# pif_LongInt

Double, triple, and quadruple-precision integers, both signed and unsigned. [More]

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Version b1.2.3.20210718
 Date added: Apr 8 2016 Last updated: Jul 19 2021

BETA VERSION. FEATURES ARE INCOMPLETE.

pif_LongInt is a library that implements both signed and unsigned double, triple, and quadruple precision (32-bit, 48-bit, and 64-bit) integers. In this beta version, only 32-bit signed and unsigned double precision integers are available.

As an example of how one could use this library, here is how you could write a function to output binomial coefficients with your desired precision.
```proc/Choose(n, k, type = /pif_LongInt/Unsigned32)  /*   * This method was found at:   * http://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/   */  var/pif_LongInt/Int = new type(1)  if(k > (n-k))    // Choose(n, k) = Choose(n, n-k) so by doing this we reduce the    // number of steps needed.    k = n-k    for(var/i = 0, i <= k-1, i ++)      Int *= n-i      Int /= i+1    return Int
```

Then to test it, we could do
```mob/Login()  ..()  for(var/i = 0, i <= 25, i ++)    world << "<tt>Choose(25, [i])\t=>\t[Choose(25, i, /pif_LongInt/Unsigned32).Print()]</tt>"
```

And this produces the following output.
```Choose(25, 0)    =>      1
Choose(25, 1)    =>      25
Choose(25, 2)    =>      300
Choose(25, 3)    =>      2300
Choose(25, 4)    =>      12650
Choose(25, 5)    =>      53130
Choose(25, 6)    =>      177100
Choose(25, 7)    =>      480700
Choose(25, 8)    =>      1081575
Choose(25, 9)    =>      2042975
Choose(25, 10)   =>      3268760
Choose(25, 11)   =>      4457400
Choose(25, 12)   =>      5200300
Choose(25, 13)   =>      5200300
Choose(25, 14)   =>      4457400
Choose(25, 15)   =>      3268760
Choose(25, 16)   =>      2042975
Choose(25, 17)   =>      1081575
Choose(25, 18)   =>      480700
Choose(25, 19)   =>      177100
Choose(25, 20)   =>      53130
Choose(25, 21)   =>      12650
Choose(25, 22)   =>      2300
Choose(25, 23)   =>      300
Choose(25, 24)   =>      25
Choose(25, 25)   =>      1
```

Upon completion of this library, when a Unsigned64 object is available, one could compute binomial coefficients Choose(n,k) for all 0 ≤ n,k ≤ 67 to perfect accuracy (where the largest in this domain is given by Choose(67, 33) = Choose(67, 34) = 14,226,520,737,620,288,370).

```Copyright (c) 2016-2021 Timothy "popisfizzy" Reilly

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```

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