Merge remote-tracking branch 'origin/main'

Schenk_Brandenberger_S2_Aufg4.py

@@ -1,8 +1,38 @@
-def maxPower(base):
-    x = 0.5
-    power = 0
-    while x > 0:
-        power = power + 1
-        x = x / base
-    return power
-print(maxPower(2))
+
+def eps(base, n): # n = Anzahl Stellen der Mantisse
+    return 0.5 * (base ** (1-n))
+
+
+def digitsMantiss(base):     # -5*10^-17
+    last_x = 0
+    x = 1.5
+    n = 1
+    while x > 1:
+        last_x = x
+        x = x - (x - 1) / base
+        n = n + 1
+    return n, last_x
+
+def largestNumber(digitsMantiss):
+    x = 0.0
+    for i in range(digitsMantiss):
+        x = x + 2 ** i
+    return x
+
+def largestNumber_eps(eps, n):
+    return eps * 2**(2*n) - 1
+
+
+
+
+digMan = digitsMantiss(2)
+epsVal = eps(2, digMan[0])
+largest = largestNumber(digMan[0])
+largest_eps = largestNumber_eps(epsVal, digMan[0])
+
+
+print(f'eps: {epsVal}')
+print(f'Digits Mantiss: {digMan[0]}')
+print(f'Smallest Number 1 + eps > 1: {digMan[1]}')
+print(f'largest Number 1 + qmax > qmax: {largest}')
+print(f'largest Number 1 + qmax > qmax (calculated by eps: {largest_eps}')