Serie 02

Kuengjoe_s02/Kuengjoe_S02_Aufg4.py

@@ -0,0 +1,37 @@
+
+
+import math
+
+def maschinengenauigkeit():
+    eps = 1.0
+    while 1.0 + eps != 1.0:
+        eps /= 2.0
+    return eps
+
+def q_min_aus_eps(eps):
+    q = 1.0/eps
+    while 1.0 + q != q:
+        q *= 2.0
+    return q
+
+eps = maschinengenauigkeit()
+eps_krit = 2.0*eps
+q_min = q_min_aus_eps(eps)
+
+bits = round(-math.log2(eps))      # ≈ 53
+decs = round(-math.log10(eps))
+
+eps = maschinengenauigkeit()
+eps_krit = 2.0 * eps         # kleinste Zahl mit 1+eps_krit != 1
+q_min = q_min_aus_eps(eps)
+
+bits = round(-math.log2(eps))     # ≈ 53
+decs = round(-math.log10(eps))    # ≈ 16
+
+print(f"Maschinengenauigkeit eps   = {eps:.20e}")
+print(f"Kontrolle: 1+eps == 1      -> {1.0 + eps == 1.0}")
+print(f"Kontrolle: 1+2*eps != 1    -> {1.0 + eps_krit != 1.0}")
+print(f"Signifikanz: ~{bits} Bits (~{decs} Dezimalstellen)")
+print(f"q_min                     = {q_min:.0f}")
+print(f"Kontrolle: 1+q_min == q_min -> {1.0 + q_min == q_min}")
+print("Zusammenhang: q_min = 1/eps (bei IEEE-754 double exakt).")