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Better Latex (?)
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Florian Deconinck committed Oct 10, 2024
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Expand Up @@ -43,9 +43,9 @@ To pass the metric has to be lower than `1e-14`, any value lower than `1e-18` wi

Moving to mixed precision code, the legacy metric didn't give enough flexibility to account for 32-bit precision errors that could accumulate. Another metric was built with the intent of breaking the one-fit-all concept and giving back flexibility. The metric is a combination of three differences:

- _Absolute Difference_ ($`\abs{computed-reference}<threshold`$): the absolute difference between the reference value and the computed value. Good for small amplitude, decays to direct comparison in higher amplitude. Default threshold is `1e-13` for 64-bit, `1e-10` at 32-bit.
- _Relative Difference_ ($`\asb{computed-reference}<threshold*max{abs{computed, abs{reference}}}`$): the difference relative to the maximum value. This can be seen at a % of error. Good for high amplitutde value, decay to direct comparison at smaller amplitude. Default is `0.0001%`
- _ULP Difference_ ($`abs{computed-reference}/spacing{max{abs{computed, abs{reference}}}}<=threshold`$): Unit of Least Precision (ULP) can be shortly describe as a way to quantify the space between two describable floating points. This is useful to measure differences that are in the "noise" of the machine representation. Default threshold is 1, meaning the two values are virtually indistiguinshible.
- _Absolute Difference_ ($`|computed-reference|<threshold`$): the absolute difference between the reference value and the computed value. Good for small amplitude, decays to direct comparison in higher amplitude. Default threshold is `1e-13` for 64-bit, `1e-10` at 32-bit.
- _Relative Difference_ ($`|computed-reference|<threshold*\max{|computed|, |reference|}`$): the difference relative to the maximum value. This can be seen at a % of error. Good for high amplitutde value, decay to direct comparison at smaller amplitude. Default is `0.0001%`
- _ULP Difference_ ($`|computed-reference|/\spacing{\max{|computed|, |reference|}}<=threshold`$): Unit of Least Precision (ULP) can be shortly describe as a way to quantify the space between two describable floating points. This is useful to measure differences that are in the "noise" of the machine representation. Default threshold is 1, meaning the two values are virtually indistiguinshible.

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