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