PHP convert decimal into fraction and back?

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, that way I can orde开发者_Python百科r by it and do other comparisons to it.

But I need to be able to convert the decimal back to a fraction when showing to the user

so basically I need a function that will convert fraction string to decimal:

fraction_to_decimal("2 1/4");// return 2.25

and a function that can convert a decimal to a faction string:

decimal_to_fraction(.5); // return "1/2"

How can I do this?

Sometimes you need to find a way to do it and rounding is acceptable. So if you decide what range of rounding works out for you you can build a function like this. To convert a decimal into the fraction that it most closely matches. You can extend the accuracy by adding more denominators to be tested.

function decToFraction($float) {
    // 1/2, 1/4, 1/8, 1/16, 1/3 ,2/3, 3/4, 3/8, 5/8, 7/8, 3/16, 5/16, 7/16,
    // 9/16, 11/16, 13/16, 15/16
    $whole = floor ( $float );
    $decimal = $float - $whole;
    $leastCommonDenom = 48; // 16 * 3;
    $denominators = array (2, 3, 4, 8, 16, 24, 48 );
    $roundedDecimal = round ( $decimal * $leastCommonDenom ) / $leastCommonDenom;
    if ($roundedDecimal == 0)
        return $whole;
    if ($roundedDecimal == 1)
        return $whole + 1;
    foreach ( $denominators as $d ) {
        if ($roundedDecimal * $d == floor ( $roundedDecimal * $d )) {
            $denom = $d;
            break;
        }
    }
    return ($whole == 0 ? '' : $whole) . " " . ($roundedDecimal * $denom) . "/" . $denom;
}

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.

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();

?>

Here is a solution that first determines a valid fraction (although not necessarily the simplest fraction). So 0.05 -> 5/100. It then determines the greatest common divisor of the numerator and denominator to reduce it down to the simplest fraction, 1/20.

function decimal_to_fraction($fraction) {
  $base = floor($fraction);
  $fraction -= $base;
  if( $fraction == 0 ) return $base;
  list($ignore, $numerator) = preg_split('/\./', $fraction, 2);
  $denominator = pow(10, strlen($numerator));
  $gcd = gcd($numerator, $denominator);
  $fraction = ($numerator / $gcd) . '/' . ($denominator / $gcd);
  if( $base > 0 ) {
    return $base . ' ' . $fraction;
  } else {
    return $fraction;
  }
}

# Borrowed from: http://www.php.net/manual/en/function.gmp-gcd.php#69189
function gcd($a,$b) {
  return ($a % $b) ? gcd($b,$a % $b) : $b;
}

This includes a pure PHP implementation of the gcd although if you are sure the gmp module is installed you could use the one that comes with gcd.

As many others have noted you need to use rational numbers. So if you convert 1/7 to a decimal then try to convert it back to a decimal you will be out of luck because the precision lost will prevent it from getting back to 1/7. For my purposes this is acceptable since all the numbers I am dealing with (standard measurements) are rational numbers anyway.

Buddies, can this help?

[]s

function toFraction($number) {
    if (!is_int($number)) {
        $number = floatval($number);
        $denominator = round(1 / $number);

        return "1/{$denominator}";
    }
    else {
        return $number;
    }
}

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;
}

An approach would be to retrieve the decimal value and multiply it by 2, 3, 4 and so on until you get an integer number.

However, I'd stick with the answer given by Derek. Guess what happens when a user inserts n/(n+1) with n high. Such an algorithm would have to scan all the numbers up to n+1. Not to mention it is likely you'll end up with approximation problems.

You'll have to face a serious problem, because floats are not precise enough.

When you'll have to deal with 1.3333, PHP will make an estimate of this value... So you will never be able to convert it to 1 1/3.

It seems to be simple to overcome, but if you want your program to differentiate 1/7901 (~ 1,2656625743576762435134793064169e-4) with 1/7907 (~ 1,2647021626406981155937776653598e-4) precisely... this will be a real hell !!

IMHO, if you want to deal with maths, you should rely on an external library... or try to make PHP communicate with Matlab.

If you want to know more, i suggest you dig in floating point problems... Starting with wikipedia.

A variation of Jir's approach could actually work if only a limited amount of denominators are used : multiply everything by the least common denominators (and round the result to discard any remaining decimals due to approximation).

I.e.: if you only have to deal with halfs, thrids and quarters, just multiply everything by 12.

And also if you know the common denominator, this should greatly reduce the search speed by knowing exactly which numbers to search instead of searching all n+1 possible.

If you have to deal with lots of unusual fractions, like 1/7, 1/13, etc. well, stick to Derek's solution and store the original value too.

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.

function dec2frac($f)
{
    $d = 1

    while (fmod($f, 1) != 0.0) {
        $f *= 2;
        $d *= 2;
    }

    $n = sprintf('%.0f', $f);
    $d = sprintf('%.0f', $d);

    return array($n, $d);
}

Then $f == $n / $d

For example:

print_r(dec2frac(3.1415926));

Outputs:

Array
(
    [0] => 3537118815677477  // $n
    [1] => 1125899906842624  // $d
)

I made a blog post with a couple solutions for this, the most recent approach I took is: http://www.carlosabundis.com/2014/03/25/converting-decimals-to-fractions-with-php-v2/

    function dec2fracso($dec){
    //Negative number flag.
    $num=$dec;
    if($num<0){
        $neg=true;
    }else{
        $neg=false;
    }

    //Extracts 2 strings from input number
    $decarr=explode('.',(string)$dec);

    //Checks for divided by zero input.
    if($decarr[1]==0){
        $decarr[1]=1;
        $fraccion[0]=$decarr[0];
        $fraccion[1]=$decarr[1];
        return $fraccion;
    }

    //Calculates the divisor before simplification.
    $long=strlen($decarr[1]);
    $div="1";
    for($x=0;$x<$long;$x++){
        $div.="0";
    }

    //Gets the greatest common divisor.
    $x=(int)$decarr[1];
    $y=(int)$div;
    $gcd=gmp_strval(gmp_gcd($x,$y));

    //Calculates the result and fills the array with the correct sign.
    if($neg){
        $fraccion[0]=((abs($decarr[0])*($y/$gcd))+($x/$gcd))*(-1);
    }else{
        $fraccion[0]=(abs($decarr[0])*($y/$gcd))+($x/$gcd);
    }
    $fraccion[1]=($y/$gcd);
    return $fraccion;
}

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;
}

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;
}

Use a 3rd party library, for example: https://packagist.org/packages/phospr/fraction

Usage:

$fraction = Fraction::fromFloat(1.5);
echo "Fraction is: " . $fraction->getNumerator() . '/' . $fraction->getDenominator();
echo "Float is: " . $fraction->toFloat();

I usually do a quick search on https://packagist.org to see if something already exists to solve what I'm trying to do, if so then I can take advantage of the many hours that the community have already put into solving the problem (this will be much much more time than I'll be able to dedicate to it) and it will also be more likely to be bug free, having been battle tested by others and maybe even have a test suite covering it.

Saves time and results in higher quality.