math_utilities.h

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//
// Created by qiayuan on 12/22/19.
//
 
#pragma once
 
#include <cmath>
template <typename T>
T angularMinus(T a, T b)
{
  a = fmod(a, 2.0 * M_PI);
  b = fmod(b, 2.0 * M_PI);
 
  T res1 = a - b;
  T res2 = (a < b) ? (a + 2 * M_PI - b) : (a - 2 * M_PI - b);
 
  return (std::abs(res1) < std::abs(res2)) ? res1 : res2;
}
 
template <typename T>
T minAbs(T a, T b)
{
  T sign = (a < 0.0) ? -1.0 : 1.0;
  return sign * fmin(fabs(a), b);
}
 
template <typename T>
int sgn(T val)
{
  return (T(0) < val) - (val < T(0));
}
 
template <typename T>
T square(T val)
{
  return val * val;
}
 
template <typename T>
T alpha(T cutoff, double freq)
{
  T tau = 1.0 / (2 * M_PI * cutoff);
  T te = 1.0 / freq;
  return 1.0 / (1.0 + tau / te);
}