foundation-sites/scss/util/_math.scss

// Foundation for Sites by ZURB
// foundation.zurb.com
// Licensed under MIT Open Source

////
/// @group functions
////

/// Finds the greatest common divisor of two integers.
///
/// @param {Number} $a - First number to compare.
/// @param {Number} $b - Second number to compare.
///
/// @returns {Number} The greatest common divisor.
@function gcd($a, $b) {
  // From: http://rosettacode.org/wiki/Greatest_common_divisor#JavaScript
  @if ($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 nth-root-algorithm for parts of the calculation
///
/// @param {Number} $base - The base number.
/// @param {Number} $exponent - The exponent.
///
/// @returns {Number} The product of the exponentiation.
@function pow($base, $exponent, $prec: 16) {
  @if (floor($exponent) != $exponent) {
    $prec2 : pow(10, $prec);
    $exponent: round($exponent * $prec2);
    $denominator: gcd($exponent, $prec2);
    @return nth-root(pow($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;
}

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

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

  @return $x;
}

/// Calculates the height as a percentage of the width for a given ratio.
/// @param {List} $ratio - Ratio to use to calculate the height, formatted as `x by y`.
/// @return {Number} A percentage value for the height relative to the width of a responsive container.
@function ratio-to-percentage($ratio) {
  $w: nth($ratio, 1);
  $h: nth($ratio, 3);
  @return $h / $w * 100%;
}