--- a/README	Sat Dec 16 23:53:28 2017 +0000
+++ b/README	Mon Jan 15 23:15:34 2018 +0000
@@ -1,7 +1,13 @@
+
+CW8A
+
+(1) There is an ontime submission (with full marks) by
+    assignment20178-fahim1997, but no late submission?
 
 
 
 
+==================================
 Calling ediff from the command line
 
 

--- a/TAs	Sat Dec 16 23:53:28 2017 +0000
+++ b/TAs	Mon Jan 15 23:15:34 2018 +0000
@@ -40,4 +40,18 @@
 6    => 1    (6)
 15   => 0    (16)
 ---------
-272 submissions
\ No newline at end of file
+272 submissions
+
+
+
+CW8, Part1 (6 marks)         Part 2 (4 Marks)
+            (late)                      (late)
+101  => 6   (101)            180 => 4   (179)
+2    => 5   (2)                1 => 3   (1)
+125  => 4   (125)             11 => 2   (11)
+8    => 3   (8)               18 => 1   (18)
+14   => 2   (14)              63 => 0   (63)
+4    => 1   (5)
+15   => 0   (14)
+---------                    ----------
+269 submissions              273 submissions (272)
\ No newline at end of file

Binary file cws/cw01.pdf has changed

--- a/cws/cw01.tex	Sat Dec 16 23:53:28 2017 +0000
+++ b/cws/cw01.tex	Mon Jan 15 23:15:34 2018 +0000
@@ -308,6 +308,9 @@
   \frac{price_{new} - price_{old}}{price_{old}}
   \]
 
+  If the change factor is defined, you should return it
+  as \texttt{Some(change factor)}; if not, you should return
+  \texttt{None}.
   
 \item[(2.b)] Write a function that calculates all change factors
   (deltas) for the prices we obtained under Task 1. For the running
@@ -320,7 +323,9 @@
 \end{verbatim}
 
   That means Google did a bit badly in 2010, while Apple did very well.
-  Both did OK in 2011.\\
+  Both did OK in 2011. Make sure you handle the cases where a company is
+  not listed in a year. In such cases the change factor should be \texttt{None}
+  (see 2.a).\\
   \mbox{}\hfill\mbox{[1 Mark]}
 
 \item[(3.a)] Write a function that calculates the ``yield'', or

--- a/handouts/scala-ho.tex	Sat Dec 16 23:53:28 2017 +0000
+++ b/handouts/scala-ho.tex	Mon Jan 15 23:15:34 2018 +0000
@@ -6,6 +6,10 @@
 %cheat sheet
 %http://worldline.github.io/scala-cheatsheet/
 
+% case class, apply, unappy
+% see https://medium.com/@thejasbabu/scala-pattern-matching-9c9e73ba9a8a
+
+
 \begin{document}
 
 \section*{A Crash-Course on Scala}

--- a/progs/lecture2.scala	Sat Dec 16 23:53:28 2017 +0000
+++ b/progs/lecture2.scala	Mon Jan 15 23:15:34 2018 +0000
@@ -295,6 +295,41 @@
 sum(add(10), 0, 2)
 
 
+
+
+// some automatic timing in each evaluation
+package wrappers {  
+
+  object wrap { 
+   
+    def timed[R](block: => R): R = {
+      val t0 = System.nanoTime()
+      val result = block
+      println("Elapsed time: " + (System.nanoTime - t0) + "ns")
+      result
+    }
+
+    def apply[A](a: => A): A = { 
+      timed(a)
+    } 
+  }
+}
+
+$intp.setExecutionWrapper("wrappers.wrap")
+
+// Iteration
+
+def fib(n: Int) : Int = 
+  if (n <= 1) 1 else fib(n - 1) + fib(n - 2)
+
+fib(10)
+
+
+Iterator.iterate((1,1)){ case (n: Int, m: Int) => (n + m, n) }.drop(9).next
+
+
+
+
 // Function Composition
 //======================
 

--- a/progs/mandelbrot.scala	Sat Dec 16 23:53:28 2017 +0000
+++ b/progs/mandelbrot.scala	Mon Jan 15 23:15:34 2018 +0000
@@ -75,8 +75,8 @@
   val delta_x = (end.a - start.a) / W
   val delta_y = (end.b - start.b) / H
    
-  for (y0 <- (0 until H).par) {
-    for (x0 <- (0 until W).par) {
+  for (y0 <- (0 until H)) {
+    for (x0 <- (0 until W)) {
     
      val c = start + Complex(x0 * delta_x, y0 * delta_y)
 
@@ -124,10 +124,21 @@
 // some more computations with example 3
 val delta = (exc2 - exc1) * 0.0333
 
-//time_needed(
-//  for (i <- (0 to 12)) 
-//     mandelbrot(exc1 + delta * i, 
-//                exc2 - delta * i, 1000))
+time_needed(
+  for (i <- (0 to 12)) 
+     mandelbrot(exc1 + delta * i, 
+                exc2 - delta * i, 1000))val exc1 = Complex(0.435396403, 0.367981352)
+val exc2 = Complex(0.451687191, 0.380210061)
+
+//time_needed(mandelbrot(exc1, exc2, 1000))
+
+// some more computations with example 3
+val delta = (exc2 - exc1) * 0.0333
+
+time_needed(
+  for (i <- (0 to 12)) 
+     mandelbrot(exc1 + delta * i, 
+                exc2 - delta * i, 1000))
 
 
 

--- a/testing1/collatz.scala	Sat Dec 16 23:53:28 2017 +0000
+++ b/testing1/collatz.scala	Mon Jan 15 23:15:34 2018 +0000
@@ -1,5 +1,7 @@
 // Part 1 about the 3n+1 conjecture
 //==================================
+package CW6a 
+
 
 object CW6a {
 
@@ -18,3 +20,4 @@
 
 }
 
+

--- a/testing1/drumb.scala	Sat Dec 16 23:53:28 2017 +0000
+++ b/testing1/drumb.scala	Mon Jan 15 23:15:34 2018 +0000
@@ -45,10 +45,10 @@
 
 
 // test case
-val prices_fb    = get_prices(List("FB"), 2012 to 2014)
-val prices_goap = get_prices(List("GOOG", "AAPL"), 2010 to 2014)
-val prices_bidu = get_prices(List("BIDU"), 2004 to 2008)
-val prices_goapfb = get_prices(List("GOOG", "AAPL", "FB"), 2010 to 2016)
+val p_fb = get_prices(List("FB"), 2012 to 2014)
+val p = get_prices(List("GOOG", "AAPL"), 2010 to 2012)
+
+val tt = get_prices(List("BIDU"), 2004 to 2008)
 
 // (2) The first function below calculates the change factor (delta) between
 // a price in year n and a price in year n+1. The second function calculates
@@ -67,11 +67,8 @@
 
 
 // test case using the prices calculated above
-val deltas_fb   = get_deltas(prices_fb)
-val deltas_goap = get_deltas(prices_goap)
-val deltas_bidu = get_deltas(prices_bidu)
-val deltas_goapfb = get_deltas(prices_goapfb)
-
+val d = get_deltas(p)
+val ttd = get_deltas(tt)
 
 // (3) Write a function that given change factors, a starting balance and a year
 // calculates the yearly yield, i.e. new balanace, according to our dump investment 
@@ -87,85 +84,17 @@
   if (somes_length == 0) balance
   else {
     val portion: Double = balance.toDouble / somes_length.toDouble
-    (for (x <- somes) yield ((1.0 + x) * portion)).sum.toLong
-    //balance + (for (x <- somes) yield (x * portion)).sum.toLong
-  }
-}
-
-def yearly_yield_double(data: List[List[Option[Double]]], balance: Double, year: Int): Double = {
-  val somes = data(year).flatten
-  val somes_length = somes.length
-  if (somes_length == 0) balance
-  else {
-    val portion: Double = balance / somes_length.toDouble
-    balance + (for (x <- somes) yield (x * portion)).sum
+    balance + (for (x <- somes) yield (x * portion)).sum.toLong
   }
 }
 
 def compound_yield(data: List[List[Option[Double]]], balance: Long, year: Int): Long = {
-  println(balance)
   if (year >= data.length) balance else {
     val new_balance = yearly_yield(data, balance, year)
     compound_yield(data, new_balance, year + 1)
   }
 }
 
-def compound_yield_double(data: List[List[Option[Double]]], balance: Double, year: Int): Long = {
-  if (year >= data.length) balance.toLong else {
-    val new_balance = yearly_yield_double(data, balance.toDouble, year)
-    compound_yield_double(data, new_balance, year + 1)
-  }
-}
-
-val prices_fb    = get_prices(List("FB"), 2012 to 2014)
-val prices_goap = get_prices(List("GOOG", "AAPL"), 2010 to 2014)
-val prices_bidu = get_prices(List("BIDU"), 2004 to 2008)
-val prices_goapfb = get_prices(List("GOOG", "AAPL", "FB"), 2010 to 2016)
-
-val deltas_fb   = get_deltas(prices_fb)
-val deltas_goap = get_deltas(prices_goap)
-val deltas_bidu = get_deltas(prices_bidu)
-val deltas_goapfb = get_deltas(prices_goapfb)
-
-
-yearly_yield(deltas_bidu, 100, 0)
-yearly_yield(deltas_bidu, 100, 1)
-yearly_yield(deltas_bidu, 100, 2)
-yearly_yield(deltas_bidu, 192, 3)
-//598
-
-yearly_yield(deltas_fb, 100, 0)
-yearly_yield(deltas_fb, 100, 1)
-//yearly_yield(deltas_fb, 195, 2)
-
-yearly_yield(deltas_goap, 100, 0)
-yearly_yield(deltas_goap, 125, 1)
-yearly_yield(deltas_goap, 146, 2)
-yearly_yield(deltas_goap, 177, 3)
-//yearly_yield(deltas_goap, 227, 4)
-
-yearly_yield(deltas_goapfb, 100, 0)
-yearly_yield(deltas_goapfb, 125, 1)
-yearly_yield(deltas_goapfb, 146, 2)
-yearly_yield(deltas_goapfb, 177, 3)
-yearly_yield(deltas_goapfb, 267, 4)
-yearly_yield(deltas_goapfb, 337, 5)
-//416
-
-compound_yield(deltas_goapfb.take(1), 100, 0)
-compound_yield(deltas_goapfb.take(2), 100, 0)
-compound_yield(deltas_goapfb.take(3), 100, 0)
-compound_yield(deltas_goapfb.take(4), 100, 0)
-compound_yield(deltas_goapfb.take(5), 100, 0)
-compound_yield(deltas_goapfb.take(6), 100, 0)
-
-compound_yield_double(deltas_goapfb.take(1), 100.0, 0)
-compound_yield_double(deltas_goapfb.take(2), 100.0, 0)
-compound_yield_double(deltas_goapfb.take(3), 100.0, 0)
-compound_yield_double(deltas_goapfb.take(4), 100.0, 0)
-compound_yield_double(deltas_goapfb.take(5), 100.0, 0)
-compound_yield_double(deltas_goapfb.take(6), 100.0, 0)
-
 //yearly_yield(d, 100, 0)
 //compound_yield(d.take(6), 100, 0)
 
@@ -183,18 +112,6 @@
   compound_yield(get_deltas(get_prices(portfolio, years)), start_balance, 0)
 }
 
-def investment_double(portfolio: List[String], years: Range, start_balance: Long): Long = {
-  compound_yield_double(get_deltas(get_prices(portfolio, years)), start_balance.toDouble, 0)
-}
-
-
-investment(rstate_portfolio, 1978 to 2017, 100)
-investment(blchip_portfolio, 1978 to 2017, 100)
-
-investment_double(rstate_portfolio, 1978 to 2017, 100)
-investment_double(blchip_portfolio, 1978 to 2017, 100)
-
-
 /*
 val q1 = get_deltas(get_prices(List("GOOG", "AAPL", "BIDU"), 2000 to 2017))
 yearly_yield(q1, 100, 0)

--- a/testing3/bf.scala	Sat Dec 16 23:53:28 2017 +0000
+++ b/testing3/bf.scala	Mon Jan 15 23:15:34 2018 +0000
@@ -48,7 +48,7 @@
   }
 }
 
-
+//jumpLeft("[******]***", 7, 0)
 
 // (2c) Complete the run function that interpretes (runs) a brainf***
 // program: the arguments are a program, a program counter,
@@ -172,6 +172,284 @@
       [<+>-[<+>-[<+>-[<[-]>>[-]+>+<<-]]]]]]]]]]<[>+<-]+>>]<<[<<]>>]""", Map())
 
 
+start("""+++++[>+++++++++<-],[[>--.++>+<<-]>+.->[<.>-]<<,]""", Map())
+
 */ 
 
+
+def splice(cs: List[Char], acc: List[(Char, Int)]) : List[(Char, Int)] = (cs, acc) match {
+  case (Nil, acc) => acc
+  case (c :: cs, Nil) => splice(cs, List((c, 1)))
+  case (c :: cs, (d, n) :: acc) => 
+    if (c == d) splice(cs, (c, n + 1) :: acc)
+    else splice(cs, (c, 1) :: (d, n) :: acc)
 }
+
+def spl(s: String) = splice(s.toList, Nil).reverse
+
+
+// simple instructions
+def instr(c: Char) : String = c match {
+  case '>' => "ptr++;"
+  case '<' => "ptr--;"
+  case '+' => "(*ptr)++;"
+  case '-' => "(*ptr)--;"
+  case '.' => "putchar(*ptr);"
+  case ',' => "*ptr = getchar();\n"
+  case '['  => "while(*ptr){"
+  case ']'  => "}"
+  case _ => ""
+}
+
+def instrs(prog: String) : String =
+  prog.toList.map(instr(_)).mkString
+
+
+//optimised instructions
+
+def instr2(c: Char, n: Int) : String = c match {
+  case '>' => "ptr += " + n.toString + ";"
+  case '<' => "ptr -= " + n.toString + ";"
+  case '+' => "(*ptr) += " + n.toString + ";"
+  case '-' => "(*ptr) -= " + n.toString + ";"
+  case '.' => "putchar(*ptr);" * n
+  case ',' => "*ptr = getchar();\n" * n
+  case '['  => "while(*ptr){" * n
+  case ']'  => "}" * n
+  case _ => ""
+}
+
+def instrs2(prog: String) : String =
+  spl(prog).map{ case (c, n) => instr2(c, n) }.mkString
+
+
+// peephole optimisers are at
+// https://github.com/Wilfred/bfc#peephole-optimisations
+// http://calmerthanyouare.org/2015/01/07/optimizing-brainfuck.html
+
+def compile_str(prog: String) : String = {
+  "#include <string.h>\n" ++
+  "#include <stdio.h>\n" ++
+  "char field[30000];\n" ++
+  "char *ptr = &field[15000];" ++
+  "int main()\n{\n" ++
+  "memset(field, '\\0', 30000);\n" ++
+  instrs2(prog) ++
+  "\n return 0;\n}"
+}
+
+def compile(name: String, prog: String) = {
+  val fw = new java.io.FileWriter(name + ".c") 
+  fw.write(compile_str(prog)) 
+  fw.close()
+}
+
+import sys.process._
+
+def compile_run(prog: String) = {
+  compile("tmp", prog)
+  "gcc -O3 -o tmp tmp.c".!
+  "./tmp".!
+  ()
+}
+
+
+compile_run("""++++++++[>++++[>++>+++>+++>+<<<<-]>+>+>->>+[<]<-]>>.>---.+++++++
+       ..+++.>>.<-.<.+++.------.--------.>>+.>++.""")
+
+compile_run("""++++++++[>+>++++<<-]>++>>+<[-[>>+<<-]+>>]>+[-<<<[
+      ->[+[-]+>++>>>-<<]<[<]>>++++++[<<+++++>>-]+<<++.[-]<<
+      ]>.>+[>>]>+]""")
+
+compile_run("""      A mandelbrot set fractal viewer in brainf*** written by Erik Bosman
++++++++++++++[->++>>>+++++>++>+<<<<<<]>>>>>++++++>--->>>>>>>>>>+++++++++++++++[[
+>>>>>>>>>]+[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-]>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+
+<<<<<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>>+>>>>>>>>>>>>>>>>>>>>>>>>>>
+>+<<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+[>>>>>>[>>>>>>>[-]>>]<<<<<<<<<[<<<<<<<<<]>>
+>>>>>[-]+<<<<<<++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<+++++++[-[->>>
+>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[[-]>>>>>>[>>>>>
+>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>
+[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<
+<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>+++++++++++++++[[
+>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[
+>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[
+-<<+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<
+<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<
+[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>
+>>>>[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+
+<<<<<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>
+>>>>>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<
++>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<
+<]<+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>
+>>>>>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
+>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<
+<<<]>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<
+<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->
+>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<
+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]<<<<<<<[->+>>>-<<<<]>>>>>>>>>+++++++++++++++++++
++++++++>>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>[<<<<<<<+<[-<+>>>>+<<[-]]>[-<<[->+>>>-
+<<<<]>>>]>>>>>>>>>>>>>[>>[-]>[-]>[-]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>>>>>>[>>>>>
+[-<<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>[-<<<<<<<<
+<+>>>>>>>>>]>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-
+]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<
+<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+>>]<
+<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>
+>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>
+[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[>>>>>>[-<
+<<<<+>>>>>]<<<<<[->>>>>+<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>+>>>>>>>>
+]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+
+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
+[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
+]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
+[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>
+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>++++++++
++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-<<<<<<<+
+>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[
+-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>>]>[-<<<<<<[->>>>>+<++<<<<]>>>>>[-<
+<<<<+>>>>>]<->+>]<[->+<]<<<<<[->>>>>+<<<<<]>>>>>>[-]<<<<<<+>>>>[-<<<<->>>>]+<<<<
+[->>>>->>>>>[>>[-<<->>]+<<[->>->[-<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]
++>>>>>>[>>>>>>>>>]>+<]]+>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<<<<<<<<<<[<<<<<
+<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<
+[<<<<<<<<<]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<
+<<<+<[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<
+<<<<<+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<
+<<<<<<<<<<]>>>>[-]<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+<]>>>>>>>>]<<<
+<<<<<+<[>[->>>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>[->>>>+<<<<]>]<[->>>>-<<<<<<<
+<<<<<<<+>>>>>>>>>>]<]>>[->>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>>+<<<<
+]<<<<<<<<<<<]>>>>>>+<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>>>>>>>>>]<<<<<<<<<
+[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<<<<<<
++>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<<<<<<
+<<<<<]]>[-]>>[-]>[-]>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<
+<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[
+[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+
+[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>
+[-<<+>>]<<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<
+<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[
+>[-]<->>>[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[
+>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>
+>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>[-]>>>>+++++++++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<
+<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<
+<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-
+<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>
+>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>>>
+[-<<<->>>]<<<[->>>+<<<]>>>>>>>>]<<<<<<<<+<[>[->+>[-<-<<<<<<<<<<+>>>>>>>>>>>>[-<<
++>>]<]>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<<<]>>[-<+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<]>
+[-<<+>>]<<<<<<<<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>
+>>>>>>]<<<<<<<<+<[>[->+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>[-<+>]>]<[-<-<<<<<<<<<<+>>>>
+>>>>>>>]<<]>>>[-<<+>[-<-<<<<<<<<<<+>>>>>>>>>>>]>]<[-<+>]<<<<<<<<<<<<]>>>>>+<<<<<
+]>>>>>>>>>[>>>[-]>[-]>[-]>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>>>[-<<<<<
+<+>>>>>>]<<<<<<[->>>>>>+<<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>
+>]>>[-<<<<<<<[->>>>>+<++<<<<]>>>>>[-<<<<<+>>>>>]<->+>>]<<[->>+<<]<<<<<[->>>>>+<<
+<<<]+>>>>[-<<<<->>>>]+<<<<[->>>>->>>>>[>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<
+<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>[-<<->>]+<<[->>->[-<<<+>>>]<
+<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<
+<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+
+<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>[->>>+<<<]>]<[->>>-
+<<<<<<<<<<<<<+>>>>>>>>>>]<]>>[->>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>+<<<
+]<<<<<<<<<<<]>>>>>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]]>>>>[-<<<<+>
+>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<<[->>>-
+<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[
+->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<<<<<]]>>>>[-]<<<<]>>>>[-<<<<+>>
+>>]<<<<[->>>>+>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>[>>>>>>
+>>>]<<<<<<<<<[>[->>>>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<
+<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<
+<<<<]]>>>>>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>[-<<<<+
+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<+>>>>>
+]<<<<<[->>>>>+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
+>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>
+>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[-<<+
+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
+[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
+]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
+[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<
+<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>
+>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<+>>>
+>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+
+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>
+>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>
+>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<<<<]
+>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<<<<<
+]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->>>+<
+<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>
+>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>->>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>]<<+>>>>[-<<<<
+->>>>]+<<<<[->>>>-<<<<<<.>>]>>>>[-<<<<<<<.>>>>>>>]<<<[-]>[-]>[-]>[-]>[-]>[-]>>>[
+>[-]>[-]>[-]>[-]>[-]>[-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-]>>>>]<<<<<<<<<
+[<<<<<<<<<]>+++++++++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+>>>>>>>>>+<<<<<<<<
+<<<<<<[<<<<<<<<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+[-]>>[>>>>>>>>>]<<<<<
+<<<<[>>>>>>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<[<<<<<<<<<]>>>>>>>[-]+>>>]<<<<
+<<<<<<]]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+>>[>+>>>>[-<<<<->>>>]<<<<[->>>
+>+<<<<]>>>>>>>>]<<+<<<<<<<[>>>>>[->>+<<]<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<
+<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<<<<<[->>>>>>+<<<<<<]<
++<<<<<<<<<]>>>>>>>-<<<<[-]+<<<]+>>>>>>>[-<<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>->>[>>
+>>>[->>+<<]>>>>]<<<<<<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<
+<<<<[->>>>>>+<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+<<<
+<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<<<<<->>>>>]+<<<<<[->>>>>->>[-<<<<<<<+>>>>>>>]<<<<
+<<<[->>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>[-<
+<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>-<<[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<<<<<<<<<[<<<
+<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<
+<<[<<<<<<<<<]>>>>[-]<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>-<<<<<[<<<<<<<
+<<]]>>>]<<<<.>>>>>>>>>>[>>>>>>[-]>>>]<<<<<<<<<[<<<<<<<<<]>++++++++++[-[->>>>>>>>
+>+<<<<<<<<<]>>>>>>>>>]>>>>>+>>>>>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-<<<<<<
+<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+[-]>[>>>>>>>>>]<<<<<<<<<[>>>>>>>>[-<<<<<<<+>>>>>>
+>]<<<<<<<[->>>>>>>+<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+>>]<<<<<<<<<<]]>>>>>>>>[-<<<<<
+<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+>[>+>>>>>[-<<<<<->>>>>]<<<<<[->>>>>+<<<<<]>>>>>>
+>>]<+<<<<<<<<[>>>>>>[->>+<<]<<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[-]<-
+>>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<
+<<<]>>>>>>>>-<<<<<[-]+<<<]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>->[>>>
+>>>[->>+<<]>>>]<<<<<<<<<[>[-]<->>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<
+<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>
++>>>>>>>>>>>>>>>>>>>>>>>>>>>+<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<<->>>>>>]+<
+<<<<<[->>>>>>->>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+<<<<<<<<<<<<<<<<<[<<<<<<<
+<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>
+-<<[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>
+>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-]<<<++++
++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>->>>>>>>>>>>>>>>>>>>>>>>>>>>-<<<<<<[<<<<
+<<<<<]]>>>]""")
+
+compile_run("""
+>+>+>+>+>++<[>[<+++>-
+
+  >>>>>
+  >+>+>+>+>++<[>[<+++>-
+
+    >>>>>
+    >+>+>+>+>++<[>[<+++>-
+
+      >>>>>
+      >+>+>+>+>++<[>[<+++>-
+
+        >>>>>
+        +++[->+++++<]>[-]<
+        <<<<<
+
+      ]<<]>[-]
+      <<<<<
+
+    ]<<]>[-]
+    <<<<<
+
+  ]<<]>[-]
+  <<<<<
+
+]<<]>.""")
+
+// benchmarks
+compile_run(""">++[<+++++++++++++>-]<[[>+>+<<-]>[<+>-]++++++++
+[>++++++++<-]>.[-]<<>++++++++++[>++++++++++[>++
+++++++++[>++++++++++[>++++++++++[>++++++++++[>+
++++++++++[-]<-]<-]<-]<-]<-]<-]<-]++++++++++.""")
+
+//
+compile_run("""++++[>++++<-]>[>+>++>[+++++++>]+++[<]>-]>>>>>>>>-.
+<<<<.<..+++.<.>>>>.<<<.+++.------.>-.<<+.<------.""")
+
+compile_run("""++++++++[->-[->-[->-[-]<]<]<]
+>++++++++[<++++++++++>-]<[>+>+<<-]>-.>-----.>""")
+
+
+
+
+// register to BF compiler
+// https://gergo.erdi.hu/blog/2010-09-06-from_register_machines_to_brainfuck,_part_1/
+}