From: Nils Forssén <nilfo359@student.liu.se>
Date: Fri, 31 Jan 2025 22:34:36 +0000 (+0100)
Subject: Added all files
X-Git-Url: https://gitweb.forssennils.se/?a=commitdiff_plain;h=a22577d35d16d46c9eb5560fbb544f1631403d66;p=gymnasiearbete.git

Added all files
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diff --git a/Buffon'sNeedle.xlsx b/Buffon'sNeedle.xlsx
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diff --git a/GyAr.pdf b/GyAr.pdf
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diff --git a/Machine's.py b/Machine's.py
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+"""
+Python3 program to calculate PI using long integers
+
+See: http://www.craig-wood.com/nick/articles/pi-machin/
+
+By Nick Craig-Wood <nick@craig-wood.com>
+"""
+
+from time import time
+
+def arctan(x, one=1000000):
+    """
+    Calculate arctan(1/x)
+
+    arctan(1/x) = 1/x - 1/3*x**3 + 1/5*x**5 - ... (x > 1)
+
+    This calculates it in fixed point, using the value for one passed in
+    """
+    power = one // x            # the +/- 1/x**n part of the term
+    total = power               # the total so far
+    x_squared = x * x           # precalculate x**2
+    divisor = 1                 # the 1,3,5,7 part of the divisor
+    while 1:
+        power = - power // x_squared
+        divisor += 2
+        power += divisor // 2   # round the division
+        delta = power // divisor
+        if delta == 0:
+            break
+        total += delta
+    return total
+
+def arctan_euler(x, one=1000000):
+    """
+    Calculate arctan(1/x) using euler's accelerated formula
+
+    arctan(1/x) =                   x / (1+x**2)
+                + (2/3)           * x / (1+x**2)**2
+                + (2*4/(3*5))     * x / (1+x**2)**3
+                + (2*4*6/(3*5*7)) * x / (1+x**2)**4
+                + ...
+
+    This calculates it in fixed point, using the value for one passed in
+    """
+    x_squared = x * x
+    x_squared_plus_1 = x_squared + 1
+    term = (x * one) // x_squared_plus_1
+    total = term
+    two_n = 2
+    while 1:
+        divisor = (two_n+1) * x_squared_plus_1
+        term *= two_n
+        term += divisor // 2    # round the division
+        term = term // divisor
+        if term == 0:
+            break
+        total += term
+        two_n += 2
+    return total
+
+def pi_machin(one):
+    return 4*(4*arctan(5, one) - arctan(239, one))
+def pi_machin_euler(one):
+    return 4*(4*arctan_euler(5, one) - arctan_euler(239, one))
+
+def pi_ferguson(one):
+    return 4*(3*arctan(4, one) + arctan(20, one) + arctan(1985, one))
+
+def pi_hutton(one):
+    return 4*(2*arctan(3, one) + arctan(7, one))
+
+def pi_gauss(one):
+    return 4*(12*arctan(18, one) + 8*arctan(57, one) - 5*arctan(239, one))
+def pi_gauss_euler(one):
+    return 4*(12*arctan_euler(18, one) + 8*arctan_euler(57, one) - 5*arctan_euler(239, one))
+
+if __name__ == "__main__":
+    for log10_digits in range(1,7):
+        digits = 10**log10_digits
+        one = 10**digits
+
+        start =time()
+        pi = pi_machin(one)
+        #print(pi)
+        print("machin: digits",digits,"time",time()-start)
+
+        start =time()
+        pi = pi_machin_euler(one)
+        #print(pi)
+        print("machin euler: digits",digits,"time",time()-start)
+
+        start =time()
+        pi = pi_gauss(one)
+        #print(pi)
+        print("gauss: digits",digits,"time",time()-start)
+
+        start =time()
+        pi = pi_gauss_euler(one)
+        #print(pi)
+        print("gauss euler: digits",digits,"time",time()-start)
+    #print(pi_ferguson(one))
+    #print(pi_hutton(one))
+    #print(pi_gauss(one))