¥اھہ'د'ن'ë'ë'خھن'ن'ثثـخھن'ٍ'¦'X°0ثـاھتثـخھت‎'‎'„(‚î&–°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$گقںقڈ'ثـُ&گھû&گقہ'اھا' ںقن'خھë'ُ&† û&î&–“*ڑ* ڑ* اھ“*“*ث”-”-يظ–-ڑطقIë¨èًزٹأ¥اھ“*¢*·*¾*¾*خھ·*·*ثîàخھ·*إ*ù)X°0îàاھتîàخھتذ*ذ*×*ˆء)–°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$³âآââ)îàب)گھخ)³â“*اھڑ* آâ·*خھ¾*ب)† خ)ء)–ظ,ع,Œ ,:‡¤¸,‡¤§,ٍہ,§,‡¤ ,:ذ.ذ. ذ. اھذ.ذ.ذاھڈسذ.ك.ô.ô. ô. خھô.ô.ذخھڈسô.‚/¶.X°0اھڈسدخھڈسدچ/چ/”/’….ڈ°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$§ç¶çں.گھŒ.ڈس’.§çذ.اھذ. ¶çô.خھô. Œ.† ’.….ڈ1®1–ى0B‡¤Œ1‡¤û0ٍہپ1û0‡¤ى0Bد3د3 د3 اھد3ع3± اھڈسع3é3‏3‏3 ‏3 خھ‏3ˆ4± خھڈسˆ4—4µ3n°0اھڈس° خھڈس° ¢4¢4©4œü2°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$›ىھى‍3گھ‹3ڈس‘3›ىد3اھد3 ھى‏3خھ‏3 ‹3† ‘3ü2؟6ہ6،†6:‡¤‍6‡¤چ6ٍہ“6چ6‡¤†6:´8´8 ´8 اھ´8´8ضاھڈس´8أ8ط8ط8 ط8 خھط8ط8ضخھڈسط8و8ڑ8X°0اھڈسصخھڈسصٌ8ٌ8ّ8§é7ڈ°0°0ًِ³0“ٌ»´0 ٌ»I9iPؤ$ڈٌ‍ٌƒ8گھً7ڈسِ7ڈٌ´8اھ´8 ‍ٌط8خھط8 ً7† ِ7é7ڈٌ:«؟:2‡¤د:‡¤ئ:ئ:‡¤؟:2´<µ< µ< اھ´<´<غاھ´<¾<س< ش< ش< خھس< س< غخھس< ـ<ڑ÷«ِ"â">™$ے÷«$آٍ#;÷«†$ٍ#;¨%÷«½%ؤپ%<÷«•%پ%<ْ-^ This crate provides type-level numbers evaluated at compile time. It depends only on libcore.ءab` The traits defined or used in this crate are used in a typical manner. They can be divided intoءfc: two categories: **marker traits** and **type operators**.ءت=ˆ^ Many of the marker traits have functions defined, but they all do essentially the same thing:ءŒaZ convert a type into its runtime counterpart, and are really just there for debugging. Forءî] example,ءجظ ```rustءف use typenum::{Integer, N4};ءé‰ assert_eq!(N4::to_i32(), -4);ءچ! ```ء¯·` **Type operators** are traits that behave as functions at the type level. These are the meat ofء»c[ this library. Where possible, traits defined in libcore have been used, but their attachedءں^% functions have not been implemented.ء‏(§[ For example, the `Add` trait is implemented for both unsigned and signed integers, but theء«^] `add` function is not. As there are never any objects of the types defined here, it wouldn'tءٹ`^ make sense to implement it. What is important is its associated type `Output`, which is whereءëa the addition happens.ءحçِ’ ë use std::ops::Add;ء÷ use typenum::{Integer, P3, P4};ءژ #² " type X = >::Output;ء¶ %) assert_eq!(::to_i32(), 7);ءـ ,ç“ ‰ ‘ [ In addition, helper aliases are defined for type operators. For example, the above snippetء• ^ could be replaced withءô ڈِ’ “% use typenum::{Integer, Sum, P3, P4};ءں(ب type X = Sum;ءج‰ڑ و,ç“ “›J Documented in each module is the full list of type operators implemented.ءںMٌتٌî Œ؛Œڈہ لگ ‍https://docs.rs/typenum/1.16.0ء ‰9—¢ِ إڈإبَ طةجٍ ‰حصforce_unix_path_separatorء×أ2ْ ¸ Type-level bits.ءC These are rather simple and are used as the building blocks of theءF" other number types in this crate.ء`%†ٹ **Type operators** implemented:ءژ#²< - From `core::ops`: `BitAnd`, `BitOr`, `BitXor`, and `Not`.ء¶?$ - From `typenum`: `Same` and `Cmp`.ءِ'ہ£V«´ؤؤةةذذظظككè è ôôے'‹‹““ڑڑ¢¢±ا†‡ھع0 Instantiates a singleton representing this bit.ء”3ل¼ٹ²گة¤ ت3—¹‡ھدصهë’ • ت ح ے ‚ ٹ²أ ة ظ ك …ˆ #½ہ $ٍُ %ں‡ھ³ٹ²تٹ²û Not of 0 (!0 = 1)ءه‡ھ‘ – ))ٹ²µ ¸ ))+‎ Not of 1 (!1 = 0)ءç ٹ²“ک,,‡ھ·؛,,.†! And with 0 ( 0 & B = 0)ءêك00پٍہ‹çٍہگ‡ھ‹‹®³//‡ھز'ص//2ٍہ¬ And with 1 ( 1 & 0 = 0)ءگٹ²ةخ33‡ھي&ً335ئ And with 1 ( 1 & 1 = 1)ءھٹ²مè66ٹ²‡&ٹ668ك Or with 0 ( 0 | 0 = 0)ءؤ‡ھû€99‡ھں%¢99;ِ Or with 0 ( 0 | 1 = 1)ءغ‡ھ’—<<ٹ²¶%¹<<>چ Or with 1 ( 1 | B = 1)ءٍك@@پ ’” —ٹ²’’´¹??ٹ²ط&غ??Bٍہ؛! Xor between 0 and 0 ( 0 ^ 0 = 0)ء•$‡ھ×ـCC‡ھû&‏CCEـ! Xor between 1 and 0 ( 1 ^ 0 = 1)ء·$ٹ²ù‏FFٹ²‌& FFH‏! Xor between 0 and 1 ( 0 ^ 1 = 1)ءظ$‡ھ› IIٹ²؟&آIIK ! Xor between 1 and 1 ( 1 ^ 1 = 0)ءû$ٹ²½آLL‡ھل&نLLN†%‡ھ %¥%OOˆةب%<ث%O¹RRو%Oپہکس%ڈہکض%Qہکس%س%‍&‡ھ¸&½&SSŒتك&<â&S¹VV‎&Sس¸ ê&و¸ ي&Uہکê&ê&´'ٹ²خ'س'WW’ثّ'<û'W¹ZZ–(Wس¸ ƒ(و¸ †(Yہکƒ(ƒ(ذ(ٹ²ê(ï([[ˆة’)<•)[¹^^°)[س¸ ‌)و¸ )]ہک‌)‌)ى) َ)ّ)‡ھ’*—*``‡ھ¶*¹*``bç*‡ھپ+†+cc‡ھ¥+¨+cceض+ٹ²ً+ُ+ff‡ھ”,—,ffhئ,ٹ²à,ه,iiٹ²„-‡-iik؛- ء-ئ-‡ھà-ه-mm‡ھ„.‡.mmoµ.‡ھد.ش.ppٹ²َ.ِ.ppr¥/ٹ²؟/ؤ/ssٹ²م/و/ssu”0ٹ²®0³0vvٹ²ز0ص0vvxإ Type-level signed integers.ء $ Type **operators** implemented:ء(#L9 From `core::ops`: `Add`, `Sub`, `Mul`, `Div`, and `Rem`.ءP<* From `typenum`: `Same`, `Cmp`, and `Pow`.ءچ-»V Rather than directly using the structs defined in this module, it is recommended thatء؟YX you import and use the relevant aliases from the [consts](../consts/index.html) module.ء™[ُL Note that operators that work on the underlying structure of the number areءùOV intentionally not implemented. This is because this implementation of signed integersءةYU does *not* use twos-complement, and implementing them would require making arbitraryء£XP choices, causing the results of such operators to be difficult to reason about.ءüSذ # Exampleءش ِ’ â) use std::ops::{Add, Div, Mul, Rem, Sub};ءî, use typenum::{Integer, N3, P2};ء›#؟3 assert_eq!(>::Output::to_i32(), -1);ءأ63 assert_eq!(>::Output::to_i32(), -5);ءْ63 assert_eq!(>::Output::to_i32(), -6);ء±63 assert_eq!(>::Output::to_i32(), -1);ءè63 assert_eq!(>::Output::to_i32(), -1);ءں6ç“ ضحç‎ٹ ùٹ ù‌ ‌ ¢ ¢ ¦ ¦ ٹ ù¸ ¸ ¼ ¼ ہ ہ ؤ ؤ ٹ ù× × ل ل ٌ ٌ € € “ “ ٹ ù« « ± ± ہ ہ إ إ ج ج ص ص غ غ ن ن é é ُ ُ ü ü ‰)••ڑڑںں¤¤©©®®»#ةںںپاشہياشأماشخœشہہءF Instantiates a singleton representing this strictly positive integer.ءهIب‍‍ اشü#ة¢¢رذ پنذ „÷ذ ڈàنپپ‚F Instantiates a singleton representing this strictly negative integer.ء¦I‰،،£اشپéُع5 Instantiates a singleton representing the integer 0.ءڈ8ل¤¤¥ƒ/ة§§رذ ˆنذ ‹÷ذ –œشˆˆ¶/ة©©رذ »نذ ¾÷ذ ةàن»»ééُ‏?ة¬¬رذ ƒنذ †÷ذ ‘ژاش› œشƒƒآéُـâٍّٹگ¢¨ٌ÷œں³رش´ˆ‹µ؟آ¶جد·ّ/ة¹¹رذ ‎نذ €÷ذ ‹œش‎‎®´¸¸بخ¸¸هë¸¸‚ˆ¸¸ـâ¸¸ژ‘¸¸؟اشعف¸¸ہاش©¬¸¸ءاشّû¸¸آاش¶ ¹ ¸¸أاش¹"/ةإإرذ ¾"نذ ء"÷ذ ج"àن¾"¾"ï"ُ"ؤؤœ#¢#ؤؤح#س#ؤؤ‏#„$ؤؤپ%‡%ؤؤة%ج%ؤؤثاش…&ˆ&ؤؤجاشؤ&ا&ؤؤحاشƒ'†'ؤؤخاش،(¤(ؤؤداشة) `-Z0 = Z0`ء؛)éُك)ن)ذذéُƒ*†*ذذزة*+ `-PInt = NInt`ء¶*ةششرذ خ*نذ ر*÷ذ ـ*œشخ*خ*û*€+سسàن¤+§+سسضاشَ++ `-NInt = PInt`ءà+ةططرذ ّ+نذ û+÷ذ †,àنّ+ّ+¥,ھ,××œشخ,ر,××عاش‏- `Z0 + I = I`ءي-ــپƒ¬ƒ.‚ƒ¬†.éُƒ.ƒ.£.¨.غغƒ¬ئ.$ة.غغقƒ¬™// `PInt + Z0 = PInt`ء‚/ةààرذ ‍/نذ ،/÷ذ ¬/œش‍/‍/د/ش/ككœشّ/#û/ككâاشز0/ `NInt + Z0 = NInt`ء»0ةننرذ ×0نذ ع0÷ذ ه0àن×0×0ˆ1چ1ممàن±1#´1ممواش•2O `P(Ul) + P(Ur) = P(Ul + Ur)`ءô1 ‚ èŒ éèé پّ°ڑ2پ‏°²2يّ°‍2مّ°©2ي‏°¶2م‏°ء2¾ّ°‏°َ2يô°™3مô°¤3ؤ²ڑ2ڑ2²2²2³3¸3ççŒ²ٍ3)ُ3ççëّ°‏°ـ4O `N(Ul) + N(Ur) = N(Ul + Ur)`ء»4 ‚ يŒ îيî ¼ë ل4دë ù4âë ه4ُë ً4ˆى ‎4›ى ˆ5®ى ؛5إى à5طى ë5½µل4ل4ù4ù4ْ5ے5ىى…µ¹6)¼6ىىًّ°‏°½7O7 `P(Ul) + N(Ur)`: We resolve this with our `PrivateAdd`ء‚7:‚ ٍŒ ٍََ¼ë آ7دë ع7âë ئ7ُë ر7ˆى ق7›ى é7¦ ّ°‏°›8أّ°÷¸‏°¥8.ؤ²آ7آ7ع7ع7غ8à8ٌٌک؛»9+¾9ٌٌُّ°‏°‡+ˆ>ِِّْ°‏°ù?@ `P + N = 0` where `P == N`ءع?¨ü¹‎ü‎پ£آ‏?پ‡آ‹@ي£آپ@ي‡آژ@‡آ‏?‏?‹@‹@ہ@إ@ûûéُه@<è@ûûے£آ‡آفAB! `P + N = Positive` where `P > N`ء¸A$¨پ¹‚پ‚أِ âAضِ ïAéِ هAüِ ٍAأ‡آ£آBي،أذBم،أغB‡آâAâAïAïAêBïB€€قأ¨C>«C€€„£آ‡آ´D?! `P + N = Negative` where `P < N`ءڈD$¨†¹‡†‡أِ ¹Dضِ ئDéِ ¼Düِ ةDأ£آ‡آپEيثإ¤Eمثإ¯E‡آ¹D¹DئDئD¾EأE……ˆئüE;ےE……‰£آ‡آضG `Z0 - Z0 = Z0`ءأGéًُGُGٹٹéُ”H#—HٹٹŒكH/ `Z0 - P = N`ءخHةژژرذ نHنذ çH÷ذ ٍHéُنHنH•IڑIچچàن¾I(ءIچچگاش—J/ `Z0 - N = P`ء†Jة’’رذ œJنذ ںJ÷ذ ھJéُœJœJحJزJ‘‘œشِJ(ùJ‘‘”اشصK/ `PInt - Z0 = PInt`ء¾Kة––رذ عKنذ فK÷ذ èKœشعKعK‹LگL••œش´L#·L••کاشژM/ `NInt - Z0 = NInt`ء÷Lةڑڑرذ “Mنذ –M÷ذ ،Màن“M“MؤMةM™™àنيM#ًM™™œاشرNO `P(Ul) - N(Ur) = P(Ul + Ur)`ء°N ‚ ‍Œ ں‍ں ¼ë ضNدë îNâë عNُë هNˆى ٍN›ى ‎N®ى ¯Oإى صOطى àOؤ²ضNضNîNîNïOôO‌‌Œ²®P)±P‌‌،ّ°‏°کQO `N(Ul) - P(Ur) = N(Ul + Ur)`ء÷P ‚ £Œ ¤¤£ ¼ë ‌Qدë µQâë ،Qُë ¬Qˆى ¹Q›ى ؤQ®ى ِQإى œRطى §R½µ‌Q‌QµQµQ¶R»R¢¢…µُR)ّR¢¢¦ّ°‏°ùSO7 `P(Ul) - P(Ur)`: We resolve this with our `PrivateAdd`ء¾S:‚ ¨Œ ©¨©¼ë ‏Sدë –Tâë ‚Tُë چTˆى ڑT›ى ¥Tسٌ ×Têٌ لT.ؤ²‏S‏S–T–T—UœU§§ک؛÷U+ْU§§«ّ°‏°أXO7 `N(Ul) - N(Ur)`: We resolve this with our `PrivateAdd`ءجW:‚ Œ ®®¼ë بXدë àXâë جXُë ×Xˆى نX›ى ïX·ô ،Yخô «Y.½µبXبXàXàXلYوY¬¬س؟ءZ+ؤZ¬¬°ّ°‏°‹] `Z0 * I = Z0`ءù\²²ئو گ]ظو “]éُگ]گ]°]µ]±±éُش]"×]±±´ƒ¬ں^/ `P * Z0 = Z0`ءچ^ة¶¶رذ ¤^نذ §^÷ذ ²^œش¤^¤^ص^ع^µµéُù^#ü^µµ¸اشإ_/ `N * Z0 = Z0`ء³_ة؛؛رذ ت_نذ ح_÷ذ ط_àنت_ت_û_€`¹¹éُں`#¢`¹¹¼اشّ`O P(Ul) * P(Ur) = P(Ul * Ur)ءظ`‚ ¾Œ ؟¾؟ ¼ë ‎`دë •aâë پaُë Œaˆى ™a›ى ¤aبّ°‏°ضaي±àüaم±à‡bؤ²‎`‎`•a•a–b›b½½إلصb)طb½½ءّ°‏°½cO N(Ul) * N(Ur) = P(Ul * Ur)ء‍c‚ أŒ ؤؤأ ¼ë آcدë عcâë ئcُë رcˆى قc›ى écï“›d†”ءd™”جd½µآcآcعcعcغdàdآآإلڑe)‌eآآئّ°‏°‚fO P(Ul) * N(Ur) = N(Ul * Ur)ءمe‚ بŒ ةبة ¼ë ‡fدë ںfâë ‹fُë –fˆى £f›ى ®fï“àf†”†g™”‘gؤ²‡f‡fںfںf g¥gااàهكg)âgااثّ°‏°اhO N(Ul) * P(Ur) = N(Ul * Ur)ء¨h‚ حŒ خحخ ¼ë جhدë نhâë ذhُë غhˆى èh›ى َhï“¥i†”ثi™”ضi½µجhجhنhنhهiêiججàه¤j)§jججذّ°‏°ٌk( `Z0 / I = Z0` where `I != 0`ءذk ززئو ِkظو ùkمƒ¬ƒléُِkِk l¥lررéُؤl"اlررشƒ¬‎lٹmض|ق| ق| ê|ê|ٍ|بع¨غعغو‘ى‘صéُ¸}پى‘ْ|‚و‘‍}حو‘ى‘¨}سو‘ى‘±}پو‘÷|و‘÷|÷|ْ|ْ|ج}ر}ظظ¦’ّ},û}ظظفو‘ى‘± 0 == 0ء¦ éُثذققˆةَ=ِقˆلل’€قپˆ‏ڈ“¢‚€à“¢‏‏ص€/ 0 > -Xءت€ ةممرذ ع€نذ ف€÷ذ è€éُع€ع€‹پگپââ’ثµپB¸پâˆووشپâپˆہپڈ®¤ؤپهاش®¤ہپہپ‌‚/ 0 < Xء“‚ ةèèرذ ¢‚نذ ¥‚÷ذ °‚éُ¢‚¢‚س‚ط‚ççŒتْ‚B‎‚çˆëë™ƒç§¤…ƒ½¤‰ƒêاش®¤…ƒ…ƒكƒ/ X > 0ءصƒ ةييرذ نƒنذ çƒ÷ذ ٍƒœشنƒنƒ•„ڑ„ىى’ث؟„=آ„ىˆًًق„ى§¤ت„½¤خ„ïاش®¤ت„ت„£…/ -X < 0ءک… ةٍٍرذ ¨…نذ «…÷ذ ¶…àن¨…¨…ظ…ق…ٌٌŒت€†=ƒ†ٌˆُُں†ٌ§¤‹†½¤ڈ†ôاش®¤‹†‹†ل†K -X < Yءض† ¹÷¨ّّ÷س¸ و†œں‎†يہکé†مہکô†يى‘€‡مى‘‹‡ظ—و†و†‎†‎†³‡¸‡ِِŒتع‡Bف‡ِˆûûù‡ِپˆه‡ڈنé‡ْہکى‘نه‡ه‡ءˆK X > - Yءµˆ¹‎¨‏‎‏س¸ ئˆœںفˆّ«ةˆŒ¬شˆ ¬àˆ´¬ëˆ•کئˆئˆفˆفˆ“‰ک‰üü’ث½‰Bہ‰üˆپپـ‰üفب‰َج‰€ہکى‘نب‰ب‰¨ٹY X <==> Yء›ٹ‏ƒˆ„„ƒپü™ٹپ”ڑدٹ¦ ü™”ڑ±ٹيü™»ٹمü™ئٹي”ڑسٹم”ڑقٹ‌›ٹٹدٹدٹˆ‹چ‹‚‚‚›آ‹Eإ‹‚ˆ‡‡ل‹‚فح‹َر‹†ü™”ڑنح‹ح‹حŒY -X <==> -Yء¾Œ®‰¸ٹ‰ٹپ‌‌زŒپ…‌êŒي‌‌ضŒم‌‌لŒ¦ …‌‌‌îŒي…‌ّŒم…‌ƒچ¦‍زŒزŒêŒêŒچ²چˆˆ‹‍çچEêچˆˆچچ†ژˆفٍچَِچŒ‌‌…‌نٍچٍچçڈ( `Z0 % I = Z0` where `I != 0`ءئڈ ڈڈئو ىڈظو ïڈ©‌ùڈéُىڈىڈ–گ›گژژéُ؛گ"½گژژ‘ƒ¬َگ€‘¾œ 0^0 = 1ء²œéُطœفœ““÷ïüœ$ےœ““•ت‌/ 0^P = 0ء¾‌ة——رذ د‌نذ ز‌÷ذ ف‌éُد‌د‌€‍…‍––éُ¤‍)§‍––™اشً‍/ 0^N = 0ءن‍ة››رذ ُ‍نذ ّ‍÷ذ ƒںéُُ‍ُ‍¦ں«ںڑڑéُتں)حںڑڑ‌اش– / 1^N = 1ءٹ ةںںرذ › نذ ‍ ÷ذ © ÷ï› › ج ر ‍‍÷ïً )َ ‍‍،اشس،/ (-1)^N = 1 if N is evenء·،ة££رذ ط،نذ غ،شْط،ط،‰¢ژ¢¢¢÷ï¢3°¢¢¢¥اشڑ£/ (-1)^N = -1 if N is oddء‏¢ة§§رذ ں£نذ ¢£شْں£ں£ذ£ص£¦¦شْô£3÷£¦¦©اشر¤/ P^0 = 1ءإ¤ة««رذ ض¤نذ ظ¤÷ذ ن¤œشض¤ض¤‡¥Œ¥ھھ÷ï«¥$®¥ھھاشù¥/ N^0 = 1ءي¥ة¯¯رذ ‏¥نذ پ¦÷ذ Œ¦àن‏¥‏¥¯¦´¦®®÷ïس¦$ض¦®®±اش°§O P(Ul)^P(Ur) = P(Ul^Ur)ء•§‚ ³Œ ´´³ ¼ë µ§دë ح§âë ¹§ُë ؤ§ˆى ر§›ى ـ§ ّ°‏°ژ¨يپة´¨مپة؟¨ؤ²µ§µ§ح§ح§خ¨س¨²²کتچ©*گ©²²¶ّ°‏°€ھO% N(Ul)^P(Ur) = P(Ul^Ur) if Ur is evenء×©(‚ ¸Œ ¹¸¹¼ë …ھدë ‌ھâë ‰ھُë ”ھˆى ،ھ ّ°إثقھي½ثک«م½ث£«½µ…ھ…ھ‌ھ‌ھ²«·«··‹حû«4‏«··»ّ°‏°÷¬O$ N(Ul)^P(Ur) = N(Ul^Ur) if Ur is oddءد¬'‚ ½Œ ¾½¾¼ë ü¬دë ”âë €ُë ‹ˆى ک ّ°مخصيغخڈ®مغخڑ®½µü¬ü¬””©®®®¼¼©ذٍ®4ُ®¼¼ہّ°‏°¬°´°´°¹°¹°ہ°éُع°ك°ؤؤéُï°ةاارذ ô°نذ ک±÷ذ £±éُô°ô°²±·±ئئœشج±ةتترذ ر±نذ ُ±÷ذ €²œشر±ر±ڈ²”²ةةœش©²ةححرذ ®²نذ ز²÷ذ ف²éُ®²®²ى²ٌ²ججœش†³ةذذرذ ‹³نذ ¯³÷ذ ؛³àن‹³‹³ة³خ³ددœشم³'½ساششس پ½è³پاى³يôز™´مôز¤´ü ôزٹس®´يٹس؟´مٹست´يôزٹس‏ ن´مˆشï´ٍ,ٍ,†طô,ڑطث ڈµهEغôزè³è³ى³ى³‏´ƒµززٍ,ٍ,†طô,ڑطث ڈµهEغˆش¢µ'½×اطط× يز§µƒس«µ™سطµسمµءسيµظس‏µيس‰¶پش£¶ ش®¶”-”-يظ–-ڑطقIë¨èًزٹôز§µ§µ«µ«µ½¶آ¶ضض¬صل¶'½غاــغ يزو¶ƒسê¶™س—·س¢·ءس¬·ظس½·يسب·پشâ· شي·³شو¶و¶ê¶ê¶ü·پ¸عع¬ص ¸'½كاààك يز¥¸ƒس©¸™سض¸سل¸ءسë¸ظسü¸يس‡¹پش،¹ ش¬¹îض¥¸¥¸©¸©¸»¹ہ¹قق¬صإ؛#ح؛ح؛ز؛ز؛غ؛غ؛à؛à؛ë؛éُ…»ٹ»ççéُ©»#¬»ççéه»ةëëرذ ê»نذ ژ¼÷ذ ™¼éُê»ê»¨¼¼êêéُج¼(د¼êêياشچ½ةïïرذ ’½نذ ¶½÷ذ ء½éُ’½’½ذ½ص½îîàنù½*ü½îîٌاش»¾ةََرذ ہ¾نذ ن¾÷ذ ï¾œشہ¾ہ¾‏¾ƒ؟ٍٍéُ¢؟%¥؟ٍٍُاشك؟ة÷÷رذ ن؟نذ ˆہ÷ذ “ہàنن؟ن؟¢ہ§ہِِàنثہ#خہِِùاش‡ء'‚ ûŒ üüû ¼ë Œءدë گءâë ½ءُë بء² ّ°‏°زءˆى مء›ى îءي÷×Œآم÷×—آؤ²ŒءŒءگءگء¦آ«آْْ·طفآ+àآْْ‏ّ°‏°دأ'‚ €Œ پ€پ¼ë شأدë طأâë …ؤُë گؤˆى ،ؤ›ى ¬ؤ½µشأشأطأطأ»ؤہؤےے½µهؤ)èؤےےƒّ°‏°§إ'‚ …Œ †…†¼ë ¬إدë °إâë فإُë èإˆى ùإ›ى „ئؤ²¬إ¬إ°إ°إ“ئکئ„„ُµ½ئ+ہئ„„ˆّ°‏°€ا'‚ ٹŒ ‹ٹ‹ ¼ë …ادë ‰اâë ¶اُë ءا¶ ّ°‏°ثاˆى ـا›ى çايکف…بمکفگب½µ…ا…ا‰ا‰اںب¤ب‰‰طفضب+ظب‰‰چّ°‏°«تéُإتتتژژéُéت#ىتژژگ¥ثة’’رذ ھثنذ خث÷ذ ظثéُھثھثèثيث‘‘œش‘ج*”ج‘‘”اشسجة––رذ طجنذ üج÷ذ ‡حéُطجطج–ح›ح••éُ؛ح(½ح••کاشûحةڑڑرذ €خنذ ¤خ÷ذ ¯خœش€خ€خ¾خأخ™™œشçخ#êخ™™œاش£دة‍‍رذ ¨دنذ جد÷ذ ×دàن¨د¨دودëد‌‌éُٹذ%چذ‌‌ اشاذ'‚ ¢Œ £¢£ ¼ë جذدë ذذâë ‎ذُë ˆر»é’رˆى £ر›ى ®رééجر‎é×رؤ²جذجذذذذذورëر،،صه‌ز+ ز،،¥ّ°‏°ڈس'‚ §Œ ¨¨§¼ë ”سدë کسâë إسُë ذسˆى لس›ى ىس½µ”س”سکسکسûس€ش¦¦ü²¥ش+¨ش¦¦ھّ°‏°èش'‚ ¬Œ ¬¼ë يشدë ٌشâë ‍صُë ©صˆى ؛ص›ى إصؤ²يشيشٌشٌششصظص««ؤ²‏ص)پض««¯ّ°‏°ہض'‚ ±Œ ²±² ¼ë إضدë ةضâë ِضُë پ×پم‹×ˆى œ×›ى §×¯مإ×أمذ×½µإضإضةضةضك×ن×°°لê–ط+™ط°°´ّ°‏°؟ظéُéظىظµµ¶کع ‍عµµµعéُàعمع¸¸¹‘غ—غ¸¸°غéُغغقغ»»¼Œـ’ـ»»«ـéُضـظـ¾¾؟‡فچف¾¾»فةآآرذ ہفنذ وف÷ذ ٌفàنہفہفژق‘قءءأاش½ق أقءءعقةئئرذ كقنذ †ك÷ذ ‘كàنكقكق®ك±كإإااشككهكإإ‏كةتترذ ƒàنذ ھà÷ذ µààنƒàƒàزàصàةةثاشƒل‰لةة¢لةخخرذ §لنذ خل÷ذ ظلàن§ل§لِلùلححداش§ââححغâةززرذ àâنذ †م÷ذ ‘مœشàâàâ®م±مررساشفم ممررْمةضضرذ ےمنذ ¦ن÷ذ ±نœشےمےمخنرنصص×اشےن…هصص‍هةععرذ £هنذ ته÷ذ صهœش£ه£هٍهُهظظغاش£و©وظظآوةققرذ اونذ îو÷ذ ùوœشاواو–ç™çففكاشاçحçففز. All of the **marker traits** used in typenum.ء12K Note that the definition here for marker traits is slightly different thanء6NM the conventional one -- we include traits with functions that convert a typeء…PH to the corresponding value, as well as associated constants that do theءضK same.ء¢ ¬J For example, the `Integer` trait includes the function (among others) `fnء°ML to_i32() -> i32` and the associated constant `I32` so that one can do this:ء‏Oخç“ ز use typenum::{Integer, N42};ءع û assert_eq!(-42, N42::to_i32());ءے# assert_eq!(-42, N42::I32);ء£ç“ آع دقّR A **marker trait** to designate that a type is not zero. All number types in thisءçU7 crate implement `NonZero` except `B0`, `U0`, and `Z0`.ء½:‚ممط‹¾ڈ‹ƒO A **marker trait** to designate that a type is zero. Only `B0`, `U0`, and `Z0`ء–R implement this trait.ءéچنن¾ڈ“¾ڈ“مA A **Marker trait** for the types `Greater`, `Equal`, and `Less`.ء‍Dيهه¾ڈٍ¾ڈٍڑ*‌ههوإڈّ0, The **marker trait** for compile time bits.ءب/‚ çç¾ڈ‡ †إڈگ ›إڈ— إڈ، ¾ڈ‡ ¸“گ ث“— ق“، ت ذ çç÷ ‎ ççئ ة¤ ژ 3ة ççêإڈّ û ççëإڈ©¬ççىإڈ‡ 59 The **marker trait** for compile time unsigned integers.ءآ<ےµب ƒ ِ’ ‘ use typenum::{Unsigned, U3};ء‌ ¾ assert_eq!(U3::to_u32(), 3);ءآ assert_eq!(U3::I32, 3);ءمç“ ے‘ يي¾ڈ› ¸“¤ ث“« ق“µ ¾ڈ› ¸“¤ ث“« ق“µ ق ن يي‹‘يي؛ہييéïييوىييڑ يياحييِüيي¥«يي¢¨ييضظييّإڈ‡ٹييùإڈ؛½ييْإڈيًييûإڈٍُييüإڈھيي‎إڈغقيي‏إڈژ‘ييےإڈءؤيي€إڈئةييپإڈ£47 The **marker trait** for compile time signed integers.ءل:œµب ِ’ ® use typenum::{Integer, P3};ء؛ع assert_eq!(P3::to_i32(), 3);ءق assert_eq!(P3::I32, 3);ءےç“ ›‚‚¾ڈ¶¸“؟ث“ئق“ذ¾ڈ¶¸“؟ث“ئق“ذùے‚‚¦¬‚‚صغ‚‚„ٹ‚‚پ‡‚‚µ¸‚‚ˆإڈوé‚‚‰إڈ™œ‚‚ٹإڈجد‚‚‹إڈرش‚‚Œإڈٹ!B The **marker trait** for type-level arrays of type-level numbers.ءىE²K Someday, it may contain an associated constant to produce a runtime array,ء¶NE like the other marker traits here. However, that is blocked by [thisء… H8 issue](https://github.com/rust-lang/rust/issues/44168).ءخ ;”! چچ¾ڈں!¾ڈں!ص%F The **marker trait** for type-level numbers which are a power of two.ءھ!Iô! # Examplesءّ!‡" Here's a working example:ء‹"©"ِ’ "# use typenum::{PowerOfTwo, P4, P8};ء¹"&à" fn only_p2() {}ءن""‡# only_p2::();ء‹# only_p2::();ء #ç“ µ#½#K Numbers which are not a power of two will fail to compile in this example:ءء#Nگ$ ```rust,compile_failء”$, use typenum::{P9, P511, P1023, PowerOfTwo};ء$/ف$ fn only_p2() { }ءل$#…% only_p2::();ء‰% only_p2::();ء‍% only_p2::();ءµ%ç“ ح%ك% ژژ¾ڈë%¾ڈë%é3 Aliases for the type operators used in this crate.ء6Z Their purpose is to increase the ergonomics of performing operations on the types definedء8]H here. For even more ergonomics, consider using the `op!` macro instead.ء–Kâ6 For example, type `X` and type `Y` are the same here:ءو9 ِ’ ¤% # #[macro_use] extern crate typenum;ء°( use std::ops::Mul;ءظ use typenum::{Prod, P5, P7};ءً ‘" type X = >::Output;ء•% type Y = Prod;ء»ض assert_type_eq!(X, Y);ءعç“ ٌُگe²²··¼¼ء ء ححزز× × ممè è ûJ‡‡ŒŒ””››££¨¨²²··¼¼ءء‍R Alias for the associated type of `BitAnd`: `And = >::Output`ءبU§“'¨œ'©¨©پ† «پ·„®† ·„û««®® O Alias for the associated type of `BitOr`: `Or = >::Output`ءحR©“'«œ'¬¬«·¶¬ت¶¯† ·„€¬¬¯¯£R Alias for the associated type of `BitXor`: `Xor = >::Output`ءحU¬“'®œ'¯®¯·¶°ت¶³† ·„…°°³³¦ O Alias for the associated type of `Shl`: `Shleft = >::Output`ءسR¯ “'±œ'²±²·¶¶ ت¶¹ † ·„ٹ¶ ¶ ¹ ¹ © P Alias for the associated type of `Shr`: `Shright = >::Output`ءص S² “'´œ'µ´µ·¶؛ ت¶½ † ·„گ؛ ؛ ½ ½ ھL Alias for the associated type of `Add`: `Sum = >::Output`ءع O³“'·œ'¸¸··¶·ت¶؛† ·„ہ··؛؛§M Alias for the associated type of `Sub`: `Diff = >::Output`ءضP°“'؛œ'»؛»·¶µت¶¸† ·„إµµ¸¸¥ M Alias for the associated type of `Mul`: `Prod = >::Output`ءشP® “'½œ'¾½¾·¶³ ت¶¶ † ·„ت³ ³ ¶ ¶ £M Alias for the associated type of `Div`: `Quot = >::Output`ءز P¬“'ہœ'ءہء·¶±ت¶´† ·„د±±´´ L Alias for the associated type of `Rem`: `Mod = >::Output`ءذO©“'أœ'ؤؤأ·¶ت¶°† ·„ص°°·! Alias for the associated type ofءح$A `PartialDiv`: `PartialQuot = >::Output`ءٍDہ“'ئœ'ائا·¶جت¶د† ·„° ججددہI Alias for the associated type of `Neg`: `Negate = ::Output`ءَLة“'ةة·¶ذ† عذذ·I Alias for the associated type of `Abs`: `AbsVal = ::Output`ءêLہ“'ثث·¶ا† — اا±L Alias for the associated type of `Pow`: `Exp = >::Output`ءلO؛“'حœ'خحخ·¶¾ت¶ء† ·„¢ ¾¾ءء¯M Alias for the associated type of `Gcd`: `Gcf = >::Output>`ءقP¸“'ذœ'رذر·¶¼ت¶؟† ·„‏ ¼¼؟؟£C Alias to make it easy to add 1: `Add1 = >::Output`ءـF¬“'سس·¶±† ٹ²ہ±±¦H Alias to make it easy to subtract 1: `Sub1 = >::Output`ءعK¯“'صص·¶´† ٹ²إ´´¦D Alias to make it easy to multiply by 2. `Double = Shleft`ءقG¯“'××·¶¶† ٹ²ٹ¶¶ E Alias to make it easy to square. `Square = >::Output`ء×H©“'ظظ·¶°† † ت°°–I Alias to make it easy to cube. `Cube = as Mul >::Output`ءةLں“'غغ·¶¤‡س† ت¤¤¢U Alias for the associated type of `SquareRoot`: `Sqrt = ::Output`ءةX«“'فف·¶°† ù °°¥P Alias for the associated type of `Cmp`: `Compare = >::Output`ءرS®“'كœ'ààك·¶¶ت¶¹‡آ¶¶¹¹£I Alias for the associated type of `Len`: `Length = ::Output`ءضL¬هââپه³دط¬ ³³،P Alias for the associated type of `Min`: `Minimum = >::Output`ءحSھ“'نœ'هنه·¶²ت¶µ† ·„´ ²²µµ¦P Alias for the associated type of `Max`: `Maximum = >::Output`ءزS¯“'çœ'èèç·¶·ت¶؛† ·„¸ ··؛؛غgّّپ پ ŒŒ‍‍¦ ¦ µ µ ™ Q Alias for the associated type of `IsLess`: `Le = >::Output`ءؤT¢ “'ٌœ'ٌٍٍ·¶¥ ت¶¨ † ·„½ ¥ ¥ ¨ ¨ ‍!S Alias for the associated type of `IsEqual`: `Eq = >::Output`ءا V§!“'ôœ'ُôُ·¶ھ!ت¶!† ·„ا ھ!ھ!!!¨"W Alias for the associated type of `IsGreater`: `Gr = >::Output`ءح!Z±"“'÷œ'ّّ÷·¶´"ت¶·"† ·„ر ´"´"·"·"ب#5 Alias for the associated type of `IsGreaterOrEqual`:ءظ"82 `GrEq = >::Output`ء’#5ر#“'ْœ'ûْû·¶ض#ت¶ظ#† ·„ï ض#ض#ظ#ظ#ç$a Alias for the associated type of `IsLessOrEqual`: `LeEq = >::Output`ء‚$dً$“'‎œ'‏‎‏·¶ُ$ت¶ّ$† ·„غ ُ$ُ$ّ$ّ$‏%\ Alias for the associated type of `IsNotEqual`: `NotEq = >::Output`ء‍%_‡&“'€œ'پ€پ·¶چ&ت¶گ&† ·„ه چ&چ&گ&گ&Œ'U Alias for the associated type of `Logarithm2`: `Log2 = ::Output`ء³&X•'“'ƒƒ·¶ڑ'† û ڑ'ڑ'ƒU **Ignore me!** This module is for things that are conceptually private but that mustءX. be made public for typenum to work correctly.ءY1‹V Unless you are working on typenum itself, **there is no need to view anything here**.ءڈYé? Certainly don't implement any of the traits here for anything.ءيB°´ Just look away.ء¸جذU Loooooooooooooooooooooooooooooooooook awaaaaaaaaaaaayyyyyyyyyyyyyyyyyyyyyyyyyyyyy...ءشX±Y If you do manage to find something of use in here, please let me know. If you can make aءµ\3 compelling case, it may be moved out of __private.ء’6ةY Note: Aliases for private type operators will all be named simply that operator followedءح\/ by an abbreviated name of its associated type.ءھ2ل؛ل؟.نë غهق‹َEَE††‹‹ڈڈَEںں¥¥¬¬‰™م·ش.^¸Iت¦°ڈڈأ م·±E Convenience trait. Calls `Invert` -> `TrimTrailingZeros` -> `Invert`ءèH»‘‘ئث‘‘طغ‘‘“إڈù‚ “'••·¶ٹ † ’ٹ ٹ ‎ + Gets rid of all zeros until it hits a one.ء¥ .‡ ––ں ¤ ––± -´ ––کإڈل ê “'ڑڑ·¶ے † —ے ے کS Converts between standard numbers and inverted ones that have the most significantء§V digit on the outside.ء‏¢››¯´››ء ؤ››‌إڈني “'ںں·¶÷† œ÷÷–X Doubly private! Called by invert to make the magic happen once its done the first step.ء” [" The Rhs is what we've got so far.ءً % ك، ،پك®®®¹¾ ث2خ £إڈ±ْ€!‰“'¥ك¦¥¦·¶ڑھْ‌† ±ْ¢ڑڑ‌‌ِ* Terminating character for `InvertedUInt`sءب-پ ¯‡I†©ےoâ¨ِپ §§¯‡ر5< Inverted `UInt` (has most significant digit on the outside)ء‘?ـ·1ھœ'«ھ«پë…éت¶ےلë…يç·„‚§“ـ!>®ً…إش¬ééےےچچ„©©ë…ڑڑ„©©·„ٍ I Does the real anding for `UInt`s; `And` just calls this and then `Trim`.ء¥Lü ®ك¯®¯ھْ‡ ‡ ‡إڈ™‍®®«/®®®±إڈ±ْفو “'³ك´´³·¶ôھْ÷† ±ْ°ôô÷÷ى I Does the real xoring for `UInt`s; `Xor` just calls this and then `Trim`.ءںLِ µك¶µ¶ھْپ پ پإڈ“کµµ¥/¨µµ¸إڈ±ْ×à “'؛ك»؛»·¶îھٌْ† ±ْ·îîٌٌë N Does the real subtraction for `UInt`s; `Sub` just calls this and then `Trim`.ء™Qُ ¼ك½¼½ھْ€ € €إڈ’—¼¼¤/§¼¼؟إڈ±ْضك “'ءكآءآ·¶يھًْ† ±ْ¾ييًًأ!5 Used for addition of signed integers; `C = P.cmp(N)`ءک83 Assumes `P = Self` is positive and `N` is negativeءر67 where `P` and `N` are both passed as unsigned integersءˆ:حأdؤ¨إؤإأپdكپ¨âككââëًأأ‎9€أأاإڈڈ‹£‹¹&آ¹ةdت¨ثةتثس¸ ×ˆ‹عœ‹فہکڈ‹£‹ئ××ععفف‹• جê4ح¨خجحخپê4 œ‹£ ££¬±جج¾1ءججذإڈ¯ژ£‹ٍû “'زê4س¨ششزس·¶‰¨ژŒœ‹ڈ† ¯ژ£‹د‰‰ŒŒڈڈں< Performs `Shl` on `Lhs` so that `SizeOf(Lhs) = SizeOf(Rhs)`ء¶?% Fails if `SizeOf(Lhs) > SizeOf(Rhs)`ءِ(© صكضصضھْ³³³¾أصصحض“'ظكعظع·¶مھْو† ±ْ×مموو³" Gives `SizeOf(Lhs) - SizeOf(Rhs)`ءچ%½غكــغھْإإإذصغغكè “'ككààك·¶َھِْ† ±ْفََِِ¹ Inverted unsigned numbersء›أللعفللâإڈٌ'¯‡°ممنصK·1وœ'çوç¹‏عت¶ًض‏قé‏َ§“ععًًµ ¸ ههèë…·„…!ڈï،!¦!éé¯‡ر!ش!ééë’"/ةيœ'îيîرذ —"ت¶¤"نذ ڑ"é‏§" اش‌‰د"-¸ٹ—"—"¤"¤"„#‰#ىى ٹع#ف#ىىًاش·„ْ$6·1ٍٍ¹‏ے$ض‏ƒ%ڈïے$ے$·%¼%ٌٌë…ـ%0ك%ٌٌôë…¤&P·1ِة÷œ'ِّّ÷¹‏©&پçŒ؟&پژچج&ض‏&يçŒآ&çژچد& çŒغچ‚'"ِژ©&©&؟&؟&ج&ج&¬'±'ُُقژ÷'0ْ'ُُْë…çŒژچژ-¯‡²-·-ûûڈïع-ف-ûû‎“.A·1ےœ'€€ے¹‏ک.ت¶®.ض‏œ.é‏±. ë…چ’م.§“ک.ک.®.®.ˆ/چ/‏‏ڈ“ط/غ/‏‏‚ë…·„è04ة„„رذ ي0نذ ً0¯‡ي0ي0£1¨1ƒƒاشا1/ت1ƒƒ†اشژ2Xةˆ·1‰œ'ٹˆ‰ٹرذ “2پ×• 2خ‌¶2نذ –2ل×•¤2‏‌¹2 ×•ة–ُ2م—“2“2 2 2¶2¶2–3›3‡‡ث—â3/ه3‡‡Œاش×•ژچ©9(¯‡ط9ف9چچ¯‡ˆ:,‹:چچڈض:E·1‘‘¹‏غ:ض‏ك:ڑڑغ:غ:¢;§;گگڑڑة;,ج;گگ“ë…ژة™™رذ £>نذ ¦>›اشب>–ـ‌ë>›ڑ‍¸?اش£>£>ئ?ث?ککك‍±@´@کک›اشؤA خA œك‌،:‍œ‌‍ھْظAپ‡ë قAظAظAقAقAëAًAœœ‎A9€BœŒBœ إڈ±ْ‡ë ¹B%آB “'¢ك£،:¤¤¢£·¶ذBھْسBث«طB† ±ْ‡ë ںذBذBسBسBطBطB”C‍C ¥¦œ'§¥¦§پذ‹¬Cخ‌¯C¬C¬C¯C¯C¸C½C¥¥تC5حC¥¥©إڈذ‹ژچ‚D"‹D¨«¬œ'¬«أِ œDـ®ںDخ‌¢DچŒœDœDںDںD¢D¢DسD#فD ®¨¯„<°چ<±–<²³°²¯±®³œںèDپ„<ëDپچ<îDپ–<ٌDپ¤·ôDèDèDëDëDîDîDٌDٌDôDôD‎D ‚E®®گE•E ®®¥EN¨E®®¶إڈى‘ ²µ²ت²¤·ùEPüE®®·إڈى‘ ²µ²ت²¤·حF&ضF¨¹„<؛چ<»–<¼½½؛¼¹»أِ هFپà¦èFپ¬¨ëFپ“تîFپٌF£آà¦¬¨“تخ¶´هFهFèFèFëFëFîFîFٌFٌF£G%¬G ¨؟„<ہچ<ء–<آأہآ؟ءأأِ ؛Gژ¶½G،¶ہG´¶أGا¶ئG£آà¦¬¨“تخ¶µ؛G؛G½G½GہGہGأGأGئGئGْG,„Hؤ¨إ„<ئچ<ا–<بة¸>تبإتاؤةئœں‘H™²”H®²—Hأ²ڑHط²‌Hپ¸> H‘H‘H”H”H—H—HڑHڑH‌H‌H H HH ²HؤؤہHإH ؤؤصH[طHؤؤحإڈى‘ ²µ²ت²¤·²»¶I]¹Iؤؤخإڈى‘ ²µ²ت²¤·²»—J/ J¨ذ„<رچ<ز–<سش¸>صذصزشرسأِ ±Jژ¶´J،¶·J´¶؛Jا¶½Jپ¸>ہJ£آà¦¬¨“تخ¶ہ؟ث±J±J´J´J·J·J؛J؛J½J½JہJہJƒK.ŒK¨×„<طچ<ظ–<عغ¸>ـطع×ـظغأِ œKژ¶ںK،¶¢K´¶¥Kا¶¨K¹؟«K£آà¦¬¨“تخ¶ہ؟جœKœKںKںK¢K¢K¥K¥K¨K¨K«K«K‡L#‘L فdق؟@كفقكˆ‹ںLپ؟@¢LںLںL¢L¢L±L¶LففأL;ئLففلإڈڈ‹ٹؤپM(ٹM“'مdن؟@هنهم·¶›Mˆ‹‍Mƒؤ،M† ڈ‹ٹؤà›M›M‍M‍M،M،M×M#لM و®Aç؟@èèوçپ®AىMƒؤٍMىMىMٍMٍMپN†Nوو“N:–Nووêإڈ–اٹؤذN(ظN “'ى®Aي؟@îىيî·¶çNڈاêNƒؤًN† –اٹؤéçNçNêNêNًNًN±O$»O ïكً¤BًٌٌïھْئOپ¤BثO ئOئOثO ثO ـOلOïïيO/ًOïïَإڈ±ْ·تںP'¨P “'ُœ'ِ¤B÷ُِ÷·¶¶Pت¶¹P°ت¼P † ·„·تٍ¶P¶P¹P¹P¼P ¼P َP$‎P ّكù¤BّْùْھْˆQ°تچQ ˆQˆQچQ چQ ‍Q£Qّّ¯Q/²Qّّüإڈ±ْ·تلQ'êQ “'‏œ'ے¤B€€‏ے·¶ّQت¶ûQ°ت‏Q † ·„·تûّQّQûQûQ‏Q ‏Q ةR*رRرRطRطRكRكRèRèRîRîRِR!€S ‡كˆ¢D‰ˆ‰‡ھْژSپ¢D“SژSژS“S“S‍S£S‡‡µS9¸S‡‡‹إڈ±ْ‍رٍS'“'چœ'ژچژ·¶÷Sت¶ْS† ÷S÷SْSْS T¥TŒŒٹ²اT7تTŒŒگ† ·„”U(“'’œ'“’“·¶™Uت¶œU† ™U™UœUœUأUبU‘‘‡ھëU8îU‘‘•† ·„¹V*“'—œ'کک—·¶¾Vت¶ءV† ¾V¾VءVءVêVïV––‡ھ’W:•W––ڑ† ·„مW"يW›كœ¢D‌œ‌›ھْüW—رپXüWüWپXپXŒX‘X››£X:¦X››ںإڈ±ْ‍رلX(“'،œ'¢،¢·¶وXت¶éX† وXوXéXéXگY•Y ‡ھ¸Y8»Y ¤† ·„†Z)“'¦œ'§¦§·¶‹Zت¶ژZ† ‹Z‹ZژZژZ¶Z»Z¥¥ٹ²فZ9àZ¥¥©† ·„¬[+“'«œ'¬¬«·¶±[ت¶´[† ±[±[´[´[ق[م[ھھ‡ھ†\;‰\ھھ®† ·„ط\$â\¯ك°¢D±°±¯ھَْ\—رّ\َ\َ\ّ\ّ\ƒ]ˆ]¯¯ڑ]<‌]¯¯³إڈ±ْ‍رع]*“'µœ'¶µ¶·¶ك]ت¶â]† ك]ك]â]â]‹^گ^´´‡ھ³^:¶^´´¸† ·„ƒ_+“'؛œ'»؛»·¶ˆ_ت¶‹_† ˆ_ˆ_‹_‹_µ_؛_¹¹‡ھف_;à_¹¹½† ·„®`-“'؟œ'ہہ؟·¶³`ت¶¶`† ³`³`¶`¶`â`ç`¾¾ٹ²‰a=Œa¾¾آ† ·„فa(çaأكؤ¢Dإؤإأھْüa—رپbüaüaپbپbŒb‘bأأ£bB¦bأأاإڈ±ْ‍رéb.“'ةœ'تةت·¶îbت¶ٌb† îbîbٌbٌb‍c£cببٹ²إc@بcببج† ·„›d/“'خœ'دخد·¶ dت¶£d† d d£d£dرdضdححٹ²ّdAûdححر† ·„دe1“'سœ'ششس·¶شeت¶×e† شeشe×e×e‡fŒfزز‡ھ¯fC²fززض† ·„‰g%“g×كط¢Dظطظ×ھْ¥g—رھg¥g¥gھgھgµg؛g××جg>دg××غإڈ±ْ‍رژh+“'فœ'قفق·¶“hت¶–h† “h“h–h–hہhإhــٹ²çh<êhــà† ·„¹i,“'âœ'مâم·¶¾iت¶ءi† ¾i¾iءiءiىiٌiلل‡ھ”j=—jلله† ·„çj.“'çœ'èèç·¶ىjت¶ïj† ىjىjïjïjœk،kووٹ²أk?ئkووê† ·„™l+£lëكى¢Dيىيëھْ»l—رہl»l»lہlہlثlذlëëâlEهlëëïإڈ±ْ‍ر«m1“'ٌœ'ٌٍٍ·¶°mت¶³m† °m°m³m³mمmèmًً‡ھ‹nCژnًًô† ·„نn2“'ِœ'÷ِ÷·¶énت¶ىn† énénىnىn‌o¢oُُٹ²ؤoDاoُُù† ·„‍p4“'ûœ'üüû·¶£pت¶¦p† £p£p¦p¦pظpقpْْٹ²€qFƒqْْ‏† ·„فqçqےےےq„rےےڈr™rپ پ ±r¶rپ پ ”? Useful **type operators** that are not defined in `core::ops`.ءBœHlHl__ii~~ƒƒ‰‰’’کک‍‍¥¥¯¯‎W A **type operator** that ensures that `Rhs` is the same as `Self`, it is mainly usefulء·ZF for writing macros that can take arbitrary binary or unary operators.ء’IـX `Same` is implemented generically for all types; it should never need to be implementedءà[ for anything else.ء¼سY Note that Rust lazily evaluates types, so this will only fail for two different types ifء×\ the `Output` is used.ء´خµب ز ِ’ à' use typenum::{Same, Unsigned, U4, U5};ءى*—3 assert_eq!(>::Output::to_u32(), 5);ء›6ز // Only an error if we use it:ءض" # #[allow(dead_code)]ءù+ type Undefined = >::Output;ء“. // Compiler error:ءآ // Undefined::to_u32();ءظç“ ُ‡گ ك‘ گ ‘ ھْŒ Œ Œإڈ¾ Should always be `Self`ء‍أگ گ خه” ” بطسدطسسêï“ “ دط¸ 5 A **type operator** that returns the absolute value.ء‏8·µب » ِ’ ة! use typenum::{Abs, Integer, N5};ءص$ْ. assert_eq!(::Output::to_i32(), 5);ء‏1ç“ ° آ – – è The absolute value.ءج ي – – ّ éُژ “ ک ک éُ£ +ة› › رذ ¨ نذ « ÷ذ ¶ œش¨ ¨ ص ع ڑ ڑ œشى +ة‍ ‍ رذ ٌ نذ ô ÷ذ ے àنٌ ٌ ‍£‌ ‌ œشژ G A **type operator** that provides exponentiation by repeated squaring.ء¸Jƒµب ‡ ِ’ •% use typenum::{Integer, Pow, N3, P3};ء،(ت4 assert_eq!(>::Output::to_i32(), -27);ءخ7ç“ † ک ً)، ، پً)œ œ œ ر " The result of the exponentiation.ء§ %ض ٍ(F This function isn't used in this crate, but may be useful for others.ءâ I" It is implemented for primitives.ء°%عµب â ِ’ ô use typenum::{Pow, U3};ء„¤ let a = 7u32.powi(U3::new());ء¬! let b = 7u32.pow(3);ءز assert_eq!(a, b);ءï‰ let x = 3.0.powi(U3::new());ء‘ let y = 27.0;ء¶ assert_eq!(x, y);ءجç“ وُ £ إڈہ‰‍« ژ&›& َ>[ A **type operator** for comparing `Self` and `Rhs`. It provides a similar functionality toءة:^ the functionء¨;` [`core::cmp::Ord::cmp`](https://doc.rust-lang.org/nightly/core/cmp/trait.Ord.html#tymethod.cmp)ء¹;c but for types.ء‌<°<µب ´< ِ’ آ<% use typenum::{Cmp, Ord, N3, P2, P5};ءخ<( use std::cmp::Ordering;ء÷<“=G assert_eq!(>::Output::to_ordering(), Ordering::Greater);ء—=JE assert_eq!(>::Output::to_ordering(), Ordering::Equal);ءâ=HD assert_eq!(>::Output::to_ordering(), Ordering::Less);ء«>G‎>¦ ك§ ¦ § ھْپ? پ? پ?إڈِ?[ The result of the comparison. It should only ever be one of `Greater`, `Less`, or `Equal`.ء“?^û?¦ ¦ ›@?ٹ@؛ٹ@َ>چ@”@ غژ@ˆ@‍@¦ ˆھ ھ ؛@¦ ف¦@َھ@© إڈ±ْن¦@¦@½A [ A **type operator** that gives the length of an `Array` or the number of bits in a `UInt`.ءق@^اA« « †B- The length as a type-level unsigned integer.ءرA0‹B« « ِB¶‰¨BIùB« ‎B« إڈبD _ Division as a partial function. This **type operator** performs division just as `Div`, but isءکCbI only defined when the result is an integer (i.e. there is no remainder).ءûCLزD ® ك¯ ® ¯ ھْفD فD فDإڈ‍E' The type of the result of the divisionءïD*£E® ® عE-# Method for performing the divisionء¯E&فE® ® ± إڈ±ْرFB A **type operator** that returns the minimum of `Self` and `Rhs`.ء‹FEغF² ك³ ² ³ ھْكF كF كFإڈ¥G, The type of the minimum of `Self` and `Rhs`ءٌF/ھG² ² غG' Method returning the minimumء¶G قG² ² µ إڈ±ْجHB A **type operator** that returns the maximum of `Self` and `Rhs`.ء†HEضH¶ ك· ¶ · ھْعH عH عHإڈ I, The type of the maximum of `Self` and `Rhs`ءىH/¥I¶ ¶ ضI' Method returning the maximumء±I ظI¶ ¶ ¹ إڈ±ْ…JŒJîJT A **type operator** that returns `True` if `Self < Rhs`, otherwise returns `False`.ء–JWّJ» ك¼ ¼ » ھْےJ ےJ ےJإڈبK/ The type representing either `True` or `False`ء‘K2حK» » ٹL+$ Method returning `True` or `False`.ءقK'چL» » ¾ إڈ±ْ½LحL ـL“'ء œ'آ ء آ ·¶لLت¶نL¦ † ·„„M‡† ·„‡آچM† لLلLنLنL´M¹Mہ ہ üآ…N(ˆNہ ہ ؤ † ·„ûOU A **type operator** that returns `True` if `Self == Rhs`, otherwise returns `False`.ء¢OX…Pإ كئ إ ئ ھْچP چP چPإڈضP¼¢ںP2غPإ إ کQ,’£ىP'›Qإ إ ب إڈ±ْجQـQىQ“'ث œ'ج ج ث ·¶ٌQت¶ôQآ¥•R›† ·„‡آ‍R † ٌQٌQôQôQئRثRت ت üئکS)›Sت ت خ † ·„ڈUT A **type operator** that returns `True` if `Self > Rhs`, otherwise returns `False`.ء·TW™U د كذ ذ د ھْ£U £U £UإڈىU¼¢µU2ٌUد د ®V.’£‚V'±V د د ز إڈ±ْنV ôV†W“'ص œ'ض ص ض ·¶‹Wت¶ژWآ¥±W¯† ·„‡آ؛W"† ‹W‹WژWژWنWéWش ش ِت¸X+»X ش ش ط † ·„´Z#U A **type operator** that returns `True` if `Self <= Rhs`, otherwise returns `False`.ءغYX¾Z ظ كع ظ ع ھْجZ جZ جZإڈ•[¼¢قZ2ڑ[ظ ظ ×[4’£«['ع[ظ ظ ـ إڈ±ْ“\$£\¹\!“'ك œ'à à ك ·¶¾\ت¶ء\آ¥è\أ† ·„‡آٌ\&† ¾\¾\ء\ء\ں]¤]ق ق ًخ÷]1ْ]ق ق â † ·„ے_ U A **type operator** that returns `True` if `Self != Rhs`, otherwise returns `False`.ء¦_X‰` م كن ن م ھْ”` ”` ”`إڈف`¼¢¦`2â`م م ںa0’£َ`'¢aم م و إڈ±ْ×a!çaْa“'é œ'ê é ê ·¶ےaت¶‚bآ¥¦b×† ·„‡آ¯b#† ےaےa‚b‚bعbكbè è êز¯c-²cè è ى † ·„¯e&U A **type operator** that returns `True` if `Self >= Rhs`, otherwise returns `False`.ءضdX¹eي كî ي î ھْتe تe تeإڈ“f¼¢ـe2کfي ي صf7’£©f'طfي ي ً إڈ±ْ”g'¤g½g$“'َ œ'ô ô َ ·¶آgت¶إgآ¥ïgë† ·„‡آّg)† آgآgإgإg©h®hٍ ٍ نض„i4‡iٍ ٍ ِ † ·„¥p‘ A convenience macro for comparing type numbers. Use `op!` instead. Due to the intricacies of the macro system, if the left-hand operand is more complex than a simple `ident`, you must place a comma between it and the comparison sign. For example, you can do `cmp!(P5 > P3)` or `cmp!(typenum::P5, > typenum::P3)` but not `cmp!(typenum::P5 > typenum::P3)`. The result of this comparison will always be one of `True` (aka `B1`) or `False` (aka `B0`). # Example ```rust #[macro_use] extern crate typenum; use typenum::consts::*; use typenum::Bit; fn main() { type Result = cmp!(P9 == op!(P1 + P2 * (P2 - N2))); assert_eq!(Result::to_bool(), true); } ``` ء¹j–زo ¥زo ‏Cـo’p ح فoمo1.9.0ءهoىo عîoَouse the `op!` macro insteadءُoذoD—pذ—pےC•p²pîہ ءœzB A **type operator** for taking the integer square root of `Self`.ء–xEـx? The integer square root of `n` is the largest integer `m` suchءàxBA that `n >= m*m`. This definition is equivalent to truncating theء£yD0 real-valued square root: `floor(real_sqrt(n))`.ءèy3¦z ّ ّ وz' The result of the integer square root.ء·z*ëzّ ّ †}G A **type operator** for taking the integer binary logarithm of `Self`.ءِzJء{D The integer binary logarighm of `n` is the largest integer `m` suchءإ{GA that `n >= 2^m`. This definition is equivalent to truncating theءچ|D0 real-valued binary logarithm: `floor(log2(n))`.ءز|3گ} ْ ْ ص}, The result of the integer binary logarithm.ء،}/ع}ْ ْ ک€Z A **type operator** that computes the [greatest common divisor][gcd] of `Self` and `Rhs`.ءه}]أ~= [gcd]: https://en.wikipedia.org/wiki/Greatest_common_divisorءا~@ˆµب Œ ڑِ’ ‍' use typenum::{Gcd, Unsigned, U12, U8};ءھ*ص3 assert_eq!(>::Output::to_i32(), 4);ءظ6ç“ گ€¢€ü ك‎ ü ‎ ھْ¦€¦€¦€ض€ The greatest common divisor.ء±€ غ€ü ü ï‚E A **type operator** for taking a concrete integer value from a type.ءو€H¯پE It returns arbitrary integer value without explicitly specifying theء³پHC type. It is useful when you pass the values to methods that acceptءüپF( distinct types without runtime casting.ءأ‚+ù‚ے ه€ € ے پهے‚ے‚ے‚آƒ2 Method returning the concrete value for the type.ءˆƒ5إƒے ے پ إڈـذ¢„B The concrete value for the type. Can be used in `const` contexts.ءطƒE¨„ے ے ـذ¬ Type-level unsigned integers.ء!"&ت، *#NM From `::core::ops`: `BitAnd`, `BitOr`, `BitXor`, `Shl`, `Shr`, `Add`, `Sub`,ءRP) `Mul`, `Div`, and `Rem`.ء£,،أ ذ-‏âأ ‚Yؤؤ ـ[¸µب ¼ ِ’ تJ use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Rem, Shl, Shr, Sub};ءضM) use typenum::{Unsigned, U1, U2, U3, U4};ء¤,ر5 assert_eq!(>::Output::to_u32(), 2);ءص84 assert_eq!(>::Output::to_u32(), 7);ءژ75 assert_eq!(>::Output::to_u32(), 1);ءئ82 assert_eq!(>::Output::to_u32(), 6);ءے52 assert_eq!(>::Output::to_u32(), 1);ءµ52 assert_eq!(>::Output::to_u32(), 5);ءë52 assert_eq!(>::Output::to_u32(), 1);ء،52 assert_eq!(>::Output::to_u32(), 6);ء×52 assert_eq!(>::Output::to_u32(), 1);ءچ52 assert_eq!(>::Output::to_u32(), 1);ءأ5ç“ ù´† ¹† ¹™ ™ ‍ ‍ ¢ ¢ † ¹´ ´ ¸ ¸ † ¹ش ش ف ف é é َ َ ƒ ƒ ڈ ڈ ‍ ‍ ² ² ء ء ش ش à à ï ï ‚ ‚ – – ¥ ¥ ± ± ہہئئععààههييôôùù‏‏„„چچںں¤¤¬¬²²¼ ¼ ببررععممççىىٌٌ÷÷ےےˆ ˆ ژ ژ ڑ ڑ ¦ ¦ ¬ ¬ ± ± ¸ ¸ إ ;ر ر ض ض ق ق ه ه ي ي ٍ ٍ ÷ ÷ ü ü ‹,¢ ¢ ®®ٍ ڈïض= Instantiates a singleton representing this unsigned integer.ءƒ@فة ة ت …ڈï£©ث ث ¹؟ث ث ر×ث ث éïث ث ¸¾ث ث صغث ث ëٌث ث ƒ‰ث ث ›،ث ث êًث ث •کث ث ض تحث ث × پ„ث ث ط ¸»ث ث ظ إبث ث ع پ„ث ث غ ¶¹ث ث ـ يًث ث ف ¤§ث ث ق ±´ث ث ك •"$ةل œ'â ل â رذ ڑ"ت¶§"نذ ‌"é‏ھ"¸ٹڑ"ڑ"§"§"“#ژلہ"@ڑ#à à م اش·„ر#1ةه œ'و ه و رذ ض#ت¶م#نذ ظ#é‏و#¸ٹض#ض#م#م#‰$ڈ$ن ن °$¶$ن ن ل$ç$ن ن ’%ک%ن ن •&›&ن ن د&ص&ن ن ü&‚'ن ن '³'ن ن ق'ن'ن ن ل(ç(ن ن ©)¬)ن ن ٌ اش·„ù)ü)ن ن ٍ اش·„×*ع*ن ن َ اش·„µ+¸+ن ن ô اش·„’-•-ن ن ُ اش·„ù-ü-ن ن ِ اش·„د.ز.ن ن ÷ اش·„/°/ن ن ّ اش·„‹0ژ0ن ن ù اش·„è1ë1ن ن ْ اش·„»20ةü œ'‎ ü ‎ رذ ہ2ت¶ح2نذ أ2é‏ذ2¸ٹہ2ہ2ح2ح2ï2ڈï‡3#¢ً®39ةپپرذ ³3نذ ¶3‰× ء3 ˆہ³3³3ث5! Length of `UTerm` by itself is 0ء¦5$ڈïن5é5‚‚ڈïˆ6‹6‚ڈ6‚„ط6, Length of a bit is 1ء؟6ة†œ'‡†‡رذ ف6ت¶ê6نذ à6é‏ي6« اش’7¾قب ٹ²¦7ي°ة ؤ7¸ٹف6ف6ê6ê6ش7ظ7……°ة …8ˆ8…Œ8…‰اش·„م9 `UTerm + B0 = UTerm`ءت9ڈï€:…:ٹٹڈï§:#ھ:ٹٹŒُ:0 `U + B0 = U`ءن:ةژœ'ڈژڈرذ ْ:ت¶‡;نذ ‎:é‏ٹ;¸ٹْ:ْ:‡;‡;¬;±;چچ¸ٹط;#غ;چچ‘اش·„¾< `UTerm + B1 = UInt`ء›<"ڈïغ<à<’’¢ًŒ=#ڈ=’’”ُ=)" `UInt + B1 = UInt`ءد=%ة––رذ ْ=نذ ‎=ˆہْ=ْ=¥>ھ>••“أز>#ص>••کاش؟?)& `UInt + B1 = UInt`ء•?)ةڑڑرذ ؤ?نذ ا?¾اشٹ²ِ?يْر Œ@“أؤ?ؤ?œ@،@™™¹س د@#ز@™™œاش‍B" `UTerm + U = U`ءٹBة‍‍رذ £Bنذ ¦Bڈï£B£BاBجB‌‌اشêB$يB‌‌ اشجC3" `UInt + UTerm = UInt`ء¦C%ة¢œ'£¢£رذ رCت¶قCنذ شCé‏لC¸ٹرCرCقCقC†D‹D،،¸ٹ²D&µD،،¥اش·„®EC2 `UInt + UInt = UInt

+ UInt = UInt<(Ul + Ur) + B1, B0>`ءŒM<‚ ¶Œ ·¶·¼ë خMدë ـMâë زMˆى àM®ى ›N¾ô°ٹ²µNأà خMخMـMـMؤNةNµµ”ن پO/„Oµµ¹ّ°‏°³Q `UTerm - B0 = Term`ء›QڈïذQصQ؛؛ڈï÷Q#ْQ؛؛¼ثR0 `UInt - B0 = UInt`ء´Rة¾œ'؟¾؟رذ ذRت¶فRنذ سRé‏àR¸ٹذRذRفRفR‚S‡S½½¸ٹ®S#±S½½ءاش·„–T:! `UInt - B1 = UInt`ءٌS$ةأœ'ؤؤأرذ ›Tت¶¨Tنذ ‍Té‏«Tہى ›T›T¨T¨T×TـTآآüë چU#گUآآئاش·„َU `UInt - B1 = UTerm`ءذU"¢ًڑVںVااڈïءV#ؤVااة¨W)& `UInt - B1 = UInt`ء‏V)ةثثرذ Wنذ °Wأاشٹ²كWيٍî ُWˆہWW…XٹXتت±ً ¸X#»Xتتحاش”Z `UTerm - UTerm = UTerm`ءّYڈï´Z¹ZخخڈïغZ&قZخخذِ[BW Subtracting unsigned integers. We just do our `PrivateSub` and then `Trim` the output.ء›[Z‚ ز›aسŒ ششزس¼ë û[پ€َ ‰\پ†َ ’\âë ے[ç€َ چ\ي†َ –\¼ةٍ †َ ر\‘¹َ †]ةٍ û[û[‰\‰\’\’\’]—]رر‚ô ـ]%ك]ررضّ°€َ †َ ئ^) `U - UTerm = U`ء²^ةططرذ ث^نذ خ^اشث^ث^ِ^û^××اشڑ_.‌_××عاش—`J2 `UInt - UInt = UInt

- UInt = UInt<(Ul - Ur) - B1, B1>`ءéb<‚ لŒ âلâ¼ë «cدë ¹câë ¯cˆى ½cض›ےcأûِ ٹ²ھd·ع «c«c¹c¹c¹d¾dàà¤û پe7„eààنّ°‏°فfJ2 `UInt - UInt = UInt

- UInt = UInt

& UInt = UInt

| UInt = UInt

^ UInt = UInt

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