PHP convert decimal into fraction and back?

Question

I want the user to be able to type in a fraction like:

 1/2
 2 1/4
 3

And convert it into its corresponding decimal, to be saved in MySQL,

Answer 1

The fraction to decimal is quite straightforward and there are lots of solutions. I'd go with trimming the string, replacing spaces with '+', and anything other than space,/,. or digits with '' then running it through 'eval'.

The decimal to fraction is virtually impossible to do correctly - not least because your decimal fraction would probably have to be converted to binary first - at which point you loose a lot of precision. As an academic exercise.....If you can live with the difference between 20976/41953 and 1/2 then you could try a fuzzy match for a predefined number of fractions:

(there's probably a neater way of implementing the same algorithm - but I'll leave that as an exercise for the reader).

define('DECIMAL_DIGITS',5);

function decimal_2_frac($inp_decimal)
{
  static $fracs;
  if (!is_array($fracs)) {
    init_fracs($fracs);
  }
  $int_part=(integer)$inp_decimal;
  $inp_decimal=$inp_decimal-$int_part;
  $candidate='';
  $distance=10;
  foreach ($fracs as $decimal=>$frac) {
     if (abs($decimal-$inp_decimal)<$distance) {
       $candidate=$frac;
       $distance=abs($decimal-$inp_decimal);
     }
  if (abs($decimal-$inp_decimal)>$distance) {
     break;
  }
 }
 return $int_part . ' ' . $candidate;
}

function init_fracs(&$fracs)
{
   $fracs=array(); 
   for ($x=2;$x<(5*DECIMAL_DIGITS);$x++) {
       // there's probably a beter way to calculate the loop limit
      for ($y=1; $y<$x; $y++) {
         $decimal=round($y/$x,DECIMAL_DIGITS);
         $frac="$x/$y";
         if (!array_key_exists($decimal,$fracs)) {
         $fracs[$decimal]=$frac;
   }
  }    
 }
}

But personally, I'd just store the original representation in a seperate field in the database.

Answer 2

function frac2dec($fraction) {
    list($whole, $fractional) = explode(' ', $fraction);

    $type = empty($fractional) ? 'improper' : 'mixed';

    list($numerator, $denominator) = explode('/', $type == 'improper' ? $whole : $fractional);

    $decimal = $numerator / ( 0 == $denominator ? 1 : $denominator );

    return $type == 'improper' ? $decimal : $whole + $decimal;
}

Answer 3

I think I'd store the string representation too, as, once you run the math, you're not getting it back!

And, here's a quick-n-dirty compute function, no guarantees:

$input = '1 1/2';
$fraction = array('whole' => 0);
preg_match('/^((?P<whole>\d+)(?=\s))?(\s*)?(?P<numerator>\d+)\/(?P<denominator>\d+)$/', $input, $fraction);
$result = $fraction['whole'] + $fraction['numerator']/$fraction['denominator'];
print_r($result);die;

Oh, for completeness, add a check to make sure $fraction['denominator'] != 0.

Answer 4

To can use PEAR's Math_Fraction class for some of your needs

<?php

include "Math/Fraction.php";

$fr = new Math_Fraction(1,2);


// print as a string
// output: 1/2
echo $fr->toString();

// print as float
// output: 0.5
echo $fr->toFloat();

?>

Answer 5

Little improvement on above, but keepin it simple.

function dec2frac($f) {
  $base = floor($f);
  if ($base) {
    $out = $base . ' ';
    $f = $f - $base;
  }
  if ($f != 0) {
    $d = 1;
    while (fmod($f, 1) != 0.0) {
      $f *= 2;
      $d *= 2;
    }
    $n = sprintf('%.0f', $f);
    $d = sprintf('%.0f', $d);
    $out .= $n . '/' . $d;
  }
  return $out;
}

Answer 6

Just adding a bit more logic to Derek's accepted answer - check for "division by zero" and whole number input check.

function fractionToDec($input) {
    if (strpos($input, '/') === FALSE) {
        $result = $input;
    } else {
        $fraction = array('whole' => 0);
        preg_match('/^((?P<whole>\d+)(?=\s))?(\s*)?(?P<numerator>\d+)\/(?P<denominator>\d+)$/', $input, $fraction);
        $result = $fraction['whole'];

        if ($fraction['denominator'] > 0)
            $result += $fraction['numerator'] / $fraction['denominator'];
    }

    return $result;
}