Some fun with arbitrary base numbers (with specific tests for base PI)

basePi.ts

describe('convert number to arbitrary base-system coefficients', () => {

  const truncateToFixed = (num: number, maxFractionalDigits: number): number => {
    const multiplier = Math.pow(10, maxFractionalDigits);
    return Math.floor(num * multiplier) / multiplier;
  }

  const toBaseCoefficients = (num: number, base: number): (number | '.')[] => {
    const maxFractionalDigits = 10; 
    let coefficients = []; 
    let i = Math.ceil(Math.log(num) / Math.log(base));

    while (
      i >= 0 ||
      (i >= -1 * maxFractionalDigits && truncateToFixed(num, maxFractionalDigits) !== 0)
    ) { 
      if (i === -1) {
        coefficients.push('.');
      }   

      const base_i = Math.pow(base, i); 
      const a_i = Math.floor(num / base_i);
      num = num - (a_i * base_i);

      if (!(coefficients.length === 0 && a_i === 0)) {
        // Don't push leading zeroes
        coefficients.push(a_i);
      }   
      i--;
    }   
    return coefficients;
  };  

  it('should convert 0 base 10 to 0 base 2', () => {
    expect(toBaseCoefficients(0, 2)).toEqual([]);
  }); 

  it('should convert 10 base 10 to 1010 base 2', () => {
    expect(toBaseCoefficients(10, 2)).toEqual([ 1, 0, 1, 0 ]); 
  }); 

  it('should convert 10 base 10 to A base 16', () => {
    expect(toBaseCoefficients(10, 16)).toEqual([ 10 ]); 
  }); 

  it('should do something with base pi', () => {
    expect(toBaseCoefficients(2 * Math.PI, Math.PI)).toEqual([ 2, 0 ]); 
  }); 

  it('should do something else with base pi', () => {
    expect(toBaseCoefficients(10, Math.PI)).toEqual([ 1, 0, 0, '.', 0, 1, 0, 2, 2, 1, 2, 2, 2, 2 ]); 
  }); 

  it('should handle fractions', () => {
    expect(toBaseCoefficients(1.12345, 10)).toEqual([ 1, '.', 1, 2, 3, 4, 5 ]); 
  }); 
});