TypeScript Types binary to decimal exploration

index.ts

// copyright 2022 Zach Hardesty

// want to check this out in the TypeScript playground?
// visit the following link to automatically see the latest version!
// https://www.typescriptlang.org/play?jsx=0#gist/4b88be5dbc4ce1d00c37df0d1811c48b

// experiments that have thus far been unsuccessful

// https://itnext.io/implementing-arithmetic-within-typescripts-type-system-a1ef140a6f6f
// https://github.com/fightingcat/sits
// https://github.com/kddnewton/typescript-parse-math
// https://github.com/ronami/meta-typing
// https://github.com/ghoullier/awesome-template-literal-types#bitwise-arithmetic
// https://www.typescriptlang.org/play?ts=4.5.0-dev.20210908#code/C4TwDgpgBAsgggDQJIwKowPpwDLYPIDqAogCIYBCeqAciXAEoCaUAvFACwCcArALABQA0JFgBDMJAAmAHgFR5UalAgAPYBAB2kgM5QNAVwC2AIwgAnADRyF9CNv0AbYMrWadUOGbOiQ0-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
// https://www.typescriptlang.org/play?ts=4.5.0-dev.20211012#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
// https://www.typescriptlang.org/play?ts=4.5.0-dev.20211012&ssl=9&ssc=25&pln=9&pc=31#code/C4TwDgpgBAsgggDQJIwKowPpwDLYPIDqAogCIYBCeqAciXAEoCaUAvFAJycCwAUL6JFgBDMJAAmAHl5QZUalAgAPYBAB2YgM5RVAVwC2AIwgAnADTTZ9CBp0AbYAuVrNUOMeNCQEnaoDWqgHsAd1UAPlYoAG0AXXMeWShwlgsZAAorG3tIgHJbNQBzYAALbOjHFXUtahSEqAB+KAy7YBqEgC5hUQhJalMogDpBpvs+4eAcvNVCkujo0JqASl5lngFoan0jY3ohKeg2GBFxCXhkNEwcfGIySho6JlCAbhX+cGgAYQDVADcTYAAVAIbQwmCT-crOLQaYDGACWU1Gu3y0CUFRcuhBxhiSQs4NRkKgvggIACADNGkjoA0dntIv8yh1VBBfsZnnxVm8oBgIp8fn9AcCthJsgBWbJ9QUmGnI8IAellUBFr0EGG5bF5LIBQM2oOyAEYAExiiU67aUuUKw1K9lAA
type decimalMapA = {
  "0000": "0"
  "0001": "1"
  "0010": "2"
  "0011": "3"
  "0100": "4"
  "0101": "5"
  "0110": "6"
  "0111": "7"
  "1000": "8"
  "1001": "9"
}
/** numbers with a carried digit in base 10 */
type decimalMapB = {
  "1010": "0"
  "1011": "1"
  "1100": "2"
  "1101": "3"
  "1110": "4"
  "1111": "5"
}

type decimalMapInc = {
  "0": "1"
  "1": "2"
  "2": "3"
  "3": "4"
  "4": "5"
  "5": "6"
  "6": "7"
  "7": "8"
  "8": "9"
  "9": "0"
}

type IncDecCarry<Dec extends string> = Dec extends keyof decimalMapInc
  ? Dec extends "9"
    ? [decimalMapInc[Dec], One]
    : [decimalMapInc[Dec], Zero]
  : never

/** note, must be multiple of 4, well exactly 4 bc this algorithm isn't how math works... */
type binToDecString<
  Bin extends string,
  Out extends string = "",
  Carry extends string = Zero,
> = Bin extends ""
  ? Carry extends One
    ? `1${Out}`
    : Out
  : Bin extends `${infer Rest}${Nibble}`
  ? Bin extends `${Rest}${infer D}`
    ? D extends keyof decimalMapA
      ? Carry extends One
        ? binToDecString<
            Rest,
            `${IncDecCarry<decimalMapA[D]>[0]}${Out}`,
            IncDecCarry<decimalMapA[D]>[1]
          >
        : binToDecString<Rest, `${decimalMapA[D]}${Out}`, Zero>
      : D extends keyof decimalMapB
      ? binToDecString<Rest, `${decimalMapB[D]}${Out}`, One>
      : never
    : never
  : never

type TEST_DEC_00 = Expect<binToDecString<"0111">, "7">
type TEST_DEC_01 = Expect<binToDecString<"0000">, "0">
type TEST_DEC_02 = Expect<binToDecString<"1010">, "10">
type TEST_DEC_03 = Expect<binToDecString<"1111">, "15">
// type TEST_DEC_04 = Expect<binToDecString<"00101010">, "42">

// subtract 9 in a loop?