package funkin.util;

/**
 * Utilities for performing mathematical operations.
 */
class MathUtil
{
  /**
   * Euler's constant and the base of the natural logarithm.
   * Math.E is not a constant in Haxe, so we'll just define it ourselves.
   */
  public static final E:Float = 2.71828182845904523536;

  /**
   * Perform linear interpolation between the base and the target, based on the current framerate.
   * @param base The starting value, when `progress <= 0`.
   * @param target The ending value, when `progress >= 1`.
   * @param ratio Value used to interpolate between `base` and `target`.
   *
   * @return The interpolated value.
   */
  @:deprecated('Use smoothLerp instead')
  public static function coolLerp(base:Float, target:Float, ratio:Float):Float
  {
    return base + cameraLerp(ratio) * (target - base);
  }

  /**
   * Perform linear interpolation based on the current framerate.
   * @param lerp Value used to interpolate between `base` and `target`.
   *
   * @return The interpolated value.
   */
  @:deprecated('Use smoothLerp instead')
  public static function cameraLerp(lerp:Float):Float
  {
    return lerp * (FlxG.elapsed / (1 / 60));
  }

  /**
   * Get the logarithm of a value with a given base.
   * @param base The base of the logarithm.
   * @param value The value to get the logarithm of.
   * @return `log_base(value)`
   */
  public static function logBase(base:Float, value:Float):Float
  {
    return Math.log(value) / Math.log(base);
  }

  /**
   * Get the base-2 logarithm of a value.
   * @param x value
   * @return `2^x`
   */
  public static function exp2(x:Float):Float
  {
    return Math.pow(2, x);
  }

  /**
   * Linearly interpolate between two values.
   *
   * @param base The starting value, when `progress <= 0`.
   * @param target The ending value, when `progress >= 1`.
   * @param progress Value used to interpolate between `base` and `target`.
   * @return The interpolated value.
   */
  public static function lerp(base:Float, target:Float, progress:Float):Float
  {
    return base + progress * (target - base);
  }

  /**
   * Perform a framerate-independent linear interpolation between the base value and the target.
   * @param current The current value.
   * @param target The target value.
   * @param elapsed The time elapsed since the last frame.
   * @param duration The total duration of the interpolation. Nominal duration until remaining distance is less than `precision`.
   * @param precision The target precision of the interpolation. Defaults to 1% of distance remaining.
   * @see https://twitter.com/FreyaHolmer/status/1757918211679650262
   *
   * @return A value between the current value and the target value.
   */
  public static function smoothLerp(current:Float, target:Float, elapsed:Float, duration:Float, precision:Float = 1 / 100):Float
  {
    // An alternative algorithm which uses a separate half-life value:
    // var halfLife:Float = -duration / logBase(2, precision);
    // lerp(current, target, 1 - exp2(-elapsed / halfLife));

    if (current == target) return target;

    var result:Float = lerp(current, target, 1 - Math.pow(precision, elapsed / duration));

    // TODO: Is there a better way to ensure a lerp which actually reaches the target?
    // Research a framerate-independent PID lerp.
    if (Math.abs(result - target) < (precision * target)) result = target;

    return result;
  }
}