Code tagged with math

An example of accurate math in PHP

// PHP Gregorian date calculation algorithm based on work by Gary Katch
 // http://alcor.concordia.ca/~gpkatch/gdate-algorithm.html
 // http://alcor.concordia.ca/~gpkatch/gdate-c.html

function dayfromdate($year,$month,$day){

  // define as floats
  $m = 0.0;
  $y = 0.0;

  #$m = ($month + 9) % 12;
  #$y = $year - $m/10;

  $m = bcmod(bcadd($month,9),12);
  $y = bcsub($year,(bcdiv($m,10)));

  # Gregorian calendar takes the length of a year to be 365.2425 days:
  # 365.0000 + 0.2500 - 0.0100 + 0.0025
  # or
  # 365 + 1/4 - 1/100 + 1/400 using integers
  # made into a discrete function this is
  # d = 365y + int(y/4) - int(y/100) + int(y/400)  

  // define as floats
  $toreturn = 0.0;
  #$toreturn = $y*365 + $y/4 - $y/100 + $y/400 + $monthoffset +$dayoffset

  $toreturn = bcmul($y,365);
  $toreturn = bcadd($toreturn,bcdiv($y,4));
  $toreturn = bcsub($toreturn,bcdiv($y,100));
  $toreturn = bcadd($toreturn,bcdiv($y,400));

  # month offset
  # length of months are not the same, feb is not fixed
  # so we start the calendar year with March
  # this makes leap days always added on to the end of the year
  # and do not change day offsets for the beginning of the months

  #$monthoffset = ($month*306 + 5) / 10;

  $monthoffset = 0.0;
  $monthoffset = bcdiv(bcadd(bcmul($m,306),5),10);
  $toreturn = bcadd($toreturn,$monthoffset);

  # day offset, start at zero 
  #$dayoffset = $day - 1;

  $dayoffset = 0.0;
  $dayoffset = bcsub($day,1);
  $toreturn = bcadd($toreturn,$dayoffset);

  return $toreturn;
}

function datediff($d1,$d2){
    // this is the main function.
    // takes two dates of the format YYYY-MM-DD
    // and displays the difference in days between the two
    // by calling 'dayfromdate', which does all the math

  $date1 = split('-',$d1);
  $date2 = split('-',$d2);

  $year1 = $date1[0];
  $month1 = $date1[1];
  $day1 = $date1[2];
  $year2 = $date2[0];
  $month2 = $date2[1];
  $day2 = $date2[2];

  $res = 0.0;
  $res =  bcsub(dayfromdate($year1,$month1,$day1),dayfromdate($year2,$month2,$day2));
  $result = (string)$res;
  
  return "$d2 is $result days after $d1
\n"; } function gendate(){ // generate a random gregorian date.. for testing $year = rand(1600,3000); $month = rand(1,12); $day = rand(1,29); if($month < 10){ $tm = "0".$month; }else{ $tm = "".$month; } if($day < 10){ $td = "0".$day; }else{ $td = "".$day; } $d1 = "$year-$tm-$td"; $d2 = array('y' => $year, 'm' => $month,'d' => $day); return array('text-date' => $d1,'num-date' => $d2); } // unit test code - shows it works for arbitary Gregorian dates.. // run it from the command line to test against mysql5's datediff version for($i<0;$i<10;$i++){ $d1 = gendate(); $d2 = gendate(); $dd = datediff($d1['text-date'],$d2['text-date']); echo "[Datediff]" . $dd; # change below to match your local mysql5 test account! :) $con = mysql_connect('localhost','seo','seo'); sleep(1); $res = mysql_query("SELECT DATEDIFF('".$d1['text-date']."','".$d2['text-date']."') as days") or die(mysql_error()); $row = mysql_fetch_array($res); echo "[MySQL] Mysql reports actual difference is = " . $row['days'] ."
\n"; if(!bccomp($row['days'],$dd)){ echo "Doesn't add up.."; break; } echo "--\n"; mysql_close($con); } // here is an example test run, showing it is working: #[Datediff]1710-09-02 is 455209 days after 2956-12-27
#[MySQL] Mysql reports actual difference is = 455209
#-- #[Datediff]2905-02-25 is -466866 days after 1626-12-01
#[MySQL] Mysql reports actual difference is = -466866
#-- #[Datediff]1605-10-23 is 113856 days after 1917-07-16
#[MySQL] Mysql reports actual difference is = 113856
#-- #[Datediff]2401-08-20 is 34469 days after 2496-01-03
#[MySQL] Mysql reports actual difference is = 34469
#-- #[Datediff]1863-09-16 is 16705 days after 1909-06-12
#[MySQL] Mysql reports actual difference is = 16705
#-- #[Datediff]2631-09-06 is 42712 days after 2748-08-15
#[MySQL] Mysql reports actual difference is = 42712
#-- #[Datediff]2714-08-09 is -12026 days after 2681-09-04
#[MySQL] Mysql reports actual difference is = -12026
#-- #[Datediff]1844-11-19 is 229379 days after 2472-11-25
#[MySQL] Mysql reports actual difference is = 229379
#-- #[Datediff]1640-02-11 is 464018 days after 2910-07-21
#[MySQL] Mysql reports actual difference is = 464018
#-- #[Datediff]1779-07-15 is 300513 days after 2602-04-25
#[MySQL] Mysql reports actual difference is = 300513
#--
Language PHP / Tagged with math, dates

Tricks with Infinity

Posted by Chad Humphries about 1 year ago / Source: http://weblog.jamisbuck.org/2007/2/7/infinity
Ruby won’t let you divide an integer by zero—you’ll get an exception. However, thanks to the IEEE 754 standard for floating point numbers, when you try to divide a float by zero you get a rather special value back:
	
puts 1.0/0
#-> Infinity

It’s not a constant though, it’s just how that floating point result is represented as a string. However, you can easily assign that value to a constant:
	
Infinity = 1.0/0

Once you have that, you can use it for all kinds of nifty things; throw it in ranges, use it in comparisons, whatever suits your fancy:

# a rather useless range
everything = -Infinity..Infinity
puts everything.include?(5) #-> true

# use it for representing an unbounded value
storage_limits => { :demo => 0,
  :standard => 250.megabytes,
  :expert => 1.gigabyte,
  :unlimited => Infinity }

if bytes_used < storage_limits[account_level]
  # add another file or something
else
  # display "out of space" message
end
Language Ruby / Tagged with math, infinity