[FIX] tools: epsilon magnitude #35565
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The following rounding is incorrect:
```
>>> float_round(6.6 * 0.175, precision_digits=2)
1.15
```
Indeed, 6.6 * 0.175 = 1.155 ≈ 1.16.
In this specific case, the `epsilon` computed is not sufficient. A
precision of 53 gives:
normalized_value = 115.49999999999997
epsilon = 1.2823075934420547e-14
=> new normalized_value = 115.49999999999999
Bad luck, this is just not enough to tip the value in the right
direction.
However, a precision of 52 is sufficient:
normalized_value = 115.49999999999997
epsilon = 2.5646151868841094e-14
=> new normalized_value = 115.5
The value of 53 was chosen from the `binary64` number format precision.
In case of Python, the corresponding machine epsilon is 2^-52 [1].
Therefore, using 52 instead of 53 does make sense.
It is worth noting that the value of the machine epsilon
2^-52 = 2.2204460492503131e-16, which is still 2 orders of magnitude
below our dynamic estimation.
[1] https://en.wikipedia.org/wiki/Machine_epsilon
[2] `numpy.finfo(float).eps = 2.2204460492503131e-16`
opw-2047368
|
robodoo r+ |
robodoo
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Aug 20, 2019
The following rounding is incorrect: ``` >>> float_round(6.6 * 0.175, precision_digits=2) 1.15 ``` Indeed, 6.6 * 0.175 = 1.155 ≈ 1.16. In this specific case, the `epsilon` computed is not sufficient. A precision of 53 gives: normalized_value = 115.49999999999997 epsilon = 1.2823075934420547e-14 => new normalized_value = 115.49999999999999 Bad luck, this is just not enough to tip the value in the right direction. However, a precision of 52 is sufficient: normalized_value = 115.49999999999997 epsilon = 2.5646151868841094e-14 => new normalized_value = 115.5 The value of 53 was chosen from the `binary64` number format precision. In case of Python, the corresponding machine epsilon is 2^-52 [1]. Therefore, using 52 instead of 53 does make sense. It is worth noting that the value of the machine epsilon 2^-52 = 2.2204460492503131e-16, which is still 2 orders of magnitude below our dynamic estimation. [1] https://en.wikipedia.org/wiki/Machine_epsilon [2] `numpy.finfo(float).eps = 2.2204460492503131e-16` opw-2047368 closes #35565 Signed-off-by: Nicolas Martinelli (nim) <nim@odoo.com>
|
Merged at 0f878e4, thanks! |
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The following rounding is incorrect:
Indeed, 6.6 * 0.175 = 1.155 ≈ 1.16.
In this specific case, the
epsiloncomputed is not sufficient. Aprecision of 53 gives:
normalized_value = 115.49999999999997
epsilon = 1.2823075934420547e-14
=> new normalized_value = 115.49999999999999
Bad luck, this is just not enough to tip the value in the right
direction.
However, a precision of 52 is sufficient:
normalized_value = 115.49999999999997
epsilon = 2.5646151868841094e-14
=> new normalized_value = 115.5
The value of 53 was chosen from the
binary64number format precision.In case of Python, the corresponding machine epsilon is 2^-52 [1].
Therefore, using 52 instead of 53 does make sense.
It is worth noting that the value of the machine epsilon
2^-52 = 2.2204460492503131e-16, which is still 2 orders of magnitude
below our dynamic estimation.
[1] https://en.wikipedia.org/wiki/Machine_epsilon
[2]
numpy.finfo(float).eps = 2.2204460492503131e-16opw-2047368
Description of the issue/feature this PR addresses:
Current behavior before PR:
Desired behavior after PR is merged:
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