DGtal 1.4.0
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testSternBrocot.cpp
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1
31#include <cstdlib>
32#include <iostream>
33#include "DGtal/base/Common.h"
34#include "DGtal/kernel/CPointPredicate.h"
35#include "DGtal/arithmetic/CPositiveIrreducibleFraction.h"
36#include "DGtal/arithmetic/IntegerComputer.h"
37#include "DGtal/arithmetic/SternBrocot.h"
38#include "DGtal/arithmetic/Pattern.h"
39#include "DGtal/arithmetic/StandardDSLQ0.h"
40#include "DGtal/geometry/curves/ArithmeticalDSSComputer.h"
42
43using namespace std;
44using namespace DGtal;
45
47// Functions for testing class SternBrocot.
49
50template <typename Quotient>
51bool
52equalCFrac( const std::vector<Quotient> & c1, const std::vector<Quotient> & c2 )
53{
54 unsigned int s = c1.size() < c2.size() ? c1.size() : c2.size();
55 if ( ( s != c1.size() ) && ( c1.back() != NumberTraits<Quotient>::ONE ) )
56 return false;
57 if ( ( s != c2.size() ) && ( c2.back() != NumberTraits<Quotient>::ONE ) )
58 return false;
59 for ( unsigned int i = 0; i < s; ++i )
60 {
61 Quotient q1 = c1[ i ];
62 if ( ( s != c1.size() ) && ( i == s - 1 ) ) q1 += c1.back();
63 Quotient q2 = c2[ i ];
64 if ( ( s != c2.size() ) && ( i == s - 1 ) ) q2 += c2.back();
65 if ( q1 != q2 ) return false;
66 }
67 return true;
68}
69
70template <typename SB>
71bool testReducedFraction()
72{
73 typedef typename SB::Integer Integer;
74 typedef typename SB::Quotient Quotient;
75 typedef typename SB::Fraction Fraction;
76 unsigned int nbok = 0;
77 unsigned int nb = 0;
78 Integer p = rand() / 10000;
79 Integer q = rand() / 10000;
80 trace.beginBlock ( "Testing block: reduced fraction." );
81 IntegerComputer<Integer> ic;
82 Integer g = ic.gcd( p, q );
83 p /= g;
84 q /= g;
85 IntegerComputer<Quotient> ics;
86 Quotient sp = NumberTraits<Integer>::castToInt64_t( p );
87 Quotient sq = NumberTraits<Integer>::castToInt64_t( q );
88 std::vector<Quotient> cf1;
89 ics.getCFrac( cf1, sp, sq );
90 Fraction f1 = SB::fraction( p, q );
91 std::vector<Quotient> cf1_bis;
92 f1.getCFrac( cf1_bis );
93 bool ok = equalCFrac<Quotient>( cf1, cf1_bis );
94 trace.info() << " - p / q = " << p << " / " << q << std::endl;
95 trace.info() << " - f1 = ";
96 SB::display( trace.info(), f1 );
97 trace.info() << std::endl;
98 ++nb; nbok += ok ? 1 : 0;
99 trace.info() << "(" << nbok << "/" << nb << ") "
100 << " cfrac"
101 << std::endl;
102 unsigned int depth = (unsigned int)cf1.size();
103 for ( unsigned int k = 1; k < depth; ++k )
104 {
105 std::vector<Quotient> cf1_red;
106 Fraction fr = f1.reduced( k );
107 fr.getCFrac( cf1_red );
108 cf1.resize( depth - k );
109 ok = equalCFrac<Quotient>( cf1, cf1_red );
110 ++nb; nbok += ok ? 1 : 0;
111 trace.info() << "(" << nbok << "/" << nb << ") "
112 << "reduced(" << k << ")=";
113 SB::display( trace.info(), fr );
114 std::cerr << std::endl;
115 }
116
117 //trace.info() << "- nbFractions = " << SB::instance().nbFractions << std::endl;
118 trace.endBlock();
119 return nbok == nb;
120}
121
122template <typename SB>
123bool testInitFraction()
124{
125 typedef typename SB::Integer Integer;
126 typedef typename SB::Fraction Fraction;
127 unsigned int nbok = 0;
128 unsigned int nb = 0;
129 Integer p = rand() / 10000;
130 Integer q = rand() / 10000;
131 trace.beginBlock ( "Testing block: init fraction." );
132 IntegerComputer<Integer> ic;
133 Integer g = ic.gcd( p, q );
134 p /= g;
135 q /= g;
136 Fraction f1 = SB::fraction( p, q );
137 trace.info() << "p / q = " << p << " / " << q << std::endl;
138 trace.info() << "f1 = ";
139 SB::display( trace.info(), f1 );
140 trace.info() << std::endl;
141 nbok += ( ( p == f1.p() ) && ( q == f1.q() ) ) ? 1 : 0;
142 ++nb;
143 trace.info() << "(" << nbok << "/" << nb << ") "
144 << "( ( p == f1.p() ) && ( q == f1.q() ) )"
145 << std::endl;
146 trace.info() << "- nbFractions = " << SB::instance().nbFractions << std::endl;
147 trace.endBlock();
148
149 return nbok == nb;
150}
151
152template <typename SB>
153bool testPattern()
154{
155 typedef typename SB::Integer Integer;
156 typedef typename SB::Quotient Quotient;
157 typedef typename SB::Fraction Fraction;
158 typedef Pattern<Fraction> MyPattern;
159 typedef typename MyPattern::Vector2I Vector2I;
160 unsigned int nbok = 0;
161 unsigned int nb = 0;
162 Integer p = rand() / 10000;
163 Integer q = rand() / 10000;
164 MyPattern pattern( p*6, q*6 );
165 trace.info() << pattern << endl;
166
167 // ODD PATTERN
168 trace.beginBlock ( "Testing block: Smallest covering subpatterns of ODD pattern." );
169 MyPattern pat_odd( 5, 12 );
170 trace.info() << "ODD " << pat_odd << " " << pat_odd.rE() << endl;
171 MyPattern sp;
172 Quotient np;
173 Vector2I start;
174
175 // Left Subpatterns
176 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
177 0, 17 );
178 trace.info() << "sub(0,17) = " << sp << " " << sp.rE() << "^" << np << endl;
179 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
180 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
181 1, 17 );
182 trace.info() << "sub(1,17) = " << sp << " " << sp.rE() << "^" << np << endl;
183 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
184 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
185 7, 17 );
186 trace.info() << "sub(7,17) = " << sp << " " << sp.rE() << "^" << np << endl;
187 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) ? 1 : 0;
188 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
189 8, 17 );
190 trace.info() << "sub(8,17) = " << sp << " " << sp.rE() << "^" << np << endl;
191 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) ? 1 : 0;
192 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
193 13, 17 );
194 trace.info() << "sub(13,17) = " << sp << " " << sp.rE() << "^" << np << endl;
195 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) ? 1 : 0;
196 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
197 14, 17 );
198 trace.info() << "sub(14,17) = " << sp << " " << sp.rE() << "^" << np << endl;
199 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) ? 1 : 0;
200 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
201 15, 17 );
202 trace.info() << "sub(15,17) = " << sp << " " << sp.rE() << "^" << np << endl;
203 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) ? 1 : 0;
204
205 trace.info() << "(" << nbok << "/" << nb << ") covering left Subpatterns." << endl;
206
207 // Right Subpatterns
208 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
209 0, 16 );
210 trace.info() << "sub(0,16) = " << sp << " " << sp.rE() << "^" << np << endl;
211 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
212 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
213 0, 15 );
214 trace.info() << "sub(0,15) = " << sp << " " << sp.rE() << "^" << np << endl;
215 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
216 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
217 0, 14 );
218 trace.info() << "sub(0,14) = " << sp << " " << sp.rE() << "^" << np << endl;
219 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
220 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
221 0, 8 );
222 trace.info() << "sub(0,8) = " << sp << " " << sp.rE() << "^" << np << endl;
223 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
224 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
225 0, 7 );
226 trace.info() << "sub(0,7) = " << sp << " " << sp.rE() << "^" << np << endl;
227 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
228 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
229 0, 1 );
230 trace.info() << "sub(0,1) = " << sp << " " << sp.rE() << "^" << np << endl;
231 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
232
233 trace.info() << "(" << nbok << "/" << nb << ") covering right Subpatterns." << endl;
234
235 // Middle Subpatterns
236 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
237 1, 16 );
238 trace.info() << "sub(1,16) = " << sp << " " << sp.rE() << "^" << np << endl;
239 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
240 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
241 2, 14 );
242 trace.info() << "sub(2,14) = " << sp << " " << sp.rE() << "^" << np << endl;
243 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
244 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
245 7, 15 );
246 trace.info() << "sub(7,15) = " << sp << " " << sp.rE() << "^" << np << endl;
247 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) && np == 1 ? 1 : 0;
248 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
249 7, 14 );
250 trace.info() << "sub(7,14) = " << sp << " " << sp.rE() << "^" << np << endl;
251 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
252 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
253 3, 6 );
254 trace.info() << "sub(3,6) = " << sp << " " << sp.rE() << "^" << np << endl;
255 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
256 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
257 6, 8 );
258 trace.info() << "sub(6,8) = " << sp << " " << sp.rE() << "^" << np << endl;
259 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
260 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
261 8, 12 );
262 trace.info() << "sub(8,12) = " << sp << " " << sp.rE() << "^" << np << endl;
263 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
264 pat_odd.getSmallestCoveringSubpattern( sp, np, start,
265 15, 16 );
266 trace.info() << "sub(15,16) = " << sp << " " << sp.rE() << "^" << np << endl;
267 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) && np == 1 ? 1 : 0;
268
269 trace.info() << "(" << nbok << "/" << nb << ") covering middle Subpatterns." << endl;
270 trace.endBlock();
271
272 // EVEN PATTERN
273 trace.beginBlock ( "Testing block: Smallest covering subpatterns of EVEN pattern." );
274 MyPattern pat_even( 12, 17 );
275 trace.info() << "EVEN " << pat_even << " " << pat_even.rE() << endl;
276
277 // Left Subpatterns
278 pat_even.getSmallestCoveringSubpattern( sp, np, start,
279 0, 29 );
280 trace.info() << "sub(0,29) = " << sp << " " << sp.rE() << "^" << np << endl;
281 ++nb; nbok += sp.slope() == SB::fraction( 12, 17 ) ? 1 : 0;
282 pat_even.getSmallestCoveringSubpattern( sp, np, start,
283 0, 25 );
284 trace.info() << "sub(0,25) = " << sp << " " << sp.rE() << "^" << np << endl;
285 ++nb; nbok += sp.slope() == SB::fraction( 12, 17 ) ? 1 : 0;
286 pat_even.getSmallestCoveringSubpattern( sp, np, start,
287 0, 17 );
288 trace.info() << "sub(0,17) = " << sp << " " << sp.rE() << "^" << np << endl;
289 ++nb; nbok += sp.slope() == SB::fraction( 7, 10 ) ? 1 : 0;
290 pat_even.getSmallestCoveringSubpattern( sp, np, start,
291 0, 6 );
292 trace.info() << "sub(0,6) = " << sp << " " << sp.rE() << "^" << np << endl;
293 ++nb; nbok += sp.slope() == SB::fraction( 7, 10 ) ? 1 : 0;
294 pat_even.getSmallestCoveringSubpattern( sp, np, start,
295 0, 5 );
296 trace.info() << "sub(0,5) = " << sp << " " << sp.rE() << "^" << np << endl;
297 ++nb; nbok += sp.slope() == SB::fraction( 2, 3 ) ? 1 : 0;
298 trace.info() << "(" << nbok << "/" << nb << ") covering left Subpatterns." << endl;
299
300 // Right Subpatterns
301 pat_even.getSmallestCoveringSubpattern( sp, np, start,
302 4, 29 );
303 trace.info() << "sub(4,29) = " << sp << " " << sp.rE() << "^" << np << endl;
304 ++nb; nbok += sp.slope() == SB::fraction( 12, 17 ) ? 1 : 0;
305 pat_even.getSmallestCoveringSubpattern( sp, np, start,
306 5, 29 );
307 trace.info() << "sub(5,29) = " << sp << " " << sp.rE() << "^" << np << endl;
308 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 2 ? 1 : 0;
309 pat_even.getSmallestCoveringSubpattern( sp, np, start,
310 16, 29 );
311 trace.info() << "sub(16,29) = " << sp << " " << sp.rE() << "^" << np << endl;
312 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 2 ? 1 : 0;
313 pat_even.getSmallestCoveringSubpattern( sp, np, start,
314 17, 29 );
315 trace.info() << "sub(17,29) = " << sp << " " << sp.rE() << "^" << np << endl;
316 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
317 trace.info() << "(" << nbok << "/" << nb << ") covering right Subpatterns." << endl;
318
319 // Middle Subpatterns
320 pat_even.getSmallestCoveringSubpattern( sp, np, start,
321 1, 27 );
322 trace.info() << "sub(1,27) = " << sp << " " << sp.rE() << "^" << np << endl;
323 ++nb; nbok += sp.slope() == SB::fraction( 12, 17 ) ? 1 : 0;
324 pat_even.getSmallestCoveringSubpattern( sp, np, start,
325 5, 24 );
326 trace.info() << "sub(5,24) = " << sp << " " << sp.rE() << "^" << np << endl;
327 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 2 ? 1 : 0;
328 pat_even.getSmallestCoveringSubpattern( sp, np, start,
329 4, 17 );
330 trace.info() << "sub(4,17) = " << sp << " " << sp.rE() << "^" << np << endl;
331 ++nb; nbok += sp.slope() == SB::fraction( 7, 10 ) && np == 1 ? 1 : 0;
332 pat_even.getSmallestCoveringSubpattern( sp, np, start,
333 5, 17 );
334 trace.info() << "sub(5,17) = " << sp << " " << sp.rE() << "^" << np << endl;
335 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
336 pat_even.getSmallestCoveringSubpattern( sp, np, start,
337 7, 12 );
338 trace.info() << "sub(7,12) = " << sp << " " << sp.rE() << "^" << np << endl;
339 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
340 pat_even.getSmallestCoveringSubpattern( sp, np, start,
341 1, 4 );
342 trace.info() << "sub(1,4) = " << sp << " " << sp.rE() << "^" << np << endl;
343 ++nb; nbok += sp.slope() == SB::fraction( 2, 3 ) && np == 1 ? 1 : 0;
344 pat_even.getSmallestCoveringSubpattern( sp, np, start,
345 18, 25 );
346 trace.info() << "sub(18,20) = " << sp << " " << sp.rE() << "^" << np << endl;
347 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
348 trace.info() << "(" << nbok << "/" << nb << ") covering middle Subpatterns." << endl;
349 trace.endBlock();
350
351
352 // GREATEST INCLUDED SUBPATTERN
353 // ODD PATTERN
354 trace.beginBlock ( "Testing block: greatest included subpatterns of ODD pattern." );
355 trace.info() << "ODD " << pat_odd << " " << pat_odd.rE() << endl;
356
357 // Left Subpatterns
358 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
359 0, 17 );
360 trace.info() << "sub(0,17) = " << sp << " " << sp.rE() << "^" << np << endl;
361 ++nb; nbok += sp.slope() == SB::fraction( 5, 12 ) ? 1 : 0;
362 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
363 1, 17 );
364 trace.info() << "sub(1,17) = " << sp << " " << sp.rE() << "^" << np << endl;
365 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) ? 1 : 0;
366 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
367 7, 17 );
368 trace.info() << "sub(7,17) = " << sp << " " << sp.rE() << "^" << np << endl;
369 ++nb; nbok += sp.slope() == SB::fraction( 3, 7 ) ? 1 : 0;
370 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
371 8, 17 );
372 trace.info() << "sub(8,17) = " << sp << " " << sp.rE() << "^" << np << endl;
373 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) ? 1 : 0;
374 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
375 13, 17 );
376 trace.info() << "sub(13,17) = " << sp << " " << sp.rE() << "^" << np << endl;
377 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) ? 1 : 0;
378 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
379 14, 17 );
380 trace.info() << "sub(14,17) = " << sp << " " << sp.rE() << "^" << np << endl;
381 ++nb; nbok += sp.slope() == SB::fraction( 1, 2 ) ? 1 : 0;
382 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
383 15, 17 );
384 trace.info() << "sub(15,17) = " << sp << " " << sp.rE() << "^" << np << endl;
385 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
386
387 trace.info() << "(" << nbok << "/" << nb << ") covering left Subpatterns." << endl;
388
389 // Right Subpatterns
390 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
391 0, 15 );
392 trace.info() << "sub(0,15) = " << sp << " " << sp.rE() << "^" << np << endl;
393 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
394 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
395 0, 14 );
396 trace.info() << "sub(0,14) = " << sp << " " << sp.rE() << "^" << np << endl;
397 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 2 ? 1 : 0;
398 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
399 0, 13 );
400 trace.info() << "sub(0,13) = " << sp << " " << sp.rE() << "^" << np << endl;
401 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
402 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
403 0, 7 );
404 trace.info() << "sub(0,7) = " << sp << " " << sp.rE() << "^" << np << endl;
405 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
406 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
407 0, 6 );
408 trace.info() << "sub(0,6) = " << sp << " " << sp.rE() << "^" << np << endl;
409 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
410 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
411 0, 1 );
412 trace.info() << "sub(0,1) = " << sp << " " << sp.rE() << "^" << np << endl;
413 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
414
415 trace.info() << "(" << nbok << "/" << nb << ") covering right Subpatterns." << endl;
416
417 // Middle Subpatterns
418 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
419 1, 16 );
420 trace.info() << "sub(1,16) = " << sp << " " << sp.rE() << "^" << np << endl;
421 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) ? 1 : 0;
422 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
423 2, 14 );
424 trace.info() << "sub(2,14) = " << sp << " " << sp.rE() << "^" << np << endl;
425 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
426 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
427 7, 15 );
428 trace.info() << "sub(7,15) = " << sp << " " << sp.rE() << "^" << np << endl;
429 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
430 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
431 7, 14 );
432 trace.info() << "sub(7,14) = " << sp << " " << sp.rE() << "^" << np << endl;
433 ++nb; nbok += sp.slope() == SB::fraction( 2, 5 ) && np == 1 ? 1 : 0;
434 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
435 3, 6 );
436 trace.info() << "sub(3,6) = " << sp << " " << sp.rE() << "^" << np << endl;
437 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
438 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
439 6, 8 );
440 trace.info() << "sub(6,8) = " << sp << " " << sp.rE() << "^" << np << endl;
441 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
442 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
443 8, 12 );
444 trace.info() << "sub(8,12) = " << sp << " " << sp.rE() << "^" << np << endl;
445 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
446 pat_odd.getGreatestIncludedSubpattern( sp, np, start,
447 15, 16 );
448 trace.info() << "sub(15,16) = " << sp << " " << sp.rE() << "^" << np << endl;
449 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
450
451 trace.info() << "(" << nbok << "/" << nb << ") covering middle Subpatterns." << endl;
452 trace.endBlock();
453
454 // EVEN PATTERN
455 trace.beginBlock ( "Testing block: Greatest included subpatterns of EVEN pattern." );
456 trace.info() << "EVEN " << pat_even << " " << pat_even.rE() << endl;
457
458 // Left Subpatterns
459 pat_even.getGreatestIncludedSubpattern( sp, np, start,
460 0, 29 );
461 trace.info() << "sub(0,29) = " << sp << " " << sp.rE() << "^" << np << endl;
462 ++nb; nbok += sp.slope() == SB::fraction( 12, 17 ) ? 1 : 0;
463 pat_even.getGreatestIncludedSubpattern( sp, np, start,
464 0, 25 );
465 trace.info() << "sub(0,25) = " << sp << " " << sp.rE() << "^" << np << endl;
466 ++nb; nbok += sp.slope() == SB::fraction( 7, 10 ) ? 1 : 0;
467 pat_even.getGreatestIncludedSubpattern( sp, np, start,
468 0, 17 );
469 trace.info() << "sub(0,17) = " << sp << " " << sp.rE() << "^" << np << endl;
470 ++nb; nbok += sp.slope() == SB::fraction( 7, 10 ) ? 1 : 0;
471 pat_even.getGreatestIncludedSubpattern( sp, np, start,
472 0, 16 );
473 trace.info() << "sub(0,16) = " << sp << " " << sp.rE() << "^" << np << endl;
474 ++nb; nbok += sp.slope() == SB::fraction( 2, 3 ) ? 1 : 0;
475 pat_even.getGreatestIncludedSubpattern( sp, np, start,
476 0, 6 );
477 trace.info() << "sub(0,6) = " << sp << " " << sp.rE() << "^" << np << endl;
478 ++nb; nbok += sp.slope() == SB::fraction( 2, 3 ) ? 1 : 0;
479 pat_even.getGreatestIncludedSubpattern( sp, np, start,
480 0, 5 );
481 trace.info() << "sub(0,5) = " << sp << " " << sp.rE() << "^" << np << endl;
482 ++nb; nbok += sp.slope() == SB::fraction( 2, 3 ) ? 1 : 0;
483 pat_even.getGreatestIncludedSubpattern( sp, np, start,
484 0, 4 );
485 trace.info() << "sub(0,4) = " << sp << " " << sp.rE() << "^" << np << endl;
486 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
487 trace.info() << "(" << nbok << "/" << nb << ") covering left Subpatterns." << endl;
488
489 // Right Subpatterns
490 pat_even.getGreatestIncludedSubpattern( sp, np, start,
491 4, 29 );
492 trace.info() << "sub(4,29) = " << sp << " " << sp.rE() << "^" << np << endl;
493 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 2 ? 1 : 0;
494 pat_even.getGreatestIncludedSubpattern( sp, np, start,
495 5, 29 );
496 trace.info() << "sub(5,29) = " << sp << " " << sp.rE() << "^" << np << endl;
497 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 2 ? 1 : 0;
498 pat_even.getGreatestIncludedSubpattern( sp, np, start,
499 16, 29 );
500 trace.info() << "sub(16,29) = " << sp << " " << sp.rE() << "^" << np << endl;
501 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
502 pat_even.getGreatestIncludedSubpattern( sp, np, start,
503 17, 29 );
504 trace.info() << "sub(17,29) = " << sp << " " << sp.rE() << "^" << np << endl;
505 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
506 pat_even.getGreatestIncludedSubpattern( sp, np, start,
507 18, 29 );
508 trace.info() << "sub(18,29) = " << sp << " " << sp.rE() << "^" << np << endl;
509 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
510 trace.info() << "(" << nbok << "/" << nb << ") covering right Subpatterns." << endl;
511
512 // Middle Subpatterns
513 pat_even.getGreatestIncludedSubpattern( sp, np, start,
514 1, 27 );
515 trace.info() << "sub(1,27) = " << sp << " " << sp.rE() << "^" << np << endl;
516 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
517 pat_even.getGreatestIncludedSubpattern( sp, np, start,
518 5, 24 );
519 trace.info() << "sub(5,24) = " << sp << " " << sp.rE() << "^" << np << endl;
520 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
521 pat_even.getGreatestIncludedSubpattern( sp, np, start,
522 4, 17 );
523 trace.info() << "sub(4,17) = " << sp << " " << sp.rE() << "^" << np << endl;
524 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
525 pat_even.getGreatestIncludedSubpattern( sp, np, start,
526 5, 17 );
527 trace.info() << "sub(5,17) = " << sp << " " << sp.rE() << "^" << np << endl;
528 ++nb; nbok += sp.slope() == SB::fraction( 5, 7 ) && np == 1 ? 1 : 0;
529 pat_even.getGreatestIncludedSubpattern( sp, np, start,
530 7, 16 );
531 trace.info() << "sub(5,16) = " << sp << " " << sp.rE() << "^" << np << endl;
532 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
533 pat_even.getGreatestIncludedSubpattern( sp, np, start,
534 1, 4 );
535 trace.info() << "sub(1,4) = " << sp << " " << sp.rE() << "^" << np << endl;
536 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
537 pat_even.getGreatestIncludedSubpattern( sp, np, start,
538 18, 25 );
539 trace.info() << "sub(18,20) = " << sp << " " << sp.rE() << "^" << np << endl;
540 ++nb; nbok += sp.slope() == Fraction() ? 1 : 0;
541 trace.info() << "(" << nbok << "/" << nb << ") covering middle Subpatterns." << endl;
542 trace.endBlock();
543
544 trace.info() << "Odd pattern " << pat_odd << endl;
545 trace.info() << " U(0)=" << pat_odd.U( 0 )
546 << " L(0)=" << pat_odd.L( 0 )
547 << " U(1)=" << pat_odd.U( 1 )
548 << " L(1)=" << pat_odd.L( 1 ) << endl;
549
550 trace.info() << "Even pattern " << pat_even << endl;
551 trace.info() << " U(0)=" << pat_even.U( 0 )
552 << " L(0)=" << pat_even.L( 0 )
553 << " U(1)=" << pat_even.U( 1 )
554 << " L(1)=" << pat_even.L( 1 ) << endl;
555
556 return nbok == nb;
557}
558
559template <typename Fraction>
560bool testStandardDSLQ0()
561{
562 typedef StandardDSLQ0<Fraction> DSL;
563 typedef typename Fraction::Integer Integer;
564 typedef typename DSL::Point Point;
565 typedef typename DSL::Vector2I Vector2I;
566
567 BOOST_CONCEPT_ASSERT(( concepts::CPointPredicate< DSL > ));
568 unsigned int nbok = 0;
569 unsigned int nb = 0;
570
571 for ( Integer mu = -5; mu < 30; ++mu )
572 {
573 DSL D1( 5, 12, mu );
574 trace.info() << "DSL D1=" << D1 << endl;
575 Point U = D1.U();
576 Point L = D1.L();
577 trace.info() << "- U=" << U << " r(U)=" << D1.r( U )
578 << ", L=" << L << " r(L)=" << D1.r( L ) << endl;
579 ++nb; nbok += D1.r( U ) == D1.mu() ? 1 : 0;
580 ++nb; nbok += D1.r( L ) == D1.mup() ? 1 : 0;
581 }
582
583 DSL D2( 12, 17, 5 );
584 for ( Integer x = -5; x < 30; ++x )
585 {
586 Point P = D2.lowestY( x );
587 ++nb; nbok += D2( P ) && ( ! D2( P - Vector2I(0,1) ) ) ? 1 : 0;
588 trace.info() << "(" << nbok << "/" << nb << ") "
589 << "D2(P) && ! D2(P-y) P=" << P << " r(P)=" << D2.r( P )
590 << endl;
591 P = D2.uppermostY( x );
592 ++nb; nbok += D2( P ) && ( ! D2( P + Vector2I(0,1) ) ) ? 1 : 0;
593 trace.info() << "(" << nbok << "/" << nb << ") "
594 << "D2(P) && ! D2(P+y) P=" << P << " r(P)=" << D2.r( P )
595 << endl;
596 }
597 for ( Integer y = -5; y < 30; ++y )
598 {
599 Point P = D2.lowestX( y );
600 ++nb; nbok += D2( P ) && ( ! D2( P - Vector2I(1,0) ) ) ? 1 : 0;
601 trace.info() << "(" << nbok << "/" << nb << ") "
602 << "D2(P) && ! D2(P-x) P=" << P << " r(P)=" << D2.r( P )
603 << endl;
604 P = D2.uppermostX( y );
605 ++nb; nbok += D2( P ) && ( ! D2( P + Vector2I(1,0) ) ) ? 1 : 0;
606 trace.info() << "(" << nbok << "/" << nb << ") "
607 << "D2(P) && ! D2(P+x) P=" << P << " r(P)=" << D2.r( P )
608 << endl;
609 }
610
611 return nbok == nb;
612}
613
614template <typename DSL>
615bool checkSubStandardDSLQ0( const DSL & D,
616 const typename DSL::Point & A,
617 const typename DSL::Point & B )
618{
619 typedef typename DSL::Integer Integer;
620 typedef typename DSL::ConstIterator ConstIterator;
621 typedef ArithmeticalDSSComputer<ConstIterator, Integer, 4> ADSS;
622
623 DSL S = D.reversedSmartDSS( A, B );
624 ConstIterator it = D.begin( A );
625 ConstIterator it_end = D.end( B );
626 ADSS dss;
627 dss.init( it );
628 while ( ( dss.end() != it_end )
629 && ( dss.extendFront() ) ) {}
630 bool ok = S.a() == dss.a()
631 && S.b() == dss.b()
632 && S.mu() == dss.mu();
633 if ( ! ok )
634 {
635 trace.info() << "-------------------------------------------------------"
636 << std::endl;
637 trace.info() << "D = " << D // << " U1=" << U1 << " U2=" << U2
638 << " " << D.pattern().rE() << endl;
639 trace.info() << "S(" << A << "," << B << ") = "
640 << S << " " << S.pattern() << endl;
641 trace.info() << "ArithDSS = " << dss << std::endl;
642 }
643 // if ( ok )
644 // trace.info() << "========================== OK =========================";
645 // else
646 // trace.info() << "eeeeeeeeeeeeeeeeeeeeeeeeee KO eeeeeeeeeeeeeeeeeeeeeeeee";
647 // std::cerr << std::endl;
648 return ok;
649}
650
651template <typename Fraction>
652bool testSubStandardDSLQ0()
653{
654 typedef StandardDSLQ0<Fraction> DSL;
655 typedef typename Fraction::Integer Integer;
656 typedef typename DSL::Point Point;
657 IntegerComputer<Integer> ic;
658 unsigned int nbok = 0;
659 unsigned int nb = 0;
660
661 trace.beginBlock( "Check ReversedSmartDSS == ArithmeticDSS" );
662 for ( unsigned int i = 0; i < 100; ++i )
663 {
664 Integer a( rand() % 12000 + 1 );
665 Integer b( rand() % 12000 + 1 );
666 if ( ic.gcd( a, b ) == 1 )
667 {
668 trace.info() << "(" << i << ")"
669 << " Test DSL has slope " << a << "/" << b << std::endl;
670 for ( Integer mu = 0; mu < 5; ++mu )
671 {
672 DSL D( a, b, rand() % 10000 );
673 for ( Integer x = 0; x < 10; ++x )
674 {
675 Integer x1 = rand() % 1000;
676 Integer x2 = x1 + 1 + ( rand() % 1000 );
677 Point A = D.lowestY( x1 );
678 Point B = D.lowestY( x2 );
679 ++nb; nbok += checkSubStandardDSLQ0<DSL>( D, A, B ) ? 1 : 0;
680 if ( nb != nbok )
681 trace.info() << "(" << nbok << "/" << nb << ") correct reversedSmartDSS."
682 << std::endl;
683 if ( nbok != nb ) assert(false);
684 }
685 }
686 }
687 }
688 trace.info() << "(" << nbok << "/" << nb << ") correct reversedSmartDSS."
689 << std::endl;
690 trace.endBlock();
691 return nbok == nb;
692}
693
694
699bool testSternBrocot()
700{
701 unsigned int nbtests = 10;
702 unsigned int nbok = 0;
703 unsigned int nb = 0;
704 typedef DGtal::BigInteger Integer;
705 typedef SternBrocot<Integer, DGtal::int32_t> SB;
706 trace.beginBlock ( "Testing block: init fractions." );
707 for ( unsigned int i = 0; i < nbtests; ++i )
708 {
709 nbok += testInitFraction<SB>() ? 1 : 0;
710 nb++;
711 }
712 trace.info() << "(" << nbok << "/" << nb << ") init fractions." << endl;
713 trace.endBlock();
714 trace.beginBlock ( "Testing block: reduced fractions." );
715 for ( unsigned int i = 0; i < nbtests; ++i )
716 {
717 nbok += testReducedFraction<SB>() ? 1 : 0;
718 nb++;
719 }
720 trace.info() << "(" << nbok << "/" << nb << ") reduced fractions." << endl;
721 trace.endBlock();
722
723 trace.beginBlock ( "Testing block: number of fractions." );
724 trace.info() << "- nbFractions = " << SB::instance().nbFractions << endl;
725 trace.endBlock();
726
727 return nbok == nb;
728}
729
730template <typename SB>
731bool testContinuedFraction()
732{
733 typedef typename SB::Quotient Quotient;
734 typedef typename SB::Fraction Fraction;
735 typedef typename SB::Fraction::ConstIterator ConstIterator;
736
737 Fraction f;
738 std::vector<Quotient> quotients;
739 std::vector<Quotient> qcfrac;
740 std::back_insert_iterator< Fraction > itout =
741 std::back_inserter( f );
742 unsigned int size = ( rand() % 20 ) + 10;
743 for ( unsigned int i = 0; i < size; ++i )
744 {
745 Quotient q = ( i == 0 )
746 ? ( rand() % 5 )
747 : ( rand() % 5 ) + 1;
748 *itout++ = std::make_pair( q, (Quotient) i );
749 quotients.push_back( q );
750 }
751 for ( ConstIterator it = f.begin(), it_end = f.end();
752 it != it_end; ++it )
753 qcfrac.push_back( (*it).first );
754 // f.getCFrac( qcfrac );
755 bool ok = equalCFrac( quotients, qcfrac );
756
757 trace.info() << ( ok ? "(OK)" : "(ERR)" );
758 for ( unsigned int i = 0; i < quotients.size(); ++i )
759 std::cerr << " " << quotients[ i ];
760 trace.info() << std::endl;
761 trace.info() << " f=";
762 f.selfDisplay( std::cerr );
763 trace.info() << std::endl;
764 return ok;
765}
766
767template <typename SB>
768bool testContinuedFractions()
769{
770 unsigned int nbtests = 1000;
771 unsigned int nbok = 0;
772 unsigned int nb = 0;
773 trace.beginBlock ( "Testing block: continued fraction." );
774 for ( unsigned int i = 0; i < nbtests; ++i )
775 {
776 ++nb; nbok += testContinuedFraction<SB>() ? 1 : 0;
777 trace.info() << "(" << nbok << "/" << nb << ")"
778 << " continued fractions." << std::endl;
779 }
780 trace.endBlock();
781 return nbok == nb;
782}
783
787template <typename SB>
788bool
789testAncestors()
790{
791 typedef typename SB::Fraction Fraction;
792 typedef StandardDSLQ0<Fraction> DSL;
793 typedef typename DSL::Point Point;
794
795 // Instanciation d'un DSL
796 DSL D(1077,1495,6081);
797
798 // Definition du sous-segment [AB] et calcul des caractéristiques
799 Point A(3,-3);
800 Point B(4,-2);
801 ASSERT( D( A ) && "Point A belongs to D." );
802 ASSERT( D( B ) && "Point A belongs to D." );
803 DSL D1 = D.reversedSmartDSS(A,B); // may raise an assert.
804 std::cerr << D1 << std::endl;
805 return D1.slope() == Fraction( 1, 1 );
806}
807
808
809//-------------------------------------------
810template <typename SB>
811bool
812testSimplestFractionInBetween()
813{
814 typedef typename SB::Fraction Fraction;
815 Fraction f,g;
816 unsigned int nb = 0;
817 unsigned int nbok = 0;
818
819 trace.beginBlock("Testing block: simplest fraction between two fractions");
820 // When the two fractions are not ancestors of one other
821 f = Fraction(1,5); g = Fraction(3,4);
822 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(1,2) ? 1 : 0;
823 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
824
825 f = Fraction(4,7); g = Fraction(5,7);
826 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(2,3) ? 1 : 0;
827 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
828
829 f = Fraction(3,8); g = Fraction(7,4);
830 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(1,1) ? 1 : 0;
831 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
832
833 f = Fraction(11,7); g = Fraction(7,4);
834 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(5,3) ? 1 : 0;
835 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
836
837 f = Fraction(8,13); g = Fraction(7,11);
838 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(5,8) ? 1 : 0;
839 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
840
841 // When f is an ancestor of g or conversely
842 f = Fraction(2,5); g = Fraction(4,9);
843 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(3,7) ? 1 : 0;
844 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
845
846 f = Fraction(2,3); g = Fraction(8,11);
847 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(5,7) ? 1 : 0;
848 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
849
850 f = Fraction(1,2); g = Fraction(5,9);
851 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(6,11) ? 1 : 0;
852 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
853
854 f = Fraction(5,9); g = Fraction(2,3);
855 ++nb; nbok += f.simplestFractionInBetween(g) == Fraction(3,5) ? 1 : 0;
856 trace.info() << "(" << nbok << "/" << nb << ")" << std::endl;
857
858 trace.endBlock();
859 return nbok == nb;
860}
861
862
863
865// Standard services - public :
866
867int main( int , char** )
868{
869 typedef SternBrocot<DGtal::int64_t,DGtal::int32_t> SB;
870 typedef SB::Fraction Fraction;
871 typedef Fraction::ConstIterator ConstIterator;
872
873 BOOST_CONCEPT_ASSERT(( concepts::CPositiveIrreducibleFraction< Fraction > ));
874 BOOST_CONCEPT_ASSERT(( boost::InputIterator< ConstIterator > ));
875
876 trace.beginBlock ( "Testing class SternBrocot" );
877 bool res = testSternBrocot()
878 && testPattern<SB>()
879 && testSubStandardDSLQ0<Fraction>()
880 && testContinuedFractions<SB>()
881 && testAncestors<SB>()
882 && testSimplestFractionInBetween<SB>();
883 trace.emphase() << ( res ? "Passed." : "Error." ) << endl;
884 trace.endBlock();
885 return res ? 0 : 1;
886}
887// //
DGtal::ArithmeticalDSSComputer
Aim: This class is a wrapper around ArithmeticalDSS that is devoted to the dynamic recognition of dig...
Definition ArithmeticalDSSComputer.h:87
DGtal::ArithmeticalDSSComputer::begin
ConstIterator begin() const
DGtal::IntegerComputer
Aim: This class gathers several types and methods to make computation with integers.
Definition IntegerComputer.h:83
DGtal::IntegerComputer::getCFrac
Integer getCFrac(std::vector< Integer > &quotients, IntegerParamType a, IntegerParamType b) const
DGtal::IntegerComputer::gcd
Integer gcd(IntegerParamType a, IntegerParamType b) const
DGtal::Pattern
Aim: This class represents a pattern, i.e. the path between two consecutive upper leaning points on a...
Definition Pattern.h:79
DGtal::StandardDSLQ0
Aim: Represents a digital straight line with slope in the first quadrant (Q0: x >= 0,...
Definition StandardDSLQ0.h:80
DGtal::SternBrocot
Aim: The Stern-Brocot tree is the tree of irreducible fractions. This class allows to construct it pr...
Definition SternBrocot.h:78
DGtal::Trace::beginBlock
void beginBlock(const std::string &keyword="")
DGtal::Trace::emphase
std::ostream & emphase()
DGtal::Trace::info
std::ostream & info()
DGtal::Trace::endBlock
double endBlock()
ConstIterator
MyDigitalSurface::ConstIterator ConstIterator
Definition greedy-plane-segmentation-ex2.cpp:93
DGtal
DGtal is the top-level namespace which contains all DGtal functions and types.
Definition ClosedIntegerHalfPlane.h:49
DGtal::trace
Trace trace
Definition Common.h:153
DGtal::BigInteger
mpz_class BigInteger
Multi-precision integer with GMP implementation.
Definition BasicTypes.h:79
std
STL namespace.
DGtal::NumberTraits
Aim: The traits class for all models of Cinteger.
Definition NumberTraits.h:564
DGtal::concepts::CPointPredicate
Aim: Defines a predicate on a point.
Definition CPointPredicate.h:81
DGtal::concepts::CPositiveIrreducibleFraction
Aim: Defines positive irreducible fractions, i.e. fraction p/q, p and q non-negative integers,...
Definition CPositiveIrreducibleFraction.h:164
boost::InputIterator
Go to http://www.sgi.com/tech/stl/InputIterator.html.
Definition Boost.dox:36
main
int main()
Definition testBits.cpp:56
Point
MyPointD Point
Definition testClone2.cpp:383
testSubStandardDSLQ0
bool testSubStandardDSLQ0()
Definition testSternBrocot.cpp:652
testSternBrocot
bool testSternBrocot()
Definition testSternBrocot.cpp:699
testReducedFraction
bool testReducedFraction()
Definition testSternBrocot.cpp:71
checkSubStandardDSLQ0
bool checkSubStandardDSLQ0(const DSL &D, const typename DSL::Point &A, const typename DSL::Point &B)
Definition testSternBrocot.cpp:615
testPattern
bool testPattern()
Definition testSternBrocot.cpp:153
testStandardDSLQ0
bool testStandardDSLQ0()
Definition testSternBrocot.cpp:560
testAncestors
bool testAncestors()
Definition testSternBrocot.cpp:789
testSimplestFractionInBetween
bool testSimplestFractionInBetween()
Definition testSternBrocot.cpp:812
testInitFraction
bool testInitFraction()
Definition testSternBrocot.cpp:123
testContinuedFraction
bool testContinuedFraction()
Definition testSternBrocot.cpp:731
testContinuedFractions
bool testContinuedFractions()
Definition testSternBrocot.cpp:768
equalCFrac
bool equalCFrac(const std::vector< Quotient > &c1, const std::vector< Quotient > &c2)
Definition testSternBrocot.cpp:52