mathjs/src/plain/number/arithmetic.js

import { isInteger, log2, log10, cbrt, expm1, sign, toFixed, log1p } from '../../utils/number'

const n1 = 'number'
const n2 = 'number, number'

export function absNumber (a) {
  return Math.abs(a)
}
absNumber.signature = n1

export function addNumber (a, b) {
  return a + b
}
addNumber.signature = n2

export function subtractNumber (a, b) {
  return a - b
}
subtractNumber.signature = n2

export function multiplyNumber (a, b) {
  return a * b
}
multiplyNumber.signature = n2

export function divideNumber (a, b) {
  return a / b
}
divideNumber.signature = n2

export function unaryMinusNumber (x) {
  return -x
}
unaryMinusNumber.signature = n1

export function unaryPlusNumber (x) {
  return x
}
unaryPlusNumber.signature = n1

export function cbrtNumber (x) {
  return cbrt(x)
}
cbrtNumber.signature = n1

export function ceilNumber (x) {
  return Math.ceil(x)
}
ceilNumber.signature = n1

export function cubeNumber (x) {
  return x * x * x
}
cubeNumber.signature = n1

export function expNumber (x) {
  return Math.exp(x)
}
expNumber.signature = n1

export function expm1Number (x) {
  return expm1(x)
}
expm1Number.signature = n1

export function fixNumber (x) {
  return (x > 0) ? Math.floor(x) : Math.ceil(x)
}
fixNumber.signature = n1

export function floorNumber (x) {
  return Math.floor(x)
}
floorNumber.signature = n1

/**
 * Calculate gcd for numbers
 * @param {number} a
 * @param {number} b
 * @returns {number} Returns the greatest common denominator of a and b
 */
export function gcdNumber (a, b) {
  if (!isInteger(a) || !isInteger(b)) {
    throw new Error('Parameters in function gcd must be integer numbers')
  }

  // https://en.wikipedia.org/wiki/Euclidean_algorithm
  let r
  while (b !== 0) {
    r = a % b
    a = b
    b = r
  }
  return (a < 0) ? -a : a
}
gcdNumber.signature = n2

/**
 * Calculate lcm for two numbers
 * @param {number} a
 * @param {number} b
 * @returns {number} Returns the least common multiple of a and b
 */
export function lcmNumber (a, b) {
  if (!isInteger(a) || !isInteger(b)) {
    throw new Error('Parameters in function lcm must be integer numbers')
  }

  if (a === 0 || b === 0) {
    return 0
  }

  // https://en.wikipedia.org/wiki/Euclidean_algorithm
  // evaluate lcm here inline to reduce overhead
  let t
  const prod = a * b
  while (b !== 0) {
    t = b
    b = a % t
    a = t
  }
  return Math.abs(prod / a)
}
lcmNumber.signature = n2

/**
 * Calculate the logarithm of a value.
 * @param {number} x
 * @return {number}
 */
export function logNumber (x) {
  return Math.log(x)
}
logNumber.signature = n1

/**
 * Calculate the 10-base logarithm of a number
 * @param {number} x
 * @return {number}
 */
export function log10Number (x) {
  return log10(x)
}
log10Number.signature = n1

/**
 * Calculate the 2-base logarithm of a number
 * @param {number} x
 * @return {number}
 */
export function log2Number (x) {
  return log2(x)
}
log2Number.signature = n1

/**
 * Calculate the natural logarithm of a `number+1`
 * @param {number} x
 * @returns {number}
 */
export function log1pNumber (x) {
  return log1p(x)
}
log1pNumber.signature = n1

/**
 * Calculate the modulus of two numbers
 * @param {number} x
 * @param {number} y
 * @returns {number} res
 * @private
 */
export function modNumber (x, y) {
  if (y > 0) {
    // We don't use JavaScript's % operator here as this doesn't work
    // correctly for x < 0 and x === 0
    // see https://en.wikipedia.org/wiki/Modulo_operation
    return x - y * Math.floor(x / y)
  } else if (y === 0) {
    return x
  } else { // y < 0
    // TODO: implement mod for a negative divisor
    throw new Error('Cannot calculate mod for a negative divisor')
  }
}
modNumber.signature = n2

/**
 * Calculate the nth root of a, solve x^root == a
 * http://rosettacode.org/wiki/Nth_root#JavaScript
 * @param {number} a
 * @param {number} root
 * @private
 */
export function nthRootNumber (a, root) {
  const inv = root < 0
  if (inv) {
    root = -root
  }

  if (root === 0) {
    throw new Error('Root must be non-zero')
  }
  if (a < 0 && (Math.abs(root) % 2 !== 1)) {
    throw new Error('Root must be odd when a is negative.')
  }

  // edge cases zero and infinity
  if (a === 0) {
    return inv ? Infinity : 0
  }
  if (!isFinite(a)) {
    return inv ? 0 : a
  }

  let x = Math.pow(Math.abs(a), 1 / root)
  // If a < 0, we require that root is an odd integer,
  // so (-1) ^ (1/root) = -1
  x = a < 0 ? -x : x
  return inv ? 1 / x : x

  // Very nice algorithm, but fails with nthRoot(-2, 3).
  // Newton's method has some well-known problems at times:
  // https://en.wikipedia.org/wiki/Newton%27s_method#Failure_analysis
  /*
  let x = 1 // Initial guess
  let xPrev = 1
  let i = 0
  const iMax = 10000
  do {
    const delta = (a / Math.pow(x, root - 1) - x) / root
    xPrev = x
    x = x + delta
    i++
  }
  while (xPrev !== x && i < iMax)

  if (xPrev !== x) {
    throw new Error('Function nthRoot failed to converge')
  }

  return inv ? 1 / x : x
  */
}
nthRootNumber.signature = n2

export function signNumber (x) {
  return sign(x)
}
signNumber.signature = n1

export function sqrtNumber (x) {
  return Math.sqrt(x)
}
sqrtNumber.signature = n1

export function squareNumber (x) {
  return x * x
}
squareNumber.signature = n1

/**
 * Calculate xgcd for two numbers
 * @param {number} a
 * @param {number} b
 * @return {number} result
 * @private
 */
export function xgcdNumber (a, b) {
  // source: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
  let t // used to swap two variables
  let q // quotient
  let r // remainder
  let x = 0
  let lastx = 1
  let y = 1
  let lasty = 0

  if (!isInteger(a) || !isInteger(b)) {
    throw new Error('Parameters in function xgcd must be integer numbers')
  }

  while (b) {
    q = Math.floor(a / b)
    r = a - q * b

    t = x
    x = lastx - q * x
    lastx = t

    t = y
    y = lasty - q * y
    lasty = t

    a = b
    b = r
  }

  let res
  if (a < 0) {
    res = [-a, -lastx, -lasty]
  } else {
    res = [a, a ? lastx : 0, lasty]
  }
  return res
}
xgcdNumber.signature = n2

/**
 * Calculates the power of x to y, x^y, for two numbers.
 * @param {number} x
 * @param {number} y
 * @return {number} res
 */
export function powNumber (x, y) {
  // x^Infinity === 0 if -1 < x < 1
  // A real number 0 is returned instead of complex(0)
  if ((x * x < 1 && y === Infinity) ||
    (x * x > 1 && y === -Infinity)) {
    return 0
  }

  return Math.pow(x, y)
}
powNumber.signature = n2

/**
 * round a number to the given number of decimals, or to zero if decimals is
 * not provided
 * @param {number} value
 * @param {number} decimals       number of decimals, between 0 and 15 (0 by default)
 * @return {number} roundedValue
 */
export function roundNumber (value, decimals = 0) {
  return parseFloat(toFixed(value, decimals))
}
roundNumber.signature = n2

/**
 * Calculate the norm of a number, the absolute value.
 * @param {number} x
 * @return {number}
 */
export function normNumber (x) {
  return Math.abs(x)
}
normNumber.signature = n1