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Merge pull request #24941 from WanliZhong:v_exp
Add support for v_exp (exponential) #24941 This PR aims to implement `v_exp(v_float16 x)`, `v_exp(v_float32 x)` and `v_exp(v_float64 x)`. ### 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
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Wanli
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@@ -1239,6 +1239,7 @@ namespace CV__SIMD_NAMESPACE {
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#define CV_SIMD 0
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#endif
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#include "intrin_math.hpp"
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#include "simd_utils.impl.hpp"
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#ifndef CV_DOXYGEN
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@@ -263,7 +263,7 @@ Most of these operations return only one value.
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### Other math
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- Some frequent operations: @ref v_sqrt, @ref v_invsqrt, @ref v_magnitude, @ref v_sqr_magnitude
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- Some frequent operations: @ref v_sqrt, @ref v_invsqrt, @ref v_magnitude, @ref v_sqr_magnitude, @ref v_exp
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- Absolute values: @ref v_abs, @ref v_absdiff, @ref v_absdiffs
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### Conversions
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@@ -363,6 +363,7 @@ Floating point:
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|reverse | x | x |
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|extract_n | x | x |
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|broadcast_element | x | |
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|exp | x | x |
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@{ */
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@@ -721,11 +722,33 @@ template<typename _Tp, int n> inline v_reg<_Tp2, n> func(const v_reg<_Tp, n>& a)
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Only for floating point types.*/
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OPENCV_HAL_IMPL_MATH_FUNC(v_sqrt, std::sqrt, _Tp)
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/**
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* @brief Exponential \f$ e^x \f$ of elements
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*
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* Only for floating point types. Core implementation steps:
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* 1. Decompose Input: Convert the input to \f$ 2^{x \cdot \log_2e} \f$ and split its exponential into integer and fractional parts:
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* \f$ x \cdot \log_2e = n + f \f$, where \f$ n \f$ is the integer part and \f$ f \f$ is the fractional part.
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* 2. Compute \f$ 2^n \f$: Calculated by shifting the bits.
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* 3. Adjust Fractional Part: Compute \f$ f \cdot \ln2 \f$ to convert the fractional part to base \f$ e \f$.
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* \f$ C1 \f$ and \f$ C2 \f$ are used to adjust the fractional part.
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* 4. Polynomial Approximation for \f$ e^{f \cdot \ln2} \f$: The closer the fractional part is to 0, the more accurate the result.
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* - For float16 and float32, use a Taylor Series with 6 terms.
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* - For float64, use Pade Polynomials Approximation with 4 terms.
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* 5. Combine Results: Multiply the two parts together to get the final result:
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* \f$ e^x = 2^n \cdot e^{f \cdot \ln2} \f$.
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*
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* @note The precision of the calculation depends on the implementation and the data type of the input vector.
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*/
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OPENCV_HAL_IMPL_MATH_FUNC(v_exp, std::exp, _Tp)
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#define OPENCV_HAL_MATH_HAVE_EXP 1
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//! @cond IGNORED
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OPENCV_HAL_IMPL_MATH_FUNC(v_sin, std::sin, _Tp)
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#define OPENCV_HAL_MATH_HAVE_SIN 1
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OPENCV_HAL_IMPL_MATH_FUNC(v_cos, std::cos, _Tp)
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OPENCV_HAL_IMPL_MATH_FUNC(v_exp, std::exp, _Tp)
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#define OPENCV_HAL_MATH_HAVE_COS 1
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OPENCV_HAL_IMPL_MATH_FUNC(v_log, std::log, _Tp)
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#define OPENCV_HAL_MATH_HAVE_LOG 1
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//! @endcond
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/** @brief Absolute value of elements
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@@ -0,0 +1,200 @@
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// This file is part of OpenCV project.
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// It is subject to the license terms in the LICENSE file found in the top-level directory
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// of this distribution and at http://opencv.org/license.html
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// This header is not standalone. Don't include directly, use "intrin.hpp" instead.
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#ifdef OPENCV_HAL_INTRIN_HPP // defined in intrin.hpp
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namespace CV__SIMD_NAMESPACE {
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/* Universal Intrinsics implementation of sin, cos, exp and log
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Inspired by Intel Approximate Math library, and based on the
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corresponding algorithms of the cephes math library
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*/
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/* Copyright (C) 2010,2011 RJVB - extensions */
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/* Copyright (C) 2011 Julien Pommier
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This software is provided 'as-is', without any express or implied
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warranty. In no event will the authors be held liable for any damages
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arising from the use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it
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freely, subject to the following restrictions:
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1. The origin of this software must not be misrepresented; you must not
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claim that you wrote the original software. If you use this software
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in a product, an acknowledgment in the product documentation would be
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appreciated but is not required.
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2. Altered source versions must be plainly marked as such, and must not be
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misrepresented as being the original software.
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3. This notice may not be removed or altered from any source distribution.
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(this is the zlib license)
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*/
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#ifndef OPENCV_HAL_MATH_HAVE_EXP
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//! @name Exponential
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//! @{
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#if defined(CV_SIMD_FP16) && CV_SIMD_FP16
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// Implementation is the same as float32 vector.
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inline v_float16 v_exp(const v_float16 &x) {
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const v_float16 _vexp_lo_f16 = vx_setall_f16(-10.7421875f);
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const v_float16 _vexp_hi_f16 = vx_setall_f16(11.f);
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const v_float16 _vexp_half_fp16 = vx_setall_f16(0.5f);
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const v_float16 _vexp_one_fp16 = vx_setall_f16(1.f);
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const v_float16 _vexp_LOG2EF_f16 = vx_setall_f16(1.44269504088896341f);
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const v_float16 _vexp_C1_f16 = vx_setall_f16(-6.93359375E-1f);
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const v_float16 _vexp_C2_f16 = vx_setall_f16(2.12194440E-4f);
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const v_float16 _vexp_p0_f16 = vx_setall_f16(1.9875691500E-4f);
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const v_float16 _vexp_p1_f16 = vx_setall_f16(1.3981999507E-3f);
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const v_float16 _vexp_p2_f16 = vx_setall_f16(8.3334519073E-3f);
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const v_float16 _vexp_p3_f16 = vx_setall_f16(4.1665795894E-2f);
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const v_float16 _vexp_p4_f16 = vx_setall_f16(1.6666665459E-1f);
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const v_float16 _vexp_p5_f16 = vx_setall_f16(5.0000001201E-1f);
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const v_int16 _vexp_bias_s16 = vx_setall_s16(0xf);
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v_float16 _vexp_, _vexp_x, _vexp_y, _vexp_xx;
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v_int16 _vexp_mm;
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// compute exponential of x
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_vexp_x = v_max(x, _vexp_lo_f16);
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_vexp_x = v_min(_vexp_x, _vexp_hi_f16);
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_vexp_ = v_fma(_vexp_x, _vexp_LOG2EF_f16, _vexp_half_fp16);
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_vexp_mm = v_floor(_vexp_);
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_vexp_ = v_cvt_f16(_vexp_mm);
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_vexp_mm = v_add(_vexp_mm, _vexp_bias_s16);
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_vexp_mm = v_shl(_vexp_mm, 10);
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_vexp_x = v_fma(_vexp_, _vexp_C1_f16, _vexp_x);
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_vexp_x = v_fma(_vexp_, _vexp_C2_f16, _vexp_x);
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_vexp_xx = v_mul(_vexp_x, _vexp_x);
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_vexp_y = v_fma(_vexp_x, _vexp_p0_f16, _vexp_p1_f16);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p2_f16);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p3_f16);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p4_f16);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p5_f16);
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_vexp_y = v_fma(_vexp_y, _vexp_xx, _vexp_x);
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_vexp_y = v_add(_vexp_y, _vexp_one_fp16);
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_vexp_y = v_mul(_vexp_y, v_reinterpret_as_f16(_vexp_mm));
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// exp(NAN) -> NAN
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v_float16 mask_not_nan = v_not_nan(x);
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return v_select(mask_not_nan, _vexp_y, v_reinterpret_as_f16(vx_setall_s16(0x7e00)));
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}
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#endif
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inline v_float32 v_exp(const v_float32 &x) {
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const v_float32 _vexp_lo_f32 = vx_setall_f32(-88.3762626647949f);
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const v_float32 _vexp_hi_f32 = vx_setall_f32(89.f);
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const v_float32 _vexp_half_fp32 = vx_setall_f32(0.5f);
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const v_float32 _vexp_one_fp32 = vx_setall_f32(1.f);
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const v_float32 _vexp_LOG2EF_f32 = vx_setall_f32(1.44269504088896341f);
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const v_float32 _vexp_C1_f32 = vx_setall_f32(-6.93359375E-1f);
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const v_float32 _vexp_C2_f32 = vx_setall_f32(2.12194440E-4f);
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const v_float32 _vexp_p0_f32 = vx_setall_f32(1.9875691500E-4f);
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const v_float32 _vexp_p1_f32 = vx_setall_f32(1.3981999507E-3f);
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const v_float32 _vexp_p2_f32 = vx_setall_f32(8.3334519073E-3f);
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const v_float32 _vexp_p3_f32 = vx_setall_f32(4.1665795894E-2f);
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const v_float32 _vexp_p4_f32 = vx_setall_f32(1.6666665459E-1f);
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const v_float32 _vexp_p5_f32 = vx_setall_f32(5.0000001201E-1f);
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const v_int32 _vexp_bias_s32 = vx_setall_s32(0x7f);
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v_float32 _vexp_, _vexp_x, _vexp_y, _vexp_xx;
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v_int32 _vexp_mm;
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// compute exponential of x
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_vexp_x = v_max(x, _vexp_lo_f32);
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_vexp_x = v_min(_vexp_x, _vexp_hi_f32);
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_vexp_ = v_fma(_vexp_x, _vexp_LOG2EF_f32, _vexp_half_fp32);
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_vexp_mm = v_floor(_vexp_);
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_vexp_ = v_cvt_f32(_vexp_mm);
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_vexp_mm = v_add(_vexp_mm, _vexp_bias_s32);
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_vexp_mm = v_shl(_vexp_mm, 23);
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_vexp_x = v_fma(_vexp_, _vexp_C1_f32, _vexp_x);
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_vexp_x = v_fma(_vexp_, _vexp_C2_f32, _vexp_x);
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_vexp_xx = v_mul(_vexp_x, _vexp_x);
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_vexp_y = v_fma(_vexp_x, _vexp_p0_f32, _vexp_p1_f32);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p2_f32);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p3_f32);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p4_f32);
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_vexp_y = v_fma(_vexp_y, _vexp_x, _vexp_p5_f32);
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_vexp_y = v_fma(_vexp_y, _vexp_xx, _vexp_x);
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_vexp_y = v_add(_vexp_y, _vexp_one_fp32);
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_vexp_y = v_mul(_vexp_y, v_reinterpret_as_f32(_vexp_mm));
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// exp(NAN) -> NAN
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v_float32 mask_not_nan = v_not_nan(x);
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return v_select(mask_not_nan, _vexp_y, v_reinterpret_as_f32(vx_setall_s32(0x7fc00000)));
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}
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#if CV_SIMD_64F || CV_SIMD_SCALABLE_64F
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inline v_float64 v_exp(const v_float64 &x) {
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const v_float64 _vexp_lo_f64 = vx_setall_f64(-709.43613930310391424428);
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const v_float64 _vexp_hi_f64 = vx_setall_f64(710.);
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const v_float64 _vexp_half_f64 = vx_setall_f64(0.5);
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const v_float64 _vexp_one_f64 = vx_setall_f64(1.0);
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const v_float64 _vexp_two_f64 = vx_setall_f64(2.0);
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const v_float64 _vexp_LOG2EF_f64 = vx_setall_f64(1.44269504088896340736);
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const v_float64 _vexp_C1_f64 = vx_setall_f64(-6.93145751953125E-1);
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const v_float64 _vexp_C2_f64 = vx_setall_f64(-1.42860682030941723212E-6);
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const v_float64 _vexp_p0_f64 = vx_setall_f64(1.26177193074810590878E-4);
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const v_float64 _vexp_p1_f64 = vx_setall_f64(3.02994407707441961300E-2);
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const v_float64 _vexp_p2_f64 = vx_setall_f64(9.99999999999999999910E-1);
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const v_float64 _vexp_q0_f64 = vx_setall_f64(3.00198505138664455042E-6);
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const v_float64 _vexp_q1_f64 = vx_setall_f64(2.52448340349684104192E-3);
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const v_float64 _vexp_q2_f64 = vx_setall_f64(2.27265548208155028766E-1);
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const v_float64 _vexp_q3_f64 = vx_setall_f64(2.00000000000000000009E0);
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const v_int64 _vexp_bias_s64 = vx_setall_s64(0x3ff);
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v_float64 _vexp_, _vexp_x, _vexp_y, _vexp_z, _vexp_xx;
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v_int64 _vexp_mm;
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// compute exponential of x
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_vexp_x = v_max(x, _vexp_lo_f64);
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_vexp_x = v_min(_vexp_x, _vexp_hi_f64);
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_vexp_ = v_fma(_vexp_x, _vexp_LOG2EF_f64, _vexp_half_f64);
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_vexp_mm = v_expand_low(v_floor(_vexp_));
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_vexp_ = v_cvt_f64(_vexp_mm);
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_vexp_mm = v_add(_vexp_mm, _vexp_bias_s64);
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_vexp_mm = v_shl(_vexp_mm, 52);
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_vexp_x = v_fma(_vexp_, _vexp_C1_f64, _vexp_x);
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_vexp_x = v_fma(_vexp_, _vexp_C2_f64, _vexp_x);
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_vexp_xx = v_mul(_vexp_x, _vexp_x);
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_vexp_y = v_fma(_vexp_xx, _vexp_p0_f64, _vexp_p1_f64);
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_vexp_y = v_fma(_vexp_y, _vexp_xx, _vexp_p2_f64);
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_vexp_y = v_mul(_vexp_y, _vexp_x);
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_vexp_z = v_fma(_vexp_xx, _vexp_q0_f64, _vexp_q1_f64);
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_vexp_z = v_fma(_vexp_xx, _vexp_z, _vexp_q2_f64);
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_vexp_z = v_fma(_vexp_xx, _vexp_z, _vexp_q3_f64);
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_vexp_z = v_div(_vexp_y, v_sub(_vexp_z, _vexp_y));
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_vexp_z = v_fma(_vexp_two_f64, _vexp_z, _vexp_one_f64);
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_vexp_z = v_mul(_vexp_z, v_reinterpret_as_f64(_vexp_mm));
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// exp(NAN) -> NAN
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v_float64 mask_not_nan = v_not_nan(x);
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return v_select(mask_not_nan, _vexp_z, v_reinterpret_as_f64(vx_setall_s64(0x7FF8000000000000)));
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}
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#endif
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#define OPENCV_HAL_MATH_HAVE_EXP 1
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//! @}
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#endif
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}
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#endif // OPENCV_HAL_INTRIN_HPP
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