Add calculate_digits.py and use Decimal instead of float

calculate_digits.py

@@ -0,0 +1,37 @@
+import sys
+from decimal import Decimal
+
+from physics import calculate_collision
+
+if len(sys.argv) != 2 or not sys.argv[1].isnumeric() or int(sys.argv[1]) < 0:
+    print(f"Usage: {sys.argv[0]} <digits>")
+    exit()
+
+m1: int = 1
+m2: int = 100 ** int(sys.argv[1])
+v1: Decimal = Decimal(0)
+v2: Decimal = Decimal(-1)
+x1: Decimal = Decimal(100)
+x2: Decimal = Decimal(200)
+w: int = 20
+collisions: int = 0
+wall: bool = False
+
+# simulate until blocks cannot collide
+while not (0 <= v1 <= v2):
+    if wall:
+        # left block collides with wall
+        time_wall_collision: float = x1 / -v1
+        x1 += time_wall_collision * v1
+        x2 += time_wall_collision * v2
+        v1 *= -1
+    else:
+        # blocks collide with each other
+        time_block_collision: float = (w + x1 - x2) / (v2 - v1)
+        x1 += time_block_collision * v1
+        x2 += time_block_collision * v2
+        v1, v2 = calculate_collision(m1, v1, m2, v2)
+    collisions += 1
+    wall = not wall
+
+print(collisions)

physics.py

@@ -1,7 +1,8 @@
+from decimal import Decimal
 from typing import Tuple
 
 
-def calculate_collision(m1: float, v1: float, m2: float, v2: float) -> Tuple[float, float]:
+def calculate_collision(m1: int, v1: Decimal, m2: int, v2: Decimal) -> Tuple[Decimal, Decimal]:
     """
     Calculates the new velocities after the two blocks collide.
 
@@ -12,11 +13,11 @@ def calculate_collision(m1: float, v1: float, m2: float, v2: float) -> Tuple[flo
     :return: The two new velocities
     """
 
-    mv: float = m1 * v1 + m2 * v2
-    s: float = m1 + m2
-    b: float = mv / s
-    d: float = (b ** 2 - (mv ** 2 - (m1 * v1 ** 2 + m2 * v2 ** 2) * m2) / (m1 * s)) ** .5
-    new_v1: float = max([b - d, b + d], key=lambda a: abs(a - v1))
-    d: float = (b ** 2 - (mv ** 2 - (m1 * v1 ** 2 + m2 * v2 ** 2) * m1) / (m2 * s)) ** .5
-    new_v2: float = max([b - d, b + d], key=lambda a: abs(a - v2))
+    mv: Decimal = m1 * v1 + m2 * v2
+    s: Decimal = m1 + m2
+    b: Decimal = mv / s
+    d: Decimal = (b ** 2 - (mv ** 2 - (m1 * v1 ** 2 + m2 * v2 ** 2) * m2) / (m1 * s)).sqrt()
+    new_v1: Decimal = max([b - d, b + d], key=lambda a: abs(a - v1))
+    d: Decimal = (b ** 2 - (mv ** 2 - (m1 * v1 ** 2 + m2 * v2 ** 2) * m1) / (m2 * s)).sqrt()
+    new_v2: Decimal = max([b - d, b + d], key=lambda a: abs(a - v2))
     return new_v1, new_v2

picollisions.py

@@ -1,6 +1,8 @@
-from PyQt5.QtCore import *
-from PyQt5.QtGui import *
-from PyQt5.QtWidgets import *
+from decimal import Decimal
+
+from PyQt5.QtCore import Qt, QBasicTimer, QTimerEvent
+from PyQt5.QtGui import QPainter, QPaintEvent, QKeyEvent, QPen, QColor, QFont, QFontMetrics
+from PyQt5.QtWidgets import QWidget, QApplication
 
 from physics import calculate_collision
 
@@ -12,14 +14,14 @@ class Window(QWidget):
         self.setWindowTitle("Pi Collisions")
         self.setFixedSize(640, 480)
 
-        self.m1: float = 1
-        self.v1: float = 0
-        self.x1: float = 150
+        self.m1: int = 1
+        self.v1: Decimal = Decimal(0)
+        self.x1: Decimal = Decimal(150)
         self.s1: int = 50
 
-        self.m2: float = 100
-        self.v2: float = -1
-        self.x2: float = 300
+        self.m2: int = 100 ** 1
+        self.v2: Decimal = Decimal(-1)
+        self.x2: Decimal = Decimal(300)
         self.s2: int = 100
 
         self.timer = QBasicTimer()