Add euler's number example

Author: edubart

README.md

@@ -74,8 +74,9 @@ For more usage examples check the
 Some interesting examples there:
 
 * [factorial.lua](https://github.com/edubart/lua-bint/blob/master/examples/factorial.lua) - calculate factorial of 100
-* [fibonnaci.lua](https://github.com/edubart/lua-bint/blob/master/examples/fibonnaci.lua) - calculate the 1001th fibonacci number
-* [pi.lua](https://github.com/edubart/lua-bint/blob/master/examples/pi.lua) - calculate the first 100 pi digits
+* [fibonnaci.lua](https://github.com/edubart/lua-bint/blob/master/examples/fibonnaci.lua) - calculate the 1001th number of the Fibonacci sequence
+* [pi.lua](https://github.com/edubart/lua-bint/blob/master/examples/pi.lua) - calculate the first 100 digits of Pi
+* [e.lua](https://github.com/edubart/lua-bint/blob/master/examples/e.lua) - calculate the first 100 digits of Euler's number
 * [rsa.lua](https://github.com/edubart/lua-bint/blob/master/examples/rsa.lua) - simple RSA example for encrypting/decrypting messages
 
 ## Tests

examples/e.lua

@@ -0,0 +1,19 @@
+-- Compute the first 100 digits of Euler's number
+-- See https://en.wikipedia.org/wiki/E_(mathematical_constant)
+
+local bint = require 'bint'
+
+bint.scale(512)
+
+local digits = 100
+local e = bint.zero()
+local one = bint.ipow(10, digits+10)
+local factorial = bint.one()
+for i=0,digits+10 do
+  e = e + (one // factorial)
+  factorial = factorial * (i+1)
+end
+e = tostring(e)
+e = e:sub(1,1) .. '.' .. e:sub(2, digits+1)
+print(e)
+assert(e == '2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274')