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