GY-63_MS5611/libraries/Complex/complex.cpp
2021-12-14 15:48:21 +01:00

414 lines
6.4 KiB
C++

//
// FILE: Complex.cpp
// AUTHOR: Rob Tillaart
// VERSION: 0.3.1
// PURPOSE: Arduino library for Complex math
// URL: https://github.com/RobTillaart/Complex
// http://arduino.cc/playground/Main/ComplexMath
//
// HISTORY
// 0.3.1 2021-12-14 update library.json, license, minor edits
// 0.3.0 2021-11-15 fix #7 adding const to operators
// 0.2.4 2021-10-19 update build-CI.
// 0.2.3 2021-09-14 fix build-CI + update readme
// 0.2.2 2020-12-16 add arduino-ci + unit test (starter)
// setReal, setImag
// 0.2.1 2020-06-05 fix library.json
// 0.2.0 2020-03-29 #pragma once, own repo
// 0.1.12 2018-04-02 - fix issue #33 double -> float
// 0.1.11 2018-01-29 - fix sin and cos formula - issue #91
// 0.1.10 2018-01-15 - uppercase #define COMPLEX_H
// 0.1.09 2016-10-15 - added (0,0) constructor
// 0.1.08 2015-06-03 - refactor
// 0.1.07 2015-06-03 - refactor interfaces
#include "Complex.h"
// PRINTING
size_t Complex::printTo(Print& p) const
{
size_t n = 0;
n += p.print(re, 3);
n += p.print(' ');
n += p.print(im, 3);
n += p.print('i');
return n;
};
void Complex::polar(const float modulus, const float phase)
{
re = modulus * cos(phase);
im = modulus * sin(phase);
}
Complex Complex::reciprocal() const
{
float f = 1.0 / (re * re + im * im);
float r = re * f;
float i = -im * f;
return Complex(r, i);
}
//
// EQUALITIES
//
bool Complex::operator == (const Complex &c) const
{
return (re == c.re) && (im == c.im);
}
bool Complex::operator != (const Complex &c) const
{
return (re != c.re) || (im != c.im);
}
//
// NEGATE
//
Complex Complex::operator - () const
{
return Complex(-re, -im);
}
//
// BASIC MATH
//
Complex Complex::operator + (const Complex &c) const
{
return Complex(re + c.re, im + c.im);
}
Complex Complex::operator - (const Complex &c) const
{
return Complex(re - c.re, im - c.im);
}
Complex Complex::operator * (const Complex &c) const
{
float r = re * c.re - im * c.im;
float i = re * c.im + im * c.re;
return Complex(r, i);
}
Complex Complex::operator / (const Complex &c) const
{
float f = 1.0/(c.re * c.re + c.im * c.im);
float r = (re * c.re + im * c.im) * f;
float i = (im * c.re - re * c.im) * f;
return Complex(r, i);
}
Complex& Complex::operator += (const Complex &c)
{
re += c.re;
im += c.im;
return *this;
}
Complex& Complex::operator -= (const Complex &c)
{
re -= c.re;
im -= c.im;
return *this;
}
Complex& Complex::operator *= (const Complex &c)
{
float r = re * c.re - im * c.im;
float i = re * c.im + im * c.re;
re = r;
im = i;
return *this;
}
Complex& Complex::operator /= (const Complex &c)
{
float f = 1.0/(c.re * c.re + c.im * c.im);
float r = (re * c.re + im * c.im) * f;
float i = (im * c.re - re * c.im) * f;
re = r;
im = i;
return *this;
}
//
// POWER FUNCTIONS
//
Complex Complex::c_sqr() const
{
float r = re * re - im * im;
float i = 2 * re * im;
return Complex(r, i);
}
Complex Complex::c_sqrt() const
{
float m = modulus();
float r = sqrt(0.5 * (m + re));
float i = sqrt(0.5 * (m - re));
if (im < 0) i = -i;
return Complex(r, i);
}
Complex Complex::c_exp() const
{
float e = exp(re);
return Complex(e * cos(im), e * sin(im));
}
Complex Complex::c_log() const
{
float m = modulus();
float p = phase();
if (p > PI) p -= 2 * PI;
return Complex(log(m), p);
}
Complex Complex::c_pow(const Complex &c) const
{
Complex t = c_log();
t = t * c;
return t.c_exp();
}
Complex Complex::c_logn(const Complex &c) const
{
Complex t = c;
return c_log()/t.c_log();
}
Complex Complex::c_log10() const
{
return c_logn(10);
}
//
// GONIO I - SIN COS TAN
//
Complex Complex::c_sin() const
{
return Complex(sin(re) * cosh(im), cos(re) * sinh(im));
}
Complex Complex::c_cos() const
{
return Complex(cos(re) * cosh(im), -sin(re) * sinh(im));
}
Complex Complex::c_tan() const
{
/* faster but 350 bytes longer!!
float s = sin(re);
float c = cos(re);
float sh = sinh(im);
float ch = cosh(im);
// return Complex(s*ch, c*sh) / Complex(c*ch, -s*sh);
float r0 = s*ch;
float i0 = c*sh;
float cre = c*ch;
float cim = -s*sh;
float f = 1.0/(cre*cre + cim*cim);
float r = r0 * cre + i0 * cim;
float i = r0 * cim - i0 * cre;
return Complex(r * f, -i * f);
*/
return c_sin() / c_cos();
}
Complex Complex::gonioHelper1(const byte mode) const
{
Complex c = (one - this->c_sqr()).c_sqrt();
if (mode == 0)
{
c = c + *this * Complex(0,-1);
}
else
{
c = *this + c * Complex(0,-1);
}
c = c.c_log() * Complex(0,1);
return c;
}
Complex Complex::c_asin() const
{
return gonioHelper1(0);
}
Complex Complex::c_acos() const
{
return gonioHelper1(1);
}
Complex Complex::c_atan() const
{
return (Complex(0,-1) * (Complex(re, im - 1)/Complex(-re, -im - 1)).c_log()) * 0.5;
}
//
// GONIO II - CSC SEC COT
//
Complex Complex::c_csc() const
{
return one / c_sin();
}
Complex Complex::c_sec() const
{
return one / c_cos();
}
Complex Complex::c_cot() const
{
return one / c_tan();
}
Complex Complex::c_acsc() const
{
return (one / *this).c_asin();
}
Complex Complex::c_asec() const
{
return (one / *this).c_acos();
}
Complex Complex::c_acot() const
{
return (one / *this).c_atan();
}
//
// GONIO HYPERBOLICUS I
//
Complex Complex::c_sinh() const
{
return Complex(cos(im) * sinh(re), sin(im) * cosh(re));
}
Complex Complex::c_cosh() const
{
return Complex(cos(im) * cosh(re), sin(im) * sinh(re));
}
Complex Complex::c_tanh() const
{
return c_sinh() / c_cosh();
}
Complex Complex::gonioHelper2(const byte mode) const
{
Complex c = c_sqr();
if (mode == 0)
{
c += 1;
}
else
{
c -= 1;
}
c = (*this + c.c_sqrt()).c_log();
return c;
}
Complex Complex::c_asinh() const
{
return gonioHelper2(0);
}
Complex Complex::c_acosh() const
{
return gonioHelper2(1);
}
Complex Complex::c_atanh() const
{
Complex c = (*this + one).c_log();
c = c - (-(*this - one)).c_log();
return c * 0.5;
}
//
// GONIO HYPERBOLICUS II
//
Complex Complex::c_csch() const
{
return one / c_sinh();
}
Complex Complex::c_sech() const
{
return one / c_cosh();
}
Complex Complex::c_coth() const
{
return one / c_tanh();
}
Complex Complex::c_acsch() const
{
return (one / *this).c_asinh();
}
Complex Complex::c_asech() const
{
return (one / *this).c_acosh();
}
Complex Complex::c_acoth() const
{
return (one / *this).c_atanh();
}
// --- END OF FILE ---