├── .gitignore
├── .vscode
    └── settings.json
├── package.json
├── license
├── readme.md
└── src
    └── ts-8-bit.ts


/.gitignore:
--------------------------------------------------------------------------------
1 | node_modules
2 | .v


--------------------------------------------------------------------------------
/.vscode/settings.json:
--------------------------------------------------------------------------------
1 | {
2 |     "typescript.tsdk": "node_modules\\typescript\\lib"
3 | }


--------------------------------------------------------------------------------
/package.json:
--------------------------------------------------------------------------------
 1 | {
 2 |   "name": "ts-8bit",
 3 |   "version": "0.8.0",
 4 |   "description": "Using TypeScript's Type System to do 8-bit Arithmetic",
 5 |   "main": "index.js",
 6 |   "keywords": ["typescript", "conditional-types", "8-bit", "math"],
 7 |   "author": "sinclairzx81",
 8 |   "license": "MIT",
 9 |   "devDependencies": {
10 |     "typescript": "^4.1.2"
11 |   }
12 | }
13 | 


--------------------------------------------------------------------------------
/license:
--------------------------------------------------------------------------------
 1 | ts-8-bit: Using TypeScript's Type System to do 8-bit Arithmetic
 2 | 
 3 | The MIT License (MIT)
 4 | 
 5 | Copyright (c) 2020 Haydn Paterson (sinclair) <haydn.developer@gmail.com>
 6 | 
 7 | Permission is hereby granted, free of charge, to any person obtaining a copy
 8 | of this software and associated documentation files (the "Software"), to deal
 9 | in the Software without restriction, including without limitation the rights
10 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
11 | copies of the Software, and to permit persons to whom the Software is
12 | furnished to do so, subject to the following conditions:
13 | 
14 | The above copyright notice and this permission notice shall be included in
15 | all copies or substantial portions of the Software.
16 | 
17 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
18 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
20 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
21 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
22 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
23 | THE SOFTWARE.


--------------------------------------------------------------------------------
/readme.md:
--------------------------------------------------------------------------------
  1 | <div align='center'>
  2 | 
  3 | <h1>TS-8-bit</h1>
  4 | 
  5 | <p>Using TypeScript's Type System to do 8-bit Arithmetic</p>
  6 | </div>
  7 | 
  8 | ```typescript
  9 | import { 
 10 |     Byte, Num, Add, Sub, Mul, Div, Mod, Eq, Lt, Gt, Lte, Gte, Lsh, Rsh, And, Xor, Or, Not 
 11 | } from './ts-8-bit'
 12 | 
 13 | // Arithmetic
 14 | type A = Num< Add < Byte<12>, Byte<22> > >  // + type A = 34
 15 | type B = Num< Sub < Byte<47>, Byte<12> > >  // - type B = 35
 16 | type C = Num< Mul < Byte<31>, Byte<4>  > >  // * type C = 124
 17 | type D = Num< Div < Byte<16>, Byte<8>  > >  // / type D = 2
 18 | type E = Num< Mod < Byte<19>, Byte<4>  > >  // % type E = 3
 19 | 
 20 | // Equality
 21 | type F = Eq < Byte<10>, Byte<10> >          // == type F = true
 22 | type G = Lt < Byte<10>, Byte<10> >          // <  type G = false
 23 | type H = Gt < Byte<20>, Byte<10> >          // >  type H = true
 24 | type I = Lte< Byte<10>, Byte<10> >          // <= type I = true
 25 | type J = Gte< Byte<20>, Byte<10> >          // >= type J = true
 26 | 
 27 | // Bitwise
 28 | type K = Num< Rsh < Byte<64>, 3 > >         // >> type K = 8
 29 | type L = Num< Lsh < Byte<23>, 2 > >         // << type L = 92
 30 | type M = Num< Or  < Byte<33>, Byte<7> > >   // |  type M = 39 
 31 | type N = Num< And < Byte<12>, Byte<5> > >   // &  type N = 4
 32 | type O = Num< Xor < Byte<22>, Byte<17 > > > // ^  type O = 7
 33 | type P = Num< Not < Byte<253> > >           // !  type P = 2
 34 | ```
 35 | 
 36 | ## Overview
 37 | 
 38 | ts-8-bit is an experimental library that does 8-bit arithmetic on TypeScript's type system. It does so by applying bitwise operations on tuples of length 8 (1 byte) and leverages TypeScript conditional type inference to give the result. This project was written as a exercise in TypeScript and is offered as is for anyone who may find it of use.
 39 | 
 40 | Requires TypeScript 4.1.2 and above. Example link [here](https://www.typescriptlang.org/play?#code/PTAEFpK6dv4YpcBQJQc6A+rv2d8tM9iTiCCM0xiAfXE7MfO4l0AHTLbYwApsASlB8aZTL1GhBjfNjaCRDVqMY5eBcROl9OpffIB8OUAB55C0AHICnKbjraJUwrmVZFw6Z7UfNoM48Vip4tFiGzMEAdLjADHSGTug6qWnpZEEAqgDOAJYAdgDmoAAuABYApqAAKgCeAA6VAMoAxgBOeQ2lZY3VOXU5pZUAtqAAZgD27aAAHOAARnk9AIadFSOVpXmtNEEZmPkFrQA2K3kzAEwADDfSALIAkjV7KRLlpaUNOQBcIEXLcoAVwW0VakxGwCOp3O7QAXgAPWYARmApRy4HmSx6B1xGX2eMJWHEyFJZPJFKgKGp4gAgutypttrtSn1QLTQABeUAAOSBIzM7IAJkLzKAAEJ1YZmZGXIwAGglUsqZkuctAJhMoHQrKa7K5oAAzAAWFC66rig18gWgZogsWS6XGgDsCqV0tlmo1GB1bMt3MNAFYzWyAMJW-mC+5Ak4O5VmQ3It2OlXGrVe7Vgc2gcPc2Wm7MAEQjNsLeQAbnGPQA2ZPx2bp72Z3p64vcy4hvUAURLUcmosFKZlAE4607G1rfd2DYbqeguwBHIErE7LOqd6oAMQNi6rKuR1zH+8PTZ0U63BtK7SBlQ3oAA4gaADI9Qfxg9HmUnrVnrNsx-cuMK45Le2YABIGver7uiqNyfh+p4SOeoAQdyV43nejzPtKMFfvB35pMhWFodeoFsgAUpBOFDnBipDghP5IX+eqUSRGHiOKywAO55CBd4ANK9qAABKOTlHuZjVmmiqGt6jHsMx1SCdysx3k+QlPmJEmXIabqXHJqTIep3LDh22b3EJADyMwSYaul0fGroGT6imgBZAbDoE2Y8kJtIFAOuGeg50qBl6P7IT53IFmyllCQAGtM2lysF+7OgZJjIbF3LOneAAKQk8pM0E0YGunOYZrn5e2c5gJueRwnC4pAg1d51Q1TUNWYNSgJUCLDP5OS4SsBR1EYJjcigACQbn9l1KVmKFJi9f1QqDUOJ4APyBNN9yzTU826UtfWVANuGbTY4z1XCCzNXC1igD8Ng3Q190-FNM1CnNuGHT1x2netJhbdYl0vcQj3WNY1LZjUyIYNybWNbdb4ehmmDITDBoAESY3eNT6QaCMdXCyOwajLkttUeNYzj0OyQTV1EyTCZk82tNYyDcI02yNTGnDoCE0juFpohrPc7z3LY7jgZ8wLnW4aFIvo9LEvPZzuPVjLDOC0OtaK65NTK6AmMczj6DRObPWlK0lsstzyKG7LxOBQrjHo-b7NXarOMkpSvt+77HHLD7-sh6H8DUr1DTTD02acT03LXNIyI1RAYdp+n4j3isww5MH6f537EcIlH7Qx36yyFaUXW-Sta3LONKBYN1y0natoCJ1tsNvU3Net4NsNbYn3eYAUlTlpU7RFyXZd6nHfmfc3f1twA2nHdHLAAug3Pct6dy-XIq1wb6Ag8PY3mCL7XoD74qyLH6fw8YJfffX8ih-3+3Z870vg3L2-oB3xPgAr+I8x4TyntHCmEpljWWrrvFea9oGlC3lyc+T9e57wPu3D+Q80G1AwSvLBgDO4gPQfA3+-8j5AK7ng5+e9-7EOAY-UAo9x6TxQJHSBsdlgJXaHAn+19EFxxQZyWhBDf5YKoQ-MR5Dr5EI-jQ7+V8-7v2oaQ-BsiVEAJweo1h4C84F0MWScQjxhjtGztMAxRjrEIAgaXKBjx-K9QNAAa0qHUSY4xQCmInhYyenD7HZlyu0Me-Cr5uI8V4nx5jSjTHGt4sxfjl41A3vvDeHDi5cLZDyZaYSX4RM8Qk3xsT2jxOiUklJf90kBJntUcpJSDQAG88HXEesvZ0t8N6KjwciNpWDLhdMwHgy4bT-6GkGdQLAho2mXEVMaCZgQsDGjaYaRUgYFl4MDG040ipqwbKwNWNpgZFTOn2ZgZ0bTqzv0VNQAAvinGxjzECB1KDxPi6AnmfNgHY2pvIip5L3kI5Y69SggrBUg8Fwj4nLzwXHSuXU0kKlhRXf5NQqlIqwHC1Fy8BkYswFiquaLxl4owAShF8ySVIPhWi9ZlKyVor2XSlFhL2lb3lCgdJGTp5QPnmYPBHJNFAtBRCkVQrIWb3ZZi8RgjgWitlWKuVwrhEoGhci0ovLl60jSXRNJbK1Uaq1XfHVd89WYuWAanFgzxSWtNfi81-kzCauXuMnV4zbWkvtZ9J18ydXzPdUgi16ydXrP9XPB1Tq9k6r2aGz1jqtWnJ1acvVnKalQNgfy6Vq95XZqVTm8VubkGSvxZmhVpa82KvSaqs1pRYFOqPjqo+Maa18KdUaiUVSm21q1QMnVAzO0tq1S69tbqmXNrjcvH17a-Wjq7cvIN7aQ0zoHcvSN7bo1LvHQm9tSakUpsyYEtkvC+VYAFQIrNBb82XorUW0lJby1lovRWlVBoYXVqPavbV7JdWjvfdatthqN5Nt-ZaxU3bAM-umI661Q7B3gZvUg4Dk6tXTvg3HYD86tWLtQzwyDH7V1avXdh0owGt3xrgxyn5UDRLlABQg+99HH1CsGVhWRjihS9W3pgFjAiO74MetRx1aK21op7bUZ1gy0WTppRJldMmt31tAME0JjwxqUezJpGjdC6OMYY1e4RipuNXzYxx1BWBDMv1491R6GnHVYLRQpoTMnRNEpk1JudMno2KiU+WMwKmjA0g+V8oL4BxCLmXKuVkVjgvWLU2yRcx7MCnuUQ+vTDGumwrvTprLqXkHPu5Ell+lotroWqI9ICJw+JcqyXqF8lkGgJYwAVwFunFU5fS1KwVLWUvXrweZ06xmER5f1LIorExgKlbwU6x4Vrl7TePpoyRH9av1dpHRLzISfN+fUVNmbc3M0MKWzWlba3FMbd82NbbWrps6r25oyhH9ysgUu7N3bgHM3yKASV9Rj3bxVYPTVquGbOvZda6D-TGXgc5ah0g9L8TltmFWxKE5-m-u-JfCqIHZ7uvY5ze14tkOwdddx+y6F8XEfijdC+BHdEjDzbPSVxUP2P5feYcvMnNPFRU-J7TzNP3FQleZ6RB6izMA-di3qKCdWGvDax0TkHTHUOZehzjwtvXpUDaG01tuo2fvPeu+227Z7FtAMl8dpHp3lMXdZ1d17dPlEHZN0d6n5vvPnZMNbl7N23sLc6UA3XHv9fWsN-b1RxWhfMLF6jqBUFpda9-ir5XEqIey-l3LkFsOqJS-J8j8X1QoIY5PUrwnqeC149vQThPxeM-cjZwuZ3FPFQx+53bl+y8GdjYq5UQXN5tvs4lG6JvNOW97z52UUi3fSsi4wJHwL0Wnl0hFMsPIkwChRbnwXXP-MYwnFpCKCetH49pc42Qo3h9Q9yNUcwrTFCz-YKAVoqhV-3u33Pw-4+T+7sv7v1tG+2j1HX4v3bl9x-3u3-321v0YV-0AQ-1PwAWAMAOgJkTPQYXgK0UQKwD0XYVTWzF3yFCl0x2SzT2L3T0VwryIIfTL28XVycQRHg1ihGyDniU3G31wP31fUS09wN0oL6zbl4yHmFDwLN3FHW0t1vn8y3mXksj3W5RwJFFjyL0rwoNIJT0TxL0rRfX5RFCzxO0kUpVwO0PN0oT0K0KEMVFmXbmMMEPrxkkPksIMOENAB2QsPg30NMNAGOWcM0KsOz1ACuU8JPRMOsNAA6U8M5Vn3Xxi3QDtAWCvBWFaG2BXzXwiLTk32YJOBOGiNiPiMgwAPPXzRESQOUUkVf2NxgJDyAO-1fkv0KNbyIVfwdzKNbxQMqN-0fxqMwQgI-jQPf3aJXkoVQNKN6IkS-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-J-Pxhr3NmiG-LhF-MVFAvAt-PSWzBgrphAvNhgvMOgqArgrZBgt5hfTQogtWVAFwsqHGUAogulhwuQp-KcMIvmRIsqA1nIrAp-I8MIvWVorSgYpgr8MIr2VotmD5mXkIpCMEuqX3V+WtAPxlRPKryrUwFAvs2HzbgHltB-K7mvkoLkqqWlSUpQuF2XnUvNhEwUv7iAQQt0v0uiBcy0pMsorMvgw0vmSsq2hguljaXMuk0cuUogo1lcrsoMtkw8pgrSh8rwQ0tOQCp-L4uCtSWsBOBOiKAqGsHeP+wtHjAAIKH5AWAnmPw0R4wwB-2KIqIKqKp6KURfj-JANvyKsquqNKtOnxnyq-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-ulVKmjunoLtFsDDno9qVsvt-pXsPoNr3pVsDG3r7pgbfsfoPrQfAeQbPuFoQfvqvsfpvvwdftrurGfp3vQfIc-qoZwa9tOmrH-r9uofZurEnoIYIaAbmqgZjv7rLpVurHgdBoAYwd8NQa-tEfIawckY7rEerDwf4f2o3rmpIaUb7tgelWdGfpgbkdrudE-t0aUbEedGYbpqkfZudA4Y0b0csd4alosdFudGEd3vMZMYkcAdsacZkc8eMf0cUa4a8ZVudDUcCb8fZtmEoZsZZrEZRFAeidAIibMerqCYYbblmGsa-ocdid4bAfCdFtmBcbydZtiYkaPtSYfrmBkfKfyZVtmEUfnuydrtmDUcaYqaIdAGHB0cQdqbScGmHEMZ6ZKdrtMkFv4Zqc0dkWHEybod6cqeHHsb9uGfZuHBcc4faYAOHA8dBsWrEeHB8Z2car2YCcOZiZGdCdOcSdFoPCiayaOdroPFoZLt2YeduDGaMZefZoPEyY+fua+euFyfXu-rEYPCKaBc+eueuDKfBb+cheqZhbOf+YaegdhZVoPFaZRcReuYPHecxaubReevTrxZUYEWerMeUeBYeeRBmewaxYJcWbpohYJbWdpfxb6YAWRG2dcaZfZeeoOe5dRd5dJtxYFbpaFYudFbZcqdlFudmalY6dlCefGaRpBYFvJrlZJa+p+Z6Z5elblrGY1bFb1bBbvq4dVehdNZVYecuHhctcpa+ctoNZEc6OtYxb4bGOuddpFfPsGpBZ9tpp9Y9bReDqddkd9YeajoJtvqDd5ZNBFejd9y+bTtpoTb-yTa5dHsVr9f5czZdaTZOfUcJr9YldzfDa+dbtDaMZjelZ7vie-sxpBaHvjZLurYVeNG1fraLYeeNEBfMbzeueXrrYAf7bRa3u9aBdbZJpdCJb7bLYHeRdcaze7bdYcZHd5afubcLcna0o-pndXbnbRb-tDd8e3dkXthpeVa7a+cgfHc7dPdJcDBZcvaXeva5bCfvaesDH5ffcTeucDALZ-bTb-YlcA-QN5YoePYSZBerCVYpY-bRuSdOfg9xvYZnbg9-bRakkrag4eaEbrZSYPfA4tYI+Q8UurFtZI4w-A4XeKao+lerDddo6A7Re0dvf3bA+lYMbQ9IcI84-JcxdI-7isfw548E4AWdAZYmbo4Vecb3dE+k5JudAzaGYU60udBzZU+Y95edALbad45k5Lc0444Vciew+fdU7PbiajaM5BdmEQ9FbE9Jo7bNrXeldmF7dmcc8KaHaWYs9JdmAtc8786etmFtaC607c4XfWf05JpaZE7tcc66c3bCeM5JoGbk4S+C7KtGeZp9emLRemZ86Toi4VYWdvYpdS+pqfby6y9xq2bM4q5Bf2fi8a4eeHAA8uaa5A869rpuFleedq51uuFg4G5K4AJuHs9Lfy-ZZuA7am8G8GhuF7d+bG+lRuBNZW8q8ZqheS7QbEZuAo9G624ERuBo4ReO-5uuEY-O-25xfVZu968JYDYe4ttlAa544u9lupZa4+9u8k5e7tvdhTYB5Vs5uU87em8qc5o04h4W45uFfu9h9W8ZuREM6R8+7qqZtDpS7h7VCVZx+R5O7Vf1sy8lv250gy5qYx51v1dy9ZfJ5NYq9x91vK51fJ7C-p968deZoI8h46bVBXc54tq9fJt59x-9dNqO-F-48LcPv28jcdtl8mN67jcR5c8J-5uTcl6V7J5V7fY+-F+-YN419lort28vep8W8NG68lf24rbp4t9x9rYJr075-G6bcR7lbt7m51ad+W995N7qsHes8d8D51rHdF4D8t45uneB9D+j7lrO7tbd7W+NGu+T9x43bV5Yf293ee4z7D8W6PZ55Ycz4vei5T8Zpvcj4L4T8fcp5z90TAXaCAA).
 41 | 
 42 | License MIT
 43 | 
 44 | ## Usage
 45 | 
 46 | The following demonstrates basic usage.
 47 | 
 48 | ```typescript
 49 | import { Byte, Num, Add, Sub, Mod } from './ts-8-bit'
 50 | 
 51 | // ------------------------------------------------------------------------
 52 | //
 53 | // Use Byte<T> and Num<T> to map between bytes and numbers
 54 | //
 55 | // ------------------------------------------------------------------------
 56 | 
 57 | type A = Byte<127>                           // type A = [1, 1, 1, 1, 1, 1, 1, 0]
 58 | 
 59 | type B = Num<[1, 1, 1, 1, 1, 1, 1, 0]>       // type B = 127
 60 | 
 61 | type C = Num< Byte<55> >                     // type C = 55
 62 | 
 63 | // ------------------------------------------------------------------------
 64 | //
 65 | // ... with math done exclusively on bytes ...
 66 | //
 67 | // ------------------------------------------------------------------------
 68 | 
 69 | type D = Add<                                // type D = [0, 1, 1, 1, 1, 1, 1, 1]
 70 |     [1, 1, 1, 1, 1, 1, 1, 0], 
 71 |     [1, 1, 1, 1, 1, 1, 1, 0]
 72 | >
 73 | 
 74 | // ------------------------------------------------------------------------
 75 | //
 76 | // ... but can be remapped this way ...
 77 | //
 78 | // ------------------------------------------------------------------------
 79 | 
 80 | type E = Num< Add< Byte<127>, Byte<127> > >  // type E = 254
 81 | 
 82 | // ------------------------------------------------------------------------
 83 | //
 84 | // ... and used for stuff like ...
 85 | //
 86 | // ------------------------------------------------------------------------
 87 | 
 88 | type FizzBuzz<T extends Byte<any>> = 
 89 |      Mod<T, Byte<5>> extends Byte<0> ? 
 90 |      Mod<T, Byte<3>> extends Byte<0> ? 'fizzbuzz' : 'buzz' :
 91 |      Mod<T, Byte<3>> extends Byte<0> ? 'fizz'     : ""
 92 | 
 93 | type T1  = FizzBuzz< Byte<1> >     // ""
 94 | type T2  = FizzBuzz< Byte<2> >     // ""
 95 | type T3  = FizzBuzz< Byte<3> >     // "fizz"
 96 | type T4  = FizzBuzz< Byte<4> >     // ""
 97 | type T5  = FizzBuzz< Byte<5> >     // "buzz"
 98 | type T6  = FizzBuzz< Byte<6> >     // "fizz"
 99 | // ... etc ...
100 | type T15 = FizzBuzz< Byte<15> >    // "fizzbuzz"
101 | 
102 | // ------------------------------------------------------------------------
103 | //
104 | // ... or something more elaborate ...
105 | //
106 | // ------------------------------------------------------------------------
107 | 
108 | type IsPrimeOp<
109 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
110 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
111 | > = Num<B>         extends 1 ? true  : 
112 |     Num<Mod<A, B>> extends 0 ? false : 
113 |     IsPrimeOp<A, Sub<B, Byte<1>>>
114 | 
115 | type IsPrime<
116 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
117 | > = IsPrimeOp<A, Sub<A, Byte<1>>>
118 | 
119 | type P3  = IsPrime< Byte<3> >      // true
120 | type P4  = IsPrime< Byte<4> >      // false
121 | type P5  = IsPrime< Byte<5> >      // true
122 | type P6  = IsPrime< Byte<6> >      // false
123 | type P7  = IsPrime< Byte<7> >      // true
124 | type P8  = IsPrime< Byte<8> >      // false
125 | type P9  = IsPrime< Byte<9> >      // false
126 | type P10 = IsPrime< Byte<10> >     // false
127 | type P11 = IsPrime< Byte<11> >     // true
128 | type P12 = IsPrime< Byte<12> >     // false
129 | type P13 = IsPrime< Byte<13> >     // true
130 | type P14 = IsPrime< Byte<14> >     // false
131 | type P15 = IsPrime< Byte<15> >     // false
132 | type P16 = IsPrime< Byte<16> >     // false
133 | type P17 = IsPrime< Byte<17> >     // true - pushing recursion limits here
134 | type P18 = IsPrime< Byte<18> >     // false
135 | 
136 | ```
137 | 


--------------------------------------------------------------------------------
/src/ts-8-bit.ts:
--------------------------------------------------------------------------------
  1 | // -------------------------------------------------------------------------
  2 | //       _______ _____       ___        _     _ _   
  3 | //      |__   __/ ____|     / _ \      | |   (_) |  
  4 | //         | | | (___ _____| (_) |_____| |__  _| |_ 
  5 | //         | |  \___ \______> _ <______| '_ \| | __|
  6 | //         | |  ____) |    | (_) |     | |_) | | |_ 
  7 | //         |_| |_____/      \___/      |_.__/|_|\__|
  8 | //                                             
  9 | //    Using the TypeScript type system for 8-bit arithmetic
 10 | //
 11 | //                    sinclair 2020 | MIT                                         
 12 | //                                        
 13 | // -------------------------------------------------------------------------
 14 | 
 15 | // -------------------------------------------------------------------------
 16 | // Bit
 17 | // -------------------------------------------------------------------------
 18 | 
 19 | export type Bit = 0 | 1
 20 | 
 21 | // -------------------------------------------------------------------------
 22 | // Gates
 23 | // -------------------------------------------------------------------------
 24 | 
 25 | export type BitNot<T extends Bit> =
 26 |     T extends 0 ? 1 :
 27 |     T extends 1 ? 0 :
 28 |     never
 29 | 
 30 | export type BitAnd<T extends [Bit, Bit]> =
 31 |     T extends [0, 0] ? 0 :
 32 |     T extends [0, 1] ? 0 :
 33 |     T extends [1, 0] ? 0 :
 34 |     T extends [1, 1] ? 1 :
 35 |     never
 36 | 
 37 | export type BitOr<T extends [Bit, Bit]> =
 38 |     T extends [0, 0] ? 0 :
 39 |     T extends [0, 1] ? 1 :
 40 |     T extends [1, 0] ? 1 :
 41 |     T extends [1, 1] ? 1 :
 42 |     never
 43 | 
 44 | export type BitXor<T extends [Bit, Bit]> =
 45 |     T extends [0, 0] ? 0 :
 46 |     T extends [0, 1] ? 1 :
 47 |     T extends [1, 0] ? 1 :
 48 |     T extends [1, 1] ? 0 :
 49 |     never
 50 | 
 51 | // -------------------------------------------------------------------------
 52 | // Iterator
 53 | // -------------------------------------------------------------------------
 54 | 
 55 | export type Index = keyof Iterator
 56 | export type Prev<T extends keyof Iterator> = Iterator[T][0]
 57 | export type Next<T extends keyof Iterator> = Iterator[T][1]
 58 | export type Iterator = {
 59 |     0: [7, 1],
 60 |     1: [0, 2],
 61 |     2: [1, 3],
 62 |     3: [2, 4],
 63 |     4: [3, 5],
 64 |     5: [4, 6],
 65 |     6: [5, 7],
 66 |     7: [6, 0],
 67 | }
 68 | 
 69 | // -------------------------------------------------------------------------
 70 | // Bitwise
 71 | // -------------------------------------------------------------------------
 72 | 
 73 | export type Not<T extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]> = [
 74 |     BitNot<T[0]>,
 75 |     BitNot<T[1]>,
 76 |     BitNot<T[2]>,
 77 |     BitNot<T[3]>,
 78 |     BitNot<T[4]>,
 79 |     BitNot<T[5]>,
 80 |     BitNot<T[6]>,
 81 |     BitNot<T[7]>,
 82 | ]
 83 | 
 84 | export type And<
 85 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
 86 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
 87 |     > = [
 88 |         BitAnd<[A[0], B[0]]>,
 89 |         BitAnd<[A[1], B[1]]>,
 90 |         BitAnd<[A[2], B[2]]>,
 91 |         BitAnd<[A[3], B[3]]>,
 92 |         BitAnd<[A[4], B[4]]>,
 93 |         BitAnd<[A[5], B[5]]>,
 94 |         BitAnd<[A[6], B[6]]>,
 95 |         BitAnd<[A[7], B[7]]>,
 96 |     ]
 97 | 
 98 | export type Or<
 99 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
100 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
101 |     > = [
102 |         BitOr<[A[0], B[0]]>,
103 |         BitOr<[A[1], B[1]]>,
104 |         BitOr<[A[2], B[2]]>,
105 |         BitOr<[A[3], B[3]]>,
106 |         BitOr<[A[4], B[4]]>,
107 |         BitOr<[A[5], B[5]]>,
108 |         BitOr<[A[6], B[6]]>,
109 |         BitOr<[A[7], B[7]]>,
110 |     ]
111 | 
112 | export type Xor<
113 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
114 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
115 |     > = [
116 |         BitXor<[B[0], A[0]]>,
117 |         BitXor<[B[1], A[1]]>,
118 |         BitXor<[B[2], A[2]]>,
119 |         BitXor<[B[3], A[3]]>,
120 |         BitXor<[B[4], A[4]]>,
121 |         BitXor<[B[5], A[5]]>,
122 |         BitXor<[B[6], A[6]]>,
123 |         BitXor<[B[7], A[7]]>,
124 |     ]
125 | 
126 | export type Rsh<T extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit], I extends Index> =
127 |     I extends 0 ? T : Rsh<[T[1], T[2], T[3], T[4], T[5], T[6], T[7], 0], Prev<I>>
128 | 
129 | export type Lsh<T extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit], I extends Index> =
130 |     I extends 0 ? T : Lsh<[0, T[0], T[1], T[2], T[3], T[4], T[5], T[6]], Prev<I>>
131 | 
132 | 
133 | // -------------------------------------------------------------------------
134 | // Equality
135 | // -------------------------------------------------------------------------
136 | 
137 | export type Eq<
138 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
139 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
140 |     > = A extends B ? true : false
141 | 
142 | export type LtOp<
143 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
144 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
145 |     I extends Index
146 |     > = A extends B ? false :
147 |     [A[I], B[I]] extends [0, 0] ? LtOp<A, B, Prev<I>> :
148 |     [A[I], B[I]] extends [1, 1] ? LtOp<A, B, Prev<I>> :
149 |     [A[I], B[I]] extends [1, 0] ? false :
150 |     [A[I], B[I]] extends [0, 1] ? true :
151 |     false
152 | 
153 | export type Lt<
154 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
155 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
156 |     > = LtOp<A, B, 7>
157 | 
158 | export type Lte<
159 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
160 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
161 |     > = [Eq<A, B>, Lt<A, B>] extends [true, false] ? true :
162 |     [Eq<A, B>, Lt<A, B>] extends [false, true] ? true :
163 |     false
164 | 
165 | export type GtOp<
166 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
167 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
168 |     I extends Index
169 |     > = A extends B ? false :
170 |     [A[I], B[I]] extends [0, 0] ? GtOp<A, B, Prev<I>> :
171 |     [A[I], B[I]] extends [1, 1] ? GtOp<A, B, Prev<I>> :
172 |     [A[I], B[I]] extends [0, 1] ? false :
173 |     [A[I], B[I]] extends [1, 0] ? true :
174 |     false
175 | 
176 | export type Gt<
177 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
178 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
179 |     > = GtOp<A, B, 7>
180 | 
181 | export type Gte<
182 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
183 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
184 |     > = [Eq<A, B>, Gt<A, B>] extends [true, false] ? true :
185 |     [Eq<A, B>, Gt<A, B>] extends [false, true] ? true :
186 |     false
187 | 
188 | // -------------------------------------------------------------------------
189 | // Addition
190 | // -------------------------------------------------------------------------
191 | 
192 | export type FullAdder<T extends [Bit, Bit, Bit]> =
193 |     T extends [0, 0, 0] ? [0, 0] :
194 |     T extends [1, 0, 0] ? [1, 0] :
195 |     T extends [0, 1, 0] ? [1, 0] :
196 |     T extends [1, 1, 0] ? [0, 1] :
197 |     T extends [0, 0, 1] ? [1, 0] :
198 |     T extends [1, 0, 1] ? [0, 1] :
199 |     T extends [0, 1, 1] ? [0, 1] :
200 |     T extends [1, 1, 1] ? [1, 1] :
201 |     never
202 | 
203 | export type AddOp<
204 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
205 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
206 |     I extends Index,
207 |     O extends Bit
208 |     > = FullAdder<[
209 |         A[I], B[I],
210 |         I extends 0 ? 0 : AddOp<A, B, Prev<I>, 1>
211 |     ]>[O]
212 | 
213 | export type Add<
214 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
215 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
216 |     > = [
217 |         AddOp<A, B, 0, 0>,
218 |         AddOp<A, B, 1, 0>,
219 |         AddOp<A, B, 2, 0>,
220 |         AddOp<A, B, 3, 0>,
221 |         AddOp<A, B, 4, 0>,
222 |         AddOp<A, B, 5, 0>,
223 |         AddOp<A, B, 6, 0>,
224 |         AddOp<A, B, 7, 0>,
225 |     ]
226 | 
227 | // -------------------------------------------------------------------------
228 | // Subtraction
229 | // -------------------------------------------------------------------------
230 | 
231 | export type FullSubtractor<T extends [Bit, Bit, Bit]> =
232 |     T extends [0, 0, 0] ? [0, 0] :
233 |     T extends [1, 0, 0] ? [1, 0] :
234 |     T extends [0, 1, 0] ? [1, 1] :
235 |     T extends [1, 1, 0] ? [0, 0] :
236 |     T extends [0, 0, 1] ? [1, 1] :
237 |     T extends [1, 0, 1] ? [0, 0] :
238 |     T extends [0, 1, 1] ? [0, 1] :
239 |     T extends [1, 1, 1] ? [1, 1] :
240 |     never
241 | 
242 | export type SubOp<
243 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
244 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
245 |     I extends Index,
246 |     O extends Bit
247 |     > = FullSubtractor<[
248 |         A[I], B[I],
249 |         I extends 0 ? 0 : SubOp<A, B, Prev<I>, 1>
250 |     ]>[O]
251 | 
252 | export type Sub<
253 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
254 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
255 |     > = [
256 |         SubOp<A, B, 0, 0>,
257 |         SubOp<A, B, 1, 0>,
258 |         SubOp<A, B, 2, 0>,
259 |         SubOp<A, B, 3, 0>,
260 |         SubOp<A, B, 4, 0>,
261 |         SubOp<A, B, 5, 0>,
262 |         SubOp<A, B, 6, 0>,
263 |         SubOp<A, B, 7, 0>,
264 |     ]
265 | 
266 | // -------------------------------------------------------------------------
267 | // Multiply
268 | // -------------------------------------------------------------------------
269 | 
270 | export type MulOp<
271 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
272 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
273 |     C extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
274 |     D extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
275 |     > = Lt<C, D> extends true ? MulOp<Add<A, B>, B, Add<C, Byte<1>>, D> : A
276 | 
277 | export type Mul<
278 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
279 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
280 |     > = MulOp<Byte<0>, A, Byte<0>, B>
281 | 
282 | // -------------------------------------------------------------------------
283 | // Division
284 | // -------------------------------------------------------------------------
285 | 
286 | export type DivOp<
287 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
288 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
289 |     C extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
290 |     > = Gte<A, B> extends true ? DivOp<Sub<A, B>, B, Add<C, Byte<1>>> : C
291 | 
292 | export type Div<
293 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
294 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
295 |     > = DivOp<A, B, Byte<0>>
296 | 
297 | // -------------------------------------------------------------------------
298 | // Modulo
299 | // -------------------------------------------------------------------------
300 | 
301 | export type ModOp<
302 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
303 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
304 |     C extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
305 |     > = Gte<A, B> extends true ? ModOp<Sub<A, B>, B, Add<C, Byte<1>>> : A
306 | 
307 | export type Mod<
308 |     A extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit],
309 |     B extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]
310 |     > = ModOp<A, B, Byte<0>>
311 | 
312 | // -------------------------------------------------------------------------
313 | // Converters
314 | // -------------------------------------------------------------------------
315 | 
316 | type Size1 = [0]
317 | type Size2 = [...Size1, ...Size1]
318 | type Size3 = [...Size2, ...Size2]
319 | type Size4 = [...Size3, ...Size3]
320 | type Size5 = [...Size4, ...Size4]
321 | type Size6 = [...Size5, ...Size5]
322 | type Size7 = [...Size6, ...Size6]
323 | type Size8 = [...Size7, ...Size7]
324 | export type Num<T extends [Bit, Bit, Bit, Bit, Bit, Bit, Bit, Bit]> = [
325 |     ...T[0] extends 1 ? Size1 : [],
326 |     ...T[1] extends 1 ? Size2 : [],
327 |     ...T[2] extends 1 ? Size3 : [],
328 |     ...T[3] extends 1 ? Size4 : [],
329 |     ...T[4] extends 1 ? Size5 : [],
330 |     ...T[5] extends 1 ? Size6 : [],
331 |     ...T[6] extends 1 ? Size7 : [],
332 |     ...T[7] extends 1 ? Size8 : [],
333 | ]['length']
334 | 
335 | export type Byte<T extends number> =
336 |     T extends 0 ? [0, 0, 0, 0, 0, 0, 0, 0] :
337 |     T extends 1 ? [1, 0, 0, 0, 0, 0, 0, 0] :
338 |     T extends 2 ? [0, 1, 0, 0, 0, 0, 0, 0] :
339 |     T extends 3 ? [1, 1, 0, 0, 0, 0, 0, 0] :
340 |     T extends 4 ? [0, 0, 1, 0, 0, 0, 0, 0] :
341 |     T extends 5 ? [1, 0, 1, 0, 0, 0, 0, 0] :
342 |     T extends 6 ? [0, 1, 1, 0, 0, 0, 0, 0] :
343 |     T extends 7 ? [1, 1, 1, 0, 0, 0, 0, 0] :
344 |     T extends 8 ? [0, 0, 0, 1, 0, 0, 0, 0] :
345 |     T extends 9 ? [1, 0, 0, 1, 0, 0, 0, 0] :
346 |     T extends 10 ? [0, 1, 0, 1, 0, 0, 0, 0] :
347 |     T extends 11 ? [1, 1, 0, 1, 0, 0, 0, 0] :
348 |     T extends 12 ? [0, 0, 1, 1, 0, 0, 0, 0] :
349 |     T extends 13 ? [1, 0, 1, 1, 0, 0, 0, 0] :
350 |     T extends 14 ? [0, 1, 1, 1, 0, 0, 0, 0] :
351 |     T extends 15 ? [1, 1, 1, 1, 0, 0, 0, 0] :
352 |     T extends 16 ? [0, 0, 0, 0, 1, 0, 0, 0] :
353 |     T extends 17 ? [1, 0, 0, 0, 1, 0, 0, 0] :
354 |     T extends 18 ? [0, 1, 0, 0, 1, 0, 0, 0] :
355 |     T extends 19 ? [1, 1, 0, 0, 1, 0, 0, 0] :
356 |     T extends 20 ? [0, 0, 1, 0, 1, 0, 0, 0] :
357 |     T extends 21 ? [1, 0, 1, 0, 1, 0, 0, 0] :
358 |     T extends 22 ? [0, 1, 1, 0, 1, 0, 0, 0] :
359 |     T extends 23 ? [1, 1, 1, 0, 1, 0, 0, 0] :
360 |     T extends 24 ? [0, 0, 0, 1, 1, 0, 0, 0] :
361 |     T extends 25 ? [1, 0, 0, 1, 1, 0, 0, 0] :
362 |     T extends 26 ? [0, 1, 0, 1, 1, 0, 0, 0] :
363 |     T extends 27 ? [1, 1, 0, 1, 1, 0, 0, 0] :
364 |     T extends 28 ? [0, 0, 1, 1, 1, 0, 0, 0] :
365 |     T extends 29 ? [1, 0, 1, 1, 1, 0, 0, 0] :
366 |     T extends 30 ? [0, 1, 1, 1, 1, 0, 0, 0] :
367 |     T extends 31 ? [1, 1, 1, 1, 1, 0, 0, 0] :
368 |     T extends 32 ? [0, 0, 0, 0, 0, 1, 0, 0] :
369 |     T extends 33 ? [1, 0, 0, 0, 0, 1, 0, 0] :
370 |     T extends 34 ? [0, 1, 0, 0, 0, 1, 0, 0] :
371 |     T extends 35 ? [1, 1, 0, 0, 0, 1, 0, 0] :
372 |     T extends 36 ? [0, 0, 1, 0, 0, 1, 0, 0] :
373 |     T extends 37 ? [1, 0, 1, 0, 0, 1, 0, 0] :
374 |     T extends 38 ? [0, 1, 1, 0, 0, 1, 0, 0] :
375 |     T extends 39 ? [1, 1, 1, 0, 0, 1, 0, 0] :
376 |     T extends 40 ? [0, 0, 0, 1, 0, 1, 0, 0] :
377 |     T extends 41 ? [1, 0, 0, 1, 0, 1, 0, 0] :
378 |     T extends 42 ? [0, 1, 0, 1, 0, 1, 0, 0] :
379 |     T extends 43 ? [1, 1, 0, 1, 0, 1, 0, 0] :
380 |     T extends 44 ? [0, 0, 1, 1, 0, 1, 0, 0] :
381 |     T extends 45 ? [1, 0, 1, 1, 0, 1, 0, 0] :
382 |     T extends 46 ? [0, 1, 1, 1, 0, 1, 0, 0] :
383 |     T extends 47 ? [1, 1, 1, 1, 0, 1, 0, 0] :
384 |     T extends 48 ? [0, 0, 0, 0, 1, 1, 0, 0] :
385 |     T extends 49 ? [1, 0, 0, 0, 1, 1, 0, 0] :
386 |     T extends 50 ? [0, 1, 0, 0, 1, 1, 0, 0] :
387 |     T extends 51 ? [1, 1, 0, 0, 1, 1, 0, 0] :
388 |     T extends 52 ? [0, 0, 1, 0, 1, 1, 0, 0] :
389 |     T extends 53 ? [1, 0, 1, 0, 1, 1, 0, 0] :
390 |     T extends 54 ? [0, 1, 1, 0, 1, 1, 0, 0] :
391 |     T extends 55 ? [1, 1, 1, 0, 1, 1, 0, 0] :
392 |     T extends 56 ? [0, 0, 0, 1, 1, 1, 0, 0] :
393 |     T extends 57 ? [1, 0, 0, 1, 1, 1, 0, 0] :
394 |     T extends 58 ? [0, 1, 0, 1, 1, 1, 0, 0] :
395 |     T extends 59 ? [1, 1, 0, 1, 1, 1, 0, 0] :
396 |     T extends 60 ? [0, 0, 1, 1, 1, 1, 0, 0] :
397 |     T extends 61 ? [1, 0, 1, 1, 1, 1, 0, 0] :
398 |     T extends 62 ? [0, 1, 1, 1, 1, 1, 0, 0] :
399 |     T extends 63 ? [1, 1, 1, 1, 1, 1, 0, 0] :
400 |     T extends 64 ? [0, 0, 0, 0, 0, 0, 1, 0] :
401 |     T extends 65 ? [1, 0, 0, 0, 0, 0, 1, 0] :
402 |     T extends 66 ? [0, 1, 0, 0, 0, 0, 1, 0] :
403 |     T extends 67 ? [1, 1, 0, 0, 0, 0, 1, 0] :
404 |     T extends 68 ? [0, 0, 1, 0, 0, 0, 1, 0] :
405 |     T extends 69 ? [1, 0, 1, 0, 0, 0, 1, 0] :
406 |     T extends 70 ? [0, 1, 1, 0, 0, 0, 1, 0] :
407 |     T extends 71 ? [1, 1, 1, 0, 0, 0, 1, 0] :
408 |     T extends 72 ? [0, 0, 0, 1, 0, 0, 1, 0] :
409 |     T extends 73 ? [1, 0, 0, 1, 0, 0, 1, 0] :
410 |     T extends 74 ? [0, 1, 0, 1, 0, 0, 1, 0] :
411 |     T extends 75 ? [1, 1, 0, 1, 0, 0, 1, 0] :
412 |     T extends 76 ? [0, 0, 1, 1, 0, 0, 1, 0] :
413 |     T extends 77 ? [1, 0, 1, 1, 0, 0, 1, 0] :
414 |     T extends 78 ? [0, 1, 1, 1, 0, 0, 1, 0] :
415 |     T extends 79 ? [1, 1, 1, 1, 0, 0, 1, 0] :
416 |     T extends 80 ? [0, 0, 0, 0, 1, 0, 1, 0] :
417 |     T extends 81 ? [1, 0, 0, 0, 1, 0, 1, 0] :
418 |     T extends 82 ? [0, 1, 0, 0, 1, 0, 1, 0] :
419 |     T extends 83 ? [1, 1, 0, 0, 1, 0, 1, 0] :
420 |     T extends 84 ? [0, 0, 1, 0, 1, 0, 1, 0] :
421 |     T extends 85 ? [1, 0, 1, 0, 1, 0, 1, 0] :
422 |     T extends 86 ? [0, 1, 1, 0, 1, 0, 1, 0] :
423 |     T extends 87 ? [1, 1, 1, 0, 1, 0, 1, 0] :
424 |     T extends 88 ? [0, 0, 0, 1, 1, 0, 1, 0] :
425 |     T extends 89 ? [1, 0, 0, 1, 1, 0, 1, 0] :
426 |     T extends 90 ? [0, 1, 0, 1, 1, 0, 1, 0] :
427 |     T extends 91 ? [1, 1, 0, 1, 1, 0, 1, 0] :
428 |     T extends 92 ? [0, 0, 1, 1, 1, 0, 1, 0] :
429 |     T extends 93 ? [1, 0, 1, 1, 1, 0, 1, 0] :
430 |     T extends 94 ? [0, 1, 1, 1, 1, 0, 1, 0] :
431 |     T extends 95 ? [1, 1, 1, 1, 1, 0, 1, 0] :
432 |     T extends 96 ? [0, 0, 0, 0, 0, 1, 1, 0] :
433 |     T extends 97 ? [1, 0, 0, 0, 0, 1, 1, 0] :
434 |     T extends 98 ? [0, 1, 0, 0, 0, 1, 1, 0] :
435 |     T extends 99 ? [1, 1, 0, 0, 0, 1, 1, 0] :
436 |     T extends 100 ? [0, 0, 1, 0, 0, 1, 1, 0] :
437 |     T extends 101 ? [1, 0, 1, 0, 0, 1, 1, 0] :
438 |     T extends 102 ? [0, 1, 1, 0, 0, 1, 1, 0] :
439 |     T extends 103 ? [1, 1, 1, 0, 0, 1, 1, 0] :
440 |     T extends 104 ? [0, 0, 0, 1, 0, 1, 1, 0] :
441 |     T extends 105 ? [1, 0, 0, 1, 0, 1, 1, 0] :
442 |     T extends 106 ? [0, 1, 0, 1, 0, 1, 1, 0] :
443 |     T extends 107 ? [1, 1, 0, 1, 0, 1, 1, 0] :
444 |     T extends 108 ? [0, 0, 1, 1, 0, 1, 1, 0] :
445 |     T extends 109 ? [1, 0, 1, 1, 0, 1, 1, 0] :
446 |     T extends 110 ? [0, 1, 1, 1, 0, 1, 1, 0] :
447 |     T extends 111 ? [1, 1, 1, 1, 0, 1, 1, 0] :
448 |     T extends 112 ? [0, 0, 0, 0, 1, 1, 1, 0] :
449 |     T extends 113 ? [1, 0, 0, 0, 1, 1, 1, 0] :
450 |     T extends 114 ? [0, 1, 0, 0, 1, 1, 1, 0] :
451 |     T extends 115 ? [1, 1, 0, 0, 1, 1, 1, 0] :
452 |     T extends 116 ? [0, 0, 1, 0, 1, 1, 1, 0] :
453 |     T extends 117 ? [1, 0, 1, 0, 1, 1, 1, 0] :
454 |     T extends 118 ? [0, 1, 1, 0, 1, 1, 1, 0] :
455 |     T extends 119 ? [1, 1, 1, 0, 1, 1, 1, 0] :
456 |     T extends 120 ? [0, 0, 0, 1, 1, 1, 1, 0] :
457 |     T extends 121 ? [1, 0, 0, 1, 1, 1, 1, 0] :
458 |     T extends 122 ? [0, 1, 0, 1, 1, 1, 1, 0] :
459 |     T extends 123 ? [1, 1, 0, 1, 1, 1, 1, 0] :
460 |     T extends 124 ? [0, 0, 1, 1, 1, 1, 1, 0] :
461 |     T extends 125 ? [1, 0, 1, 1, 1, 1, 1, 0] :
462 |     T extends 126 ? [0, 1, 1, 1, 1, 1, 1, 0] :
463 |     T extends 127 ? [1, 1, 1, 1, 1, 1, 1, 0] :
464 |     T extends 128 ? [0, 0, 0, 0, 0, 0, 0, 1] :
465 |     T extends 129 ? [1, 0, 0, 0, 0, 0, 0, 1] :
466 |     T extends 130 ? [0, 1, 0, 0, 0, 0, 0, 1] :
467 |     T extends 131 ? [1, 1, 0, 0, 0, 0, 0, 1] :
468 |     T extends 132 ? [0, 0, 1, 0, 0, 0, 0, 1] :
469 |     T extends 133 ? [1, 0, 1, 0, 0, 0, 0, 1] :
470 |     T extends 134 ? [0, 1, 1, 0, 0, 0, 0, 1] :
471 |     T extends 135 ? [1, 1, 1, 0, 0, 0, 0, 1] :
472 |     T extends 136 ? [0, 0, 0, 1, 0, 0, 0, 1] :
473 |     T extends 137 ? [1, 0, 0, 1, 0, 0, 0, 1] :
474 |     T extends 138 ? [0, 1, 0, 1, 0, 0, 0, 1] :
475 |     T extends 139 ? [1, 1, 0, 1, 0, 0, 0, 1] :
476 |     T extends 140 ? [0, 0, 1, 1, 0, 0, 0, 1] :
477 |     T extends 141 ? [1, 0, 1, 1, 0, 0, 0, 1] :
478 |     T extends 142 ? [0, 1, 1, 1, 0, 0, 0, 1] :
479 |     T extends 143 ? [1, 1, 1, 1, 0, 0, 0, 1] :
480 |     T extends 144 ? [0, 0, 0, 0, 1, 0, 0, 1] :
481 |     T extends 145 ? [1, 0, 0, 0, 1, 0, 0, 1] :
482 |     T extends 146 ? [0, 1, 0, 0, 1, 0, 0, 1] :
483 |     T extends 147 ? [1, 1, 0, 0, 1, 0, 0, 1] :
484 |     T extends 148 ? [0, 0, 1, 0, 1, 0, 0, 1] :
485 |     T extends 149 ? [1, 0, 1, 0, 1, 0, 0, 1] :
486 |     T extends 150 ? [0, 1, 1, 0, 1, 0, 0, 1] :
487 |     T extends 151 ? [1, 1, 1, 0, 1, 0, 0, 1] :
488 |     T extends 152 ? [0, 0, 0, 1, 1, 0, 0, 1] :
489 |     T extends 153 ? [1, 0, 0, 1, 1, 0, 0, 1] :
490 |     T extends 154 ? [0, 1, 0, 1, 1, 0, 0, 1] :
491 |     T extends 155 ? [1, 1, 0, 1, 1, 0, 0, 1] :
492 |     T extends 156 ? [0, 0, 1, 1, 1, 0, 0, 1] :
493 |     T extends 157 ? [1, 0, 1, 1, 1, 0, 0, 1] :
494 |     T extends 158 ? [0, 1, 1, 1, 1, 0, 0, 1] :
495 |     T extends 159 ? [1, 1, 1, 1, 1, 0, 0, 1] :
496 |     T extends 160 ? [0, 0, 0, 0, 0, 1, 0, 1] :
497 |     T extends 161 ? [1, 0, 0, 0, 0, 1, 0, 1] :
498 |     T extends 162 ? [0, 1, 0, 0, 0, 1, 0, 1] :
499 |     T extends 163 ? [1, 1, 0, 0, 0, 1, 0, 1] :
500 |     T extends 164 ? [0, 0, 1, 0, 0, 1, 0, 1] :
501 |     T extends 165 ? [1, 0, 1, 0, 0, 1, 0, 1] :
502 |     T extends 166 ? [0, 1, 1, 0, 0, 1, 0, 1] :
503 |     T extends 167 ? [1, 1, 1, 0, 0, 1, 0, 1] :
504 |     T extends 168 ? [0, 0, 0, 1, 0, 1, 0, 1] :
505 |     T extends 169 ? [1, 0, 0, 1, 0, 1, 0, 1] :
506 |     T extends 170 ? [0, 1, 0, 1, 0, 1, 0, 1] :
507 |     T extends 171 ? [1, 1, 0, 1, 0, 1, 0, 1] :
508 |     T extends 172 ? [0, 0, 1, 1, 0, 1, 0, 1] :
509 |     T extends 173 ? [1, 0, 1, 1, 0, 1, 0, 1] :
510 |     T extends 174 ? [0, 1, 1, 1, 0, 1, 0, 1] :
511 |     T extends 175 ? [1, 1, 1, 1, 0, 1, 0, 1] :
512 |     T extends 176 ? [0, 0, 0, 0, 1, 1, 0, 1] :
513 |     T extends 177 ? [1, 0, 0, 0, 1, 1, 0, 1] :
514 |     T extends 178 ? [0, 1, 0, 0, 1, 1, 0, 1] :
515 |     T extends 179 ? [1, 1, 0, 0, 1, 1, 0, 1] :
516 |     T extends 180 ? [0, 0, 1, 0, 1, 1, 0, 1] :
517 |     T extends 181 ? [1, 0, 1, 0, 1, 1, 0, 1] :
518 |     T extends 182 ? [0, 1, 1, 0, 1, 1, 0, 1] :
519 |     T extends 183 ? [1, 1, 1, 0, 1, 1, 0, 1] :
520 |     T extends 184 ? [0, 0, 0, 1, 1, 1, 0, 1] :
521 |     T extends 185 ? [1, 0, 0, 1, 1, 1, 0, 1] :
522 |     T extends 186 ? [0, 1, 0, 1, 1, 1, 0, 1] :
523 |     T extends 187 ? [1, 1, 0, 1, 1, 1, 0, 1] :
524 |     T extends 188 ? [0, 0, 1, 1, 1, 1, 0, 1] :
525 |     T extends 189 ? [1, 0, 1, 1, 1, 1, 0, 1] :
526 |     T extends 190 ? [0, 1, 1, 1, 1, 1, 0, 1] :
527 |     T extends 191 ? [1, 1, 1, 1, 1, 1, 0, 1] :
528 |     T extends 192 ? [0, 0, 0, 0, 0, 0, 1, 1] :
529 |     T extends 193 ? [1, 0, 0, 0, 0, 0, 1, 1] :
530 |     T extends 194 ? [0, 1, 0, 0, 0, 0, 1, 1] :
531 |     T extends 195 ? [1, 1, 0, 0, 0, 0, 1, 1] :
532 |     T extends 196 ? [0, 0, 1, 0, 0, 0, 1, 1] :
533 |     T extends 197 ? [1, 0, 1, 0, 0, 0, 1, 1] :
534 |     T extends 198 ? [0, 1, 1, 0, 0, 0, 1, 1] :
535 |     T extends 199 ? [1, 1, 1, 0, 0, 0, 1, 1] :
536 |     T extends 200 ? [0, 0, 0, 1, 0, 0, 1, 1] :
537 |     T extends 201 ? [1, 0, 0, 1, 0, 0, 1, 1] :
538 |     T extends 202 ? [0, 1, 0, 1, 0, 0, 1, 1] :
539 |     T extends 203 ? [1, 1, 0, 1, 0, 0, 1, 1] :
540 |     T extends 204 ? [0, 0, 1, 1, 0, 0, 1, 1] :
541 |     T extends 205 ? [1, 0, 1, 1, 0, 0, 1, 1] :
542 |     T extends 206 ? [0, 1, 1, 1, 0, 0, 1, 1] :
543 |     T extends 207 ? [1, 1, 1, 1, 0, 0, 1, 1] :
544 |     T extends 208 ? [0, 0, 0, 0, 1, 0, 1, 1] :
545 |     T extends 209 ? [1, 0, 0, 0, 1, 0, 1, 1] :
546 |     T extends 210 ? [0, 1, 0, 0, 1, 0, 1, 1] :
547 |     T extends 211 ? [1, 1, 0, 0, 1, 0, 1, 1] :
548 |     T extends 212 ? [0, 0, 1, 0, 1, 0, 1, 1] :
549 |     T extends 213 ? [1, 0, 1, 0, 1, 0, 1, 1] :
550 |     T extends 214 ? [0, 1, 1, 0, 1, 0, 1, 1] :
551 |     T extends 215 ? [1, 1, 1, 0, 1, 0, 1, 1] :
552 |     T extends 216 ? [0, 0, 0, 1, 1, 0, 1, 1] :
553 |     T extends 217 ? [1, 0, 0, 1, 1, 0, 1, 1] :
554 |     T extends 218 ? [0, 1, 0, 1, 1, 0, 1, 1] :
555 |     T extends 219 ? [1, 1, 0, 1, 1, 0, 1, 1] :
556 |     T extends 220 ? [0, 0, 1, 1, 1, 0, 1, 1] :
557 |     T extends 221 ? [1, 0, 1, 1, 1, 0, 1, 1] :
558 |     T extends 222 ? [0, 1, 1, 1, 1, 0, 1, 1] :
559 |     T extends 223 ? [1, 1, 1, 1, 1, 0, 1, 1] :
560 |     T extends 224 ? [0, 0, 0, 0, 0, 1, 1, 1] :
561 |     T extends 225 ? [1, 0, 0, 0, 0, 1, 1, 1] :
562 |     T extends 226 ? [0, 1, 0, 0, 0, 1, 1, 1] :
563 |     T extends 227 ? [1, 1, 0, 0, 0, 1, 1, 1] :
564 |     T extends 228 ? [0, 0, 1, 0, 0, 1, 1, 1] :
565 |     T extends 229 ? [1, 0, 1, 0, 0, 1, 1, 1] :
566 |     T extends 230 ? [0, 1, 1, 0, 0, 1, 1, 1] :
567 |     T extends 231 ? [1, 1, 1, 0, 0, 1, 1, 1] :
568 |     T extends 232 ? [0, 0, 0, 1, 0, 1, 1, 1] :
569 |     T extends 233 ? [1, 0, 0, 1, 0, 1, 1, 1] :
570 |     T extends 234 ? [0, 1, 0, 1, 0, 1, 1, 1] :
571 |     T extends 235 ? [1, 1, 0, 1, 0, 1, 1, 1] :
572 |     T extends 236 ? [0, 0, 1, 1, 0, 1, 1, 1] :
573 |     T extends 237 ? [1, 0, 1, 1, 0, 1, 1, 1] :
574 |     T extends 238 ? [0, 1, 1, 1, 0, 1, 1, 1] :
575 |     T extends 239 ? [1, 1, 1, 1, 0, 1, 1, 1] :
576 |     T extends 240 ? [0, 0, 0, 0, 1, 1, 1, 1] :
577 |     T extends 241 ? [1, 0, 0, 0, 1, 1, 1, 1] :
578 |     T extends 242 ? [0, 1, 0, 0, 1, 1, 1, 1] :
579 |     T extends 243 ? [1, 1, 0, 0, 1, 1, 1, 1] :
580 |     T extends 244 ? [0, 0, 1, 0, 1, 1, 1, 1] :
581 |     T extends 245 ? [1, 0, 1, 0, 1, 1, 1, 1] :
582 |     T extends 246 ? [0, 1, 1, 0, 1, 1, 1, 1] :
583 |     T extends 247 ? [1, 1, 1, 0, 1, 1, 1, 1] :
584 |     T extends 248 ? [0, 0, 0, 1, 1, 1, 1, 1] :
585 |     T extends 249 ? [1, 0, 0, 1, 1, 1, 1, 1] :
586 |     T extends 250 ? [0, 1, 0, 1, 1, 1, 1, 1] :
587 |     T extends 251 ? [1, 1, 0, 1, 1, 1, 1, 1] :
588 |     T extends 252 ? [0, 0, 1, 1, 1, 1, 1, 1] :
589 |     T extends 253 ? [1, 0, 1, 1, 1, 1, 1, 1] :
590 |     T extends 254 ? [0, 1, 1, 1, 1, 1, 1, 1] :
591 |     T extends 255 ? [1, 1, 1, 1, 1, 1, 1, 1] :
592 |     never


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