Auto extending mixin based on GCD of width ratios

SassMeister-input.scss

// ----
// Sass (v3.4.6)
// Compass (v1.0.1)
// ----

// auto-extending includes for width ratios
// determines match by reducing argument fraction

@function gcd($a, $b) {
  @if $b == 0 { @return abs($a); }
  @return gcd($b, $a % $b);
}

@function reduce($n, $d) {
  $g: gcd($n, $d);
  @return ($n/$g, $d/$g)
}

@mixin col-size($n, $d) {
  @if not variable-exists(col-size) { $col-size: () !global; }
  $args: reduce($n, $d); $id: map-get($col-size, $args);
  @if $id { @extend %#{$id}; }
  @else {
    $id: unique-id();
    $col-size: map-merge($col-size, ($args: $id)) !global;
    @at-root { %#{$id} { width: percentage($n / $d); } }
    @extend %#{$id};
  }
}

.foo { @include col-size(1, 2); }
.bar { @include col-size(5, 10); }
.baz { @include col-size(3, 4); }
.bif { @include col-size(9, 12); }

.debug { out: inspect($col-size); }

SassMeister-output.css

.foo, .bar {
  width: 50%;
}

.baz, .bif {
  width: 75%;
}

.debug {
  out: ((1, 2): u0n11365f, (3, 4): u0n11365i);
}