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209 lines
6.3 KiB
C++
209 lines
6.3 KiB
C++
/****************************************************************************
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*
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* Copyright (c) 2017 PX4 Development Team. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* 3. Neither the name PX4 nor the names of its contributors may be
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* used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
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* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
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* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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****************************************************************************/
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/**
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* @file Functions.hpp
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*
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* collection of rather simple mathematical functions that get used over and over again
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*/
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#pragma once
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#include "Limits.hpp"
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namespace math
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{
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// Type-safe signum function
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template<typename T>
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int sign(T val)
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{
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return (T(FLT_EPSILON) < val) - (val < T(FLT_EPSILON));
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}
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// Type-safe signum function with zero treated as positive
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template<typename T>
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int signNoZero(T val)
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{
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return (T(0) <= val) - (val < T(0));
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}
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/*
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* So called exponential curve function implementation.
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* It is essentially a linear combination between a linear and a cubic function.
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* @param value [-1,1] input value to function
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* @param e [0,1] function parameter to set ratio between linear and cubic shape
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* 0 - pure linear function
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* 1 - pure cubic function
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* @return result of function output
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*/
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template<typename T>
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const T expo(const T &value, const T &e)
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{
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T x = constrain(value, (T) - 1, (T) 1);
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T ec = constrain(e, (T) 0, (T) 1);
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return (1 - ec) * x + ec * x * x * x;
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}
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/*
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* So called SuperExpo function implementation.
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* It is a 1/(1-x) function to further shape the rc input curve intuitively.
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* I enhanced it compared to other implementations to keep the scale between [-1,1].
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* @param value [-1,1] input value to function
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* @param e [0,1] function parameter to set ratio between linear and cubic shape (see expo)
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* @param g [0,1) function parameter to set SuperExpo shape
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* 0 - pure expo function
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* 0.99 - very strong bent curve, stays zero until maximum stick input
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* @return result of function output
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*/
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template<typename T>
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const T superexpo(const T &value, const T &e, const T &g)
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{
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T x = constrain(value, (T) - 1, (T) 1);
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T gc = constrain(g, (T) 0, (T) 0.99);
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return expo(x, e) * (1 - gc) / (1 - fabsf(x) * gc);
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}
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/*
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* Deadzone function being linear and continuous outside of the deadzone
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* 1 ------
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* /
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* --
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* /
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* -1 ------
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* -1 -dz +dz 1
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* @param value [-1,1] input value to function
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* @param dz [0,1) ratio between deazone and complete span
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* 0 - no deadzone, linear -1 to 1
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* 0.5 - deadzone is half of the span [-0.5,0.5]
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* 0.99 - almost entire span is deadzone
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*/
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template<typename T>
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const T deadzone(const T &value, const T &dz)
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{
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T x = constrain(value, (T) - 1, (T) 1);
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T dzc = constrain(dz, (T) 0, (T) 0.99);
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// Rescale the input such that we get a piecewise linear function that will be continuous with applied deadzone
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T out = (x - sign(x) * dzc) / (1 - dzc);
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// apply the deadzone (values zero around the middle)
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return out * (fabsf(x) > dzc);
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}
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template<typename T>
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const T expo_deadzone(const T &value, const T &e, const T &dz)
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{
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return expo(deadzone(value, dz), e);
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}
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/*
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* Constant, linear, constant function with the two corner points as parameters
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* y_high -------
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* /
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* /
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* /
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* y_low -------
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* x_low x_high
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*/
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template<typename T>
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const T gradual(const T &value, const T &x_low, const T &x_high, const T &y_low, const T &y_high)
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{
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if (value < x_low) {
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return y_low;
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} else if (value > x_high) {
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return y_high;
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} else {
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/* linear function between the two points */
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T a = (y_high - y_low) / (x_high - x_low);
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T b = y_low - a * x_low;
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return a * value + b;
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}
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}
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/*
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* Exponential function of the form Y_out = a*b^X + c
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*
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* Y_max | *
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* | *
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* | *
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* | *
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* | *
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* Y_middle | *
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* | *
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* Y_min | * *
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* | __________________________________
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* 0 1 2
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*
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*
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* @param X in the range [0,2]
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* @param Y_min minimum output at X = 2
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* @param Y_mid middle output at X = 1
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* @param Y_max maximum output at X = 0
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*/
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template<typename T>
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const T expontialFromLimits(const T &X_in, const T &Y_min, const T &Y_mid, const T &Y_max)
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{
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const T delta = (T)0.001;
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// constrain X_in to the range of 0 and 2
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T X = math::constrain(X_in, (T)0, (T)2);
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// If Y_mid is exactly in the middle, then just apply linear approach.
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bool use_linear_approach = false;
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if (((Y_max + Y_min) * (T)0.5) - Y_mid < delta) {
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use_linear_approach = true;
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}
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T Y_out;
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if (use_linear_approach) {
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// Y_out = m*x+q
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float slope = -(Y_max - Y_min) / (T)2.0;
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Y_out = slope * X + Y_max;
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} else {
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// Y_out = a*b^X + c with constraints Y_max = 0, Y_middle = 1, Y_min = 2
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T a = -((Y_mid - Y_max) * (Y_mid - Y_max))
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/ ((T)2.0 * Y_mid - Y_max - Y_min);
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T c = Y_max - a;
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T b = (Y_mid - c) / a;
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Y_out = a * powf(b, X) + c;
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}
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// Y_out needs to be in between max and min
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return constrain(Y_out, Y_min, Y_max);
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}
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} /* namespace math */
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