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
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake
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
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake
[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.
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [ ] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
Fixed the simd bugs of iPow8u and iPow16u #26061
Add the following cases in opencv_perf_core:
* OCL_PowFixture_iPow.iPow/0, where GetParam() = (640x480, 8UC1)
* OCL_PowFixture_iPow.iPow/2, where GetParam() = (640x480, 16UC1)
iPow8u and iPow16u failed to call to simd accelerating while executing.
Fix the bug by changing the input type of iPow_SIMD function.
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [ ] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
Check range for type-dependant function tables #25598
Address https://github.com/opencv/opencv/issues/24703
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
Added in-place support for cartToPolar and polarToCart #24893
- a fused hal::cartToPolar[32|64]f() is used instead of sequential hal::magnitude[32|64]f/hal::fastAtan[32|64]f
- ipp_polarToCart is skipped for in-place processing (it seems not to support it correctly)
relates to #24891
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [X] I agree to contribute to the project under Apache 2 License.
- [X] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [X] The PR is proposed to the proper branch
- [X] There is a reference to the original bug report and related work
- [X] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
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Backport to 4.x: patchNaNs() SIMD acceleration #24480
backport from #23098
connected PR in extra: [#1118@extra](https://github.com/opencv/opencv_extra/pull/1118)
### This PR contains:
* new SIMD code for `patchNaNs()`
* CPU perf test
<details>
<summary>Performance comparison</summary>
Geometric mean (ms)
|Name of Test|noopt|sse2|avx2|sse2 vs noopt (x-factor)|avx2 vs noopt (x-factor)|
|---|:-:|:-:|:-:|:-:|:-:|
|PatchNaNs::OCL_PatchNaNsFixture::(640x480, 32FC1)|0.019|0.017|0.018|1.11|1.07|
|PatchNaNs::OCL_PatchNaNsFixture::(640x480, 32FC4)|0.037|0.037|0.033|1.00|1.10|
|PatchNaNs::OCL_PatchNaNsFixture::(1280x720, 32FC1)|0.032|0.032|0.033|0.99|0.98|
|PatchNaNs::OCL_PatchNaNsFixture::(1280x720, 32FC4)|0.072|0.072|0.070|1.00|1.03|
|PatchNaNs::OCL_PatchNaNsFixture::(1920x1080, 32FC1)|0.051|0.051|0.050|1.00|1.01|
|PatchNaNs::OCL_PatchNaNsFixture::(1920x1080, 32FC4)|0.137|0.138|0.128|0.99|1.06|
|PatchNaNs::OCL_PatchNaNsFixture::(3840x2160, 32FC1)|0.137|0.128|0.129|1.07|1.06|
|PatchNaNs::OCL_PatchNaNsFixture::(3840x2160, 32FC4)|0.450|0.450|0.448|1.00|1.01|
|PatchNaNs::PatchNaNsFixture::(640x480, 32FC1)|0.149|0.029|0.020|5.13|7.44|
|PatchNaNs::PatchNaNsFixture::(640x480, 32FC2)|0.304|0.058|0.040|5.25|7.65|
|PatchNaNs::PatchNaNsFixture::(640x480, 32FC3)|0.448|0.086|0.059|5.22|7.55|
|PatchNaNs::PatchNaNsFixture::(640x480, 32FC4)|0.601|0.133|0.083|4.51|7.23|
|PatchNaNs::PatchNaNsFixture::(1280x720, 32FC1)|0.451|0.093|0.060|4.83|7.52|
|PatchNaNs::PatchNaNsFixture::(1280x720, 32FC2)|0.892|0.184|0.126|4.85|7.06|
|PatchNaNs::PatchNaNsFixture::(1280x720, 32FC3)|1.345|0.311|0.230|4.32|5.84|
|PatchNaNs::PatchNaNsFixture::(1280x720, 32FC4)|1.831|0.546|0.436|3.35|4.20|
|PatchNaNs::PatchNaNsFixture::(1920x1080, 32FC1)|1.017|0.250|0.160|4.06|6.35|
|PatchNaNs::PatchNaNsFixture::(1920x1080, 32FC2)|2.077|0.646|0.605|3.21|3.43|
|PatchNaNs::PatchNaNsFixture::(1920x1080, 32FC3)|3.134|1.053|0.961|2.97|3.26|
|PatchNaNs::PatchNaNsFixture::(1920x1080, 32FC4)|4.222|1.436|1.288|2.94|3.28|
|PatchNaNs::PatchNaNsFixture::(3840x2160, 32FC1)|4.225|1.401|1.277|3.01|3.31|
|PatchNaNs::PatchNaNsFixture::(3840x2160, 32FC2)|8.310|2.953|2.635|2.81|3.15|
|PatchNaNs::PatchNaNsFixture::(3840x2160, 32FC3)|12.396|4.455|4.252|2.78|2.92|
|PatchNaNs::PatchNaNsFixture::(3840x2160, 32FC4)|17.174|5.831|5.824|2.95|2.95|
</details>
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake
Rewrite Universal Intrinsic code by using new API: Core module. #23980
The goal of this PR is to match and modify all SIMD code blocks guarded by `CV_SIMD` macro in the `opencv/modules/core` folder and rewrite them by using the new Universal Intrinsic API.
The patch is almost auto-generated by using the [rewriter](https://github.com/hanliutong/rewriter), related PR #23885.
Most of the files have been rewritten, but I marked this PR as draft because, the `CV_SIMD` macro also exists in the following files, and the reasons why they are not rewrited are:
1. ~~code design for fixed-size SIMD (v_int16x8, v_float32x4, etc.), need to manually rewrite.~~ Rewrited
- ./modules/core/src/stat.simd.hpp
- ./modules/core/src/matrix_transform.cpp
- ./modules/core/src/matmul.simd.hpp
2. Vector types are wrapped in other class/struct, that are not supported by the compiler in variable-length backends. Can not be rewrited directly.
- ./modules/core/src/mathfuncs_core.simd.hpp
```cpp
struct v_atan_f32
{
explicit v_atan_f32(const float& scale)
{
...
}
v_float32 compute(const v_float32& y, const v_float32& x)
{
...
}
...
v_float32 val90; // sizeless type can not used in a class
v_float32 val180;
v_float32 val360;
v_float32 s;
};
```
3. The API interface does not support/does not match
- ./modules/core/src/norm.cpp
Use `v_popcount`, ~~waiting for #23966~~ Fixed
- ./modules/core/src/has_non_zero.simd.hpp
Use illegal Universal Intrinsic API: For float type, there is no logical operation `|`. Further discussion needed
```cpp
/** @brief Bitwise OR
Only for integer types. */
template<typename _Tp, int n> CV_INLINE v_reg<_Tp, n> operator|(const v_reg<_Tp, n>& a, const v_reg<_Tp, n>& b);
template<typename _Tp, int n> CV_INLINE v_reg<_Tp, n>& operator|=(v_reg<_Tp, n>& a, const v_reg<_Tp, n>& b);
```
```cpp
#if CV_SIMD
typedef v_float32 v_type;
const v_type v_zero = vx_setzero_f32();
constexpr const int unrollCount = 8;
int step = v_type::nlanes * unrollCount;
int len0 = len & -step;
const float* srcSimdEnd = src+len0;
int countSIMD = static_cast<int>((srcSimdEnd-src)/step);
while(!res && countSIMD--)
{
v_type v0 = vx_load(src);
src += v_type::nlanes;
v_type v1 = vx_load(src);
src += v_type::nlanes;
....
src += v_type::nlanes;
v0 |= v1; //Illegal ?
....
//res = v_check_any(((v0 | v4) != v_zero));//beware : (NaN != 0) returns "false" since != is mapped to _CMP_NEQ_OQ and not _CMP_NEQ_UQ
res = !v_check_all(((v0 | v4) == v_zero));
}
v_cleanup();
#endif
```
### Pull Request Readiness Checklist
See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request
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- [ ] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [ ] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
- to reduce binaries size of FFmpeg Windows wrapper
- MinGW linker doesn't support -ffunction-sections (used for FFmpeg Windows wrapper)
- move code to improve locality with its used dependencies
- move UMat::dot() to matmul.dispatch.cpp (Mat::dot() is already there)
- move UMat::inv() to lapack.cpp
- move UMat::mul() to arithm.cpp
- move UMat:eye() to matrix_operations.cpp (near setIdentity() implementation)
- move normalize(): convert_scale.cpp => norm.cpp
- move convertAndUnrollScalar(): arithm.cpp => copy.cpp
- move scalarToRawData(): array.cpp => copy.cpp
- move transpose(): matrix_operations.cpp => matrix_transform.cpp
- move flip(), rotate(): copy.cpp => matrix_transform.cpp (rotate90 uses flip and transpose)
- add 'OPENCV_CORE_EXCLUDE_C_API' CMake variable to exclude compilation of C-API functions from the core module
- matrix_wrap.cpp: add compile-time checks for CUDA/OpenGL calls
- the steps above allow to reduce FFmpeg wrapper size for ~1.5Mb (initial size of OpenCV part is about 3Mb)
backport is done to improve merge experience (less conflicts)
backport of commit: 65eb946756
- to reduce binaries size of FFmpeg Windows wrapper
- MinGW linker doesn't support -ffunction-sections (used for FFmpeg Windows wrapper)
- move code to improve locality with its used dependencies
- move UMat::dot() to matmul.dispatch.cpp (Mat::dot() is already there)
- move UMat::inv() to lapack.cpp
- move UMat::mul() to arithm.cpp
- move UMat:eye() to matrix_operations.cpp (near setIdentity() implementation)
- move normalize(): convert_scale.cpp => norm.cpp
- move convertAndUnrollScalar(): arithm.cpp => copy.cpp
- move scalarToRawData(): array.cpp => copy.cpp
- move transpose(): matrix_operations.cpp => matrix_transform.cpp
- move flip(), rotate(): copy.cpp => matrix_transform.cpp (rotate90 uses flip and transpose)
- add 'OPENCV_CORE_EXCLUDE_C_API' CMake variable to exclude compilation of C-API functions from the core module
- matrix_wrap.cpp: add compile-time checks for CUDA/OpenGL calls
- the steps above allow to reduce FFmpeg wrapper size for ~1.5Mb (initial size of OpenCV part is about 3Mb)
* js: update build script
- support emscipten 1.38.12 (wasm is ON by default)
- verbose build messages
* js: use builtin Math functions
* js: disable tracing code completelly
Updated integrations for:
cv::split
cv::merge
cv::insertChannel
cv::extractChannel
cv::Mat::convertTo - now with scaled conversions support
cv::LUT - disabled due to performance issues
Mat::copyTo
Mat::setTo
cv::flip
cv::copyMakeBorder - currently disabled
cv::polarToCart
cv::pow - ipp pow function was removed due to performance issues
cv::hal::magnitude32f/64f - disabled for <= SSE42, poor performance
cv::countNonZero
cv::minMaxIdx
cv::norm
cv::canny - new integration. Disabled for threaded;
cv::cornerHarris
cv::boxFilter
cv::bilateralFilter
cv::integral
Maxim Smolskiy
Alexander Alekhin
Alexander Smorkalov
GenshinImpactStarts
Alexander Smorkalov
penghuiho
Alexander Smorkalov
Pierre Chatelier
Rostislav Vasilikhin
HAN Liutong
Maksim Shabunin
Nikita Shulga
Vitaly Tuzov
Hamdi Sahloul
Alexander Alekhin
Tomoaki Teshima
Pavel Vlasov
Maksim Shabunin
Alexander Alekhin
Vadim Pisarevsky
hoangviet1985
Vladislav Vinogradov
Ilya Lavrenov