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1 #
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2 # Determine if floating point numbers are very close
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3 ###########
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4
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5 import math
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6
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7 DEFAULT_SANITY_CHECK_EPSILON = 1e-6
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8
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9 def floateq(a, b, epsilon=DEFAULT_SANITY_CHECK_EPSILON):
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10 """
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11 Compare two floats, with some epsilon tolerance.
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12 """
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13 return absolute_relative_error(a, b) < epsilon
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14
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15 def absolute_relative_error(a, b, epsilon=DEFAULT_SANITY_CHECK_EPSILON):
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16 return abs(a - b) / (abs(a) + abs(b) + epsilon)
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17
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18 def double_epsilon_multiplicative_eq(a, b, epsilon=DEFAULT_SANITY_CHECK_EPSILON):
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19 """
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20 Determine if doubles are equal to within a multiplicative factor of
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21 L{epsilon}.
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22 @note: This function should be preferred over
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23 L{double_epsilon_additive_eq}, unless the values to be compared may
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24 have differing signs.
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25 @precondition: sign(a) == sign(b)
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26 @rtype: bool
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27 """
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28 if a == b: return True
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29 if a == 0 and b == 0: return True
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30 assert a != 0
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31 assert b != 0
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32 assert sign(a) == sign(b)
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33 if a > b: d = a / b
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34 else: d = b / a
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35 assert d >= 1
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36 return True if d <= 1 + SANITY_CHECK_EPSILON else False
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37
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38 def double_epsilon_additive_eq(a, b):
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39 """
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40 Determine if doubles are equal to within an additive factor of
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41 L{SANITY_CHECK_EPSILON}.
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42 @note: Prefer L{double_epsilon_multiplicative_eq} to this function
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43 unless the values to be compared may have differing signs.
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44 """
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45 if a == b: return True
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46 if a == 0 and b == 0: return True
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47 assert sign(a) != sign(b) # Should use SANITY_CHECK_EPSILON
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48 d = math.fabs(a - b)
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49 return d <= SANITY_CHECK_EPSILON
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