TypeScript Type‑Level Implementation of Large Integer Addition

Result

The final output is a type‑level addition that can handle very large numbers without runtime computation, displayed directly in VSCode's type hinting.

How It Works

Typical TS tricks for addition are limited; this solution uses a systematic approach to support large numbers.

String → Number[]

type DigitRangeMap = [0,1,2,3,4,5,6,7,8,9];
type Digit = DigitRangeMap[number];
type ToDigit
= T extends keyof DigitRangeMap ? DigitRangeMap[T] : never;
type ToDigitList
=
  T extends `${infer First}${infer Rest}`
    ? ToDigitList
, ...R]>
    : R; // converts string to reversed digit array

The conversion stores digits in reverse order to simplify per‑digit addition.

One‑Digit Addition

type AdditionMap = [
  [0,1,2,3,4,5,6,7,8,9],
  [1,2,3,4,5,6,7,8,9,10],
  [2,3,4,5,6,7,8,9,10,11],
  ...
];
type AddOneDigit
= AdditionMap[A][B];

Because there are only 100 possible pairs, a lookup table is used for speed; the table is symmetric, so the size is halved by ordering A > B.

Carry Handling

type RoundMap = {10:0;11:1;12:2;13:3;14:4;15:5;16:6;17:7;18:8;19:9};
type Carry
=
  T extends keyof RoundMap
    ? [1, [RoundMap[T], ...R]]
    : [0, [T, ...R]];

Carry returns a tuple where the first element is the carry (0 or 1) and the second element is the updated digit list.

Multi‑Digit Addition

type IncMap = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19];
type Shift
= T extends [infer First, ...infer Rest] ? Rest : never;
type AddDigitList
=
  A['length'] extends 0
    ? B['length'] extends 0
      ? ACC[0] extends 1
        ? AddDigitList<[1], [], [0, ACC[1]]>
        : ACC[1]
      : AddDigitList
, Carry
, ACC[0]>>
    : B['length'] extends 0
      ? AddDigitList
, B, Carry
, ACC[0]>>
      : AddDigitList
, Shift
, Carry
: IncMap[AddOneDigit
], ACC[1]>>;

The recursive type walks through both digit arrays, adds corresponding digits with carry, and builds the result.

Number[] → String

type StrDigitRangeMap = ['0','1','2','3','4','5','6','7','8','9'];
type DigitListToString
=
  T extends [infer First, ...infer Rest]
    ? DigitListToString
: R;

type Add
= DigitListToString
, ToDigitList
>>;

The final step converts the resulting digit array back to a string, producing the compile‑time sum.

Full Code

/* (Full source code as shown in the article, including all type definitions and helper utilities) */

The complete type definitions are provided, allowing developers to paste them into a TypeScript file and see the addition result instantly in the editor.