added "mypy stack size" experiment

Author: OriRoth

README.md

@@ -18,7 +18,6 @@ Here is one possible script (also found in `typing_machines/app.py`):
 
 ```python
 from typing_machines.app import *  # import application
-
 with open("example.py", "w") as python_file:  # write palindromes machine and input "abbabba"
     python_file.write(encode(Algorithm.Grigore, palindromes, "abbabba"))
 sleep(1)  # wait for write operation
@@ -45,16 +44,9 @@ makes `mypy` throw a segmentation fault:
 
 ```python
 from typing import TypeVar, Generic
-
 T = TypeVar("T", contravariant=True)
-
-
 class N(Generic[T]): ...
-
-
 class C(N[N["C"]]): ...
-
-
 _: N[C] = C()
 ```
 
@@ -64,5 +56,5 @@ certain programs is unavoidable.
 ## What's new?
 
 We introduce an alternative construction that is supposed to compile much faster for large inputs. You can try the new
-construction by typing `R` instead of
-`G` in the first argument to `app.py`.
+construction by using `Algorithm.Roth` instead of
+`Algorithm.Grigore` in the script above.

typing_machines/experiment/__init__.py

@@ -0,0 +1,96 @@
+from os import remove
+from random import Random
+from resource import RLIMIT_STACK, setrlimit
+from subprocess import Popen, DEVNULL
+from time import sleep
+from typing import Callable, List, Tuple, Iterable
+
+import matplotlib.pyplot as plt
+
+from typing_machines.app import encode, Algorithm
+from typing_machines.examples.machines import palindromes
+
+
+def binary_search(le: Callable[[int], bool]) -> int:
+    """
+    Finds a natural number according to the given "lower equals" predicate.
+    Returns -1 if no number is found.
+    """
+    l: int = -1
+    u: int = 1
+    while le(u):
+        l = u
+        u *= 2
+    u -= 1
+    while l < u:
+        m: int = (l + u) // 2 + (l + u) % 2
+        if le(m):
+            l = m
+        else:
+            u = m - 1
+    return l
+
+
+def get_random_palindrome(n: int) -> str:
+    """
+    Returns a random palindrome over {a, b} of length n.
+    Always returns the same word for a given n.
+    """
+    random: Random = Random(n)
+    palindrome: str = ""
+    while n > 0:
+        l: str = "a" if random.getrandbits(1) else "b"
+        palindrome = l + palindrome + l
+        n -= 1
+    return palindrome
+
+
+def get_stack_size(algorithm: Algorithm, input_word: str) -> int:
+    """
+    Get the call stack size mypy requires to compile the palindromes typing machine with the given
+    algorithm and input palindrome.
+    """
+
+    def compiles(n: int) -> bool:
+        with open("test.py", "w") as python_file:
+            python_file.write(encode(algorithm, palindromes, input_word))
+        sleep(1)
+        stack_size: int = (n + 5) * 1000000
+        with Popen(["mypy", "test.py"], preexec_fn=lambda: setrlimit(RLIMIT_STACK, (stack_size, stack_size)),
+                   stdout=DEVNULL, stderr=DEVNULL) as p:
+            retcode = p.wait(timeout=10)
+        remove("test.py")
+        return retcode != 0
+
+    depth: int = binary_search(compiles)
+    depth = 5 if depth == -1 else depth + 5
+    return depth
+
+
+def run_experiment(algorithm: Algorithm, input_lengths: Iterable[int]) -> List[Tuple[int, int]]:
+    """
+    Find mypy stack sizes for given algorithm and input lengths.
+    """
+    results: List[Tuple[int, int]] = []
+    for n in input_lengths:
+        s: int = get_stack_size(algorithm, get_random_palindrome(n))
+        results.append((n * 2, s))
+        print(f"mypy requires {s}M stack size with algorithm {algorithm.name} and palindrome of length {n * 2}")
+    return results
+
+
+if __name__ == '__main__':
+    grigore_results: List[Tuple[int, int]] = run_experiment(Algorithm.Grigore, range(5, 9))
+    print("Grigore's results:")
+    for n, s in grigore_results:
+        print(f"Grigore\t{n}\t{s}")
+    roth_results: List[Tuple[int, int]] = run_experiment(Algorithm.Roth, range(5, 46, 5))
+    print("Roth's results:")
+    for n, s in roth_results:
+        print(f"Roth\t{n}\t{s}")
+    plt.plot([n for n, _ in grigore_results], [s for _, s in grigore_results], color="blue", label="Grigore")
+    plt.scatter([n for n, _ in grigore_results], [s for _, s in grigore_results], color="blue", marker="o")
+    plt.plot([n for n, _ in roth_results], [s for _, s in roth_results], color="green", label="Roth")
+    plt.scatter([n for n, _ in roth_results], [s for _, s in roth_results], color="green", marker="x")
+    plt.legend(loc="upper right")
+    plt.show()