/**
 * https://github.com/gre/bezier-easing
 * BezierEasing - use bezier curve for transition easing function
 * by Gaëtan Renaudeau 2014 - 2015 – MIT License
 */

// These values are established by empiricism with tests (tradeoff: performance VS precision)
const NEWTON_ITERATIONS = 4
const NEWTON_MIN_SLOPE = 0.001
const SUBDIVISION_PRECISION = 0.0000001
const SUBDIVISION_MAX_ITERATIONS = 10

const kSplineTableSize = 11
const kSampleStepSize = 1.0 / (kSplineTableSize - 1.0)

const float32ArraySupported = typeof Float32Array === 'function'

function A(aA1: number, aA2: number) {
  return 1.0 - 3.0 * aA2 + 3.0 * aA1
}
function B(aA1: number, aA2: number) {
  return 3.0 * aA2 - 6.0 * aA1
}
function C(aA1: number) {
  return 3.0 * aA1
}

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
function calcBezier(aT: number, aA1: number, aA2: number) {
  return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT
}

// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
function getSlope(aT: number, aA1: number, aA2: number) {
  return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1)
}

function binarySubdivide(aX: number, aA: number, aB: number, mX1: number, mX2: number) {
  let currentX: number
  let currentT: number
  let i = 0
  do {
    currentT = aA + (aB - aA) / 2.0
    currentX = calcBezier(currentT, mX1, mX2) - aX
    if (currentX > 0.0) {
      aB = currentT
    } else {
      aA = currentT
    }
  } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS)
  return currentT
}

function newtonRaphsonIterate(aX: number, aGuessT: number, mX1: number, mX2: number) {
  for (let i = 0; i < NEWTON_ITERATIONS; ++i) {
    const currentSlope = getSlope(aGuessT, mX1, mX2)
    if (currentSlope === 0.0) {
      return aGuessT
    }
    const currentX = calcBezier(aGuessT, mX1, mX2) - aX
    aGuessT -= currentX / currentSlope
  }
  return aGuessT
}

function LinearEasing(x: number): number {
  return x
}

export function bezier(
  mX1: number,
  mY1: number,
  mX2: number,
  mY2: number
): (x: number) => number {
  if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) {
    throw new Error('bezier x values must be in [0, 1] range')
  }

  if (mX1 === mY1 && mX2 === mY2) {
    return LinearEasing
  }

  // Precompute samples table
  const sampleValues = float32ArraySupported
    ? new Float32Array(kSplineTableSize)
    : new Array(kSplineTableSize)
  for (let i = 0; i < kSplineTableSize; ++i) {
    sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2)
  }

  function getTForX(aX) {
    let intervalStart = 0.0
    let currentSample = 1
    const lastSample = kSplineTableSize - 1

    for (
      ;
      currentSample !== lastSample && sampleValues[currentSample] <= aX;
      ++currentSample
    ) {
      intervalStart += kSampleStepSize
    }
    --currentSample

    // Interpolate to provide an initial guess for t
    const dist =
      (aX - sampleValues[currentSample]) /
      (sampleValues[currentSample + 1] - sampleValues[currentSample])
    const guessForT = intervalStart + dist * kSampleStepSize

    const initialSlope = getSlope(guessForT, mX1, mX2)
    if (initialSlope >= NEWTON_MIN_SLOPE) {
      return newtonRaphsonIterate(aX, guessForT, mX1, mX2)
    }
    if (initialSlope === 0.0) {
      return guessForT
    }
    return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2)
  }

  return function BezierEasing(x: number) {
    // Because JavaScript number are imprecise, we should guarantee the extremes are right.
    if (x === 0 || x === 1) {
      return x
    }
    return calcBezier(getTForX(x), mY1, mY2)
  }
}