acerix / cnum

import {MAX_LOOPS} from './config'

import {ZERO, ONE} from './bigint'

import {Rat} from './Rat'

/**

 * Traverse the tree, returning the rational number that best approximates the floating point number.

 */

export function rationalApproximation(n: number): Rat {

  const r = new Rat(ONE)

  const m = [ONE, ZERO, ZERO, ONE]

  for (let i=0; i<MAX_LOOPS; i++) {

    if (r.approximates(n)) break

    if (+r > n) {

      m[0] += m[1]

      m[2] += m[3]

    }

    else {

      m[1] += m[0]

      m[3] += m[2]

    }

    r.n = m[0] + m[1]

    r.d = m[2] + m[3]

  }

  return r

}

/**

 * Traverse the tree towards the float, yielding false for each left and true for each right.

 */

export function *pathToValue(n: number): Generator<boolean> {

  const r = new Rat(ONE)

  const m = [ONE, ZERO, ZERO, ONE]

  for (let i=0; i<MAX_LOOPS; i++) {

    if (r.approximates(n)) break

    if (+r > n) {

      yield false

      m[0] += m[1]

      m[2] += m[3]

    }

    else {

      yield true

      m[1] += m[0]

      m[3] += m[2]

    }

    r.n = m[0] + m[1]

    r.d = m[2] + m[3]

  }

}

/**

 * Traverse the tree towards the float, yielding the values of the continued fraction, ie. the length of runs left/right.

 */

export function *continuedFraction(n: number): Generator<number> {

  let last = true

  let run = 0

  for (const direction of pathToValue(n)) {

    if (direction === last) {

      run++

    }

    else {

      yield run

      run = 1

      last = direction

    }

  }

}