--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/testing5/bf.scala Thu Dec 06 18:56:26 2018 +0000
@@ -0,0 +1,225 @@
+// Part 1 about an Interpreter for the Brainf*** language
+//========================================================
+
+object CW10a { // only for generating the Jar file
+
+
+type Mem = Map[Int, Int]
+
+
+import io.Source
+import scala.util._
+
+// (1) Write a function that takes a file name as argument and
+// and requests the corresponding file from disk. It returns the
+// content of the file as a String. If the file does not exists,
+// the function should return the empty string.
+
+def load_bff(name: String) : String =
+ Try(Source.fromFile(name)("ISO-8859-1").mkString).getOrElse("")
+
+
+// (2) Complete the functions for safely reading
+// and writing brainf*** memory. Safely read should
+// Return the value stored in the Map for a given memory
+// pointer, provided it exists; otherwise it Returns 0. The
+// writing function generates a new Map with the
+// same data, except at the given memory pointer the
+// value v is stored.
+
+
+def sread(mem: Mem, mp: Int) : Int =
+ mem.getOrElse(mp, 0)
+
+def write(mem: Mem, mp: Int, v: Int) : Mem =
+ mem.updated(mp, v)
+
+
+// (3) Implement the two jumping instructions in the
+// brainf*** language. In jumpRight, given a program and
+// a program counter move the program counter to the right
+// until after the *matching* ]-command. Similarly,
+// jumpLeft implements the move to the left to just after
+// the *matching* [-command.
+
+def jumpRight(prog: String, pc: Int, level: Int) : Int = {
+ if (prog.length <= pc) pc
+ else (prog(pc), level) match {
+ case (']', 0) => pc + 1
+ case (']', l) => jumpRight(prog, pc + 1, l - 1)
+ case ('[', l) => jumpRight(prog, pc + 1, l + 1)
+ case (_, l) => jumpRight(prog, pc + 1, l)
+ }
+}
+
+def jumpLeft(prog: String, pc: Int, level: Int) : Int = {
+ if (pc < 0) pc
+ else (prog(pc), level) match {
+ case ('[', 0) => pc + 1
+ case ('[', l) => jumpLeft(prog, pc - 1, l - 1)
+ case (']', l) => jumpLeft(prog, pc - 1, l + 1)
+ case (_, l) => jumpLeft(prog, pc - 1, l)
+ }
+}
+
+// test cases
+//jumpRight("""--[..+>--],>,++""", 3, 0) // => 10
+//jumpLeft("""--[..+>--],>,++""", 8, 0) // => 3
+//jumpRight("""--[..[+>]--],>,++""", 3, 0) // => 12
+//jumpRight("""--[..[[-]+>[.]]--],>,++""", 3, 0) // => 18
+//jumpRight("""--[..[[-]+>[.]]--,>,++""", 3, 0) // => 22 (outside)
+//jumpLeft("""[******]***""", 7, 0) // => -1 (outside)
+
+// (4) Complete the compute function that interprets (runs) a brainf***
+// program: the arguments are a program (represented as a string), a program
+// counter, a memory counter and a brainf*** memory. It Returns the
+// memory at the stage when the execution of the brainf*** program
+// finishes. The interpretation finishes once the program counter
+// pc is pointing to something outside the program string.
+// If the pc points to a character inside the program, the pc,
+// memory pointer and memory need to be updated according to
+// rules of the brainf*** language. Then, recursively, the compute
+// function continues with the command at the new program
+// counter.
+// Implement the run function that calls compute with the program
+// counter and memory counter set to 0.
+
+def compute(prog: String, pc: Int, mp: Int, mem: Mem) : Mem = {
+ if (0 <= pc && pc < prog.length) {
+ val (new_pc, new_mp, new_mem) = prog(pc) match {
+ case '>' => (pc + 1, mp + 1, mem)
+ case '<' => (pc + 1, mp - 1, mem)
+ case '+' => (pc + 1, mp, write(mem, mp, sread(mem, mp) + 1))
+ case '-' => (pc + 1, mp, write(mem, mp, sread(mem, mp) - 1))
+ case '.' => { print(sread(mem, mp).toChar); (pc + 1, mp, mem) }
+ case ',' => (pc + 1, mp, write(mem, mp, Console.in.read().toByte))
+ case '[' =>
+ if (sread(mem, mp) == 0) (jumpRight(prog, pc + 1, 0), mp, mem) else (pc + 1, mp, mem)
+ case ']' =>
+ if (sread(mem, mp) != 0) (jumpLeft(prog, pc - 1, 0), mp, mem) else (pc + 1, mp, mem)
+ case _ => (pc + 1, mp, mem)
+ }
+ compute(prog, new_pc, new_mp, new_mem)
+ }
+ else mem
+}
+
+def run(prog: String, m: Mem = Map()) = compute(prog, 0, 0, m)
+
+
+/*
+
+// some sample bf-programs collected from the Internet
+//=====================================================
+
+
+// first some contrived (small) programs
+
+// clears the 0-cell
+run("[-]", Map(0 -> 100)) // Map will be 0 -> 0
+
+// copies content of the 0-cell to 1-cell
+run("[->+<]", Map(0 -> 10)) // Map will be 0 -> 0, 1 -> 10
+
+
+// copies content of the 0-cell to 2-cell and 4-cell
+run("[>>+>>+<<<<-]", Map(0 -> 42))
+
+
+// prints out numbers 0 to 9
+run("""+++++[->++++++++++<]>--<+++[->>++++++++++<<]>>++<<----------[+>.>.<+<]""")
+
+
+// some more "useful" programs
+
+// hello world program 1
+run("""++++++++[>++++[>++>+++>+++>+<<<<-]>+>+>->>+[<]<-]>>.>---.+++++++
+ ..+++.>>.<-.<.+++.------.--------.>>+.>++.""")
+
+// hello world program 2
+run("""++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>+
+ +.<<+++++++++++++++.>.+++.------.--------.>+.>.""")
+
+
+// draws the Sierpinski triangle
+run("""++++++++[>+>++++<<-]>++>>+<[-[>>+<<-]+>>]>+[-<<<[
+ ->[+[-]+>++>>>-<<]<[<]>>++++++[<<+++++>>-]+<<++.[-]<<
+ ]>.>+[>>]>+]""")
+
+run(load_bff("sierpinski.bf"))
+
+
+//fibonacci numbers below 100
+run("""+++++++++++
+ >+>>>>++++++++++++++++++++++++++++++++++++++++++++
+ >++++++++++++++++++++++++++++++++<<<<<<[>[>>>>>>+>
+ +<<<<<<<-]>>>>>>>[<<<<<<<+>>>>>>>-]<[>++++++++++[-
+ <-[>>+>+<<<-]>>>[<<<+>>>-]+<[>[-]<[-]]>[<<[>>>+<<<
+ -]>>[-]]<<]>>>[>>+>+<<<-]>>>[<<<+>>>-]+<[>[-]<[-]]
+ >[<<+>>[-]]<<<<<<<]>>>>>[+++++++++++++++++++++++++
+ +++++++++++++++++++++++.[-]]++++++++++<[->-<]>++++
+ ++++++++++++++++++++++++++++++++++++++++++++.[-]<<
+ <<<<<<<<<<[>>>+>+<<<<-]>>>>[<<<<+>>>>-]<-[>>.>.<<<
+ [-]]<<[>>+>+<<<-]>>>[<<<+>>>-]<<[<+>-]>[<+>-]<<<-]""")
+
+
+//outputs the square numbers up to 10000
+run("""++++[>+++++<-]>[<+++++>-]+<+[
+ >[>+>+<<-]++>>[<<+>>-]>>>[-]++>[-]+
+ >>>+[[-]++++++>>>]<<<[[<++++++++<++>>-]+<.<[>----<-]<]
+ <<[>>>>>[>>>[-]+++++++++<[>-<-]+++++++++>[-[<->-]+[<<<]]<[>+<-]>]<<-]<<-]""")
+
+//collatz numbers (needs a number to be typed in)
+run(""">,[[----------[
+ >>>[>>>>]+[[-]+<[->>>>++>>>>+[>>>>]++[->+<<<<<]]<<<]
+ ++++++[>------<-]>--[>>[->>>>]+>+[<<<<]>-],<]>]>>>++>+>>[
+ <<[>>>>[-]+++++++++<[>-<-]+++++++++>[-[<->-]+[<<<<]]<[>+<-]>]
+ >[>[>>>>]+[[-]<[+[->>>>]>+<]>[<+>[<<<<]]+<<<<]>>>[->>>>]+>+[<<<<]]
+ >[[>+>>[<<<<+>>>>-]>]<<<<[-]>[-<<<<]]>>>>>>>
+ ]>>+[[-]++++++>>>>]<<<<[[<++++++++>-]<.[-]<[-]<[-]<]<,]""")
+
+
+// infinite collatz (never stops)
+run(""">>+>+<[[->>[>>]>>>[>>]+[<<]<<<[<<]>[>[>>]>>+>[>>]<+<[<<]<<<[<
+ <]>-]>[>>]>>[<<<<[<<]>+>[>>]>>-]<<<<[<<]+>>]<<[+++++[>+++++++
+ +<-]>.<++++++[>--------<-]+<<]>>[>>]+[>>>>[<<+>+>-]<-[>+<-]+<
+ [<<->>-[<<+>>[-]]]>>>[<<<+<<+>>>>>-]<<<[>>>+<<<-]<<[[-]>+>>->
+ [<+<[<<+>>-]<[>+<-]<[>+<-]>>>>-]<[>+<-]+<[->[>>]<<[->[<+++>-[
+ <+++>-[<+++>-[<[-]++>>[-]+>+<<-[<+++>-[<+++>-[<[-]+>>>+<<-[<+
+ ++>-[<+++>-]]]]]]]]]<[>+<-]+<<]>>>+<[->[<+>-[<+>-[<+>-[<+>-[<
+ +>-[<+>-[<+>-[<+>-[<+>-[<[-]>>[-]+>+<<-[<+>-]]]]]]]]]]]<[>+<-
+ ]+>>]<<[<<]>]<[->>[->+>]<[-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<-
+ >>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>
+ -[<->>+<-[<+>-[<->>+<-[<+>-]]]]]]]]]]]]]]]]]]]>[<+>-]<+<[<+++
+ +++++++>-]<]>>[<+>->>]<<[>+>+<<-]>[<+>-]+>[<->[-]]<[-<<-]<<[<
+ <]]++++++[>+++++++<-]>++.------------.[-]>[>>]<<[+++++[>+++++
+ +++<-]>.<++++++[>--------<-]+<<]+<]>[<+>-]<]>>>[>>]<<[>[-]<-<
+ <]++++++++++.[-]<<<[<<]>>>+<[->[<+>-[<+>-[<+>-[<+>-[<+>-[<+>-
+ [<+>-[<+>-[<+>-[<[-]>>[-]+>+<<-]]]]]]]]]]<[>+<-]+>>]<<[<<]>>]""")
+
+
+
+// a Mandelbrot set generator in brainf*** written by Erik Bosman
+// (http://esoteric.sange.fi/brainfuck/utils/mandelbrot/)
+
+run(load_bff("mandelbrot.bf"))
+
+
+// a benchmark program (counts down from 'Z' to 'A')
+val b1 = """>++[<+++++++++++++>-]<[[>+>+<<-]>[<+>-]++++++++
+ [>++++++++<-]>.[-]<<>++++++++++[>++++++++++[>++
+ ++++++++[>++++++++++[>++++++++++[>++++++++++[>+
+ +++++++++[-]<-]<-]<-]<-]<-]<-]<-]++++++++++."""
+
+
+def time_needed[T](n: Int, code: => T) = {
+ val start = System.nanoTime()
+ for (i <- 0 until n) code
+ val end = System.nanoTime()
+ (end - start)/(n * 1.0e9)
+}
+
+time_needed(1, run(b1))
+*/
+
+}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/testing5/bfc.scala Thu Dec 06 18:56:26 2018 +0000
@@ -0,0 +1,309 @@
+// Part 2 about a "Compiler" for the Brainf*** language
+//======================================================
+
+object CW10b {
+
+// !!! Copy any function you need from file bf.scala !!!
+//
+// If you need any auxiliary function, feel free to
+// implement it, but do not make any changes to the
+// templates below.
+
+
+def time_needed[T](n: Int, code: => T) = {
+ val start = System.nanoTime()
+ for (i <- 0 until n) code
+ val end = System.nanoTime()
+ (end - start)/(n * 1.0e9)
+}
+
+type Mem = Map[Int, Int]
+
+
+import io.Source
+import scala.util._
+
+def load_bff(name: String) : String =
+ Try(Source.fromFile(name)("ISO-8859-1").mkString).getOrElse("")
+
+def sread(mem: Mem, mp: Int) : Int =
+ mem.getOrElse(mp, 0)
+
+def write(mem: Mem, mp: Int, v: Int) : Mem =
+ mem.updated(mp, v)
+
+def jumpRight(prog: String, pc: Int, level: Int) : Int = {
+ if (prog.length <= pc) pc
+ else (prog(pc), level) match {
+ case (']', 0) => pc + 1
+ case (']', l) => jumpRight(prog, pc + 1, l - 1)
+ case ('[', l) => jumpRight(prog, pc + 1, l + 1)
+ case (_, l) => jumpRight(prog, pc + 1, l)
+ }
+}
+
+def jumpLeft(prog: String, pc: Int, level: Int) : Int = {
+ if (pc < 0) pc
+ else (prog(pc), level) match {
+ case ('[', 0) => pc + 1
+ case ('[', l) => jumpLeft(prog, pc - 1, l - 1)
+ case (']', l) => jumpLeft(prog, pc - 1, l + 1)
+ case (_, l) => jumpLeft(prog, pc - 1, l)
+ }
+}
+
+def compute(prog: String, pc: Int, mp: Int, mem: Mem) : Mem = {
+ if (0 <= pc && pc < prog.length) {
+ val (new_pc, new_mp, new_mem) = prog(pc) match {
+ case '>' => (pc + 1, mp + 1, mem)
+ case '<' => (pc + 1, mp - 1, mem)
+ case '+' => (pc + 1, mp, write(mem, mp, sread(mem, mp) + 1))
+ case '-' => (pc + 1, mp, write(mem, mp, sread(mem, mp) - 1))
+ case '.' => { print(sread(mem, mp).toChar); (pc + 1, mp, mem) }
+ case ',' => (pc + 1, mp, write(mem, mp, Console.in.read().toByte))
+ case '[' =>
+ if (sread(mem, mp) == 0) (jumpRight(prog, pc + 1, 0), mp, mem) else (pc + 1, mp, mem)
+ case ']' =>
+ if (sread(mem, mp) != 0) (jumpLeft(prog, pc - 1, 0), mp, mem) else (pc + 1, mp, mem)
+ case _ => (pc + 1, mp, mem)
+ }
+ compute(prog, new_pc, new_mp, new_mem)
+ }
+ else mem
+}
+
+def run(prog: String, m: Mem = Map()) = compute(prog, 0, 0, m)
+
+
+// The baseline to what we can compare our "compiler"
+// implemented below. It should require something like
+// 60 seconds for the calculation on my laptop
+//
+//time_needed(1, run(load_bff("benchmark.bf")))
+
+
+
+// DEBUGGING INFORMATION!!!
+//
+// Compiler, even real ones, are fiedishly difficult to get
+// to prduce correct code. The point is that for example for
+// the sierpinski program, they need to still generate code
+// that displays such a triangle. If yes, then one usually
+// can take comfort that all is well. If not, then something
+// went wrong during the optimisations.
+
+
+
+// (5) Write a function jtable that precomputes the "jump
+// table" for a bf-program. This function takes a bf-program
+// as an argument and Returns a Map[Int, Int]. The
+// purpose of this map is to record the information
+// that given on the position pc is a '[' or a ']',
+// then to which pc-position do we need to jump next?
+//
+// For example for the program
+//
+// "+++++[->++++++++++<]>--<+++[->>++++++++++<<]>>++<<----------[+>.>.<+<]"
+//
+// we obtain the map
+//
+// Map(69 -> 61, 5 -> 20, 60 -> 70, 27 -> 44, 43 -> 28, 19 -> 6)
+//
+// This states that for the '[' on position 5, we need to
+// jump to position 20, which is just after the corresponding ']'.
+// Similarly, for the ']' on position 19, we need to jump to
+// position 6, which is just after the '[' on position 5, and so
+// on. The idea is to not calculate this information each time
+// we hit a bracket, but just look up this information in the
+// jtable. You can use the jumpLeft and jumpRight functions
+// from Part 1 for calculating the jtable.
+//
+// Then adapt the compute and run functions from Part 1 in order
+// to take advantage of the information stored in the jtable.
+// This means whenever jumpLeft and jumpRight was called previously,
+// you should look up the jump address in the jtable.
+
+
+def jtable(pg: String) : Map[Int, Int] =
+ (0 until pg.length).collect { pc => pg(pc) match {
+ case '[' => (pc -> jumpRight(pg, pc + 1, 0))
+ case ']' => (pc -> jumpLeft(pg, pc - 1, 0))
+ }}.toMap
+
+
+// testcase
+// jtable("""+++++[->++++++++++<]>--<+++[->>++++++++++<<]>>++<<----------[+>.>.<+<]""")
+// => Map(69 -> 61, 5 -> 20, 60 -> 70, 27 -> 44, 43 -> 28, 19 -> 6)
+
+
+def compute2(pg: String, tb: Map[Int, Int], pc: Int, mp: Int, mem: Mem) : Mem = {
+ if (0 <= pc && pc < pg.length) {
+ val (new_pc, new_mp, new_mem) = pg(pc) match {
+ case '>' => (pc + 1, mp + 1, mem)
+ case '<' => (pc + 1, mp - 1, mem)
+ case '+' => (pc + 1, mp, write(mem, mp, sread(mem, mp) + 1))
+ case '-' => (pc + 1, mp, write(mem, mp, sread(mem, mp) - 1))
+ case '.' => { print(sread(mem, mp).toChar); (pc + 1, mp, mem) }
+ case ',' => (pc + 1, mp, write(mem, mp, Console.in.read().toByte))
+ case '[' =>
+ if (sread(mem, mp) == 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case ']' =>
+ if (sread(mem, mp) != 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case _ => (pc + 1, mp, mem)
+ }
+ compute2(pg, tb, new_pc, new_mp, new_mem)
+ }
+ else mem
+}
+
+
+def run2(pg: String, m: Mem = Map()) =
+ compute2(pg, jtable(pg), 0, 0, m)
+
+//time_needed(1, run2(load_bff("benchmark.bf")))
+
+
+
+// (6) Write a function optimise which deletes "dead code" (everything
+// that is not a bf-command) and also replaces substrings of the form
+// [-] by a new command 0. The idea is that the loop [-] just resets the
+// memory at the current location to 0. In the compute3 and run3 functions
+// below you implement this command by writing the number 0 to mem(mp),
+// that is write(mem, mp, 0).
+//
+// The easiest way to modify a string in this way is to use the regular
+// expression """[^<>+-.,\[\]]""", which recognises everything that is
+// not a bf-command and replace it by the empty string. Similarly the
+// regular expression """\[-\]""" finds all occurences of [-] and
+// by using the Scala method .replaceAll you can repplace it with the
+// string "0" standing for the new bf-command.
+
+def optimise(s: String) : String =
+ s.replaceAll("""[^<>+-.,\[\]]""","").replaceAll("""\[-\]""", "0")
+
+
+def compute3(pg: String, tb: Map[Int, Int], pc: Int, mp: Int, mem: Mem) : Mem = {
+ if (0 <= pc && pc < pg.length) {
+ val (new_pc, new_mp, new_mem) = pg(pc) match {
+ case '0' => (pc + 1, mp, write(mem, mp, 0))
+ case '>' => (pc + 1, mp + 1, mem)
+ case '<' => (pc + 1, mp - 1, mem)
+ case '+' => (pc + 1, mp, write(mem, mp, sread(mem, mp) + 1))
+ case '-' => (pc + 1, mp, write(mem, mp, sread(mem, mp) - 1))
+ case '.' => { print(sread(mem, mp).toChar); (pc + 1, mp, mem) }
+ case ',' => (pc + 1, mp, write(mem, mp, Console.in.read().toByte))
+ case '[' =>
+ if (sread(mem, mp) == 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case ']' =>
+ if (sread(mem, mp) != 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case _ => (pc + 1, mp, mem)
+ }
+ compute3(pg, tb, new_pc, new_mp, new_mem)
+ }
+ else mem
+}
+
+def run3(pg: String, m: Mem = Map()) = {
+ val pg_opt = optimise(pg)
+ compute3(pg_opt, jtable(pg_opt), 0, 0, m)
+}
+
+
+// testcases
+
+//optimise(load_bff("benchmark.bf")) // should have inserted 0's
+//optimise(load_bff("mandelbrot.bf")).length // => 11203
+
+//time_needed(1, run3(load_bff("benchmark.bf")))
+
+
+
+// (7) Write a function combine which replaces sequences
+// of repated increment and decrement commands by appropriate
+// two-character commands. For example for sequences of +
+//
+// orig bf-cmds | replacement
+// ------------------------------
+// + | +A
+// ++ | +B
+// +++ | +C
+// |
+// ... |
+// |
+// +++....+++ | +Z
+// (where length = 26)
+//
+// Similar for the bf-command -, > and <. All other commands should
+// be unaffected by this change.
+//
+// Adapt the compute4 and run4 functions such that they can deal
+// appropriately with such two-character commands.
+
+def splice(cs: List[Char], acc: List[(Char, Int)]) : List[(Char, Int)] = (cs, acc) match {
+ case (Nil, acc) => acc
+ case ('[' :: cs, acc) => splice(cs, ('[', 1) :: acc)
+ case (']' :: cs, acc) => splice(cs, (']', 1) :: acc)
+ case ('.' :: cs, acc) => splice(cs, ('.', 1) :: acc)
+ case (',' :: cs, acc) => splice(cs, (',', 1) :: acc)
+ case ('0' :: cs, acc) => splice(cs, ('0', 1) :: acc)
+ case (c :: cs, Nil) => splice(cs, List((c, 1)))
+ case (c :: cs, (d, n) :: acc) =>
+ if (c == d && n < 26) splice(cs, (c, n + 1) :: acc)
+ else splice(cs, (c, 1) :: (d, n) :: acc)
+}
+
+def spl(s: String) = splice(s.toList, Nil).reverse
+
+//spl(load_bff("benchmark.bf"))
+
+def combine(s: String) : String = {
+ (for ((c, n) <- spl(s)) yield c match {
+ case '>' => List('>', (n + '@').toChar)
+ case '<' => List('<', (n + '@').toChar)
+ case '+' => List('+', (n + '@').toChar)
+ case '-' => List('-', (n + '@').toChar)
+ case _ => List(c)
+ }).flatten.mkString
+}
+
+
+//combine(load_bff("benchmark.bf"))
+
+def compute4(pg: String, tb: Map[Int, Int], pc: Int, mp: Int, mem: Mem) : Mem = {
+ if (0 <= pc && pc < pg.length) {
+ val (new_pc, new_mp, new_mem) = pg(pc) match {
+ case '0' => (pc + 1, mp, write(mem, mp, 0))
+ case '>' => (pc + 2, mp + (pg(pc + 1) - '@'), mem)
+ case '<' => (pc + 2, mp - (pg(pc + 1) - '@'), mem)
+ case '+' => (pc + 2, mp, write(mem, mp, sread(mem, mp) + (pg(pc + 1) - '@')))
+ case '-' => (pc + 2, mp, write(mem, mp, sread(mem, mp) - (pg(pc + 1) - '@')))
+ case '.' => { print(sread(mem, mp).toChar); (pc + 1, mp, mem) }
+ case ',' => (pc + 1, mp, write(mem, mp, Console.in.read().toByte))
+ case '[' =>
+ if (sread(mem, mp) == 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case ']' =>
+ if (sread(mem, mp) != 0) (tb(pc), mp, mem) else (pc + 1, mp, mem)
+ case _ => (pc + 1, mp, mem)
+ }
+ compute4(pg, tb, new_pc, new_mp, new_mem)
+ }
+ else mem
+}
+
+def run4(pg: String, m: Mem = Map()) = {
+ val pg_opt = combine(optimise(pg))
+ compute4(pg_opt, jtable(pg_opt), 0, 0, m)
+}
+
+// testcases
+//combine(optimise(load_bff("benchmark.bf"))) // => """>A+B[<A+M>A-A]<A[[....."""
+
+//time_needed(1, run4(load_bff("benchmark.bf")))
+
+//time_needed(1, run(load_bff("sierpinski.bf")))
+//time_needed(1, run4(load_bff("sierpinski.bf")))
+
+//time_needed(1, run4(load_bff("mandelbrot.bf")))
+
+
+}