4aa74d9c0b
Defines `mergeSort`, a naive stable merge sort algorithm, replaces it via a `@[csimp]` lemma with something faster at runtime, and proves the following results: * `mergeSort_sorted`: `mergeSort` produces a sorted list. * `mergeSort_perm`: `mergeSort` is a permutation of the input list. * `mergeSort_of_sorted`: `mergeSort` does not change a sorted list. * `mergeSort_cons`: proves `mergeSort le (x :: xs) = l₁ ++ x :: l₂` for some `l₁, l₂` so that `mergeSort le xs = l₁ ++ l₂`, and no `a ∈ l₁` satisfies `le a x`. * `mergeSort_stable`: if `c` is a sorted sublist of `l`, then `c` is still a sublist of `mergeSort le l`.
38 lines
1.3 KiB
Python
38 lines
1.3 KiB
Python
import subprocess
|
|
import numpy as np
|
|
from scipy.optimize import curve_fit
|
|
import matplotlib.pyplot as plt
|
|
|
|
# Function to run the command and capture the elapsed time from stdout
|
|
def benchmark(i):
|
|
result = subprocess.run([f'./.lake/build/bin/mergeSort', str(i)], capture_output=True, text=True)
|
|
elapsed_time_ms = int(result.stdout.strip()) # Assuming the time is printed as a single integer in ms
|
|
return elapsed_time_ms / 1e3 # Convert milliseconds to seconds
|
|
|
|
# Benchmark for i = 0.1, 0.2, ..., 1.0 with 5 runs each
|
|
i_values = []
|
|
times = []
|
|
|
|
for i in range(1, 11):
|
|
run_times = sorted([benchmark(i) for _ in range(5)])
|
|
middle_three_avg = np.mean(run_times[1:4]) # Take the average of the middle 3 times
|
|
times.append(middle_three_avg)
|
|
i_values.append(i / 1e1)
|
|
|
|
# Fit the data to A*i + B*i*log(i)
|
|
def model(i, A, B):
|
|
return A * i + B * i * np.log(i)
|
|
|
|
popt, _ = curve_fit(model, i_values, times)
|
|
A, B = popt
|
|
|
|
# Print the fit parameters
|
|
print(f"Best fit parameters: A = {A}, B = {B}")
|
|
|
|
# Plot the results
|
|
plt.plot(i_values, times, 'o', label='Benchmark Data (Avg of Middle 3)')
|
|
plt.plot(i_values, model(np.array(i_values), *popt), '-', label=f'Fit: A*i + B*i*log(i)\nA={A:.3f}, B={B:.3f}')
|
|
plt.xlabel('i')
|
|
plt.ylabel('Time (s)')
|
|
plt.legend()
|
|
plt.show()
|