This file is indexed.

/usr/include/cln/rational.h is in libcln-dev 1.3.2-1.1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
// Public rational number operations.

#ifndef _CL_RATIONAL_H
#define _CL_RATIONAL_H

#include "cln/number.h"
#include "cln/rational_class.h"
#include "cln/integer_class.h"
#include "cln/exception.h"

namespace cln {

CL_DEFINE_AS_CONVERSION(cl_RA)


// numerator(r) liefert den Zähler der rationalen Zahl r.
extern const cl_I numerator (const cl_RA& r);

// denominator(r) liefert den Nenner (> 0) der rationalen Zahl r.
extern const cl_I denominator (const cl_RA& r);


// Liefert (- r), wo r eine rationale Zahl ist.
extern const cl_RA operator- (const cl_RA& r);

// (+ r s), wo r und s rationale Zahlen sind.
extern const cl_RA operator+ (const cl_RA& r, const cl_RA& s);
// Dem C++-Compiler muß man auch das Folgende sagen:
inline const cl_RA operator+ (const int x, const cl_RA& y)
	{ return cl_I(x) + y; }
inline const cl_RA operator+ (const unsigned int x, const cl_RA& y)
	{ return cl_I(x) + y; }
inline const cl_RA operator+ (const long x, const cl_RA& y)
	{ return cl_I(x) + y; }
inline const cl_RA operator+ (const unsigned long x, const cl_RA& y)
	{ return cl_I(x) + y; }
#ifdef HAVE_LONGLONG
inline const cl_RA operator+ (const long long x, const cl_RA& y)
	{ return cl_I(x) + y; }
inline const cl_RA operator+ (const unsigned long long x, const cl_RA& y)
	{ return cl_I(x) + y; }
#endif
inline const cl_RA operator+ (const cl_RA& x, const int y)
	{ return x + cl_I(y); }
inline const cl_RA operator+ (const cl_RA& x, const unsigned int y)
	{ return x + cl_I(y); }
inline const cl_RA operator+ (const cl_RA& x, const long y)
	{ return x + cl_I(y); }
inline const cl_RA operator+ (const cl_RA& x, const unsigned long y)
	{ return x + cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_RA operator+ (const cl_RA& x, const long long y)
	{ return x + cl_I(y); }
inline const cl_RA operator+ (const cl_RA& x, const unsigned long long y)
	{ return x + cl_I(y); }
#endif

// (- r s), wo r und s rationale Zahlen sind.
extern const cl_RA operator- (const cl_RA& r, const cl_RA& s);
// Dem C++-Compiler muß man auch das Folgende sagen:
inline const cl_RA operator- (const int x, const cl_RA& y)
	{ return cl_I(x) - y; }
inline const cl_RA operator- (const unsigned int x, const cl_RA& y)
	{ return cl_I(x) - y; }
inline const cl_RA operator- (const long x, const cl_RA& y)
	{ return cl_I(x) - y; }
inline const cl_RA operator- (const unsigned long x, const cl_RA& y)
	{ return cl_I(x) - y; }
#ifdef HAVE_LONGLONG
inline const cl_RA operator- (const long long x, const cl_RA& y)
	{ return cl_I(x) - y; }
inline const cl_RA operator- (const unsigned long long x, const cl_RA& y)
	{ return cl_I(x) - y; }
#endif
inline const cl_RA operator- (const cl_RA& x, const int y)
	{ return x - cl_I(y); }
inline const cl_RA operator- (const cl_RA& x, const unsigned int y)
	{ return x - cl_I(y); }
inline const cl_RA operator- (const cl_RA& x, const long y)
	{ return x - cl_I(y); }
inline const cl_RA operator- (const cl_RA& x, const unsigned long y)
	{ return x - cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_RA operator- (const cl_RA& x, const long long y)
	{ return x - cl_I(y); }
inline const cl_RA operator- (const cl_RA& x, const unsigned long long y)
	{ return x - cl_I(y); }
#endif

// (1+ r), wo r eine rationale Zahl ist.
extern const cl_RA plus1 (const cl_RA& r);

// (1- r), wo r eine rationale Zahl ist.
extern const cl_RA minus1 (const cl_RA& r);

// (abs r), wo r eine rationale Zahl ist.
extern const cl_RA abs (const cl_RA& r);

// equal(r,s) vergleicht zwei rationale Zahlen r und s auf Gleichheit.
extern bool equal (const cl_RA& r, const cl_RA& s);
// equal_hashcode(r) liefert einen equal-invarianten Hashcode für r.
extern uint32 equal_hashcode (const cl_RA& r);

// compare(r,s) vergleicht zwei rationale Zahlen r und s.
// Ergebnis: 0 falls r=s, +1 falls r>s, -1 falls r<s.
extern cl_signean compare (const cl_RA& r, const cl_RA& s);

inline bool operator== (const cl_RA& x, const cl_RA& y)
	{ return equal(x,y); }
inline bool operator!= (const cl_RA& x, const cl_RA& y)
	{ return !equal(x,y); }
inline bool operator<= (const cl_RA& x, const cl_RA& y)
	{ return compare(x,y)<=0; }
inline bool operator< (const cl_RA& x, const cl_RA& y)
	{ return compare(x,y)<0; }
inline bool operator>= (const cl_RA& x, const cl_RA& y)
	{ return compare(x,y)>=0; }
inline bool operator> (const cl_RA& x, const cl_RA& y)
	{ return compare(x,y)>0; }

// minusp(x) == (< x 0)
extern bool minusp (const cl_RA& x);

// zerop(x) stellt fest, ob eine rationale Zahl = 0 ist.
extern bool zerop (const cl_RA& x);

// plusp(x) == (> x 0)
extern bool plusp (const cl_RA& x);

// Kehrwert (/ r), wo r eine rationale Zahl ist.
extern const cl_RA recip (const cl_RA& r);

// Liefert (* r s), wo r und s rationale Zahlen sind.
extern const cl_RA operator* (const cl_RA& r, const cl_RA& s);
// Dem C++-Compiler muß man auch das Folgende sagen:
inline const cl_RA operator* (const int x, const cl_RA& y)
	{ return cl_I(x) * y; }
inline const cl_RA operator* (const unsigned int x, const cl_RA& y)
	{ return cl_I(x) * y; }
inline const cl_RA operator* (const long x, const cl_RA& y)
	{ return cl_I(x) * y; }
inline const cl_RA operator* (const unsigned long x, const cl_RA& y)
	{ return cl_I(x) * y; }
#ifdef HAVE_LONGLONG
inline const cl_RA operator* (const long long x, const cl_RA& y)
	{ return cl_I(x) * y; }
inline const cl_RA operator* (const unsigned long long x, const cl_RA& y)
	{ return cl_I(x) * y; }
#endif
inline const cl_RA operator* (const cl_RA& x, const int y)
	{ return x * cl_I(y); }
inline const cl_RA operator* (const cl_RA& x, const unsigned int y)
	{ return x * cl_I(y); }
inline const cl_RA operator* (const cl_RA& x, const long y)
	{ return x * cl_I(y); }
inline const cl_RA operator* (const cl_RA& x, const unsigned long y)
	{ return x * cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_RA operator* (const cl_RA& x, const long long y)
	{ return x * cl_I(y); }
inline const cl_RA operator* (const cl_RA& x, const unsigned long long y)
	{ return x * cl_I(y); }
#endif

// Quadrat (* r r), wo r eine rationale Zahl ist.
extern const cl_RA square (const cl_RA& r);

// Liefert (/ r s), wo r und s rationale Zahlen sind.
extern const cl_RA operator/ (const cl_RA& r, const cl_RA& s);
// Dem C++-Compiler muß man auch das Folgende sagen:
inline const cl_RA operator/ (const int x, const cl_RA& y)
	{ return cl_I(x) / y; }
inline const cl_RA operator/ (const unsigned int x, const cl_RA& y)
	{ return cl_I(x) / y; }
inline const cl_RA operator/ (const long x, const cl_RA& y)
	{ return cl_I(x) / y; }
inline const cl_RA operator/ (const unsigned long x, const cl_RA& y)
	{ return cl_I(x) / y; }
#ifdef HAVE_LONGLONG
inline const cl_RA operator/ (const long long x, const cl_RA& y)
	{ return cl_I(x) / y; }
inline const cl_RA operator/ (const unsigned long long x, const cl_RA& y)
	{ return cl_I(x) / y; }
#endif
inline const cl_RA operator/ (const cl_RA& x, const int y)
	{ return x / cl_I(y); }
inline const cl_RA operator/ (const cl_RA& x, const unsigned int y)
	{ return x / cl_I(y); }
inline const cl_RA operator/ (const cl_RA& x, const long y)
	{ return x / cl_I(y); }
inline const cl_RA operator/ (const cl_RA& x, const unsigned long y)
	{ return x / cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_RA operator/ (const cl_RA& x, const long long y)
	{ return x / cl_I(y); }
inline const cl_RA operator/ (const cl_RA& x, const unsigned long long y)
	{ return x / cl_I(y); }
#endif

// Return type for rounding operators.
// x / y  --> (q,r) with x = y*q+r.
struct cl_RA_div_t {
	cl_I quotient;
	cl_RA remainder;
// Constructor.
	cl_RA_div_t () {}
	cl_RA_div_t (const cl_I& q, const cl_RA& r) : quotient(q), remainder(r) {}
};

// Liefert ganzzahligen und gebrochenen Anteil einer rationalen Zahl.
// (q,r) := (floor x)
// floor2(x)
// > x: rationale Zahl
// < q,r: Quotient q, ein Integer, Rest r, eine rationale Zahl
  extern const cl_RA_div_t floor2 (const cl_RA& x);
  extern const cl_I floor1 (const cl_RA& x);

// Liefert ganzzahligen und gebrochenen Anteil einer rationalen Zahl.
// (q,r) := (ceiling x)
// ceiling2(x)
// > x: rationale Zahl
// < q,r: Quotient q, ein Integer, Rest r, eine rationale Zahl
  extern const cl_RA_div_t ceiling2 (const cl_RA& x);
  extern const cl_I ceiling1 (const cl_RA& x);

// Liefert ganzzahligen und gebrochenen Anteil einer rationalen Zahl.
// (q,r) := (truncate x)
// truncate2(x)
// > x: rationale Zahl
// < q,r: Quotient q, ein Integer, Rest r, eine rationale Zahl
  extern const cl_RA_div_t truncate2 (const cl_RA& x);
  extern const cl_I truncate1 (const cl_RA& x);

// Liefert ganzzahligen und gebrochenen Anteil einer rationalen Zahl.
// (q,r) := (round x)
// round2(x)
// > x: rationale Zahl
// < q,r: Quotient q, ein Integer, Rest r, eine rationale Zahl
  extern const cl_RA_div_t round2 (const cl_RA& x);
  extern const cl_I round1 (const cl_RA& x);

// floor2(x,y) liefert (floor x y).
extern const cl_RA_div_t floor2 (const cl_RA& x, const cl_RA& y);
extern const cl_I floor1 (const cl_RA& x, const cl_RA& y);

// ceiling2(x,y) liefert (ceiling x y).
extern const cl_RA_div_t ceiling2 (const cl_RA& x, const cl_RA& y);
extern const cl_I ceiling1 (const cl_RA& x, const cl_RA& y);

// truncate2(x,y) liefert (truncate x y).
extern const cl_RA_div_t truncate2 (const cl_RA& x, const cl_RA& y);
extern const cl_I truncate1 (const cl_RA& x, const cl_RA& y);

// round2(x,y) liefert (round x y).
extern const cl_RA_div_t round2 (const cl_RA& x, const cl_RA& y);
extern const cl_I round1 (const cl_RA& x, const cl_RA& y);

// max(x,y) liefert (max x y), wo x und y rationale Zahlen sind.
extern const cl_RA max (const cl_RA& x, const cl_RA& y);

// min(x,y) liefert (min x y), wo x und y rationale Zahlen sind.
extern const cl_RA min (const cl_RA& x, const cl_RA& y);

// signum(x) liefert (signum x), wo x eine rationale Zahl ist.
extern const cl_RA signum (const cl_RA& x);

// (expt x y), wo x eine rationale Zahl und y ein Integer >0 ist.
extern const cl_RA expt_pos (const cl_RA& x, uintL y);
extern const cl_RA expt_pos (const cl_RA& x, const cl_I& y);

// (expt x y), wo x eine rationale Zahl und y ein Integer ist.
extern const cl_RA expt (const cl_RA& x, sintL y);
extern const cl_RA expt (const cl_RA& x, const cl_I& y);

// Stellt fest, ob eine rationale Zahl >=0 das Quadrat einer rationalen Zahl
// ist.
// sqrtp(x,&w)
// > x: eine rationale Zahl >=0
// < w: rationale Zahl (sqrt x) falls x Quadratzahl
// < ergebnis: true      ..................., false sonst
  extern bool sqrtp (const cl_RA& x, cl_RA* w);

// Stellt fest, ob eine rationale Zahl >=0 die n-te Potenz einer rationalen Zahl
// ist.
// rootp(x,n,&w)
// > x: eine rationale Zahl >=0
// > n: ein Integer >0
// < w: exakte n-te Wurzel (expt x (/ n)) falls x eine n-te Potenz
// < ergebnis: true                       ........................, false sonst
  extern bool rootp (const cl_RA& x, uintL n, cl_RA* w);
  extern bool rootp (const cl_RA& x, const cl_I& n, cl_RA* w);

// Liefert zu Integers a>0, b>1 den Logarithmus log(a,b),
// falls er eine rationale Zahl ist.
// logp(a,b,&l)
// > a: ein Integer >0
// > b: ein Integer >1
// < l: log(a,b)       falls er eine exakte rationale Zahl ist
// < ergebnis: true    ......................................., false sonst
  extern bool logp (const cl_I& a, const cl_I& b, cl_RA* l);

// Liefert zu rationalen Zahlen a>0, b>0 den Logarithmus log(a,b),
// falls er eine rationale Zahl ist.
// logp(a,b,&l)
// > a: eine rationale Zahl >0
// > b: eine rationale Zahl >0, /=1
// < l: log(a,b)       falls er eine exakte rationale Zahl ist
// < ergebnis: true    ......................................., false sonst
  extern bool logp (const cl_RA& a, const cl_RA& b, cl_RA* l);

// Konversion zu einem C "float".
extern float float_approx (const cl_RA& x);

// Konversion zu einem C "double".
extern double double_approx (const cl_RA& x);


// This could be optimized to use in-place operations.
inline cl_RA& operator+= (cl_RA& x, const cl_RA& y) { return x = x + y; }
inline cl_RA& operator+= (cl_RA& x, const int y) { return x = x + y; }
inline cl_RA& operator+= (cl_RA& x, const unsigned int y) { return x = x + y; }
inline cl_RA& operator+= (cl_RA& x, const long y) { return x = x + y; }
inline cl_RA& operator+= (cl_RA& x, const unsigned long y) { return x = x + y; }
#ifdef HAVE_LONGLONG
inline cl_RA& operator+= (cl_RA& x, const long long y) { return x = x + y; }
inline cl_RA& operator+= (cl_RA& x, const unsigned long long y) { return x = x + y; }
#endif
inline cl_RA& operator++ /* prefix */ (cl_RA& x) { return x = plus1(x); }
inline void operator++ /* postfix */ (cl_RA& x, int dummy) { (void)dummy; x = plus1(x); }
inline cl_RA& operator-= (cl_RA& x, const cl_RA& y) { return x = x - y; }
inline cl_RA& operator-= (cl_RA& x, const int y) { return x = x - y; }
inline cl_RA& operator-= (cl_RA& x, const unsigned int y) { return x = x - y; }
inline cl_RA& operator-= (cl_RA& x, const long y) { return x = x - y; }
inline cl_RA& operator-= (cl_RA& x, const unsigned long y) { return x = x - y; }
#ifdef HAVE_LONGLONG
inline cl_RA& operator-= (cl_RA& x, const long long y) { return x = x - y; }
inline cl_RA& operator-= (cl_RA& x, const unsigned long long y) { return x = x - y; }
#endif
inline cl_RA& operator-- /* prefix */ (cl_RA& x) { return x = minus1(x); }
inline void operator-- /* postfix */ (cl_RA& x, int dummy) { (void)dummy; x = minus1(x); }
inline cl_RA& operator*= (cl_RA& x, const cl_RA& y) { return x = x * y; }
inline cl_RA& operator/= (cl_RA& x, const cl_RA& y) { return x = x / y; }


// Runtime typing support.
extern cl_class cl_class_ratio;


// Debugging support.
#ifdef CL_DEBUG
extern int cl_RA_debug_module;
CL_FORCE_LINK(cl_RA_debug_dummy, cl_RA_debug_module)
#endif

}  // namespace cln

#endif /* _CL_RATIONAL_H */