@use 'sass:math';

$PI: 3.14159265359;

@function pow($number, $exp) {
  $value: 1;

  @if $exp > 0 {
    @for $i from 1 through $exp {
      $value: $value * $number;
    }
  } @else if $exp < 0 {
    @for $i from 1 through -$exp {
      $value: $value / $number;
    }
  }

  @return $value;
}

@function fact($number) {
  $value: 1;

  @if $number > 0 {
    @for $i from 1 through $number {
      $value: $value * $i;
    }
  }

  @return $value;
}

// round to number of decimals
// toFixed(0.12345, 100) -> 0.12
// toFixed(0.12345, 1000) -> 0.123
@function toFixed($number, $power) {
  // @return round($number * $power) / $power;
  @return math.div(round($number * $power), $power);
}

@function sin($angle) {
  $sin: 0;

  // angle -> radians
  $rad: $angle / 180 * $PI;

  // interval determines precision
  @for $i from 0 through 25 {
    $sin: $sin + pow(-1, $i) * pow($rad, 2 * $i + 1) / fact(2 * $i + 1);
  }

  @return $sin;
}

@function cos($angle) {
  $cos: 0;

  // angle -> radians
  $rad: $angle / 180 * $PI;

  // interval determines precision
  @for $i from 0 through 25 {
    $cos: $cos + pow(-1, $i) * pow($rad, 2 * $i) / fact(2 * $i);
  }

  @return $cos;
}