arithmetic.ts

// ============================================================================
// Fermat.js | Utility Functions
// (c) Mathigon
// ============================================================================


const PRECISION = 0.000001;


// -----------------------------------------------------------------------------
// Checks and Comparisons

/** Checks if two numbers are nearly equals. */
export function nearlyEquals(a: number, b: number, t = PRECISION) {
  if (isNaN(a) || isNaN(b)) return false;
  return Math.abs(a - b) < t;
}

/* Checks if an object is an integer. */
export function isInteger(x: number, t = PRECISION) {
  return nearlyEquals(x, Math.round(x), t);
}

/** Checks if a number x is between two numbers a and b. */
export function isBetween(value: number, a: number, b: number, t = PRECISION) {
  if (a > b) [a, b] = [b, a];
  return value > a + t && value < b - t;
}

/** Returns the sign of a number x, as +1, 0 or –1. */
export function sign(value: number, t = PRECISION) {
  return nearlyEquals(value, 0, t) ? 0 : (value > 0 ? 1 : -1);
}


// -----------------------------------------------------------------------------
// String Conversion

const NUM_REGEX = /(\d+)(\d{3})/;
const POWER_SUFFIX = ['', 'k', 'm', 'b', 't', 'q'];

function addThousandSeparators(x: string) {
  let [n, dec] = x.split('.');
  while (NUM_REGEX.test(n)) {
    n = n.replace(NUM_REGEX, '$1,$2');
  }
  return n + (dec ? `.${dec}` : '');
}

function addPowerSuffix(n: number, places = 6, fixed?: number) {
  if (!places) return fixed !== undefined ? n.toFixed(fixed) : `${n}`;

  // Trim short numbers to the appropriate number of decimal places.
  const digits = (`${Math.abs(Math.floor(n))}`).length;
  const chars = digits + (n < 0 ? 1 : 0);
  if (chars <= places) return fixed !== undefined ? n.toFixed(fixed) : `${round(n, places - chars)}`;

  // Append a power suffix to longer numbers.
  const x = Math.floor(Math.log10(Math.abs(n)) / 3);
  const suffix = POWER_SUFFIX[x];
  const decimalPlaces = places - ((digits % 3) || 3) - (suffix ? 1 : 0) - (n < 0 ? 1 : 0);
  return round(n / Math.pow(10, 3 * x), decimalPlaces) + suffix;
}

/**
 * Converts a number to a clean string, by rounding, adding power suffixes, and
 * adding thousands separators. `places` is the number of digits to show in the
 * result.
 */
export function numberFormat(n: number, places = 0, separators = true, fixed?: number) {
  const str = addPowerSuffix(n, places, fixed).replace('-', '–');
  return separators ? addThousandSeparators(str) : str;
}

export function scientificFormat(value: number, places = 6, fixed?: number) {
  const abs = Math.abs(value);
  if (isBetween(abs, Math.pow(10, -places), Math.pow(10, places))) {
    return numberFormat(value, places, true, fixed);
  }

  // TODO Decide how we want to handle these special cases
  if (abs > Number.MAX_VALUE) return `${Math.sign(value) < 0 ? '–' : ''}∞`;
  if (abs < Number.MIN_VALUE) return fixed !== undefined ? Number(0).toFixed(fixed) : '0';

  const [str, exponent] = value.toExponential().split('e');
  const top = exponent.replace('+', '').replace('-', '–');
  const isNegative = top.startsWith('–');
  return `${str.slice(0, 5)} × 10^${(isNegative ? '(' : '') + top + (isNegative ? ')' : '')}`;
}

// Numbers like 0,123 are decimals, even though they match POINT_DECIMAL.
const SPECIAL_DECIMAL = /^-?0,[0-9]+$/;

// Points as decimal points, Commas as 1k separators, allow starting .
const POINT_DECIMAL = /^-?([0-9]+(,[0-9]{3})*)?\.?[0-9]*$/;

// Commas as decimal points, Points as 1k separators, don't allow starting ,
const COMMA_DECIMAL = /^-?[0-9]+(\.[0-9]{3})*,?[0-9]*$/;

/**
 * Converts a number to a string, including . or , decimal points and
 * thousands separators.
 * @param {string} str
 * @returns {number}
 */
export function parseNumber(str: string) {
  str = str.replace(/^–/, '-').trim();
  if (!str || str.match(/[^0-9.,-]/)) return NaN;

  if (SPECIAL_DECIMAL.test(str)) {
    return parseFloat(str.replace(/,/, '.'));
  }

  if (POINT_DECIMAL.test(str)) {
    return parseFloat(str.replace(/,/g, ''));
  }

  if (COMMA_DECIMAL.test(str)) {
    return parseFloat(str.replace(/\./g, '').replace(/,/, '.'));
  }

  return NaN;
}

/**
 * Converts a number to an ordinal.
 * @param {number} x
 * @returns {string}
 */
export function toOrdinal(x: number) {
  if (Math.abs(x) % 100 >= 11 && Math.abs(x) % 100 <= 13) {
    return `${x}th`;
  }

  switch (x % 10) {
    case 1:
      return `${x}st`;
    case 2:
      return `${x}nd`;
    case 3:
      return `${x}rd`;
    default:
      return `${x}th`;
  }
}

// TODO Translate this function into other languages.

const ONES = ['', 'one', 'two', 'three', 'four', 'five', 'six', 'seven',
  'eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen', 'fourteen',
  'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen'];

const TENS = ['', '', 'twenty', 'thirty', 'forty', 'fifty', 'sixty',
  'seventy', 'eighty', 'ninety'];

const MULTIPLIERS = ['', ' thousand', ' million', ' billion', ' trillion',
  ' quadrillion', ' quintillion', ' sextillion'];

function toWordSingle(number: string) {
  const [h, t, o] = number.split('');
  const hundreds = (h === '0') ? '' : ` ${ONES[+h]} hundred`;
  if (t + o === '00') return hundreds;
  if (+t < 2) return `${hundreds} ${ONES[+(t + o)]}`;
  if (o === '0') return `${hundreds} ${TENS[+t]}`;
  return `${hundreds} ${TENS[+t]}-${ONES[+o]}`;
}

/** Spells a number as an English word. */
export function toWord(n: number) {
  if (n === 0) return 'zero';

  const str = Math.round(Math.abs(n)).toString();
  const chunks = Math.ceil(str.length / 3);

  const padded = str.padStart(3 * chunks, '0');
  let result = '';

  for (let i = 0; i < chunks; i += 1) {
    const chunk = padded.substr(i * 3, 3);
    if (chunk === '000') continue;
    result += toWordSingle(chunk) + MULTIPLIERS[chunks - 1 - i];
  }

  return result.trim();
}


// -----------------------------------------------------------------------------
// Rounding, Decimals and Fractions

/** Returns the digits of a number n. */
export function digits(n: number) {
  const str = `${Math.abs(n)}`;
  return str.split('').reverse().map(x => +x);
}

/** Rounds a number `n` to `precision` decimal places. */
export function round(n: number, precision = 0) {
  const factor = Math.pow(10, precision);
  return Math.round(n * factor) / factor;
}

/** Round a number `n` to the nearest multiple of `increment`. */
export function roundTo(n: number, increment = 1) {
  return Math.round(n / increment) * increment;
}


// -----------------------------------------------------------------------------
// Simple Operations

/** Bounds a number between a lower and an upper limit. */
export function clamp(x: number, min = -Infinity, max = Infinity) {
  return Math.min(max, Math.max(min, x));
}

/** Linear interpolation */
export function lerp(a: number, b: number, t = 0.5) {
  return a + (b - a) * t;
}

/** Squares a number. */
export function square(x: number) {
  return x * x;
}

/** Cubes a number. */
export function cube(x: number) {
  return x * x * x;
}

/**
 * Calculates `a mod m`. The JS implementation of the % operator returns the
 * symmetric modulo. Both are identical if a >= 0 and m >= 0 but the results
 * differ if a or m < 0.
 */
export function mod(a: number, m: number) {
  return ((a % m) + m) % m;
}

/** Calculates the logarithm of `x` with base `b`. */
export function log(x: number, b?: number) {
  return (b === undefined) ? Math.log(x) : Math.log(x) / Math.log(b);
}

/** Solves the quadratic equation a x^2 + b x + c = 0 */
export function quadratic(a: number, b: number, c: number): number[] {
  if (nearlyEquals(a, 0) && nearlyEquals(b, 0)) return [];
  if (nearlyEquals(a, 0)) return [-c / b];

  const p = -b / 2 / a;
  const q = Math.sqrt(b * b - 4 * a * c) / 2 / a;
  return [p + q, p - q];
}

export function polynomial(x: number, coefficients: number[]) {
  let total = 0;
  let xi = 1;

  for (const c of coefficients) {
    total += xi * c;
    xi *= x;
  }

  return total;
}