Merge pull request opencv#25892 from WanliZhong:v_sincos

Add support for v_sin and v_cos (Sine and Cosine) opencv#25892

This PR aims to implement `v_sincos(v_float16 x)`, `v_sincos(v_float32 x)` and `v_sincos(v_float64 x)`. 
Merged after opencv#25891 and opencv#26023

**NOTE:** 
Also, the patch changes already added `v_exp`, `v_log` and `v_erf` to pass parameters by reference instead of by value, to match API of other universal intrinsics.

TODO:
- [x] double and half float precision
- [x] tests for them
- [x] doc to explain the implementation

### 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
- [ ] 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

Author: WanliZhong

modules/core/include/opencv2/core/hal/intrin_avx.hpp

@@ -3167,12 +3167,18 @@ inline void v_pack_store(hfloat* ptr, const v_float32x8& a)
 inline void v256_cleanup() { _mm256_zeroall(); }
 
 #include "intrin_math.hpp"
-inline v_float32x8 v_exp(v_float32x8 x) { return v_exp_default_32f<v_float32x8, v_int32x8>(x); }
-inline v_float32x8 v_log(v_float32x8 x) { return v_log_default_32f<v_float32x8, v_int32x8>(x); }
-inline v_float32x8 v_erf(v_float32x8 x) { return v_erf_default_32f<v_float32x8, v_int32x8>(x); }
-
-inline v_float64x4 v_exp(v_float64x4 x) { return v_exp_default_64f<v_float64x4, v_int64x4>(x); }
-inline v_float64x4 v_log(v_float64x4 x) { return v_log_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float32x8 v_exp(const v_float32x8& x) { return v_exp_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_log(const v_float32x8& x) { return v_log_default_32f<v_float32x8, v_int32x8>(x); }
+inline void v_sincos(const v_float32x8& x, v_float32x8& s, v_float32x8& c) { v_sincos_default_32f<v_float32x8, v_int32x8>(x, s, c); }
+inline v_float32x8 v_sin(const v_float32x8& x) { return v_sin_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_cos(const v_float32x8& x) { return v_cos_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_erf(const v_float32x8& x) { return v_erf_default_32f<v_float32x8, v_int32x8>(x); }
+
+inline v_float64x4 v_exp(const v_float64x4& x) { return v_exp_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float64x4 v_log(const v_float64x4& x) { return v_log_default_64f<v_float64x4, v_int64x4>(x); }
+inline void v_sincos(const v_float64x4& x, v_float64x4& s, v_float64x4& c) { v_sincos_default_64f<v_float64x4, v_int64x4>(x, s, c); }
+inline v_float64x4 v_sin(const v_float64x4& x) { return v_sin_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float64x4 v_cos(const v_float64x4& x) { return v_cos_default_64f<v_float64x4, v_int64x4>(x); }
 
 CV_CPU_OPTIMIZATION_HAL_NAMESPACE_END
 

modules/core/include/opencv2/core/hal/intrin_avx512.hpp

@@ -3079,12 +3079,18 @@ inline int v_scan_forward(const v_float64x8& a) { return trailingZeros32(v_signm
 inline void v512_cleanup() { _mm256_zeroall(); }
 
 #include "intrin_math.hpp"
-inline v_float32x16 v_exp(v_float32x16 x) { return v_exp_default_32f<v_float32x16, v_int32x16>(x); }
-inline v_float32x16 v_log(v_float32x16 x) { return v_log_default_32f<v_float32x16, v_int32x16>(x); }
-inline v_float32x16 v_erf(v_float32x16 x) { return v_erf_default_32f<v_float32x16, v_int32x16>(x); }
-
-inline v_float64x8 v_exp(v_float64x8 x) { return v_exp_default_64f<v_float64x8, v_int64x8>(x); }
-inline v_float64x8 v_log(v_float64x8 x) { return v_log_default_64f<v_float64x8, v_int64x8>(x); }
+inline v_float32x16 v_exp(const v_float32x16& x) { return v_exp_default_32f<v_float32x16, v_int32x16>(x); }
+inline v_float32x16 v_log(const v_float32x16& x) { return v_log_default_32f<v_float32x16, v_int32x16>(x); }
+inline void v_sincos(const v_float32x16& x, v_float32x16& s, v_float32x16& c) { v_sincos_default_32f<v_float32x16, v_int32x16>(x, s, c); }
+inline v_float32x16 v_sin(const v_float32x16& x) { return v_sin_default_32f<v_float32x16, v_int32x16>(x); }
+inline v_float32x16 v_cos(const v_float32x16& x) { return v_cos_default_32f<v_float32x16, v_int32x16>(x); }
+inline v_float32x16 v_erf(const v_float32x16& x) { return v_erf_default_32f<v_float32x16, v_int32x16>(x); }
+
+inline v_float64x8 v_exp(const v_float64x8& x) { return v_exp_default_64f<v_float64x8, v_int64x8>(x); }
+inline v_float64x8 v_log(const v_float64x8& x) { return v_log_default_64f<v_float64x8, v_int64x8>(x); }
+inline void v_sincos(const v_float64x8& x, v_float64x8& s, v_float64x8& c) { v_sincos_default_64f<v_float64x8, v_int64x8>(x, s, c); }
+inline v_float64x8 v_sin(const v_float64x8& x) { return v_sin_default_64f<v_float64x8, v_int64x8>(x); }
+inline v_float64x8 v_cos(const v_float64x8& x) { return v_cos_default_64f<v_float64x8, v_int64x8>(x); }
 
 CV_CPU_OPTIMIZATION_HAL_NAMESPACE_END
 

modules/core/include/opencv2/core/hal/intrin_cpp.hpp

@@ -264,7 +264,7 @@ Most of these operations return only one value.
 ### Other math
 
 - Some frequent operations: @ref v_sqrt, @ref v_invsqrt, @ref v_magnitude, @ref v_sqr_magnitude, @ref v_exp, @ref v_log,
-                            @ref v_erf
+                            @ref v_erf, @ref v_sin, @ref v_cos
 - Absolute values: @ref v_abs, @ref v_absdiff, @ref v_absdiffs
 
 ### Conversions
@@ -366,6 +366,7 @@ Floating point:
 |broadcast_element  | x |   |
 |exp                | x | x |
 |log                | x | x |
+|sin, cos           | x | x |
 
  @{ */
 
@@ -745,10 +746,41 @@ OPENCV_HAL_IMPL_MATH_FUNC(v_log, std::log, _Tp)
  */
 OPENCV_HAL_IMPL_MATH_FUNC(v_erf, std::erf, _Tp)
 
-//! @cond IGNORED
+/**
+ * @brief Compute sine \f$ sin(x) \f$ and cosine \f$ cos(x) \f$ of elements at the same time
+ *
+ * Only for floating point types. Core implementation steps:
+ * 1. Input Normalization: Scale the periodicity from 2π to 4 and reduce the angle to the range \f$ [0, \frac{\pi}{4}] \f$ using periodicity and trigonometric identities.
+ * 2. Polynomial Approximation for \f$ sin(x) \f$ and \f$ cos(x) \f$:
+ *   - For float16 and float32, use a Taylor series with 4 terms for sine and 5 terms for cosine.
+ *   - For float64, use a Taylor series with 7 terms for sine and 8 terms for cosine.
+ * 3. Select Results: select and convert the final sine and cosine values for the original input angle.
+ *
+ * @note The precision of the calculation depends on the implementation and the data type of the input vector.
+ */
+template<typename _Tp, int n>
+inline void v_sincos(const v_reg<_Tp, n>& x, v_reg<_Tp, n>& s, v_reg<_Tp, n>& c)
+{
+    for( int i = 0; i < n; i++ )
+    {
+        s.s[i] = std::sin(x.s[i]);
+        c.s[i] = std::cos(x.s[i]);
+    }
+}
+
+/**
+ * @brief Sine \f$ sin(x) \f$ of elements
+ *
+ * Only for floating point types. Core implementation the same as @ref v_sincos.
+ */
 OPENCV_HAL_IMPL_MATH_FUNC(v_sin, std::sin, _Tp)
+
+/**
+ * @brief Cosine \f$ cos(x) \f$ of elements
+ *
+ * Only for floating point types. Core implementation the same as @ref v_sincos.
+ */
 OPENCV_HAL_IMPL_MATH_FUNC(v_cos, std::cos, _Tp)
-//! @endcond
 
 /** @brief Absolute value of elements
 

modules/core/include/opencv2/core/hal/intrin_lasx.hpp

@@ -3014,12 +3014,18 @@ inline void v_pack_store(hfloat* ptr, const v_float32x8& a)
 inline void v256_cleanup() {}
 
 #include "intrin_math.hpp"
-inline v_float32x8 v_exp(v_float32x8 x) { return v_exp_default_32f<v_float32x8, v_int32x8>(x); }
-inline v_float32x8 v_log(v_float32x8 x) { return v_log_default_32f<v_float32x8, v_int32x8>(x); }
-inline v_float32x8 v_erf(v_float32x8 x) { return v_erf_default_32f<v_float32x8, v_int32x8>(x); }
-
-inline v_float64x4 v_exp(v_float64x4 x) { return v_exp_default_64f<v_float64x4, v_int64x4>(x); }
-inline v_float64x4 v_log(v_float64x4 x) { return v_log_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float32x8 v_exp(const v_float32x8& x) { return v_exp_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_log(const v_float32x8& x) { return v_log_default_32f<v_float32x8, v_int32x8>(x); }
+inline void v_sincos(const v_float32x8& x, v_float32x8& s, v_float32x8& c) { v_sincos_default_32f<v_float32x8, v_int32x8>(x, s, c); }
+inline v_float32x8 v_sin(const v_float32x8& x) { return v_sin_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_cos(const v_float32x8& x) { return v_cos_default_32f<v_float32x8, v_int32x8>(x); }
+inline v_float32x8 v_erf(const v_float32x8& x) { return v_erf_default_32f<v_float32x8, v_int32x8>(x); }
+
+inline v_float64x4 v_exp(const v_float64x4& x) { return v_exp_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float64x4 v_log(const v_float64x4& x) { return v_log_default_64f<v_float64x4, v_int64x4>(x); }
+inline void v_sincos(const v_float64x4& x, v_float64x4& s, v_float64x4& c) { v_sincos_default_64f<v_float64x4, v_int64x4>(x, s, c); }
+inline v_float64x4 v_sin(const v_float64x4& x) { return v_sin_default_64f<v_float64x4, v_int64x4>(x); }
+inline v_float64x4 v_cos(const v_float64x4& x) { return v_cos_default_64f<v_float64x4, v_int64x4>(x); }
 
 CV_CPU_OPTIMIZATION_HAL_NAMESPACE_END
 

modules/core/include/opencv2/core/hal/intrin_lsx.hpp

@@ -2524,12 +2524,18 @@ inline void v_pack_store(hfloat* ptr, const v_float32x4& a)
 inline void v_cleanup() {}
 
 #include "intrin_math.hpp"
-inline v_float32x4 v_exp(v_float32x4 x) { return v_exp_default_32f<v_float32x4, v_int32x4>(x); }
-inline v_float32x4 v_log(v_float32x4 x) { return v_log_default_32f<v_float32x4, v_int32x4>(x); }
-inline v_float32x4 v_erf(v_float32x4 x) { return v_erf_default_32f<v_float32x4, v_int32x4>(x); }
-
-inline v_float64x2 v_exp(v_float64x2 x) { return v_exp_default_64f<v_float64x2, v_int64x2>(x); }
-inline v_float64x2 v_log(v_float64x2 x) { return v_log_default_64f<v_float64x2, v_int64x2>(x); }
+inline v_float32x4 v_exp(const v_float32x4& x) { return v_exp_default_32f<v_float32x4, v_int32x4>(x); }
+inline v_float32x4 v_log(const v_float32x4& x) { return v_log_default_32f<v_float32x4, v_int32x4>(x); }
+inline void v_sincos(const v_float32x4& x, v_float32x4& s, v_float32x4& c) { v_sincos_default_32f<v_float32x4, v_int32x4>(x, s, c); }
+inline v_float32x4 v_sin(const v_float32x4& x) { return v_sin_default_32f<v_float32x4, v_int32x4>(x); }
+inline v_float32x4 v_cos(const v_float32x4& x) { return v_cos_default_32f<v_float32x4, v_int32x4>(x); }
+inline v_float32x4 v_erf(const v_float32x4& x) { return v_erf_default_32f<v_float32x4, v_int32x4>(x); }
+
+inline v_float64x2 v_exp(const v_float64x2& x) { return v_exp_default_64f<v_float64x2, v_int64x2>(x); }
+inline v_float64x2 v_log(const v_float64x2& x) { return v_log_default_64f<v_float64x2, v_int64x2>(x); }
+inline void v_sincos(const v_float64x2& x, v_float64x2& s, v_float64x2& c) { v_sincos_default_64f<v_float64x2, v_int64x2>(x, s, c); }
+inline v_float64x2 v_sin(const v_float64x2& x) { return v_sin_default_64f<v_float64x2, v_int64x2>(x); }
+inline v_float64x2 v_cos(const v_float64x2& x) { return v_cos_default_64f<v_float64x2, v_int64x2>(x); }
 
 CV_CPU_OPTIMIZATION_HAL_NAMESPACE_END