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Adjust test tolerance (microsoft#19947)
### Description Improve the precision of tests. Changes include: (1) Update checkers.cc to use consistent default tolerance. (2) Allow different default tolerances for different providers at runtime (Previously, threshold of a test is decided during compiling). (3) Explicitly set absolute and relative error tolerances for tests that failed to pass new default threshold. #### Default Thresholds Change Note that the formula of testing is `abs(expected - value) < absolute + relative * expected` Default test thresholds when both absolute and relative tolerance are not set: type | provider | absolute (before) | absolute (after) | relative (before) | relative (after) -- | -- | -- | -- | -- | -- double | CPU | 0.001 | 0.00001 | 0 | 0.00001 double | CUDA | 0.005 | 0.00001 | 0 | 0.00001 double | TRT | 0.005 | 0.00001 | 0 | 0.00001 double | ROCM | 0.005 | 0.00001 | 0 | 0.00001 double | DML | 0.005 | 0.00001 | 0 | 0.00001 | | | | | float | CPU | 0.0001 | 0.00001 | 0 | 0.0001 float | CUDA | 0.005 | 0.00001 | 0 | 0.0001 float | TRT | 0.005 | 0.00001 | 0 | 0.0001 float | ROCM | 0.005 | 0.00001 | 0 | 0.0001 float | DML | 0.005 | 0.00001 | 0 | 0.0001 float | Training* | 0.005 | 0.001 | 0 | 0.0001 | | | | | half | CPU | 0.001 | 0.0025 | 0 | 0.001 half | CUDA | 0.005 | 0.0025 | 0 | 0.001 half | TRT | 0.005 | 0.0025 | 0 | 0.001 half | ROCM | 0.005 | 0.0025 | 0 | 0.001 half | DML | 0.02 | 0.005 | 0 | 0.001 half | Training* | 0.005 | 0.005 | 0 | 0.001 | | | | | bfloat16 | CPU | 0.0001 | 0.02 | 0 | 0.01 bfloat16 | CUDA | 0.0001 | 0.02 | 0.05 | 0.01 bfloat16 | TRT | 0.0001 | 0.02 | 0.05 | 0.01 bfloat16 | ROCM | 0.0001 | 0.02 | 0.05 | 0.01 bfloat16 | DML | 0.0001 | 0.02 | 0.05 | 0.01 bfloat16 | Training* | 0.0001 | 0.02 | 0.05 | 0.01 *Training mean a build flag ENABLE_TRAINING_CORE is defined. The provider can be any one. #### Threshold for provider Previously, the threshold might change according to build flags: ``` #if defined(USE_CUDA) || defined(USE_ROCM) || defined(USE_DML) constexpr float threshold = 0.005f; #else constexpr float threshold = 0.0001f; #endif ``` For a cpu only build, the threshold is 0.0001. For a cuda build, the threshold for CPU provider (some tests in cuda build actually run with CPU provider) is changed to 0.005. After this change, the threshold only depends on data type and provider used in the test. It will not change by build flags for non-training builds. Default thresholds for training might be different from inference (please refer to the above table). There are a few factors there: Training has gradient outputs; TF32 is not disabled in training; Some training tests has iterations, and error might accumulate. How to set different thresholds based on these factors could be a future task.
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