// ____________________________________________________________________________
//
//    Unit Conversion v.2.1.13
//    npm install unitconversion 
//    https://github.com/jakob-e/unitconversion
// ____________________________________________________________________________
//
//   Function               Input units
//
//   Absolute length
//   px(input);             px, pt, pc, in, mm, cm, em, rem, number
//   pt(input);             px, pt, pc, in, mm, cm, em, rem, number
//   pc(input);             px, pt, pc, in, mm, cm, em, rem, number
//   in(input);             px, pt, pc, in, mm, cm, em, rem, number
//   mm(input);             px, pt, pc, in, mm, cm, em, rem, number
//   cm(input);             px, pt, pc, in, mm, cm, em, rem, number
//
//   Relative length
//   em(input);             px, pt, pc, in, mm, cm, em, rem, number
//   rem(input);            px, pt, pc, in, mm, cm, em, rem, number
//   ex(input);             ex, number
//   ch(input);             ch, number
//   vw(input);             vw, number
//   vh(input);             vh, number
//   vmin(input);           vmin, number
//   vmax(input);           vmax, number
//
//   Angle
//   deg(input);            deg, rad, grad, turn, number
//   rad(input);            deg, rad, grad, turn, number
//   grad(input);           deg, rad, grad, turn, number
//   turn(input);           deg, rad, grad, turn, number
//
//   Resolution
//   dpi(input);            dpi, dpcm, dppx, number
//   dpcm(input);           dpi, dpcm, dppx, number
//   dppx(input);           dpi, dpcm, dppx, number
//
//   Time
//   s(input);              s, ms, number
//   ms(input);             s, ms, number
//
//   Frequency
//   hz(input);             hz, khz, number
//   khz(input);            hz, khz, number
//
//   String
//   str(input);            anything not null
//
//   Number, int and uint
//   num(input);            px, pt, pc, in, mm, cm, em, rem, ex, ch,
//                          vw, vh, vmin, vmax, deg, rad, grad, turn,
//                          dpi, dpcm, dppx, s, ms, hz, khz, number
//   int(input);            as number
//   uint(input);           as number
//
//   ratio                  number to fraction
//
//   Aliases
//   string(input);
//   number(input);
//
// ____________________________________________________________________________

// Base font size in pixel for converting em and rem to absolute lengths.
$root-font-size: 16px !default;
$base-font-size: $root-font-size !default;


// Absolute lengths
@function px($input){ @return to-unit(px, $input); }
@function pt($input){ @return to-unit(pt, $input); }
@function pc($input){ @return to-unit(pc, $input); }
@function in($input){ @return to-unit(in, $input); }
@function mm($input){ @return to-unit(mm, $input); }
@function cm($input){ @return to-unit(cm, $input); }

// Angles
@function deg($input){ @return to-unit(deg, $input); }
@function rad($input){ @return to-unit(rad, $input); }
@function grad($input){ @return to-unit(grad, $input); }
@function turn($input){ @return to-unit(turn, $input); }

// Resolution
@function dpi($input){ @return to-unit(dpi, $input); }
@function dpcm($input){ @return to-unit(dpcm, $input); }
@function dppx($input){ @return to-unit(dppx, $input); }

// Time
@function ms($input){ @return to-unit(ms, $input); }
@function s($input){ @return to-unit(s, $input); }

// Frequencies
@function hz($input){ @return to-unit(hz, $input);}
@function khz($input){ @return to-unit(khz, $input); }

// Relative lengths
@function em($input...){
  $em: to-unit(em, nth($input,1));
  // Adjust for compounds (visual size)
  @if length($input) > 1 {
    @for $i from 2 through length($input){
      $em: $em / num(em(nth($input,$i)));
    }
  }
  @return $em;
}
@function rem($input){ @return to-unit(rem, $input); }

// Inconvertible relative lengths – depends on font
@function ex($input){ @return to-unit(ex, $input); }
@function ch($input){ @return to-unit(ch, $input); }

// Viewport
@function vw($input){ @return to-unit(vw, $input); }
@function vh($input){ @return to-unit(vh, $input); }
@function vmin($input){ @return to-unit(vmin, $input); }
@function vmax($input){ @return to-unit(vmax, $input); }

// Strings and numbers
@function str($input){ @return #{$input};  }
@function num($input){
  @if type-of($input) != number {
    @error 'Could not convert `#{$input}` - must be `type-of number`';
    @return null;
  }
  @return $input/($input*0+1);
}
@function int($input){
  $num: num($input);
  @return if($num<0, ceil($num), floor($num));
}
@function uint($input){ @return abs(int($input)); }

// Aliases
@function string($input){ @return str($input);}
@function number($input){ @return num($input);}


// Conversion function
@function to-unit($unit, $input){
  // Test against valid CSS units
  $to-unit: map-get((
      px: 0px, pt: 0pt, pc: 0pc, in: 0in, mm: 0mm, cm: 0cm, // absolute length
      em: 0em, rem: 0rem, ch: 0ch, ex: 0ex,                 // relative length - font based
      vw: 0vw, vh: 0vh, vmin: 0vmin, vmax: 0vmax,           // relative length - viewport based
      deg: 0deg, turn: 0turn, grad: 0grad, rad: 0rad,       // angle
      s: 0s, ms: 0ms,                                       // time
      hz: 0Hz, khz: 0kHz,                                   // frequency
      dpi: 0dpi, dpcm: 0dpcm, dppx: 0dppx,                  // resolution
      pct: 0%, percent: 0%, num: 0, number: 0               // percent or number
  ), $unit);

  // Error handling – wrong $unit
  // Incomparable units are caught in convertion
  @if not $to-unit {
    @error 'Could not convert to `#{$unit}` – must be a valid CSS unit';
    @return null;
  }

  // Number/incomparable conversion
  @if index(num number ex ch vw vh vmin vmax, $unit) {
    $value: num($input);
  }

  // EM convertion using px as base
  @if index(em, unit($input)) {
    $input: 0px + num($input) * $base-font-size/1px;
  }
  @if index(em, $unit) and not unitless($input) {
    $input: 0px + px($input);
    $input: num($input) * 1px/$base-font-size;
  }

  // REM convertion using px as base
  @if index(rem, unit($input)) {
    $input: 0px + num($input) * $root-font-size/1px;
  }
  @if index(rem, $unit) and not unitless($input) {
    $input: 0px + $input;
    $input: num($input) * 1px/$root-font-size;
  }

  // Bug fix – resolution units seems to be flipped
  @if index(dpi dpcm dppx, $unit){
    $units: (dppx: 0dppx, dpcm: 0dpcm, dpi: 0dpi);
    $input-unit: map-get($units, unit($input));
    $input: if(1dppx < 95dpi,num($input-unit + (num($input) + $to-unit)),$input);
  }

  // Convert
  @return $to-unit + $input;
}

//  Convert number to ratio (fraction)
//  ratio(1.7777778) =>   16/9
@function ratio($x, $y: null){
  @if not $y {
    $n: $x; $y: 1;
    @while $y < 10 {
      $x:  $n * 10 - ((10 - $y) * $n);
      @if $x == round($x){ @return #{$x}/#{$y}; }
      @else { $y: $y + 1; }
    }
    $x: round($n * 1000000); $y: 1000000;
    @while $x % 10 == 0 { $x: $x/10; $y: $y/10; }
    @while $x % 5 == 0 { $x: $x/5; $y: $y/5; }
    @while $x % 2 == 0 { $x: $x/2; $y: $y/2; }
    @return #{$x}/#{$y};
  }
  @else if $x == round($x) and $y == round($y){ @return #{$x}/#{$y}; }
  @warn 'X and Y must be integers'; @return false;
}