Convert numbers to custom bases using unique characters and convert back to numbers using custom bases.

fromUniqueBase.js

/**
 * @overload
 * @param {string} uniqueBaseChars
 * @returns {(str: string) => number}
 */
/**
 * @overload
 * @param {string} uniqueBaseChars
 * @param {string} str
 * @returns {number}
 */
/**
 * Converts a custom-base string back into a number.
 * @param {string} uniqueBaseChars 
 * @param {string=} str 
 */
function fromUniqueBase(uniqueBaseChars, str) {
  // Turn unique characters string into an array of characters.
  uniqueBaseChars = [...uniqueBaseChars];

  const len = uniqueBaseChars.length;

  if (!len) {
    throw new Error('You must specify at least one character for the unique characters.');
  }

  if (new Set(uniqueBaseChars).size !== len) {
    throw new Error('Not all of the characters passed are unique.');
  }

  const charToIndex = new Map(uniqueBaseChars.map((c, i) => [c, i]));

  /**
   * @param {string} str
   * @returns {number}
   */
  function fromThisUniqueBase(str) {
    let num = 0;
    for (const char of str) {
      const index = charToIndex.get(char);
      if (index === undefined) {
        throw new Error(`Invalid character: \u201C${char}\u201D`);
      }
      num = num * len + index;
    }
    return num;
  }

  return str === undefined ? fromThisUniqueBase : fromThisUniqueBase(str);
}

toUniqueBase.js

/**
 * @overload
 * @param {string} uniqueBaseChars
 * @returns {(num: number) => string}
 */
/**
 * @overload
 * @param {string} uniqueBaseChars
 * @param {number} num
 * @returns {string}
 */
/**
 * Converts a number to a custom base using the supplied unique characters.
 * @param {string} uniqueBaseChars 
 * @param {number=} num 
 */
function toUniqueBase(uniqueBaseChars, num) {
  // Turn unique characters string into an array of characters.
  uniqueBaseChars = [...uniqueBaseChars];
  
  const len = uniqueBaseChars.length;

  if (!len) {
    throw new Error('You must specify at least one character for the unique characters.');
  }

  if (new Set(uniqueBaseChars).size !== len) {
    throw new Error('Not all of the characters passed are unique.');
  }

  /**
   * @param {number} num
   * @returns {string}
   */
  function toThisUniqueBase(num) {
    if (num === 0) return uniqueBaseChars[0];

    if (num !== Math.floor(num) || num < 0) {
      throw new Error('Number must be non-negative integer.');
    }

    let result = '';
    while (num > 0) {
      const remainder = num % len;
      result = uniqueBaseChars[remainder] + result;
      num = Math.floor(num / len);
    }
    return result;
  }

  return num === undefined ? toThisUniqueBase : toThisUniqueBase(num);
}