Ytdyklly

I have written code in Kotlin with the objective of computing Pi in few enough lines so that it looks good on a t-shirt.

Can be cut and paste into http://try.kotlinlang.org under "My Programs" and run from browser - I just tested it with version 1.2.41 and it's working.

import kotlin.math.*

import java.math.BigInteger 



fun main(args: Array<String>) { 

  val r = (4*(4*arccot(5) - arccot(239))).toString()

  println("314 digits of Pi ${r[0]}.${r.substring(1).dropLast(5)}")

}



fun arccot(x:BigInteger):BigInteger {

  var precision = 10.toBigInteger().pow(319) / x

  var total = precision

  var divisor = 1.toBigInteger()



  while(precision.abs() >= divisor) {

    precision = -precision / x.pow(2)

    divisor += 2

    total += precision / divisor

  }

  return total

}



fun arccot(x:Int) = arccot(x.toBigInteger())

operator fun Int.times(x: BigInteger) = this.toBigInteger() * x

operator fun BigInteger.plus(x: Int) = this + x.toBigInteger()

Currently it's longer than I'd like. I would like to shorten without making it less understandable. My vision is to have code that is readable enough it wouldn't be out of place in a production code base.

To give an idea, here's the significantly shorter Python version (which has been printed on a t-shirt and in my opinion looks good and is short enough but also quite readable). Can be run in browser here: https://repl.it/@sek/314-Digits - (there's also a link from there to the t-shirt if you are curious how that looks - the length in question isn't only the number of lines but also the width of the longest line as that determines the font size that can be used)

def pi():

  r = 4*(4*arccot(5) - arccot(239))

  return str(r)[0]+'.'+str(r)[1:-5]



def arccot(x):

  total = power = 10**319 // x

  divisor = 1

  while abs(power) >= divisor:

    power = -power // x**2

    divisor += 2

    total += power // divisor

  return total



print("314 digits of Pi " + pi())

I noticed that you are calculating to 314 decimal places instead of 314 digits, so drop 6 instead of 5.

• 
  

  You really don't need the extra functions. You can remove

  
  
  

  fun arccot(x:Int) = arccot(x.toBigInteger())
  
  

  
  
  

  if you convert Int to BigInteger inside your arctan method.

  
  


• 
  

  You can remove

  
  
  

  operator fun Int.times(x: BigInteger) = this.toBigInteger() * x
  
  

  
  
  

  if you shl(2) instead of * 4.

  
  


• 
  

  You can remove

  
  
  

  operator fun BigInteger.plus(x: Int) = this + x.toBigInteger()
  
  

  
  
  

  if you change

  
  
  

  divisor += 2
  
  

  
  
  

  to

  
  
  

  divisor += BigInteger("2")
  
  

  
  


• 
  

  You can shorten

  
  
  

  println("314 digits of Pi ${r[0]}.${r.substring(1).dropLast(5)}")
  
  

  
  
  

  to

  
  
  

  println("314 digits of Pi ${r[0]}.${r.substring(1,314)}")
  
  

  
  


• 
  

  Now, you can change the imports to

  
  
  

  import java.math.*
  
  

  
  



• You don't have to declare the type for val r.

The final code I came up with by doing that is:

import java.math.*

fun main(args: Array<String>) {

  val r = (acot(5).shl(2)-acot(239)).shl(2).toString()

  println("314 digits of Pi ${r[0]}.${r.substring(1,314)}")

}

fun acot(x:Int):BigInteger {

  var precision = BigInteger.TEN.pow(319)/x.toBigInteger()

  var total = precision

  var divisor = BigInteger.ONE;

  while(precision.abs() >= divisor) {

    precision = -precision/(x.toBigInteger().pow(2))

    divisor += BigInteger("2")

    total += precision / divisor

  }

  return total

}

I also came up with shorter code, with decreased width, by calculating a different way:

import java.math.*

fun main(args:Array<String>) {

  val b4 = BigDecimal(4)

  val r = ((atan(5)*b4-atan(239))*b4).toString()

  println("314 digits of Pi ${r.substring(0,315)}")

}

fun atan(xInv:Int):BigDecimal {

  var x = BigDecimal(1).divide(BigDecimal(xInv),330,3)

  var (numer, total) = arrayOf(x, x)

  for (i in 3..450 step 2) {

    numer = -numer * x * x

    total += numer / BigDecimal(i)

  }

  return total

}