This file is indexed.

/usr/include/cln/real.h is in libcln-dev 1.3.4-1.

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
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
// Public real number operations.

#ifndef _CL_REAL_H
#define _CL_REAL_H

#include "cln/number.h"
#include "cln/real_class.h"
#include "cln/rational_class.h"
#include "cln/integer_class.h"
#include "cln/float.h"
#include "cln/floatformat.h"
#include "cln/random.h"

namespace cln {

CL_DEFINE_AS_CONVERSION(cl_R)


// zerop(x) testet, ob (= x 0).
extern bool zerop (const cl_R& x);

// minusp(x) testet, ob (< x 0).
extern bool minusp (const cl_R& x);

// plusp(x) testet, ob (> x 0).
extern bool plusp (const cl_R& x);


// R_to_SF(x) wandelt eine reelle Zahl x in ein Short-Float um.
// < ergebnis: (coerce x 'short-float)
extern const cl_SF cl_R_to_SF (const cl_R& x);

// R_to_FF(x) wandelt eine reelle Zahl x in ein Single-Float um.
// < ergebnis: (coerce x 'single-float)
extern const cl_FF cl_R_to_FF (const cl_R& x);

// R_to_DF(x) wandelt eine reelle Zahl x in ein Double-Float um.
// < ergebnis: (coerce x 'double-float)
extern const cl_DF cl_R_to_DF (const cl_R& x);

// R_to_LF(x,len) wandelt eine reelle Zahl x in ein Long-Float mit len Digits um.
// > uintC len: gewünschte Anzahl Digits, >=LF_minlen
// < ergebnis: (coerce x `(long-float ,len))
extern const cl_LF cl_R_to_LF (const cl_R& x, uintC len);

// cl_float(x,y) wandelt eine reelle Zahl x in das Float-Format des
// Floats y um und rundet dabei nötigenfalls.
// > x: eine reelle Zahl
// > y: ein Float
// < ergebnis: (float x y)
extern const cl_F cl_float (const cl_R& x, const cl_F& y);

// cl_float(x,f) wandelt eine reelle Zahl x in das Float-Format f um
// und rundet dabei nötigenfalls.
// > x: eine reelle Zahl
// > f: eine Float-Format-Spezifikation
// < ergebnis: (float x f)
extern const cl_F cl_float (const cl_R& x, float_format_t f);

// cl_float(x) wandelt eine reelle Zahl x in ein Float um
// und rundet dabei nötigenfalls.
// > x: eine reelle Zahl
// < ergebnis: (float x)
// Abhängig von default_float_format.
extern const cl_F cl_float (const cl_R& x);


// Liefert (- x), wo x eine reelle Zahl ist.
extern const cl_R operator- (const cl_R& x);

// Liefert (+ x y), wo x und y reelle Zahlen sind.
extern const cl_R operator+ (const cl_R& x, const cl_R& y);
// Spezialfall: x oder y Float -> Ergebnis Float
inline const cl_F operator+ (const cl_R& x, const cl_F& y)
	{ return The(cl_F)(x + The(cl_R)(y)); }
inline const cl_F operator+ (const cl_F& x, const cl_R& y)
	{ return The(cl_F)(The(cl_R)(x) + y); }
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R operator+ (const int x, const cl_R& y)
	{ return cl_I(x) + y; }
inline const cl_R operator+ (const unsigned int x, const cl_R& y)
	{ return cl_I(x) + y; }
inline const cl_R operator+ (const long x, const cl_R& y)
	{ return cl_I(x) + y; }
inline const cl_R operator+ (const unsigned long x, const cl_R& y)
	{ return cl_I(x) + y; }
#ifdef HAVE_LONGLONG
inline const cl_R operator+ (const long long x, const cl_R& y)
	{ return cl_I(x) + y; }
inline const cl_R operator+ (const unsigned long long x, const cl_R& y)
	{ return cl_I(x) + y; }
#endif
inline const cl_F operator+ (const float x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) + y); }
inline const cl_F operator+ (const double x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) + y); }
inline const cl_R operator+ (const cl_R& x, const int y)
	{ return x + cl_I(y); }
inline const cl_R operator+ (const cl_R& x, const unsigned int y)
	{ return x + cl_I(y); }
inline const cl_R operator+ (const cl_R& x, const long y)
	{ return x + cl_I(y); }
inline const cl_R operator+ (const cl_R& x, const unsigned long y)
	{ return x + cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_R operator+ (const cl_R& x, const long long y)
	{ return x + cl_I(y); }
inline const cl_R operator+ (const cl_R& x, const unsigned long long y)
	{ return x + cl_I(y); }
#endif
inline const cl_F operator+ (const cl_R& x, const float y)
	{ return The(cl_F)(x + cl_R(y)); }
inline const cl_F operator+ (const cl_R& x, const double y)
	{ return The(cl_F)(x + cl_R(y)); }

// Liefert (- x y), wo x und y reelle Zahlen sind.
extern const cl_R operator- (const cl_R& x, const cl_R& y);
// Spezialfall: x oder y Float -> Ergebnis Float
inline const cl_F operator- (const cl_R& x, const cl_F& y)
	{ return The(cl_F)(x - The(cl_R)(y)); }
inline const cl_F operator- (const cl_F& x, const cl_R& y)
	{ return The(cl_F)(The(cl_R)(x) - y); }
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R operator- (const int x, const cl_R& y)
	{ return cl_I(x) - y; }
inline const cl_R operator- (const unsigned int x, const cl_R& y)
	{ return cl_I(x) - y; }
inline const cl_R operator- (const long x, const cl_R& y)
	{ return cl_I(x) - y; }
inline const cl_R operator- (const unsigned long x, const cl_R& y)
	{ return cl_I(x) - y; }
#ifdef HAVE_LONGLONG
inline const cl_R operator- (const long long x, const cl_R& y)
	{ return cl_I(x) - y; }
inline const cl_R operator- (const unsigned long long x, const cl_R& y)
	{ return cl_I(x) - y; }
#endif
inline const cl_F operator- (const float x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) - y); }
inline const cl_F operator- (const double x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) - y); }
inline const cl_R operator- (const cl_R& x, const int y)
	{ return x - cl_I(y); }
inline const cl_R operator- (const cl_R& x, const unsigned int y)
	{ return x - cl_I(y); }
inline const cl_R operator- (const cl_R& x, const long y)
	{ return x - cl_I(y); }
inline const cl_R operator- (const cl_R& x, const unsigned long y)
	{ return x - cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_R operator- (const cl_R& x, const long long y)
	{ return x - cl_I(y); }
inline const cl_R operator- (const cl_R& x, const unsigned long long y)
	{ return x - cl_I(y); }
#endif
inline const cl_F operator- (const cl_R& x, const float y)
	{ return The(cl_F)(x - cl_R(y)); }
inline const cl_F operator- (const cl_R& x, const double y)
	{ return The(cl_F)(x - cl_R(y)); }

// Liefert (* x y), wo x und y reelle Zahlen sind.
extern const cl_R operator* (const cl_R& x, const cl_R& y);
// Dem C++-Compiler muß man auch das Folgende sagen (wg. `int * cl_F' u.ä.):
inline const cl_R operator* (const int x, const cl_R& y)
	{ return cl_I(x) * y; }
inline const cl_R operator* (const unsigned int x, const cl_R& y)
	{ return cl_I(x) * y; }
inline const cl_R operator* (const long x, const cl_R& y)
	{ return cl_I(x) * y; }
inline const cl_R operator* (const unsigned long x, const cl_R& y)
	{ return cl_I(x) * y; }
#ifdef HAVE_LONGLONG
inline const cl_R operator* (const long long x, const cl_R& y)
	{ return cl_I(x) * y; }
inline const cl_R operator* (const unsigned long long x, const cl_R& y)
	{ return cl_I(x) * y; }
#endif
inline const cl_R operator* (const float x, const cl_R& y)
	{ return cl_R(x) * y; }
inline const cl_R operator* (const double x, const cl_R& y)
	{ return cl_R(x) * y; }
inline const cl_R operator* (const cl_R& x, const int y)
	{ return x * cl_I(y); }
inline const cl_R operator* (const cl_R& x, const unsigned int y)
	{ return x * cl_I(y); }
inline const cl_R operator* (const cl_R& x, const long y)
	{ return x * cl_I(y); }
inline const cl_R operator* (const cl_R& x, const unsigned long y)
	{ return x * cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_R operator* (const cl_R& x, const long long y)
	{ return x * cl_I(y); }
inline const cl_R operator* (const cl_R& x, const unsigned long long y)
	{ return x * cl_I(y); }
#endif
inline const cl_R operator* (const cl_R& x, const float y)
	{ return x * cl_R(y); }
inline const cl_R operator* (const cl_R& x, const double y)
	{ return x * cl_R(y); }

// Liefert (* x x), wo x eine reelle Zahl ist.
extern const cl_R square (const cl_R& x);

// Liefert (/ x y), wo x und y reelle Zahlen sind.
extern const cl_R operator/ (const cl_R& x, const cl_R& y);
// Spezialfall: x Float -> Ergebnis Float
inline const cl_F operator/ (const cl_F& x, const cl_R& y)
	{ return The(cl_F)(The(cl_R)(x) / y); }
// Dem C++-Compiler muß man auch das Folgende sagen (wg. `int / cl_F' u.ä.):
inline const cl_R operator/ (const int x, const cl_R& y)
	{ return cl_I(x) / y; }
inline const cl_R operator/ (const unsigned int x, const cl_R& y)
	{ return cl_I(x) / y; }
inline const cl_R operator/ (const long x, const cl_R& y)
	{ return cl_I(x) / y; }
inline const cl_R operator/ (const unsigned long x, const cl_R& y)
	{ return cl_I(x) / y; }
#ifdef HAVE_LONGLONG
inline const cl_R operator/ (const long long x, const cl_R& y)
	{ return cl_I(x) / y; }
inline const cl_R operator/ (const unsigned long long x, const cl_R& y)
	{ return cl_I(x) / y; }
#endif
inline const cl_F operator/ (const float x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) / y); }
inline const cl_F operator/ (const double x, const cl_R& y)
	{ return The(cl_F)(cl_R(x) / y); }
inline const cl_R operator/ (const cl_R& x, const int y)
	{ return x / cl_I(y); }
inline const cl_R operator/ (const cl_R& x, const unsigned int y)
	{ return x / cl_I(y); }
inline const cl_R operator/ (const cl_R& x, const long y)
	{ return x / cl_I(y); }
inline const cl_R operator/ (const cl_R& x, const unsigned long y)
	{ return x / cl_I(y); }
#ifdef HAVE_LONGLONG
inline const cl_R operator/ (const cl_R& x, const long long y)
	{ return x / cl_I(y); }
inline const cl_R operator/ (const cl_R& x, const unsigned long long y)
	{ return x / cl_I(y); }
#endif
inline const cl_R operator/ (const cl_R& x, const float y)
	{ return x / cl_R(y); }
inline const cl_R operator/ (const cl_R& x, const double y)
	{ return x / cl_R(y); }

// Liefert (abs x), wo x eine reelle Zahl ist.
extern const cl_R abs (const cl_R& x);

// recip(x) liefert (/ x), wo x eine reelle Zahl ist.
extern const cl_R recip (const cl_R& x);

// (1+ x), wo x eine reelle Zahl ist.
extern const cl_R plus1 (const cl_R& x);

// (1- x), wo x eine reelle Zahl ist.
extern const cl_R minus1 (const cl_R& x);


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

// floor2(x) liefert (floor x), wo x eine reelle Zahl ist.
extern const cl_R_div_t floor2 (const cl_R& x);
extern const cl_I floor1 (const cl_R& x);

// ceiling2(x) liefert (ceiling x), wo x eine reelle Zahl ist.
extern const cl_R_div_t ceiling2 (const cl_R& x);
extern const cl_I ceiling1 (const cl_R& x);

// truncate2(x) liefert (truncate x), wo x eine reelle Zahl ist.
extern const cl_R_div_t truncate2 (const cl_R& x);
extern const cl_I truncate1 (const cl_R& x);

// round2(x) liefert (round x), wo x eine reelle Zahl ist.
extern const cl_R_div_t round2 (const cl_R& x);
extern const cl_I round1 (const cl_R& x);

// floor2(x,y) liefert (floor x y), wo x und y reelle Zahlen sind.
extern const cl_R_div_t floor2 (const cl_R& x, const cl_R& y);
extern const cl_I floor1 (const cl_R& x, const cl_R& y);

// ceiling2(x,y) liefert (ceiling x y), wo x und y reelle Zahlen sind.
extern const cl_R_div_t ceiling2 (const cl_R& x, const cl_R& y);
extern const cl_I ceiling1 (const cl_R& x, const cl_R& y);

// truncate2(x,y) liefert (truncate x y), wo x und y reelle Zahlen sind.
extern const cl_R_div_t truncate2 (const cl_R& x, const cl_R& y);
extern const cl_I truncate1 (const cl_R& x, const cl_R& y);

// round2(x,y) liefert (round x y), wo x und y reelle Zahlen sind.
extern const cl_R_div_t round2 (const cl_R& x, const cl_R& y);
extern const cl_I round1 (const cl_R& x, const cl_R& y);


// Return type for frounding operators.
// x / y  --> (q,r) with x = y*q+r.
struct cl_R_fdiv_t {
	cl_F quotient;
	cl_R remainder;
// Constructor.
	cl_R_fdiv_t () {}
	cl_R_fdiv_t (const cl_F& q, const cl_R& r) : quotient(q), remainder(r) {}
	cl_R_fdiv_t (const struct cl_F_fdiv_t &);
};

// ffloor2(x) liefert (ffloor x), wo x eine reelle Zahl ist.
extern const cl_R_fdiv_t ffloor2 (const cl_R& x);
extern const cl_F ffloor (const cl_R& x);

// fceiling2(x) liefert (fceiling x), wo x eine reelle Zahl ist.
extern const cl_R_fdiv_t fceiling2 (const cl_R& x);
extern const cl_F fceiling (const cl_R& x);

// ftruncate2(x) liefert (ftruncate x), wo x eine reelle Zahl ist.
extern const cl_R_fdiv_t ftruncate2 (const cl_R& x);
extern const cl_F ftruncate (const cl_R& x);

// fround2(x) liefert (fround x), wo x eine reelle Zahl ist.
extern const cl_R_fdiv_t fround2 (const cl_R& x);
extern const cl_F fround (const cl_R& x);

// ffloor2(x,y) liefert (ffloor x y), wo x und y reelle Zahlen sind.
extern const cl_R_fdiv_t ffloor2 (const cl_R& x, const cl_R& y);
extern const cl_F ffloor (const cl_R& x, const cl_R& y);

// fceiling2(x,y) liefert (fceiling x y), wo x und y reelle Zahlen sind.
extern const cl_R_fdiv_t fceiling2 (const cl_R& x, const cl_R& y);
extern const cl_F fceiling (const cl_R& x, const cl_R& y);

// ftruncate2(x,y) liefert (ftruncate x y), wo x und y reelle Zahlen sind.
extern const cl_R_fdiv_t ftruncate2 (const cl_R& x, const cl_R& y);
extern const cl_F ftruncate (const cl_R& x, const cl_R& y);

// fround2(x,y) liefert (fround x y), wo x und y reelle Zahlen sind.
extern const cl_R_fdiv_t fround2 (const cl_R& x, const cl_R& y);
extern const cl_F fround (const cl_R& x, const cl_R& y);


// mod(x,y) = (mod x y), wo x und y reelle Zahlen sind.
extern const cl_R mod (const cl_R& x, const cl_R& y);

// rem(x,y) = (rem x y), wo x und y reelle Zahlen sind.
extern const cl_R rem (const cl_R& x, const cl_R& y);


// rational(x) liefert (rational x), wo x eine reelle Zahl ist.
extern const cl_RA rational (const cl_R& x);
// Spezialfall:
inline const cl_RA rational (const cl_RA& x) { return x; }


// equal(x,y) vergleicht zwei reelle Zahlen x und y auf Gleichheit.
extern bool equal (const cl_R& x, const cl_R& y);
// equal_hashcode(x) liefert einen equal-invarianten Hashcode für x.
extern uint32 equal_hashcode (const cl_R& x);

// compare(x,y) vergleicht zwei reelle Zahlen x und y.
// Ergebnis: 0 falls x=y, +1 falls x>y, -1 falls x<y.
extern cl_signean compare (const cl_R& x, const cl_R& y);

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

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

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

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

// sqrt(x) = (sqrt x) zieht die Wurzel aus einer reellen Zahl x >=0.
extern const cl_R sqrt (const cl_R& x);
// sqrt(x) = (sqrt x) zieht die Wurzel aus einer rationalen Zahl x >=0.
extern const cl_R sqrt (const cl_RA& x);

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

// rationalize(x) liefert (rationalize x), wo x eine reelle Zahl ist.
extern const cl_RA rationalize (const cl_R& x);


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

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


// Transcendental functions


// atan(x,y) liefert zu zwei reellen Zahlen x, y den Winkel von (x,y)
// in Polarkoordinaten. Ergebnis rational nur, wenn x>0 und y=0.
extern const cl_R atan (const cl_R& x, const cl_R& y);
// Spezialfall: y Float -> Ergebnis Float
inline const cl_F atan (const cl_R& x, const cl_F& y)
	{ return The(cl_F)(atan(x,The(cl_R)(y))); }
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R atan (const cl_R& x, const int y)
	{ return atan(x,cl_I(y)); }
inline const cl_R atan (const cl_R& x, const unsigned int y)
	{ return atan(x,cl_I(y)); }
inline const cl_R atan (const cl_R& x, const long y)
	{ return atan(x,cl_I(y)); }
inline const cl_R atan (const cl_R& x, const unsigned long y)
	{ return atan(x,cl_I(y)); }

// atan(x) liefert den Arctan einer reellen Zahl x.
// Ergebnis rational nur, wenn x=0.
extern const cl_R atan (const cl_R& x);
// Spezialfall: x Float -> Ergebnis Float
inline const cl_F atan (const cl_F& x) { return The(cl_F)(atan(The(cl_R)(x))); }
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R atan (const int x) { return atan(cl_I(x)); }
inline const cl_R atan (const unsigned int x) { return atan(cl_I(x)); }
inline const cl_R atan (const long x) { return atan(cl_I(x)); }
inline const cl_R atan (const unsigned long x) { return atan(cl_I(x)); }

// sin(x) liefert den Sinus (sin x) einer reellen Zahl x.
extern const cl_R sin (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R sin (const int x) { return sin(cl_I(x)); }
inline const cl_R sin (const unsigned int x) { return sin(cl_I(x)); }
inline const cl_R sin (const long x) { return sin(cl_I(x)); }
inline const cl_R sin (const unsigned long x) { return sin(cl_I(x)); }

// cos(x) liefert den Cosinus (cos x) einer reellen Zahl x.
extern const cl_R cos (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R cos (const int x) { return cos(cl_I(x)); }
inline const cl_R cos (const unsigned int x) { return cos(cl_I(x)); }
inline const cl_R cos (const long x) { return cos(cl_I(x)); }
inline const cl_R cos (const unsigned long x) { return cos(cl_I(x)); }

// cos_sin(x) liefert ((cos x),(sin x)), beide Werte.
extern const cos_sin_t cos_sin (const cl_R& x);

// tan(x) liefert den Tangens (tan x) einer reellen Zahl x.
extern const cl_R tan (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R tan (const int x) { return tan(cl_I(x)); }
inline const cl_R tan (const unsigned int x) { return tan(cl_I(x)); }
inline const cl_R tan (const long x) { return tan(cl_I(x)); }
inline const cl_R tan (const unsigned long x) { return tan(cl_I(x)); }

// ln(x) liefert zu einer reellen Zahl x>0 die Zahl ln(x).
extern const cl_R ln (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R ln (const int x) { return ln(cl_I(x)); }
inline const cl_R ln (const unsigned int x) { return ln(cl_I(x)); }
inline const cl_R ln (const long x) { return ln(cl_I(x)); }
inline const cl_R ln (const unsigned long x) { return ln(cl_I(x)); }

// log(a,b) liefert zu reellen Zahlen a>0, b>0 die Zahl
// log(a,b)=ln(a)/ln(b).
// Ergebnis rational nur, wenn a=1 oder a und b rational.
extern const cl_R log (const cl_R& a, const cl_R& b);

// exp(x) liefert zu einer reellen Zahl x die Zahl exp(x).
extern const cl_R exp (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R exp (const int x) { return exp(cl_I(x)); }
inline const cl_R exp (const unsigned int x) { return exp(cl_I(x)); }
inline const cl_R exp (const long x) { return exp(cl_I(x)); }
inline const cl_R exp (const unsigned long x) { return exp(cl_I(x)); }

// sinh(x) liefert zu einer reellen Zahl x die Zahl sinh(x).
extern const cl_R sinh (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R sinh (const int x) { return sinh(cl_I(x)); }
inline const cl_R sinh (const unsigned int x) { return sinh(cl_I(x)); }
inline const cl_R sinh (const long x) { return sinh(cl_I(x)); }
inline const cl_R sinh (const unsigned long x) { return sinh(cl_I(x)); }

// cosh(x) liefert zu einer reellen Zahl x die Zahl cosh(x).
extern const cl_R cosh (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R cosh (const int x) { return cosh(cl_I(x)); }
inline const cl_R cosh (const unsigned int x) { return cosh(cl_I(x)); }
inline const cl_R cosh (const long x) { return cosh(cl_I(x)); }
inline const cl_R cosh (const unsigned long x) { return cosh(cl_I(x)); }

// cosh_sinh(x) liefert ((cosh x),(sinh x)), beide Werte.
extern const cosh_sinh_t cosh_sinh (const cl_R& x);

// tanh(x) liefert zu einer reellen Zahl x die Zahl tanh(x).
extern const cl_R tanh (const cl_R& x);
// Dem C++-Compiler muß man nun auch das Folgende sagen:
inline const cl_R tanh (const int x) { return tanh(cl_I(x)); }
inline const cl_R tanh (const unsigned int x) { return tanh(cl_I(x)); }
inline const cl_R tanh (const long x) { return tanh(cl_I(x)); }
inline const cl_R tanh (const unsigned long x) { return tanh(cl_I(x)); }


// random_R(randomstate,n) liefert zu einer reellen Zahl n>0 eine Zufallszahl
// x mit 0 <= x < n.
extern const cl_R random_R (random_state& randomstate, const cl_R& n);

inline const cl_R random_R (const cl_R& n)
	{ return random_R(default_random_state,n); }


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


// Complex operations, trivial for reals

inline const cl_R realpart (const cl_R& x)
{
	return x;
}
inline const cl_R imagpart (const cl_R& x)
{
	(void)x; // unused x
	return 0;
}
inline const cl_R conjugate (const cl_R& x)
{
	return x;
}


// Debugging support.
#ifdef CL_DEBUG
extern int cl_R_debug_module;
CL_FORCE_LINK(cl_R_debug_dummy, cl_R_debug_module)
#endif

}  // namespace cln

#endif /* _CL_REAL_H */