├── .gitmodules
├── 1st order digital low pass filter.pdf
├── README.md
├── DigitalFilters.h
└── LICENSE


/.gitmodules:
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1 | [submodule "CircularDelay"]
2 | 	path = CircularDelay
3 | 	url = https://github.com/overlord1123/CircularDelay.git
4 | 


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/1st order digital low pass filter.pdf:
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https://raw.githubusercontent.com/jimmyberg/DigitalFilters/HEAD/1st order digital low pass filter.pdf


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/README.md:
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 1 | # DigitalFilters
 2 | 
 3 | Collection of different filters that can be used in real time applications. This library will be extented in the future.
 4 | 
 5 | # Example In use
 6 | `main.cpp`
 7 | ``` C++
 8 | #include <iostream>
 9 | #include <fstream>
10 | #include "DigitalFilters.h"
11 | using namespace std;
12 | 
13 | int main(int argc, char** argv){
14 | 	// Set sample time = 1 / sample frequency
15 | 	constexpr float dtUsed = 0.01;
16 | 	// Set cutoffFrequency. Note that digital filters inherently rely on the angular cutoff frequency.
17 | 	constexpr float cutoffFrequeny = 0.5;
18 | 	
19 | 	// Construct various filter with cutoff frequency of 0.5 Hz.
20 | 	LowPassFilter lpf1(dtUsed, 2 * M_PI * cutoffFrequeny);
21 | 	LowPassFilter2 lpf2(dtUsed, 1/(2 * M_PI * cutoffFrequeny));
22 | 	LowPassFilter3 lpf3(dtUsed, 2 * M_PI * cutoffFrequeny);
23 | 	HighPassFilter hpf1(dtUsed, 2 * M_PI * cutoffFrequeny);
24 | 	HighPassFilter3 hpf3(dtUsed, 2 * M_PI * cutoffFrequeny);
25 | 	double input;
26 | 
27 | 	for (int i = 0; i < 1000; ++i)
28 | 	{
29 | 		// Create 1 unit step after 1 second.
30 | 		if(i < 100)
31 | 			input = 0;
32 | 		else
33 | 			input = 1;
34 | 		cout.width(8);
35 | 		cout << i * dtUsed
36 | 		<< ", " << input
37 | 		<< ", " << lpf1.update(input)
38 | 		<< ", " << lpf2.update(input)
39 | 		<< ", " << lpf3.update(input)
40 | 		<< ", " << hpf1.update(input)
41 | 		<< ", " << hpf3.update(input)
42 | 		<< endl;
43 | 	}
44 | 	return 0;
45 | }
46 | 
47 | ```
48 | 


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/DigitalFilters.h:
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  1 | #ifndef _DIGITAL_FILTERS_H_
  2 | #define _DIGITAL_FILTERS_H_
  3 | 
  4 | #include <stdexcept>
  5 | #include <cmath>
  6 | #include "CircularDelay/CircularDelay.hpp"
  7 | 
  8 | template<typename T>
  9 | constexpr T squareOf(T input){return input * input;}
 10 | 
 11 | namespace tps{
 12 | 	template<typename T>
 13 | 	constexpr T pow(T input, unsigned int power){return (power == 0 ? 1 : input * (power <= 1 ? 1 : tps::pow(input, power-1)));}
 14 | }
 15 | 
 16 | template<typename T>
 17 | constexpr T calcC_Cr(T k, T m){return 2 * sqrt(k * m);}
 18 | 
 19 | /**
 20 |  * @brief      Abstract base class for digital moving filters.
 21 |  *
 22 |  *             Moving filter are real time filter used for applications where
 23 |  *             continuous filtering is necessary as it can be part of an control
 24 |  *             system.
 25 |  *
 26 |  * @tparam     Type  Floating point type used.
 27 |  */
 28 | template<typename Type>
 29 | class DigitalFilter{
 30 | public:
 31 | 	virtual Type update(Type newValue) = 0;
 32 | 	virtual Type getOutput() = 0;
 33 | };
 34 | 
 35 | /**
 36 |  * @brief      Class for differentiator.
 37 |  */
 38 | template<typename T>
 39 | class Differentiator : public DigitalFilter<T> {
 40 | public:
 41 | 	Differentiator(T sampleTime):
 42 | 		sampleTime(sampleTime)
 43 | 	{}
 44 | 	T update(T input){
 45 | 		y = (input - x1) / sampleTime;
 46 | 		x1 = input;
 47 | 		return y;
 48 | 	}
 49 | 	T getOutput(){return y;}
 50 | private:
 51 | 	const T sampleTime;
 52 | 	T y = 0;
 53 | 	T x1 = 0;
 54 | };
 55 | 
 56 | /**
 57 |  * @brief      Class for a low pass filter.
 58 |  *
 59 |  *             Design to be a first order Butterworth low pass filter.
 60 |  *             Transformation done using the matched-Z-transform method
 61 |  */
 62 | class LowPassFilter : public DigitalFilter<double> {
 63 | public:
 64 | 	/**
 65 | 	 * @brief      Constructor to set sample time and the tau constant
 66 | 	 *
 67 | 	 * @param[in]  idt     Sample time for the low pass filter
 68 | 	 * @param[in]  itua_c  Or
 69 | 	 *             @f$ \tau_c
 70 | 	 *             @f$ The time constant for the filter. Note that
 71 | 	 *             @f$ \tau_c = \frac{1}{2 pi f_c}@f$  where @f$ f_c @f$ is the cutoff frequency
 72 | 	 */
 73 | 	LowPassFilter(double idt, double omega_c, double ioutput = 0):
 74 | 		epow(exp(-idt * omega_c)),
 75 | 		dt(idt),
 76 | 		output(ioutput){
 77 | 			if(omega_c < idt){
 78 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
 79 | 			}
 80 | 		}
 81 | 	/**
 82 | 	 * @brief      Update function to push new value into the low pass filter
 83 | 	 *
 84 | 	 * @param[in]  newValue  The new value after dt time
 85 | 	 *
 86 | 	 * @return     The new output value
 87 | 	 */
 88 | 	double update(double newValue) final{return output = (output-newValue) * epow + newValue;}
 89 | 	/**
 90 | 	 * @brief      Gets the output.
 91 | 	 *
 92 | 	 * @return     The output.
 93 | 	 */
 94 | 	double getOutput() final{return output;}
 95 | 	/**
 96 | 	 * @brief      Force the output to a desired value
 97 | 	 *
 98 | 	 *             This can be useful when the output needs to be forced in case
 99 | 	 *             of extreme inputs or such
100 | 	 *
101 | 	 * @param[in]  newOutput  The new output
102 | 	 */
103 | 	void configOutput(double newOutput){output = newOutput;}
104 | 	const double* outputPointer(){return &output;}
105 | private:
106 | 	const double epow; /// one time calculation constant
107 | 	const double dt;
108 | 	double output;
109 | };
110 | 
111 | /**
112 |  * @brief      Class for a 2nd order low pass filter.
113 | 	*
114 |  *             Design to be a 2nd order Butterworth low pass filter.
115 |  *             Transformation done using the bilinear transform method
116 |  */
117 | class LowPassFilter2 : public DigitalFilter<double> {
118 | public:
119 | 	/**
120 | 	 * @brief      Constructor to set sample time and the tau constant
121 | 	 *
122 | 	 * @param[in]  idt     Sample time for the low pass filter
123 | 	 * @param[in]  itua_c  Or
124 | 	 *             @f$ \tau_c
125 | 	 *             @f$ The time constant for the filter. Note that
126 | 	 *             @f$ \tau_c = \frac{1}{2 pi f_c}@f$  where @f$ f_c @f$ is the cutoff frequency
127 | 	 */
128 | 	LowPassFilter2(double dt, double tau_c, double ioutput = 0):
129 | 		yc{
130 | 			-2 * (pow(dt, 2) - 4 * pow(tau_c, 2)) / (pow(dt, 2) + 2 * sqrt(2) * tau_c * dt + 4 * pow(tau_c, 2)),
131 | 			(-pow(dt, 2) + 2 * sqrt(2) * tau_c * dt - 4 * pow(tau_c, 2)) / (pow(dt, 2) + 2 * sqrt(2) * tau_c * dt + 4 * pow(tau_c, 2))
132 | 		},
133 | 		xc{
134 | 			pow(dt, 2) / (pow(dt, 2) + 2 * sqrt(2) * tau_c * dt + 4 * pow(tau_c, 2)),
135 | 			2 * pow(dt, 2) / (pow(dt, 2) + 2 * sqrt(2) * tau_c * dt + 4 * pow(tau_c, 2)),
136 | 			pow(dt, 2) / (pow(dt, 2) + 2 * sqrt(2) * tau_c * dt + 4 * pow(tau_c, 2))
137 | 		}
138 | 		{
139 | 			if(tau_c < M_PI * dt){
140 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
141 | 			}
142 | 		}
143 | 	/**
144 | 	 * @brief      Update function to push new value into the low pass filter
145 | 	 *
146 | 	 * @param[in]  newValue  The new value after dt time
147 | 	 *
148 | 	 * @return     The new output value
149 | 	 */
150 | 	double update(double newValue) final{
151 | 		x.push(newValue);
152 | 		double output = 0;
153 | 		for (int i = 0; i < 2; ++i)
154 | 			output += y.get(i) * yc[i];
155 | 		for (int i = 0; i < 3; ++i)
156 | 			output += x.get(i) * xc[i];
157 | 		return y.push(output);
158 | 	}
159 | 	/**
160 | 	 * @brief      Gets the output.
161 | 	 *
162 | 	 * @return     The output.
163 | 	 */
164 | 	double getOutput() final{return y.get(0);}
165 | 	/**
166 | 	 * @brief      Force the output to a desired value
167 | 	 *
168 | 	 *             This can be useful when the output needs to be forced in case
169 | 	 *             of extreme inputs or such
170 | 	 *
171 | 	 * @param[in]  newOutput  The new output
172 | 	 */
173 | 	void configOutput(double newOutput){
174 | 		for(auto& it : x){
175 | 			it = newOutput;
176 | 		}
177 | 		for(auto& it : y){
178 | 			it = newOutput;
179 | 		}
180 | 	}
181 | private:
182 | 	const double yc[2];
183 | 	const double xc[3];
184 | 	CircularDelay<double, 2> y;
185 | 	CircularDelay<double, 3> x;
186 | };
187 | 
188 | /**
189 |  * @brief      Class for high pass filter using bilinear transform.
190 |  */
191 | class HighPassFilter : public DigitalFilter<double> {
192 | public:
193 | 	/**
194 | 	 * @brief      Constructor to set sample time and the tau constant
195 | 	 *
196 | 	 * @param[in]  idt     Sample time for the low pass filter
197 | 	 * @param[in]  itua_c  Or
198 | 	 *             @f$ \tau_c
199 | 	 *             @f$ The time constant for the filter. Note that
200 | 	 *             @f$ \tau_c = \frac{1}{2 pi f_c}@f$  where @f$ f_c @f$ is the cutoff frequency
201 | 	 */
202 | 	HighPassFilter(double idt, double omega_c):
203 | 		amplFac(1/((idt * omega_c / 2) + 1)),
204 | 		y1c((idt * omega_c / 2) - 1),
205 | 		dt(idt){
206 | 			if(omega_c < idt){
207 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
208 | 			}
209 | 		}
210 | 	/**
211 | 	 * @brief      Update function to push new value into the low pass filter
212 | 	 *
213 | 	 * @param[in]  newValue  The new value after dt time
214 | 	 *
215 | 	 * @return     The new output value
216 | 	 */
217 | 	double update(double newValue) final{
218 | 		// Note that output before assignment equals y1 being y[n-1]
219 | 		output = amplFac * (newValue - x1 - output * y1c);
220 | 		x1 = newValue;
221 | 		return output;
222 | 	}
223 | 	/**
224 | 	 * @brief      Gets the output.
225 | 	 *
226 | 	 * @return     The output.
227 | 	 */
228 | 	double getOutput() final{return output;}
229 | 	/**X
230 | 	 * @brief      Force the output to a desired value
231 | 	 *
232 | 	 *             This can be useful when the output needs to be forced in case
233 | 	 *             of extreme inputs or such
234 | 	 *
235 | 	 * @param[in]  newOutput  The new output
236 | 	 */
237 | 	void configOutput(double newOutput){output = newOutput;}
238 | 	const double* outputPointer(){return &output;}
239 | private:
240 | 	const double amplFac; // one time calculation constant
241 | 	const double y1c; // one time calculation constant
242 | 	const double dt;
243 | 	double x1 = 0;
244 | 	double output = 0;
245 | };
246 | 
247 | /**
248 |  * @brief      Class for third order high pass filter. This is designed using
249 |  *             the bilinear transform.
250 |  */
251 | class HighPassFilter3 : public DigitalFilter<double> {
252 | public:
253 | 	HighPassFilter3(double sampleTime, double omega_c, double ioutput = 0):
254 | 		xc{
255 | 			8
256 | 			,
257 | 			-24
258 | 			,
259 | 			24
260 | 			,
261 | 			-8
262 | 		},
263 | 		yc{
264 | 			1 / (1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8),
265 | 			     3 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) - 8 * sampleTime * omega_c - 24,
266 | 			     3 * tps::pow(sampleTime * omega_c, 3) - 4 * tps::pow(sampleTime * omega_c, 2) - 8 * sampleTime * omega_c + 24,
267 | 			     1 * tps::pow(sampleTime * omega_c, 3) - 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c - 8
268 | 		}
269 | 		{
270 | 			if(omega_c < sampleTime){
271 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
272 | 			}
273 | 		}
274 | 	double update(double newValue) final{
275 | 		x.push(newValue);
276 | 		double y0 = 0;
277 | 		const double* doubleP = xc;
278 | 		for (auto it = x.rbegin(); it != x.rend(); it++)
279 | 		{
280 | 			y0 += *it * *doubleP++;
281 | 		}
282 | 		doubleP = yc + 1;
283 | 		for (auto it = y.rbegin(); it != y.rend(); it++)
284 | 		{
285 | 			y0 -= *it * *doubleP++;
286 | 		}
287 | 		return y.push(yc[0] * y0);
288 | 		// return y.push(yc[0] * (
289 | 		// 		x.get(0) * xc[0] + x.get(1) * xc[1] + x.get(2) * xc[2] + x.get(3) * xc[3] -
290 | 		// 		y.get(0) * yc[1] - y.get(1) * yc[2] - y.get(2) * yc[3]
291 | 		// 	)
292 | 		// );
293 | 	}
294 | 	double getOutput() final{return y.get(0);}
295 | private:
296 | 	const double xc[4];
297 | 	const double yc[4];
298 | 	CircularDelay<double, 3> y;
299 | 	CircularDelay<double, 4> x;
300 | };
301 | 
302 | /**
303 |  * @brief      Class for third order high pass filter. This is designed using
304 |  *             the bilinear transform.
305 |  */
306 | class LowPassFilter3 : public DigitalFilter<double> {
307 | public:
308 | 	LowPassFilter3(long double sampleTime, long double omega_c, long double ioutput = 0):
309 | 		yc{
310 | 			1
311 | 			,
312 | 			(double)((3 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) - 8 * sampleTime * omega_c - 24)
313 | 			/
314 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
315 | 			,
316 | 			(double)((3 * tps::pow(sampleTime * omega_c, 3) - 4 * tps::pow(sampleTime * omega_c, 2) - 8 * sampleTime * omega_c + 24)
317 | 			/
318 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
319 | 			,
320 | 			(double)((1 * tps::pow(sampleTime * omega_c, 3) - 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c - 8)
321 | 			/
322 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
323 | 		},
324 | 		xc{
325 | 			(double)(1 * tps::pow(sampleTime * omega_c, 3)
326 | 			/
327 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
328 | 			,
329 | 			(double)(3 * tps::pow(sampleTime * omega_c, 3)
330 | 			/
331 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
332 | 			,
333 | 			(double)(3 * tps::pow(sampleTime * omega_c, 3)
334 | 			/
335 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
336 | 			,
337 | 			(double)(1 * tps::pow(sampleTime * omega_c, 3)
338 | 			/
339 | 			(1 * tps::pow(sampleTime * omega_c, 3) + 4 * tps::pow(sampleTime * omega_c, 2) + 8 * sampleTime * omega_c + 8))
340 | 		}
341 | 		{
342 | 			if(omega_c < sampleTime){
343 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
344 | 			}
345 | 		}
346 | 	double update(double newValue) final{
347 | 		x.push(newValue);
348 | 		double y0 = 0;
349 | 		const double* doubleP = xc;
350 | 		for (auto it = x.rbegin(); it != x.rend(); it++)
351 | 		{
352 | 			y0 += *it * *doubleP++;
353 | 		}
354 | 		doubleP = yc + 1;
355 | 		for (auto it = y.rbegin(); it != y.rend(); it++)
356 | 		{
357 | 			y0 -= *it * *doubleP++;
358 | 		}
359 | 		return y.push(yc[0] * y0);
360 | 	}
361 | 	double getOutput() final{return y.get(0);}
362 | private:
363 | 	const double yc[4];
364 | 	const double xc[4];
365 | 	CircularDelay<double, 3> y;
366 | 	CircularDelay<double, 4> x;
367 | };
368 | 
369 | /**
370 |  * @brief      Class for third order high pass filter. This is designed using
371 |  *             the matched Z transform.
372 |  */
373 | class LowPassFilter3MatchedZ : public DigitalFilter<double> {
374 | public:
375 | 	LowPassFilter3MatchedZ(long double sampleTime, long double omega_c):
376 | 		amplFac(-(2*(expl(3 * omega_c * sampleTime) - expl(2 * omega_c * sampleTime))*cosl(sqrtl(3) * omega_c * sampleTime / 2) - expl(7 * omega_c * sampleTime / 2) + expl(3 * omega_c * sampleTime / 2))*expl(-7 * omega_c * sampleTime / 2)),
377 | 		yc{
378 | 			(double)(-(2 * cosl(sqrtl(3) * omega_c * sampleTime / 2) * expl(omega_c * sampleTime * 5 / 2) + expl(2 * omega_c * sampleTime)) * expl(-3 * omega_c * sampleTime))
379 | 			,
380 | 			(double)((2 * cosl(sqrtl(3) * omega_c * sampleTime / 2) * expl(omega_c * sampleTime * 3 / 2) + expl(2 * omega_c * sampleTime)) * expl(-3 * omega_c * sampleTime))
381 | 			,
382 | 			(double)(-expl(-2 * omega_c * sampleTime))
383 | 		}
384 | 		{
385 | 			if(omega_c / (2 * M_PI) < sampleTime){
386 | 				throw std::domain_error("LowPassFilter3MatchedZ constructor error: tua_c is smaller than the sample time dt.");
387 | 			}
388 | 		}
389 | 	double update(double newValue) final{
390 | 		double y0 = newValue * amplFac;
391 | 		const double* doubleP = yc;
392 | 		for (auto it = y.rbegin(); it != y.rend(); it++)
393 | 		{
394 | 			y0 -= *it * *doubleP++;
395 | 		}
396 | 		return y.push(y0);
397 | 	}
398 | 	double getOutput() final{return y.get(0);}
399 | private:
400 | 	const double amplFac;
401 | 	const double yc[3];
402 | 	CircularDelay<double, 3> y;
403 | };
404 | 
405 | /**
406 |  * @brief      Class for third order high pass filter. This is designed using
407 |  *             the approximated differtial approuch where s=(Z-1)/(Z*T).
408 |  */
409 | class LowPassFilter3DiffApprox : public DigitalFilter<double> {
410 | public:
411 | 	LowPassFilter3DiffApprox(double sampleTime, double omega_c, double ioutput = 0):
412 | 		xc{
413 | 			1 * tps::pow(sampleTime * omega_c, 3)
414 | 			,
415 | 			0
416 | 			,
417 | 			0
418 | 			,
419 | 			0
420 | 		},
421 | 		yc{
422 | 			1 / (1 * tps::pow(sampleTime * omega_c, 3) + 2 * tps::pow(sampleTime * omega_c, 2) + 2 * sampleTime * omega_c + 1),
423 | 			     0 * tps::pow(sampleTime * omega_c, 3) - 2 * tps::pow(sampleTime * omega_c, 2) - 4 * sampleTime * omega_c - 3,
424 | 			     0 * tps::pow(sampleTime * omega_c, 3) + 0 * tps::pow(sampleTime * omega_c, 2) + 2 * sampleTime * omega_c + 3,
425 | 			     0 * tps::pow(sampleTime * omega_c, 3) - 0 * tps::pow(sampleTime * omega_c, 2) + 0 * sampleTime * omega_c - 1
426 | 		}
427 | 		{
428 | 			if(omega_c < sampleTime){
429 | 				throw std::domain_error("LowPassFilter constructor error: tua_c is smaller than the sample time dt.");
430 | 			}
431 | 		}
432 | 	double update(double newValue) final{
433 | 		x.push(newValue);
434 | 		double y0 = 0;
435 | 		const double* doubleP = xc;
436 | 		for (auto it = x.rbegin(); it != x.rend(); it++)
437 | 		{
438 | 			y0 += *it * *doubleP++;
439 | 		}
440 | 		doubleP = yc + 1;
441 | 		for (auto it = y.rbegin(); it != y.rend(); it++)
442 | 		{
443 | 			y0 -= *it * *doubleP++;
444 | 		}
445 | 		return y.push(yc[0] * y0);
446 | 	}
447 | 	double getOutput() final{return y.get(0);}
448 | private:
449 | 	const double xc[4];
450 | 	const double yc[4];
451 | 	CircularDelay<double, 3> y;
452 | 	CircularDelay<double, 4> x;
453 | };
454 | 
455 | template<size_t size>
456 | class MovingAvarageFilter{
457 | public:
458 | 	double update(double input){
459 | 		input *= 1000;
460 | 		output += int64_t(input) - *buffer.rbegin();
461 | 		buffer.push(input);
462 | 		return double(output) / (1000);
463 | 	}
464 | private:
465 | 	int64_t output = 0;
466 | 	CircularDelay<int64_t, size> buffer;
467 | };
468 | 
469 | #endif
470 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
  1 |                     GNU GENERAL PUBLIC LICENSE
  2 |                        Version 3, 29 June 2007
  3 | 
  4 |  Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
  5 |  Everyone is permitted to copy and distribute verbatim copies
  6 |  of this license document, but changing it is not allowed.
  7 | 
  8 |                             Preamble
  9 | 
 10 |   The GNU General Public License is a free, copyleft license for
 11 | software and other kinds of works.
 12 | 
 13 |   The licenses for most software and other practical works are designed
 14 | to take away your freedom to share and change the works.  By contrast,
 15 | the GNU General Public License is intended to guarantee your freedom to
 16 | share and change all versions of a program--to make sure it remains free
 17 | software for all its users.  We, the Free Software Foundation, use the
 18 | GNU General Public License for most of our software; it applies also to
 19 | any other work released this way by its authors.  You can apply it to
 20 | your programs, too.
 21 | 
 22 |   When we speak of free software, we are referring to freedom, not
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 71 |                        TERMS AND CONDITIONS
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 73 |   0. Definitions.
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 75 |   "This License" refers to version 3 of the GNU General Public License.
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 77 |   "Copyright" also means copyright-like laws that apply to other kinds of
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154 |   2. Basic Permissions.
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158 | conditions are met.  This License explicitly affirms your unlimited
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164 |   You may make, run and propagate covered works that you do not
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181 |   No covered work shall be deemed part of an effective technological
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195 |   4. Conveying Verbatim Copies.
196 | 
197 |   You may convey verbatim copies of the Program's source code as you
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202 | keep intact all notices of the absence of any warranty; and give all
203 | recipients a copy of this License along with the Program.
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205 |   You may charge any price or no price for each copy that you convey,
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207 | 
208 |   5. Conveying Modified Source Versions.
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214 |     a) The work must carry prominent notices stating that you modified
215 |     it, and giving a relevant date.
216 | 
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220 |     "keep intact all notices".
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222 |     c) You must license the entire work, as a whole, under this
223 |     License to anyone who comes into possession of a copy.  This
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228 |     invalidate such permission if you have separately received it.
229 | 
230 |     d) If the work has interactive user interfaces, each must display
231 |     Appropriate Legal Notices; however, if the Program has interactive
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233 |     work need not make them do so.
234 | 
235 |   A compilation of a covered work with other separate and independent
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237 | and which are not combined with it such as to form a larger program,
238 | in or on a volume of a storage or distribution medium, is called an
239 | "aggregate" if the compilation and its resulting copyright are not
240 | used to limit the access or legal rights of the compilation's users
241 | beyond what the individual works permit.  Inclusion of a covered work
242 | in an aggregate does not cause this License to apply to the other
243 | parts of the aggregate.
244 | 
245 |   6. Conveying Non-Source Forms.
246 | 
247 |   You may convey a covered work in object code form under the terms
248 | of sections 4 and 5, provided that you also convey the
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250 | in one of these ways:
251 | 
252 |     a) Convey the object code in, or embodied in, a physical product
253 |     (including a physical distribution medium), accompanied by the
254 |     Corresponding Source fixed on a durable physical medium
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256 | 
257 |     b) Convey the object code in, or embodied in, a physical product
258 |     (including a physical distribution medium), accompanied by a
259 |     written offer, valid for at least three years and valid for as
260 |     long as you offer spare parts or customer support for that product
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262 |     copy of the Corresponding Source for all the software in the
263 |     product that is covered by this License, on a durable physical
264 |     medium customarily used for software interchange, for a price no
265 |     more than your reasonable cost of physically performing this
266 |     conveying of source, or (2) access to copy the
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268 | 
269 |     c) Convey individual copies of the object code with a copy of the
270 |     written offer to provide the Corresponding Source.  This
271 |     alternative is allowed only occasionally and noncommercially, and
272 |     only if you received the object code with such an offer, in accord
273 |     with subsection 6b.
274 | 
275 |     d) Convey the object code by offering access from a designated
276 |     place (gratis or for a charge), and offer equivalent access to the
277 |     Corresponding Source in the same way through the same place at no
278 |     further charge.  You need not require recipients to copy the
279 |     Corresponding Source along with the object code.  If the place to
280 |     copy the object code is a network server, the Corresponding Source
281 |     may be on a different server (operated by you or a third party)
282 |     that supports equivalent copying facilities, provided you maintain
283 |     clear directions next to the object code saying where to find the
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285 |     Corresponding Source, you remain obligated to ensure that it is
286 |     available for as long as needed to satisfy these requirements.
287 | 
288 |     e) Convey the object code using peer-to-peer transmission, provided
289 |     you inform other peers where the object code and Corresponding
290 |     Source of the work are being offered to the general public at no
291 |     charge under subsection 6d.
292 | 
293 |   A separable portion of the object code, whose source code is excluded
294 | from the Corresponding Source as a System Library, need not be
295 | included in conveying the object code work.
296 | 
297 |   A "User Product" is either (1) a "consumer product", which means any
298 | tangible personal property which is normally used for personal, family,
299 | or household purposes, or (2) anything designed or sold for incorporation
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302 | product received by a particular user, "normally used" refers to a
303 | typical or common use of that class of product, regardless of the status
304 | of the particular user or of the way in which the particular user
305 | actually uses, or expects or is expected to use, the product.  A product
306 | is a consumer product regardless of whether the product has substantial
307 | commercial, industrial or non-consumer uses, unless such uses represent
308 | the only significant mode of use of the product.
309 | 
310 |   "Installation Information" for a User Product means any methods,
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313 | a modified version of its Corresponding Source.  The information must
314 | suffice to ensure that the continued functioning of the modified object
315 | code is in no case prevented or interfered with solely because
316 | modification has been made.
317 | 
318 |   If you convey an object code work under this section in, or with, or
319 | specifically for use in, a User Product, and the conveying occurs as
320 | part of a transaction in which the right of possession and use of the
321 | User Product is transferred to the recipient in perpetuity or for a
322 | fixed term (regardless of how the transaction is characterized), the
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324 | by the Installation Information.  But this requirement does not apply
325 | if neither you nor any third party retains the ability to install
326 | modified object code on the User Product (for example, the work has
327 | been installed in ROM).
328 | 
329 |   The requirement to provide Installation Information does not include a
330 | requirement to continue to provide support service, warranty, or updates
331 | for a work that has been modified or installed by the recipient, or for
332 | the User Product in which it has been modified or installed.  Access to a
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335 | protocols for communication across the network.
336 | 
337 |   Corresponding Source conveyed, and Installation Information provided,
338 | in accord with this section must be in a format that is publicly
339 | documented (and with an implementation available to the public in
340 | source code form), and must require no special password or key for
341 | unpacking, reading or copying.
342 | 
343 |   7. Additional Terms.
344 | 
345 |   "Additional permissions" are terms that supplement the terms of this
346 | License by making exceptions from one or more of its conditions.
347 | Additional permissions that are applicable to the entire Program shall
348 | be treated as though they were included in this License, to the extent
349 | that they are valid under applicable law.  If additional permissions
350 | apply only to part of the Program, that part may be used separately
351 | under those permissions, but the entire Program remains governed by
352 | this License without regard to the additional permissions.
353 | 
354 |   When you convey a copy of a covered work, you may at your option
355 | remove any additional permissions from that copy, or from any part of
356 | it.  (Additional permissions may be written to require their own
357 | removal in certain cases when you modify the work.)  You may place
358 | additional permissions on material, added by you to a covered work,
359 | for which you have or can give appropriate copyright permission.
360 | 
361 |   Notwithstanding any other provision of this License, for material you
362 | add to a covered work, you may (if authorized by the copyright holders of
363 | that material) supplement the terms of this License with terms:
364 | 
365 |     a) Disclaiming warranty or limiting liability differently from the
366 |     terms of sections 15 and 16 of this License; or
367 | 
368 |     b) Requiring preservation of specified reasonable legal notices or
369 |     author attributions in that material or in the Appropriate Legal
370 |     Notices displayed by works containing it; or
371 | 
372 |     c) Prohibiting misrepresentation of the origin of that material, or
373 |     requiring that modified versions of such material be marked in
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375 | 
376 |     d) Limiting the use for publicity purposes of names of licensors or
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378 | 
379 |     e) Declining to grant rights under trademark law for use of some
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381 | 
382 |     f) Requiring indemnification of licensors and authors of that
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384 |     it) with contractual assumptions of liability to the recipient, for
385 |     any liability that these contractual assumptions directly impose on
386 |     those licensors and authors.
387 | 
388 |   All other non-permissive additional terms are considered "further
389 | restrictions" within the meaning of section 10.  If the Program as you
390 | received it, or any part of it, contains a notice stating that it is
391 | governed by this License along with a term that is a further
392 | restriction, you may remove that term.  If a license document contains
393 | a further restriction but permits relicensing or conveying under this
394 | License, you may add to a covered work material governed by the terms
395 | of that license document, provided that the further restriction does
396 | not survive such relicensing or conveying.
397 | 
398 |   If you add terms to a covered work in accord with this section, you
399 | must place, in the relevant source files, a statement of the
400 | additional terms that apply to those files, or a notice indicating
401 | where to find the applicable terms.
402 | 
403 |   Additional terms, permissive or non-permissive, may be stated in the
404 | form of a separately written license, or stated as exceptions;
405 | the above requirements apply either way.
406 | 
407 |   8. Termination.
408 | 
409 |   You may not propagate or modify a covered work except as expressly
410 | provided under this License.  Any attempt otherwise to propagate or
411 | modify it is void, and will automatically terminate your rights under
412 | this License (including any patent licenses granted under the third
413 | paragraph of section 11).
414 | 
415 |   However, if you cease all violation of this License, then your
416 | license from a particular copyright holder is reinstated (a)
417 | provisionally, unless and until the copyright holder explicitly and
418 | finally terminates your license, and (b) permanently, if the copyright
419 | holder fails to notify you of the violation by some reasonable means
420 | prior to 60 days after the cessation.
421 | 
422 |   Moreover, your license from a particular copyright holder is
423 | reinstated permanently if the copyright holder notifies you of the
424 | violation by some reasonable means, this is the first time you have
425 | received notice of violation of this License (for any work) from that
426 | copyright holder, and you cure the violation prior to 30 days after
427 | your receipt of the notice.
428 | 
429 |   Termination of your rights under this section does not terminate the
430 | licenses of parties who have received copies or rights from you under
431 | this License.  If your rights have been terminated and not permanently
432 | reinstated, you do not qualify to receive new licenses for the same
433 | material under section 10.
434 | 
435 |   9. Acceptance Not Required for Having Copies.
436 | 
437 |   You are not required to accept this License in order to receive or
438 | run a copy of the Program.  Ancillary propagation of a covered work
439 | occurring solely as a consequence of using peer-to-peer transmission
440 | to receive a copy likewise does not require acceptance.  However,
441 | nothing other than this License grants you permission to propagate or
442 | modify any covered work.  These actions infringe copyright if you do
443 | not accept this License.  Therefore, by modifying or propagating a
444 | covered work, you indicate your acceptance of this License to do so.
445 | 
446 |   10. Automatic Licensing of Downstream Recipients.
447 | 
448 |   Each time you convey a covered work, the recipient automatically
449 | receives a license from the original licensors, to run, modify and
450 | propagate that work, subject to this License.  You are not responsible
451 | for enforcing compliance by third parties with this License.
452 | 
453 |   An "entity transaction" is a transaction transferring control of an
454 | organization, or substantially all assets of one, or subdividing an
455 | organization, or merging organizations.  If propagation of a covered
456 | work results from an entity transaction, each party to that
457 | transaction who receives a copy of the work also receives whatever
458 | licenses to the work the party's predecessor in interest had or could
459 | give under the previous paragraph, plus a right to possession of the
460 | Corresponding Source of the work from the predecessor in interest, if
461 | the predecessor has it or can get it with reasonable efforts.
462 | 
463 |   You may not impose any further restrictions on the exercise of the
464 | rights granted or affirmed under this License.  For example, you may
465 | not impose a license fee, royalty, or other charge for exercise of
466 | rights granted under this License, and you may not initiate litigation
467 | (including a cross-claim or counterclaim in a lawsuit) alleging that
468 | any patent claim is infringed by making, using, selling, offering for
469 | sale, or importing the Program or any portion of it.
470 | 
471 |   11. Patents.
472 | 
473 |   A "contributor" is a copyright holder who authorizes use under this
474 | License of the Program or a work on which the Program is based.  The
475 | work thus licensed is called the contributor's "contributor version".
476 | 
477 |   A contributor's "essential patent claims" are all patent claims
478 | owned or controlled by the contributor, whether already acquired or
479 | hereafter acquired, that would be infringed by some manner, permitted
480 | by this License, of making, using, or selling its contributor version,
481 | but do not include claims that would be infringed only as a
482 | consequence of further modification of the contributor version.  For
483 | purposes of this definition, "control" includes the right to grant
484 | patent sublicenses in a manner consistent with the requirements of
485 | this License.
486 | 
487 |   Each contributor grants you a non-exclusive, worldwide, royalty-free
488 | patent license under the contributor's essential patent claims, to
489 | make, use, sell, offer for sale, import and otherwise run, modify and
490 | propagate the contents of its contributor version.
491 | 
492 |   In the following three paragraphs, a "patent license" is any express
493 | agreement or commitment, however denominated, not to enforce a patent
494 | (such as an express permission to practice a patent or covenant not to
495 | sue for patent infringement).  To "grant" such a patent license to a
496 | party means to make such an agreement or commitment not to enforce a
497 | patent against the party.
498 | 
499 |   If you convey a covered work, knowingly relying on a patent license,
500 | and the Corresponding Source of the work is not available for anyone
501 | to copy, free of charge and under the terms of this License, through a
502 | publicly available network server or other readily accessible means,
503 | then you must either (1) cause the Corresponding Source to be so
504 | available, or (2) arrange to deprive yourself of the benefit of the
505 | patent license for this particular work, or (3) arrange, in a manner
506 | consistent with the requirements of this License, to extend the patent
507 | license to downstream recipients.  "Knowingly relying" means you have
508 | actual knowledge that, but for the patent license, your conveying the
509 | covered work in a country, or your recipient's use of the covered work
510 | in a country, would infringe one or more identifiable patents in that
511 | country that you have reason to believe are valid.
512 | 
513 |   If, pursuant to or in connection with a single transaction or
514 | arrangement, you convey, or propagate by procuring conveyance of, a
515 | covered work, and grant a patent license to some of the parties
516 | receiving the covered work authorizing them to use, propagate, modify
517 | or convey a specific copy of the covered work, then the patent license
518 | you grant is automatically extended to all recipients of the covered
519 | work and works based on it.
520 | 
521 |   A patent license is "discriminatory" if it does not include within
522 | the scope of its coverage, prohibits the exercise of, or is
523 | conditioned on the non-exercise of one or more of the rights that are
524 | specifically granted under this License.  You may not convey a covered
525 | work if you are a party to an arrangement with a third party that is
526 | in the business of distributing software, under which you make payment
527 | to the third party based on the extent of your activity of conveying
528 | the work, and under which the third party grants, to any of the
529 | parties who would receive the covered work from you, a discriminatory
530 | patent license (a) in connection with copies of the covered work
531 | conveyed by you (or copies made from those copies), or (b) primarily
532 | for and in connection with specific products or compilations that
533 | contain the covered work, unless you entered into that arrangement,
534 | or that patent license was granted, prior to 28 March 2007.
535 | 
536 |   Nothing in this License shall be construed as excluding or limiting
537 | any implied license or other defenses to infringement that may
538 | otherwise be available to you under applicable patent law.
539 | 
540 |   12. No Surrender of Others' Freedom.
541 | 
542 |   If conditions are imposed on you (whether by court order, agreement or
543 | otherwise) that contradict the conditions of this License, they do not
544 | excuse you from the conditions of this License.  If you cannot convey a
545 | covered work so as to satisfy simultaneously your obligations under this
546 | License and any other pertinent obligations, then as a consequence you may
547 | not convey it at all.  For example, if you agree to terms that obligate you
548 | to collect a royalty for further conveying from those to whom you convey
549 | the Program, the only way you could satisfy both those terms and this
550 | License would be to refrain entirely from conveying the Program.
551 | 
552 |   13. Use with the GNU Affero General Public License.
553 | 
554 |   Notwithstanding any other provision of this License, you have
555 | permission to link or combine any covered work with a work licensed
556 | under version 3 of the GNU Affero General Public License into a single
557 | combined work, and to convey the resulting work.  The terms of this
558 | License will continue to apply to the part which is the covered work,
559 | but the special requirements of the GNU Affero General Public License,
560 | section 13, concerning interaction through a network will apply to the
561 | combination as such.
562 | 
563 |   14. Revised Versions of this License.
564 | 
565 |   The Free Software Foundation may publish revised and/or new versions of
566 | the GNU General Public License from time to time.  Such new versions will
567 | be similar in spirit to the present version, but may differ in detail to
568 | address new problems or concerns.
569 | 
570 |   Each version is given a distinguishing version number.  If the
571 | Program specifies that a certain numbered version of the GNU General
572 | Public License "or any later version" applies to it, you have the
573 | option of following the terms and conditions either of that numbered
574 | version or of any later version published by the Free Software
575 | Foundation.  If the Program does not specify a version number of the
576 | GNU General Public License, you may choose any version ever published
577 | by the Free Software Foundation.
578 | 
579 |   If the Program specifies that a proxy can decide which future
580 | versions of the GNU General Public License can be used, that proxy's
581 | public statement of acceptance of a version permanently authorizes you
582 | to choose that version for the Program.
583 | 
584 |   Later license versions may give you additional or different
585 | permissions.  However, no additional obligations are imposed on any
586 | author or copyright holder as a result of your choosing to follow a
587 | later version.
588 | 
589 |   15. Disclaimer of Warranty.
590 | 
591 |   THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
592 | APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
596 | PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
597 | IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
599 | 
600 |   16. Limitation of Liability.
601 | 
602 |   IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
610 | SUCH DAMAGES.
611 | 
612 |   17. Interpretation of Sections 15 and 16.
613 | 
614 |   If the disclaimer of warranty and limitation of liability provided
615 | above cannot be given local legal effect according to their terms,
616 | reviewing courts shall apply local law that most closely approximates
617 | an absolute waiver of all civil liability in connection with the
618 | Program, unless a warranty or assumption of liability accompanies a
619 | copy of the Program in return for a fee.
620 | 
621 |                      END OF TERMS AND CONDITIONS
622 | 


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