Fix cdf on micropython

.idea/.gitignore

@@ -6,3 +6,5 @@
 # Datasource local storage ignored files
 /dataSources/
 /dataSources.local.xml
+# GitHub Copilot persisted chat sessions
+/copilot/chatSessions

.idea/casio-calculator.iml

@@ -1,7 +1,9 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <module type="PYTHON_MODULE" version="4">
   <component name="NewModuleRootManager">
-    <content url="file://$MODULE_DIR$" />
+    <content url="file://$MODULE_DIR$">
+      <excludeFolder url="file://$MODULE_DIR$/.idea/copilot/chatSessions" />
+    </content>
     <orderEntry type="jdk" jdkName="Pipenv (casio-calculator)" jdkType="Python SDK" />
     <orderEntry type="sourceFolder" forTests="false" />
   </component>

Pipfile

@@ -9,4 +9,3 @@ name = "pypi"
 
 [requires]
 python_version = "3.11"
-python_full_version = "3.11.7"

Pipfile.lock

@@ -1,11 +1,10 @@
 {
     "_meta": {
         "hash": {
-            "sha256": "bc82cd27f07d4e24b750064464bbc233a141778868b9a387125705e2d4e8a830"
+            "sha256": "ed6d5d614626ae28e274e453164affb26694755170ccab3aa5866f093d51d3e4"
         },
         "pipfile-spec": 6,
         "requires": {
-            "python_full_version": "3.11.7",
             "python_version": "3.11"
         },
         "sources": [

cdf.py

@@ -0,0 +1,79 @@
+import math
+
+
+def normal_dist_cdf(x, mu=0.0, sigma=1.0):
+    return 0.5 * (1.0 + math.erf((x - mu) / (sigma * (2 ** 0.5))))
+
+
+def normal_dist_inv_cdf(p, mu=0.0, sigma=1.0):
+    # There is no closed-form solution to the inverse CDF for the normal
+    # distribution, so we use a rational approximation instead:
+    # Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
+    # Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
+    # (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
+    q = p - 0.5
+    if math.fabs(q) <= 0.425:
+        r = 0.180625 - q * q
+        # Hash sum: 55.88319_28806_14901_4439
+        num = (((((((2.5090809287301226727e+3 * r +
+                     3.3430575583588128105e+4) * r +
+                    6.7265770927008700853e+4) * r +
+                   4.5921953931549871457e+4) * r +
+                  1.3731693765509461125e+4) * r +
+                 1.9715909503065514427e+3) * r +
+                1.3314166789178437745e+2) * r +
+               3.3871328727963666080e+0) * q
+        den = (((((((5.2264952788528545610e+3 * r +
+                     2.8729085735721942674e+4) * r +
+                    3.9307895800092710610e+4) * r +
+                   2.1213794301586595867e+4) * r +
+                  5.3941960214247511077e+3) * r +
+                 6.8718700749205790830e+2) * r +
+                4.2313330701600911252e+1) * r +
+               1.0)
+        x = num / den
+        return mu + (x * sigma)
+    r = p if q <= 0.0 else 1.0 - p
+    r = math.sqrt(-math.log(r))
+    if r <= 5.0:
+        r = r - 1.6
+        # Hash sum: 49.33206_50330_16102_89036
+        num = (((((((7.74545014278341407640e-4 * r +
+                     2.27238449892691845833e-2) * r +
+                    2.41780725177450611770e-1) * r +
+                   1.27045825245236838258e+0) * r +
+                  3.64784832476320460504e+0) * r +
+                 5.76949722146069140550e+0) * r +
+                4.63033784615654529590e+0) * r +
+               1.42343711074968357734e+0)
+        den = (((((((1.05075007164441684324e-9 * r +
+                     5.47593808499534494600e-4) * r +
+                    1.51986665636164571966e-2) * r +
+                   1.48103976427480074590e-1) * r +
+                  6.89767334985100004550e-1) * r +
+                 1.67638483018380384940e+0) * r +
+                2.05319162663775882187e+0) * r +
+               1.0)
+    else:
+        r = r - 5.0
+        # Hash sum: 47.52583317549289671629
+        num = (((((((2.01033439929228813265e-7 * r +
+                     2.71155556874348757815e-5) * r +
+                    1.24266094738807843860e-3) * r +
+                   2.65321895265761230930e-2) * r +
+                  2.96560571828504891230e-1) * r +
+                 1.78482653991729133580e+0) * r +
+                5.46378491116411436990e+0) * r +
+               6.65790464350110377720e+0)
+        den = (((((((2.04426310338993978564e-15 * r +
+                     1.42151175831644588870e-7) * r +
+                    1.84631831751005468180e-5) * r +
+                   7.86869131145613259100e-4) * r +
+                  1.48753612908506148525e-2) * r +
+                 1.36929880922735805310e-1) * r +
+                5.99832206555887937690e-1) * r +
+               1.0)
+    x = num / den
+    if q < 0.0:
+        x = -x
+    return mu + (x * sigma)

distribution.py

@@ -1,4 +1,5 @@
 import math
+import cdf
 
 
 def factorial(n):
@@ -371,14 +372,116 @@ def pd_gt(x, l):
     return 1 - pd_leq(x, l)
 
 
+def sample_mean_e(u):
+    """
+    Computes the expected value of the sample mean.
+    :param u: The population mean.
+    :return: Returns the expected value of the sample mean.
+    """
+    return u
+
+
+def sample_mean_std(u, n):
+    """
+    Computes the standard deviation of the sample mean.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the standard deviation of the sample mean.
+    """
+    return u / n ** 0.5
+
+
+def sample_mean_var(u, n):
+    """
+    Computes the variance of the sample mean.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the variance of the sample mean.
+    """
+    return (sample_mean_std(u, n) ** 2) / n
+
+
+def z_score(x, u, s):
+    """
+    Computes the z-score of a sample.
+    :param x: The sample mean.
+    :param u: The population mean.
+    :param s: The standard deviation of the sample mean.
+    :return: Returns the z-score of the sample.
+    """
+    return (x - u) / s
+
+
+def z_to_p(z):
+    """
+    Computes the probability of a z-score.
+    :param z: The z-score.
+    :return: Returns the probability of the z-score.
+    """
+
+    return cdf.normal_dist_cdf(z)
+
+
+def p_to_z(p):
+    """
+    Computes the z-score of a probability.
+    :param p: The probability.
+    :return: Returns the z-score of the probability.
+    """
+    return cdf.normal_dist_inv_cdf(p)
+
+
+def gamma(u, n):
+    """
+    Computes the gamma of a sample.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the gamma of the sample.
+    """
+    return sample_mean_var(u, n) / sample_mean_e(u)
+
+
+def alpha(u, n):
+    """
+    Computes the alpha of a sample.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the alpha of the sample.
+    """
+    return sample_mean_e(u) / gamma(u, n)
+
+
+def margin_of_error(a, s, n):
+    """
+    Computes the margin of error of a sample.
+    :param a: The alpha of the sample.
+    :param s: The standard deviation of the sample mean.
+    :param n: The sample size.
+    :return: Returns the margin of error of the sample.
+    """
+    return abs((p_to_z(a / 2)) * (s / (n ** 0.5)))
+
+
+def confidence_interval(x, a, s, n):
+    """
+    Computes the confidence interval of a sample.
+    :param x: The sample mean.
+    :param a: The alpha of the sample.
+    :param s: The standard deviation of the sample mean.
+    :param n: The sample size.
+    :return: Returns the confidence interval of the sample.
+    """
+    return x - margin_of_error(a, s, n), x + margin_of_error(a, s, n)
+
+
 def man():
     """
     Prints the manual for the module.
     """
-	seperator = "-" * 20
+    separator = "-" * 20
     print("This module contains functions for computing the total probability of events.")
     print("The functions are:")
-	print(seperator)
+    print(separator)
     print("Binomial Distribution")
     print("bnd(x, n, p)")
     print("bnd_mean(n, p)")
@@ -388,7 +491,7 @@ def man():
     print("bnd_lt(x, n, p)")
     print("bnd_geq(x, n, p)")
     print("bnd_gt(x, n, p)")
-	print(seperator)
+    print(separator)
     print("Geometric Distribution")
     print("gd(x, p, q)")
     print("gd_mean(p)")
@@ -398,7 +501,7 @@ def man():
     print("gd_lt(x, p, q)")
     print("gd_geq(x, p, q)")
     print("gd_gt(x, p, q)")
-	print(seperator)
+    print(separator)
     print("Hyper Geometric Distribution")
     print("hgd(x, N, n, k)")
     print("hgd_mean(N, n, k)")
@@ -408,7 +511,7 @@ def man():
     print("hgd_lt(x, N, n, k)")
     print("hgd_geq(x, N, n, k)")
     print("hgd_gt(x, N, n, k)")
-	print(seperator)
+    print(separator)
     print("Poisson Distribution")
     print("pd(x, l)")
     print("pd_mean(l)")
@@ -418,3 +521,15 @@ def man():
     print("pd_lt(x, l)")
     print("pd_geq(x, l)")
     print("pd_gt(x, l)")
+    print(separator)
+    print("Sample Mean")
+    print("sample_mean_e(u)")
+    print("sample_mean_std(u, n)")
+    print("sample_mean_var(u, n)")
+    print("z_score(x, u, s)")
+    print("z_to_p(z)")
+    print("p_to_z(p)")
+    print("gamma(u, n)")
+    print("alpha(u, n)")
+    print("margin_of_error(a, s, n)")
+    print("confidence_interval(x, a, s, n)")

netcentric.py

@@ -0,0 +1,105 @@
+# Calculate internet checksum for any arbitrary length variable amount of binary numbers
+def checksum(*args):
+	length = len(bin(args[0])) - 2
+	result = 0
+	for arg in args:
+		result += arg
+		if result > (2 ** length) - 1:
+			result = (result & ((2 ** length) - 1)) + 1
+	return result ^ ((2 ** length) - 1)
+
+
+def e2e_delay(P, L, N, R):
+	# P = propagation speed
+	# L = packet length
+	# N = number of packets
+	# R = transmission rate
+	return (P - 1) * (L / R) + N * (L / R)
+
+
+def estimate_e2e_delay(PS, T):
+	# PS = packet size
+	# T = Throughput
+	return PS / T
+
+
+def trans_delay(L, R):
+	# L = packet length
+	# R = transmission rate
+	return L / R
+
+
+def prop_delay(P, L):
+	# P = propagation speed
+	# L = packet length
+	return P * L
+
+
+def traffic_intensity(L, pps, R):
+	# L = packet length
+	# pps = packets per second
+	# R = transmission rate
+	return (L * pps) / R
+
+
+def cs_time(N, F, U):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	return (N * F) / U
+
+
+def cs_time_n_clients(N, F, U, D):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	# D = Client download rate
+	return max(cs_time(N, F, U), F / D)
+
+
+def p2p_time(N, F, U, CD, D):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	# CU = Client upload rate
+	# D = Client download rate
+	return max((F / U), (N * F) / (U + (N * CD)), F / D)
+
+
+def utilisation(L, R, RTT):
+	# L = packet length
+	# R = transmission rate
+	# RTT = round trip time
+	return (L / R) / (L / R + RTT)
+
+
+def utilisation_pipeline(L, R, RTT, N):
+	# L = packet length
+	# R = transmission rate
+	# RTT = round trip time
+	# N = window size
+	return N / (1 + (RTT / (L / R)))
+
+
+def print_byte_tables():
+	print("Byte Conversion Table")
+	print("1 B = 8 bits")
+	print("kB = 1024 bytes")
+	print("MB = 1024 kB")
+	print("GB = 1024 MB")
+	print("TB = 1024 GB")
+
+
+def man():
+	print("checksum(0b, 0b,)")
+	print("e2e_delay(P, L, N, R)")
+	print("estimate_e2e_delay(PS, T)")
+	print("trans_delay(L, R)")
+	print("prop_delay(P, L)")
+	print("traffic_intensity(L, pps, R)")
+	print("cs_time(N, F, U)")
+	print("cs_time_n_clients(N, F, U, D)")
+	print("p2p_time(N, F, U, CD, D)")
+	print("utilisation(L, R, RTT)")
+	print("utilisation_pipeline(L, R, RTT, N)")
+	print("print_byte_tables()")