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…-numbers-tolerance 78 testcase floating point numbers tolerance
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| Original file line number | Diff line number | Diff line change |
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| # Tolerance value in IDS | ||
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| ## Equality tolerance | ||
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| Because of rounding errors, a tolerance value must always be considered for the equality of floating-point numbers (doubles in ids:simpleValue and xs:restriction). | ||
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| To support both low numbers, like an area of a wire expressed in square meters, and high numbers, like a length of a railway, the IDS uses both a relative and a fixed component, following the formula: | ||
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| `x == v ⇒ (v - abs(v) × ϵ - ϵ) < x < (v + abs(v) × ϵ + ϵ)` | ||
| with a tolerance value being: `ϵ = 1.0e⁻⁶` | ||
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| The table below demonstrates characteristic ranges of values within the tolerance: | ||
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| |v|lower bound<br>`(v - abs(v) × ε - ε)`| upper bound<br>`(v + abs(v) × ε + ε)`| absolute delta| | ||
| |---:|-------------:|-------------:|--:| | ||
| | 100000.0 | 99999.899999 | 100000.100001 | 0.200002 | | ||
| | 10000.0 | 9999.989999 | 10000.010001 | 0.020002 | | ||
| | 1000.0 | 999.998999 | 1000.001001 | 0.002002 | | ||
| | 100.0 | 99.999899 | 100.000101 | 0.000202 | | ||
| | 10.0 | 9.999989 | 10.000011 | 2.2E-05 | | ||
| | 1.0 | 0.999998 | 1.000002 | 4E-06 | | ||
| | 0.1 | 0.0999989 | 0.1000011 | 2.2E-06 | | ||
| | 0.01 | 0.00999899 | 0.01000101 | 2.02E-06 | | ||
| | 0.001 | 0.000998999 | 0.001001001 | 2.002E-06 | | ||
| | 0.0001 | 0.0000989999 | 0.0001010001 | 2.0002E-06 | | ||
| | 0.00001 | 0.00000899999 | 0.00001100001 | 2.00002E-06 | | ||
| | 0.000001 | -0.000000000001 | 0.000002000001 | 2.000002E-06 | | ||
| | 0.0000001 | -0.0000009000001 | 0.0000011000001 | 2.0000002E-06 | | ||
| | 0 | -0.000001 | 0.000001 | 2.0E-06 | | ||
| | -0.0000001 | -0.0000011000001 | 0.0000009000001 | 2.0000002E-06 | | ||
| | -0.000001 | -0.0000020000 | 0.000000000001 | 2.000002E-06 | | ||
| | -0.00001 | -0.0000110000 | -0.00000899999 | 2.00002E-06 | | ||
| | -0.0001 | -0.0001010001 | -0.0000989999 | 2.0002E-06 | | ||
| | -0.001 | -0.0010010010 | -0.000998999 | 2.002E-06 | | ||
| | -0.01 | -0.0100010100 | -0.00999899 | 2.02E-06 | | ||
| | -0.1 | -0.1000011000 | -0.0999989 | 2.2E-06 | | ||
| | -1.0 | -1.0000020000 | -0.999998 | 4E-06 | | ||
| | -10.0 | -10.0000110000 | -9.999989 | 2.2E-05 | | ||
| | -100.0 | -100.0001010000 | -99.999899 | 0.000202 | | ||
| | -1000.0 | -1000.0010010000 | -999.998999 | 0.002002 | | ||
| | -10000.0 | -10000.0100010000 | -9999.989999 | 0.020002 | | ||
| | -100000.0 | -100000.1000010000 | -99999.899999 | 0.200002 | | ||
| | -1000000.0 | -1000001.0000010000 * | -999998.999999 | 2.000002 | | ||
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| \* If the least significant digits are beyond the precision of a IEEE74 double (approximately 17 digits), it might result in a false positive. For example, -1000001.00000100001 would still pass as being equal to -1000000.0, even though being below the lower bound. | ||
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| Note: the tolerance value is not configurable, as it is specific only for rounding errors, not for construction-related tolerances, for which users need to provide an explicit range. | ||
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| ## Range tolerance | ||
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| Adding tolerance to range checks would open up all kinds of strange edge cases like 41.999958 being both in the range 42-50 inclusive, but also < 42 exclusive. For that reason, **exclusive ranges should be shrunk, while inclusive ranges should be stretched**. | ||
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| For example: | ||
| - `x > 0 ⇒ x > 1.0e⁻⁶` | ||
| - `x >= 0 ⇒ x >= -1.0e⁻⁶` | ||
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| If a numeric range constraint's spread is lower than the agreed limit, the Audit-tool should raise a warning. | ||
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| # | ||
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| Note: the history of these agreements can be traced in the history of [issue 78](https://github.com/buildingSMART/IDS/issues/78), [issue 36](https://github.com/buildingSMART/IDS/issues/36), and in [the summary by @giuseppeverduciALMA](https://github.com/buildingSMART/IDS/blob/0d50fd8f2dbd5b388f6fafb67da255cc3ce2b4ca/Documentation/tolerance.md). |