Improve solveCubic accuracy #27347
### Pull Request Readiness Checklist
Fix#27323
```
2e-13 * x^3 + x^2 - 2 * x + 1 = 0 -> x^3 + 5e12 * x^2 - 1e13 * x + 5e12 = 0
```
The problem that coefficients have quite big magnitudes and current calculations are subject to round-off error
```
Q = (a1 * a1 - 3 * a2) * (1./9)
R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) * (1./54)
Qcubed = Q * Q * Q = a1^6/729 - (a1^4 a2)/81 + (a1^2 a2^2)/27 - a2^3/27
R * R = R^2 = a1^6/729 - (a1^4 a2)/81 + (a1^2 a2^2)/36 + (a1^3 a3)/27 - (a1 a2 a3)/6 + a3^2/4
d = Qcubed - R * R
```
Let `a1`, `a2`, `a3` have quite big same magnitudes, then we see that `Qcubed` and `R * R` have same terms `a1^6/729` and `-(a1^4 a2)/81` (which will be reduced in `d`), but they level out the other terms (these terms have `6`th and `5`th degree and other terms - less or equal than `4`th degree).
So, if these terms will participate in the calculation, this will lead to a huge round-off error.
But if we expand the expression, then round-off error should be less
```
d = Qcubed - R * R = 1/108 (a1^2 a2^2 - 4 a2^3 - 4 a1^3 a3 + 18 a1 a2 a3 - 27 a3^2)
```
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
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build: fix more warnings from recent gcc versions after #27337#27343
More fixings after https://github.com/opencv/opencv/pull/27337
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build: fix warnings from recent gcc versions #27337
This PR addresses the following found warnings:
- [x] -Wmaybe-uninitialized
- [x] -Wunused-variable
- [x] -Wsign-compare
Tested building with GCC 14.2 (RISC-V 64).
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Add tests for solveCubic #27331
### Pull Request Readiness Checklist
Related to #27323
I found only randomized tests with number of roots always equal to `1` or `3`, `x^3 = 0` and some simple test for Java and Swift.
Obviously, they don't cover all cases (implementation has strong branching and number of roots can be equal to `-1`, `0` and `2` additionally).
So, I think it will be useful to try explicitly cover more cases (and implementation branches correspondingly)
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
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Make sure to not access outside normDiffTabMake sure to not access outside normDiffTab #27321
If the norm is outside the array (e.g. Hamming), memory is read outside of the array, which does not matter because the invalid pointer is not used oustide of the function (e.g. the Hamming path is taken) but it triggers the sanitizer.
### Pull Request Readiness Checklist
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hal_rvv: further optimized flip #27257
Checklist:
- [x] flipX
- [x] flipY
- [x] flipXY
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FastCV gemm hal #27184
FastCV hal for gemm 32f
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HAL: implemented cv_hal_transpose in hal_rvv #27229
Checklists:
- [x] transpose2d_8u
- [x] transpose2d_16u
- [ ] ~transpose2d_8uC3~
- [x] transpose2d_32s
- [ ] ~transpose2d_16uC3~
- [x] transpose2d_32sC2
- [ ] ~transpose_32sC3~
- [ ] ~transpose_32sC4~
- [ ] ~transpose_32sC6~
- [ ] ~transpose_32sC8~
- [ ] ~inplace transpose~
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core: further vectorize copyTo with mask #27145
Merge with https://github.com/opencv/opencv_extra/pull/1247.
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HAL: added copyToMask and implemented in hal_rvv #27162
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User-defined logger callback, C-style. #27154
This is a competing PR, an alternative to #27140
Both functions accept C-style pointer to static functions. Both functions allow restoring the OpenCV built-in implementation by passing in a nullptr.
- replaceWriteLogMessage
- replaceWriteLogMessageEx
This implementation is not compatible with C++ log handler objects.
This implementation has minimal thread safety, in the sense that the function pointer are stored and read atomically. But otherwise, the user-defined static functions must accept calls at all times, even after having been deregistered, because some log calls may have started before deregistering.
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core: refactored normDiff in hal_rvv and extended with support of more data types #27115
Merge wtih https://github.com/opencv/opencv_extra/pull/1246.
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Move IPP norm and normDiff to HAL #27128
Continues https://github.com/opencv/opencv/pull/26880
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Initial version of IPP-based HAL for x86 and x86_64 platforms #26880
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core: improve norm of hal rvv #26991
Merge with https://github.com/opencv/opencv_extra/pull/1241
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[HAL RVV] unify and impl polar_to_cart | add perf test #26999
### Summary
1. Implement through the existing `cv_hal_polarToCart32f` and `cv_hal_polarToCart64f` interfaces.
2. Add `polarToCart` performance tests
3. Make `cv::polarToCart` use CALL_HAL in the same way as `cv::cartToPolar`
4. To achieve the 3rd point, the original implementation was moved, and some modifications were made.
Tested through:
```sh
opencv_test_core --gtest_filter="*PolarToCart*:*Core_CartPolar_reverse*"
opencv_perf_core --gtest_filter="*PolarToCart*" --perf_min_samples=300 --perf_force_samples=300
```
### HAL performance test
***UPDATE***: Current implementation is no more depending on vlen.
**NOTE**: Due to the 4th point in the summary above, the `scalar` and `ui` test is based on the modified code of this PR. The impact of this patch on `scalar` and `ui` is evaluated in the next section, `Effect of Point 4`.
Vlen 256 (Muse Pi):
```
Name of Test scalar ui rvv ui rvv
vs vs
scalar scalar
(x-factor) (x-factor)
PolarToCart::PolarToCartFixture::(127x61, 32FC1) 0.315 0.110 0.034 2.85 9.34
PolarToCart::PolarToCartFixture::(127x61, 64FC1) 0.423 0.163 0.045 2.59 9.34
PolarToCart::PolarToCartFixture::(640x480, 32FC1) 13.695 4.325 1.278 3.17 10.71
PolarToCart::PolarToCartFixture::(640x480, 64FC1) 17.719 7.118 2.105 2.49 8.42
PolarToCart::PolarToCartFixture::(1280x720, 32FC1) 40.678 13.114 3.977 3.10 10.23
PolarToCart::PolarToCartFixture::(1280x720, 64FC1) 53.124 21.298 6.519 2.49 8.15
PolarToCart::PolarToCartFixture::(1920x1080, 32FC1) 95.158 29.465 8.894 3.23 10.70
PolarToCart::PolarToCartFixture::(1920x1080, 64FC1) 119.262 47.743 14.129 2.50 8.44
```
### Effect of Point 4
To make `cv::polarToCart` behave the same as `cv::cartToPolar`, the implementation detail of the former has been moved to the latter's location (from `mathfuncs.cpp` to `mathfuncs_core.simd.hpp`).
#### Reason for Changes:
This function works as follows:
$y = \text{mag} \times \sin(\text{angle})$ and $x = \text{mag} \times \cos(\text{angle})$. The original implementation first calculates the values of $\sin$ and $\cos$, storing the results in the output buffers $x$ and $y$, and then multiplies the result by $\text{mag}$.
However, when the function is used as an in-place operation (one of the output buffers is also an input buffer), the original implementation allocates an extra buffer to store the $\sin$ and $\cos$ values in case the $\text{mag}$ value gets overwritten. This extra buffer allocation prevents `cv::polarToCart` from functioning in the same way as `cv::cartToPolar`.
Therefore, the multiplication is now performed immediately without storing intermediate values. Since the original implementation also had AVX2 optimizations, I have applied the same optimizations to the AVX2 version of this implementation.
***UPDATE***: UI use v_sincos from #25892 now. The original implementation has AVX2 optimizations but is slower much than current UI so it's removed, and AVX2 perf test is below. Scalar implementation isn't changed because it's faster than using UI's method.
#### Test Result
`scalar` and `ui` test is done on Muse PI, and AVX2 test is done on Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz.
`scalar` test:
```
Name of Test orig pr pr
vs
orig
(x-factor)
PolarToCart::PolarToCartFixture::(127x61, 32FC1) 0.333 0.294 1.13
PolarToCart::PolarToCartFixture::(127x61, 64FC1) 0.385 0.403 0.96
PolarToCart::PolarToCartFixture::(640x480, 32FC1) 14.749 12.343 1.19
PolarToCart::PolarToCartFixture::(640x480, 64FC1) 19.419 16.743 1.16
PolarToCart::PolarToCartFixture::(1280x720, 32FC1) 44.155 37.822 1.17
PolarToCart::PolarToCartFixture::(1280x720, 64FC1) 62.108 50.358 1.23
PolarToCart::PolarToCartFixture::(1920x1080, 32FC1) 99.011 85.769 1.15
PolarToCart::PolarToCartFixture::(1920x1080, 64FC1) 127.740 112.874 1.13
```
`ui` test:
```
Name of Test orig pr pr
vs
orig
(x-factor)
PolarToCart::PolarToCartFixture::(127x61, 32FC1) 0.306 0.110 2.77
PolarToCart::PolarToCartFixture::(127x61, 64FC1) 0.455 0.163 2.79
PolarToCart::PolarToCartFixture::(640x480, 32FC1) 13.381 4.325 3.09
PolarToCart::PolarToCartFixture::(640x480, 64FC1) 21.851 7.118 3.07
PolarToCart::PolarToCartFixture::(1280x720, 32FC1) 39.975 13.114 3.05
PolarToCart::PolarToCartFixture::(1280x720, 64FC1) 67.006 21.298 3.15
PolarToCart::PolarToCartFixture::(1920x1080, 32FC1) 90.362 29.465 3.07
PolarToCart::PolarToCartFixture::(1920x1080, 64FC1) 129.637 47.743 2.72
```
AVX2 test:
```
Name of Test orig pr pr
vs
orig
(x-factor)
PolarToCart::PolarToCartFixture::(127x61, 32FC1) 0.019 0.009 2.11
PolarToCart::PolarToCartFixture::(127x61, 64FC1) 0.022 0.013 1.74
PolarToCart::PolarToCartFixture::(640x480, 32FC1) 0.788 0.355 2.22
PolarToCart::PolarToCartFixture::(640x480, 64FC1) 1.102 0.618 1.78
PolarToCart::PolarToCartFixture::(1280x720, 32FC1) 2.383 1.042 2.29
PolarToCart::PolarToCartFixture::(1280x720, 64FC1) 3.758 2.316 1.62
PolarToCart::PolarToCartFixture::(1920x1080, 32FC1) 5.577 2.559 2.18
PolarToCart::PolarToCartFixture::(1920x1080, 64FC1) 9.710 6.424 1.51
```
A slight performance loss occurs because the check for whether $mag$ is nullptr is performed with every calculation, instead of being done once per batch. This is to reuse current `SinCos_32f` function.
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[HAL RVV] reuse atan | impl cart_to_polar | add perf test #27000
Implement through the existing `cv_hal_cartToPolar32f` and `cv_hal_cartToPolar64f` interfaces.
Add `cartToPolar` performance tests.
cv_hal_rvv::fast_atan is modified to make it more reusable because it's needed in cartToPolar.
**UPDATE**: UI enabled. Since the vec type of RVV can't be stored in struct. UI implementation of `v_atan_f32` is modified. Both `fastAtan` and `cartToPolar` are affected so the test result for `atan` is also appended. I have tested the modified UI on RVV and AVX2 and no regressions appears.
Perf test done on MUSE-PI. AVX2 test done on Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz.
```sh
$ opencv_test_core --gtest_filter="*CartToPolar*:*Core_CartPolar_reverse*:*Phase*"
$ opencv_perf_core --gtest_filter="*CartToPolar*:*phase*" --perf_min_samples=300 --perf_force_samples=300
```
Test result between enabled UI and HAL:
```
Name of Test ui rvv rvv
vs
ui
(x-factor)
CartToPolar::CartToPolarFixture::(127x61, 32FC1) 0.106 0.059 1.80
CartToPolar::CartToPolarFixture::(127x61, 64FC1) 0.155 0.070 2.20
CartToPolar::CartToPolarFixture::(640x480, 32FC1) 4.188 2.317 1.81
CartToPolar::CartToPolarFixture::(640x480, 64FC1) 6.593 2.889 2.28
CartToPolar::CartToPolarFixture::(1280x720, 32FC1) 12.600 7.057 1.79
CartToPolar::CartToPolarFixture::(1280x720, 64FC1) 19.860 8.797 2.26
CartToPolar::CartToPolarFixture::(1920x1080, 32FC1) 28.295 15.809 1.79
CartToPolar::CartToPolarFixture::(1920x1080, 64FC1) 44.573 19.398 2.30
phase32f::VectorLength::128 0.002 0.002 1.20
phase32f::VectorLength::1000 0.008 0.006 1.32
phase32f::VectorLength::131072 1.061 0.731 1.45
phase32f::VectorLength::524288 3.997 2.976 1.34
phase32f::VectorLength::1048576 8.001 5.959 1.34
phase64f::VectorLength::128 0.002 0.002 1.33
phase64f::VectorLength::1000 0.012 0.008 1.58
phase64f::VectorLength::131072 1.648 0.931 1.77
phase64f::VectorLength::524288 6.836 3.837 1.78
phase64f::VectorLength::1048576 14.060 7.540 1.86
```
Test result before and after enabling UI on RVV:
```
Name of Test perf perf perf
ui ui ui
orig pr pr
vs
perf
ui
orig
(x-factor)
CartToPolar::CartToPolarFixture::(127x61, 32FC1) 0.141 0.106 1.33
CartToPolar::CartToPolarFixture::(127x61, 64FC1) 0.187 0.155 1.20
CartToPolar::CartToPolarFixture::(640x480, 32FC1) 5.990 4.188 1.43
CartToPolar::CartToPolarFixture::(640x480, 64FC1) 8.370 6.593 1.27
CartToPolar::CartToPolarFixture::(1280x720, 32FC1) 18.214 12.600 1.45
CartToPolar::CartToPolarFixture::(1280x720, 64FC1) 25.365 19.860 1.28
CartToPolar::CartToPolarFixture::(1920x1080, 32FC1) 40.437 28.295 1.43
CartToPolar::CartToPolarFixture::(1920x1080, 64FC1) 56.699 44.573 1.27
phase32f::VectorLength::128 0.003 0.002 1.54
phase32f::VectorLength::1000 0.016 0.008 1.90
phase32f::VectorLength::131072 2.048 1.061 1.93
phase32f::VectorLength::524288 8.219 3.997 2.06
phase32f::VectorLength::1048576 16.426 8.001 2.05
phase64f::VectorLength::128 0.003 0.002 1.44
phase64f::VectorLength::1000 0.020 0.012 1.60
phase64f::VectorLength::131072 2.621 1.648 1.59
phase64f::VectorLength::524288 10.780 6.836 1.58
phase64f::VectorLength::1048576 22.723 14.060 1.62
```
Test result before and after modifying UI on AVX2:
```
Name of Test perf perf perf
avx2 avx2 avx2
orig pr pr
vs
perf
avx2
orig
(x-factor)
CartToPolar::CartToPolarFixture::(127x61, 32FC1) 0.006 0.005 1.14
CartToPolar::CartToPolarFixture::(127x61, 64FC1) 0.010 0.009 1.08
CartToPolar::CartToPolarFixture::(640x480, 32FC1) 0.273 0.264 1.03
CartToPolar::CartToPolarFixture::(640x480, 64FC1) 0.511 0.487 1.05
CartToPolar::CartToPolarFixture::(1280x720, 32FC1) 0.760 0.723 1.05
CartToPolar::CartToPolarFixture::(1280x720, 64FC1) 2.009 1.937 1.04
CartToPolar::CartToPolarFixture::(1920x1080, 32FC1) 1.996 1.923 1.04
CartToPolar::CartToPolarFixture::(1920x1080, 64FC1) 5.721 5.509 1.04
phase32f::VectorLength::128 0.000 0.000 0.98
phase32f::VectorLength::1000 0.001 0.001 0.97
phase32f::VectorLength::131072 0.105 0.111 0.95
phase32f::VectorLength::524288 0.402 0.402 1.00
phase32f::VectorLength::1048576 0.775 0.767 1.01
phase64f::VectorLength::128 0.000 0.000 1.00
phase64f::VectorLength::1000 0.001 0.001 1.01
phase64f::VectorLength::131072 0.163 0.162 1.01
phase64f::VectorLength::524288 0.669 0.653 1.02
phase64f::VectorLength::1048576 1.660 1.634 1.02
```
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[HAL RVV] impl magnitude | add perf test #27002
Implement through the existing `cv_hal_magnitude32f` and `cv_hal_magnitude64f` interfaces.
**UPDATE**: UI is enabled. The only difference between UI and HAL now is HAL use a approximate `sqrt`.
Perf test done on MUSE-PI.
```sh
$ opencv_test_core --gtest_filter="*Magnitude*"
$ opencv_perf_core --gtest_filter="*Magnitude*" --perf_min_samples=300 --perf_force_samples=300
```
Test result between enabled UI and HAL:
```
Name of Test ui rvv rvv
vs
ui
(x-factor)
Magnitude::MagnitudeFixture::(127x61, 32FC1) 0.029 0.016 1.75
Magnitude::MagnitudeFixture::(127x61, 64FC1) 0.057 0.036 1.57
Magnitude::MagnitudeFixture::(640x480, 32FC1) 1.063 0.648 1.64
Magnitude::MagnitudeFixture::(640x480, 64FC1) 2.261 1.530 1.48
Magnitude::MagnitudeFixture::(1280x720, 32FC1) 3.261 2.118 1.54
Magnitude::MagnitudeFixture::(1280x720, 64FC1) 6.802 4.682 1.45
Magnitude::MagnitudeFixture::(1920x1080, 32FC1) 7.287 4.738 1.54
Magnitude::MagnitudeFixture::(1920x1080, 64FC1) 15.226 10.334 1.47
```
Test result before and after enabling UI:
```
Name of Test orig pr pr
vs
orig
(x-factor)
Magnitude::MagnitudeFixture::(127x61, 32FC1) 0.032 0.029 1.11
Magnitude::MagnitudeFixture::(127x61, 64FC1) 0.067 0.057 1.17
Magnitude::MagnitudeFixture::(640x480, 32FC1) 1.228 1.063 1.16
Magnitude::MagnitudeFixture::(640x480, 64FC1) 2.786 2.261 1.23
Magnitude::MagnitudeFixture::(1280x720, 32FC1) 3.762 3.261 1.15
Magnitude::MagnitudeFixture::(1280x720, 64FC1) 8.549 6.802 1.26
Magnitude::MagnitudeFixture::(1920x1080, 32FC1) 8.408 7.287 1.15
Magnitude::MagnitudeFixture::(1920x1080, 64FC1) 18.884 15.226 1.24
```
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core: vectorize normDiff with universal intrinsics #27042
Merge with https://github.com/opencv/opencv_extra/pull/1242.
Performance results on Desktop Intel i7-12700K, Apple M2, Jetson Orin and SpaceMIT K1:
[perf-normDiff.zip](https://github.com/user-attachments/files/19178689/perf-normDiff.zip)
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Update tutorials #26441
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Add RISC-V HAL implementation for cv::dft and cv::dct #26865
This patch implements `static cv::DFT` function in RVV_HAL using native intrinsic, optimizing the performance for `cv::dft` and `cv::dct` with data types `32FC1/64FC1/32FC2/64FC2`.
The reason I chose to create a new `cv_hal_dftOcv` interface is that if I were to use the existing interfaces (`cv_hal_dftInit1D` and `cv_hal_dft1D`), it would require handling and parsing the dft flags within HAL, as well as performing preprocessing operations such as handling unit roots. Since these operations are not performance hotspots and do not require optimization, reusing the existing interfaces would result in copying approximately 300 lines of code from `core/src/dxt.cpp` into HAL, which I believe is unnecessary.
Moreover, if I insert the new interface into `static cv::DFT`, both `static cv::RealDFT` and `static cv::DCT` can be optimized as well. The processing performed before and after calling `static cv::DFT` in these functions is also not a performance hotspot.
Tested on MUSE-PI (Spacemit X60) for both gcc 14.2 and clang 20.0.
```
$ opencv_test_core --gtest_filter="*DFT*"
$ opencv_perf_core --gtest_filter="*dft*:*dct*" --perf_min_samples=30 --perf_force_samples=30
```
The head of the perf table is shown below since the table is too long.
View the full perf table here: [hal_rvv_dxt.pdf](https://github.com/user-attachments/files/18622645/hal_rvv_dxt.pdf)
<img width="1017" alt="Untitled" src="https://github.com/user-attachments/assets/609856e7-9c7d-4a95-9923-45c1b77eb3a2" />
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Impl hal_rvv LUT | Add more LUT test #26941
Implement through the existing `cv_hal_lut` interfaces.
Add more LUT accuracy and performance tests:
- **Accuracy test**: Multi-channel table tests are added, and the boundary of `randu` used for generating test data is broadened to make the test more robust.
- **Performance test**: Multi-channel input and multi-channel table tests are added.
Perf test done on
- MUSE-PI (vlen=256)
- Compiler: gcc 14.2 (riscv-collab/riscv-gnu-toolchain Nightly: December 16, 2024)
```sh
$ opencv_test_core --gtest_filter="Core_LUT*"
$ opencv_perf_core --gtest_filter="SizePrm_LUT*" --perf_min_samples=300 --perf_force_samples=300
```
```sh
Geometric mean (ms)
Name of Test scalar ui rvv ui rvv
vs vs
scalar scalar
(x-factor) (x-factor)
LUT::SizePrm::320x240 0.248 0.249 0.052 1.00 4.74
LUT::SizePrm::640x480 0.277 0.275 0.085 1.01 3.28
LUT::SizePrm::1920x1080 0.950 0.947 0.634 1.00 1.50
LUT_multi2::SizePrm::320x240 2.051 2.045 2.049 1.00 1.00
LUT_multi2::SizePrm::640x480 2.128 2.134 2.125 1.00 1.00
LUT_multi2::SizePrm::1920x1080 7.397 7.380 7.390 1.00 1.00
LUT_multi::SizePrm::320x240 0.715 0.747 0.154 0.96 4.64
LUT_multi::SizePrm::640x480 0.741 0.766 0.257 0.97 2.88
LUT_multi::SizePrm::1920x1080 2.766 2.765 1.925 1.00 1.44
```
This optimization is achieved by loading the entire lookup table into vector registers. Due to register size limitations, the optimization is only effective under the following conditions:
- For the U8C1 table type, the optimization works when `vlen >= 256`
- For U16C1, it works when `vlen >= 512`
- For U32C1, it works when `vlen >= 1024`
Since I don’t have real hardware with `vlen > 256`, the corresponding accuracy tests were conducted on QEMU built from the `riscv-collab/riscv-gnu-toolchain`.
This patch does not implement optimizations for multi-channel tables.
Previous attempts:
1. For the U8C1 table type, when `vlen = 128`, it is possible to use four `u8m4` vectors to load the entire table, perform gathering, and merge the results. However, the performance is almost the same as the scalar version.
2. Loading part of the table and repeatedly loading the source data is faster for small sizes. But as the table size grows, the performance quickly degrades compared to the scalar version.
3. Using `vluxei8` as a general solution does not show any performance improvement.
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Fix issues in RISC-V Vector (RVV) Universal Intrinsic #27006
This PR aims to make `opencv_test_core` pass on RVV, via following two parts:
1. Fix bug in Universal Intrinsic when VLEN >= 512:
- `max_nlanes` should be multiplied by 2, because we use LMUL=2 in RVV Universal Intrinsic since #26318.
- Related tests are also expanded to match longer registers
- Relax the precision threshold of `v_erf` to make the tests pass
2. Temporary fix #26936
- Disable 3 Universal Intrinsic code blocks on GCC
- This is just a temporary fix until we figure out if it's our issue or GCC/something else's
This patch is tested under the following conditions:
- Compier: GCC 14.2, Clang 19.1.7
- Device: Muse-Pi (VLEN=256), QEMU (VLEN=512, 1024)
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