math.scss

// The luminance function requires some math functions be added to sass as shown below
@function luminance($color) {
  // Formula: http://www.w3.org/TR/2008/REC-WCAG20-20081211/#relativeluminancedef
  $rgba: red($color), green($color), blue($color);
  $rgba2: ();

  @for $i from 1 through 3 {
    $rgb: nth($rgba, $i);
    $rgb: $rgb / 255;

    $rgb: if($rgb < .03928, $rgb / 12.92, pow(($rgb + .055) / 1.055, 2.4));

    $rgba2: append($rgba2, $rgb);
  }

  @return .2126 * nth($rgba2, 1) + .7152 * nth($rgba2, 2) + 0.0722 * nth($rgba2, 3);
}


// Greatest common devisor
// From: http://rosettacode.org/wiki/Greatest_common_divisor#JavaScript
@function gcd($a, $b) {
  @if ($b != 0) {
    @return gcd($b, $a % $b);
  } @else {
    @return abs($a);
  }
}

// Handles decimal exponents by trying to convert them into a fraction and then
// use a nthRoot-algorithm for parts of the calculation
@function pow($base, $exponent, $prec: 12) {
  @if (floor($exponent) != $exponent) {
    $prec2 : pow(10, $prec);
    $exponent: round($exponent * $prec2);
    $denominator: gcd($exponent, $prec2);
    @return nthRoot(pow($base, $exponent / $denominator), $prec2 / $denominator, $prec);
  }

  $value: $base;
  @if $exponent > 1 {
    @for $i from 2 through $exponent {
      $value: $value * $base;
    }
  } @else if $exponent < 1 {
    @for $i from 0 through -$exponent {
      $value: $value / $base;
    }
  }

  @return $value;
}

// From: http://rosettacode.org/wiki/Nth_root#JavaScript
@function nthRoot($num, $n: 2, $prec: 12) {
  $x: 1;

  @for $i from 0 through $prec {
    $x: 1 / $n * (($n - 1) * $x + ($num / pow($x, $n - 1)));
  }

  @return $x;
}