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The reason the bitwise AND ("&") operator works to determine whether a number is odd or even is because odd numbers expressed in binary always have the rightmost (2^0) bit = 1 and even numbers always have the 2^0 bit = 0.

So if you do a " 1 & $num", it will return zero if the number is even (since xxxxxxx0 [the even number in binary] and 00000001 [the 1]) don't share any bits, and will return 1 if the number is odd (xxxxxx01).a clever way of doing things, but$num % 2 would work as well i think :). Here is a further modified version which should work for all numbers.

This won't work on floating point numbers accurately though.

If you want a floating point one, you need to have at least PHP 4, and the code would befunction gcd($n,$m) Please note that shorter is not always better (meaning that really short faculty implementation above).

Der Ableitungsrechner kann die erste, zweite, …, fünfte Ableitung berechnen.

Ableitungen von Funktionen mit mehreren Variablen (partielle Ableitungen), implizite Ableitungen sowie die Berechnung von Nullstellen sind kein Problem. Interaktive Funktionsgraphen erleichtern das Verständnis. Mehr zur Bedienung des Ableitungsrechners gibt's unter "

If you need to deal with polar co-ordinates for somereason you will need to convert to and from x,y for input and output in most situations: here are some functions to convert cartesian to polar and polar to cartesian To add to what Cornelius had, I have written a function that will take an array of numbers and return the least common multiple of them:function lcm_arr($items)//His Code below with$'s added for varsfunction gcd($n,$m) function lcm($n,$m) If you're an aviator and needs to calculate windcorrection angles and groundspeed (e.g. $windcorrection = rad2deg(asin((($windspeed * (sin(deg2rad($tt - ($winddirection-180))))/$tas))));$groundspeed = $tas*cos(deg2rad($windcorrection)) $windspeed*cos(deg2rad($tt-($winddirection-180))); You can probably write these lines more beautiful, but they work!Tim's fix of Evan's ordinal function causes another problem, it no longer works for number above 100. If you're really concerned about speed, you could compute the factorial of large numbers using the Gamma function of n-1.Integral y^(t-1)*Exp(-y) for y from 0 to Infinity For Fibonacci numbers, there's a better-than-recursive way.((1 sqrt(5))/2)^(n/sqrt(5)) - ((1-sqrt(5))/2)^(n/sqrt(5)) I found that when dealing with tables, a 'least common multiple' function is sometimes useful for abusing tablespan and the likes.Here is how to calculate standard deviation in PHP where$samples is an array of incrementing numeric keys and the values are your samples:$sample_count = count($samples);for ($current_sample = 0;$sample_count $current_sample;$current_sample) $sample_square[$current_sample] = pow($samples[$current_sample], 2);$standard_deviation = sqrt(array_sum($sample_square) / $sample_count - pow((array_sum($samples) / $sample_count), 2)); Here's yet another greatest common denominator (gcd) function, a reeeeally small one.function gcd($n,$m)It works by recursion.Not really sure about it's speed, but it's really small! .7x$ $-\fracx$ $x 1$ $x-1$ $-x$ $x^2$ $\frac$ $a(x^2 b)$ $a_1x a_2$ $x^$ $\mathrm^$ $\sqrt$ $\sqrt[7]$ $\ln(x)$ $\log_(x)$ $|x|$ $\sin(x)$ $\cos(x)$ $\tan(x)$ $\arcsin(x)$ $\arccos(x)$ $\arctan(x)$ $\sec(x)$ $\sinh(x)$ $\operatorname(x)$ $\operatorname(x)$ $\operatorname(x,y)$ $\operatorname(x)$ $\operatorname(x)$ $\mathrm$ $\mathrm$ $\mathrm$ Mit dem Aufgabengenerator kannst du dir beliebig viele zufällige Übungsaufgaben generieren.

If you need to deal with polar co-ordinates for somereason you will need to convert to and from x,y for input and output in most situations: here are some functions to convert cartesian to polar and polar to cartesian To add to what Cornelius had, I have written a function that will take an array of numbers and return the least common multiple of them:function lcm_arr($items)//His Code below with$'s added for varsfunction gcd($n,$m) function lcm($n,$m) If you're an aviator and needs to calculate windcorrection angles and groundspeed (e.g. $windcorrection = rad2deg(asin((($windspeed * (sin(deg2rad($tt - ($winddirection-180))))/$tas))));$groundspeed = $tas*cos(deg2rad($windcorrection)) $windspeed*cos(deg2rad($tt-($winddirection-180))); You can probably write these lines more beautiful, but they work! Tim's fix of Evan's ordinal function causes another problem, it no longer works for number above 100. If you're really concerned about speed, you could compute the factorial of large numbers using the Gamma function of n-1. Integral y^(t-1)*Exp(-y) for y from 0 to Infinity For Fibonacci numbers, there's a better-than-recursive way.((1 sqrt(5))/2)^(n/sqrt(5)) - ((1-sqrt(5))/2)^(n/sqrt(5)) I found that when dealing with tables, a 'least common multiple' function is sometimes useful for abusing tablespan and the likes. Here is how to calculate standard deviation in PHP where$samples is an array of incrementing numeric keys and the values are your samples:$sample_count = count($samples);for ($current_sample = 0;$sample_count $current_sample;$current_sample) $sample_square[$current_sample] = pow($samples[$current_sample], 2);$standard_deviation = sqrt(array_sum($sample_square) / $sample_count - pow((array_sum($samples) / $sample_count), 2)); Here's yet another greatest common denominator (gcd) function, a reeeeally small one.function gcd($n,\$m)It works by recursion.

Not really sure about it's speed, but it's really small!