MathUtil.h

#ifndef _MATH_UTIL_H
#define _MATH_UTIL_H

#define _USE_MATH_DEFINES
#include <cmath>
#include <vector>
#include <algorithm>    // std::binary_search, std::sort
#include <iostream>
#include <stdio.h>
#include <conio.h>

const double pi         = M_PI;         // pi
const double pi_2       = M_PI_2;       // pi/2
const double pi_4       = M_PI_4;       // pi/4
const double p1_pi      = M_1_PI;       // 1/pi
const double p2_pi      = M_2_PI;       // 2/pi
const double p2_sqrtpi  = M_2_SQRTPI;   // 2/sqrt(pi)
const double sqrt2      = M_SQRT2;      // sqrt(2)
const double sqrt1_2    = M_SQRT1_2;    // 1/sqrt(2)
const double e          = M_E;          // e
const double log2e      = M_LOG2E;      // log_2(e)
const double log10e     = M_LOG10E;     // log_10(e)
const double ln2        = M_LN2;        // log_e(2)
const double ln10       = M_LN10;       // log_e(10)
const double epsD       = std::numeric_limits<double>::epsilon();
const double inf        = std::numeric_limits<double>::infinity();
//const double nan        = std::numeric_limits<double>::quiet_NaN()
const double g          = 9.806650;      //m/s
const double gUS        = 32.17405;      //ft/s

const long double piL = 3.141592653589793238462643383279502884L; /* pi */

const double incTOm      = 0.0254; //Length 1.0 in = 0.0254 m  (exact)
const double ftTOinc     = 12.0; //Length 1.0 in = 0.0254 m  (exact)
const double incTOmm     = 25.4; //Length 1.0 in = 25.4 mm  (exact)
const double lbmTOkg     = 0.45359237; //Mass 1.0 lbm = 0.45359237 kg (exact)
const double lbmolTOkmol = 0.45359237; //Moles 1.0 lbmol = 0.45359237 kmol (exact)

const double psiTOmpa    = 0.006894757; //Pressure 1.0 psia = 0.006894757 MPa
const double mpaTOpsi    = 1.0/psiTOmpa;
const double psiTObar    = 0.06894757; //Pressure 1.0 psia = 0.006894757 MPa
const double barTOpsi    = 1.0/psiTObar;
const double psiTOkpa    = 6.894757; //Pressure 1.0 psia = 0.006894757 MPa
const double kpaTOpsi    = 1.0/psiTOkpa;
const double paTObar     = 1.0/100000.0;
const double barTOpa     = 100000.0;

const double cpTOpas     = 0.001; // 1 CP centipoise = 0.001 pascal second

const double degTOrad    = pi/180.0;
const double radTOdeg    = 180.0/pi;

const double atm      = 0.101325;  //MPa
const double atmUS    = 14.696;  //Psi
const double atmMMHG  = 760.0;  //mm Hg
const double atmINCHG = 29.9212;  //inc Hg

double Tcon(char in, double val, char out);

template <typename T> void bubbleSort(T arr[], int n);
template <class T> inline size_t binarySearch(const std::vector<T>& xd, T x, size_t low, size_t high);
template <class T> inline size_t linearSearch(const std::vector<T>& xd, T x, size_t low, size_t high);
int cubicRoot(double a1, double b1, double c1, double d1, double root[], double& img);
double kahanSum(std::vector<double> &fa);
void matrixDump(std::vector<std::vector<double>>& m);
bool checkSymmetric(std::vector<std::vector<double>>& m);
int nofDecimals(const double val);

template <typename T> inline T pow2(const T a){return a*a;}
template <typename T> inline T pow3(const T a){return a*a*a;}
template <typename T> inline T pow4(const T a){T a2 = a*a;   return a2*a2;}
template <typename T> inline T pow5(const T a){T a2 = a*a;   return a2*a2*a;}
template <typename T> inline T pow6(const T a){T a3 = a*a*a; return a3*a3;}

bool inline close_enough(double a, double b){
    if (fabs(a - b) <= epsD * std::fmax(fabs(a), fabs(b))) return true;
    return false;
}

int lagrange_value_1d (double x, double& y, const std::vector<double>& xd, const std::vector<double>& yd, int extrapolate = 1);

#endif