Use numpy and pmf function to speed up gen

Numpy has a built-in way to sum probability mass functions (pmf).
This shaves of 60% of the generation time :D

worlds/yachtdice/Rules.py

@@ -7,6 +7,7 @@ from BaseClasses import MultiWorld
 from worlds.generic.Rules import set_rule
 
 from .YachtWeights import yacht_weights
+import numpy as np
 
 
 # This module adds logic to the apworld.
@@ -69,8 +70,6 @@ class Category:
         return mean_score * self.quantity
 
 
-
-
 class ListState:
     def __init__(self, state: List[str]):
         self.state = state
@@ -99,19 +98,25 @@ def extract_progression(state, player, options):
     )
     number_of_fixed_mults = state.count("Fixed Score Multiplier", player)
     number_of_step_mults = state.count("Step Score Multiplier", player)
-    
+
     categories = [
         Category(category_value, state.count(category_name, player))
         for category_name, category_value in category_mappings.items()
         if state.count(category_name, player)  # want all categories that have count >= 1
-    ]        
-            
+    ]
+
     extra_points_in_logic = state.count("1 Point", player)
     extra_points_in_logic += state.count("10 Points", player) * 10
     extra_points_in_logic += state.count("100 Points", player) * 100
 
-    return categories, number_of_dice, number_of_rerolls, number_of_fixed_mults * 0.1, number_of_step_mults * 0.01, extra_points_in_logic,
-    
+    return (
+        categories,
+        number_of_dice,
+        number_of_rerolls,
+        number_of_fixed_mults * 0.1,
+        number_of_step_mults * 0.01,
+        extra_points_in_logic,
+    )
 
 
 # We will store the results of this function as it is called often for the same parameters.
@@ -140,18 +145,44 @@ def dice_simulation_strings(categories, num_dice, num_rolls, fixed_mult, step_mu
     # sort categories because for the step multiplier, you will want low-scoring categories first
     categories.sort(key=lambda category: category.mean_score(num_dice, num_rolls))
 
-    # function to add two discrete distribution.
-    # defaultdict is a dict where you don't need to check if an id is present, you can just use += (lot faster)
-    def add_distributions(dist1, dist2):
-        combined_dist = defaultdict(float)
-        for val1, prob1 in dist1.items():
-            for val2, prob2 in dist2.items():
-                combined_dist[val1 + val2] += prob1 * prob2
-        return dict(combined_dist)
+    # we have two ways to store a distribution (example, 0 with probability 0.4, 10 with probability 0.6):
+    # dict: {0: 0.4, 10: 0.6}
+    # pmf (probability mass function): [0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.6] (numpy array)
+    # adding two distributions works fast with pmf's and numpy's convolve method.
+    # maximizing two distributions (with multipliers) seems to work fastest with dictionaries.
+
+    def dict_to_pmf(dist):
+        """
+        Convert dict-distribution to pmf-distribution
+        """
+        max_value = max(dist) + 1
+        return np.array([dist.get(i, 0) for i in range(max_value)])
+
+    def pmf_to_dict(pmf):
+        """
+        Convert pmf-distribution to dict-distribution
+        """
+        sum_values = np.arange(0, len(pmf) + 1)
+        sum_dist = {v: p for v, p in zip(sum_values, pmf)}
+        return sum_dist
+
+    def add_distributions(pmf1, dic2):
+        """
+        function to add two discrete distributions. The first in pmf form, the second in dict form, returns pmf.
+        """
+        pmf2 = dict_to_pmf(dic2)
+
+        # Sum the two distributions using convolution
+        sum_pmf = np.convolve(pmf1, pmf2)
+
+        return sum_pmf
 
-    # function to take the maximum of "times" i.i.d. dist1.
-    # (I have tried using defaultdict here too but this made it slower.)
     def max_dist(dist1, mults):
+        """
+        function to take the maximum of "times" i.i.d. dist1.
+        dist1 is a dict-distribution
+        (I have tried using defaultdict here too but this made it slower.)
+        """
         new_dist = {0: 1}
         for mult in mults:
             c = new_dist.copy()
@@ -171,16 +202,10 @@ def dice_simulation_strings(categories, num_dice, num_rolls, fixed_mult, step_mu
 
     # Returns percentile value of a distribution.
     def percentile_distribution(dist, percentile):
-        sorted_values = sorted(dist.keys())
-        cumulative_prob = 0
-
-        for val in sorted_values:
-            cumulative_prob += dist[val]
-            if cumulative_prob >= percentile:
-                return val
+        cumdist = np.cumsum(dist)
 
         # Return the last value if percentile is higher than all probabilities
-        return sorted_values[-1]
+        return np.argmax(cumdist > percentile)
 
     # parameters for logic.
     # perc_return is, per difficulty, the percentages of total score it returns (it averages out the values)
@@ -188,8 +213,8 @@ def dice_simulation_strings(categories, num_dice, num_rolls, fixed_mult, step_mu
     perc_return = [[0], [0.1, 0.5], [0.3, 0.7], [0.55, 0.85], [0.85, 0.95]][diff]
     diff_divide = [0, 9, 7, 3, 2][diff]
 
-    # calculate total distribution
-    total_dist = {0: 1}
+    # calculate total distribution, start in pmf-form
+    total_dist = [1]
     for j, category in enumerate(categories):
         if num_dice == 0 or num_rolls == 0:
             dist = {0: 100000}
@@ -208,12 +233,12 @@ def dice_simulation_strings(categories, num_dice, num_rolls, fixed_mult, step_mu
 
         total_dist = add_distributions(total_dist, dist)
 
-    # save result into the cache, then return it
+    # note, total_dist is in pmf-form
     outcome = sum([percentile_distribution(total_dist, perc) for perc in perc_return]) / len(perc_return)
+    # save result into the cache, then return it
     yachtdice_cache[tup] = max(5, math.floor(outcome))  # at least 5.
-    
-    return yachtdice_cache[tup]
 
+    return yachtdice_cache[tup]
 
 
 def dice_simulation(state, player, options):
@@ -243,7 +268,6 @@ def dice_simulation(state, player, options):
     return state.prog_items[player]["maximum_achievable_score"]
 
 
-
 def set_yacht_rules(world: MultiWorld, player: int, options):
     """
     Sets rules on entrances and advancements that are always applied
@@ -262,4 +286,3 @@ def set_yacht_completion_rules(world: MultiWorld, player: int):
     Sets rules on completion condition
     """
     world.completion_condition[player] = lambda state: state.has("Victory", player)
-