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
|
// -*- C++ -*-
// Fix.h : variable length fixed point data type
//
#ifndef _Fix_h
#ifdef __GNUG__
#pragma interface
#endif
#define _Fix_h 1
#include <stream.h>
#include <std.h>
#include <stddef.h>
#include <Integer.h>
#include <builtin.h>
class Fix
{
struct Rep // internal Fix representation
{
_G_uint16_t len; // length in bits
_G_uint16_t siz; // allocated storage
_G_int16_t ref; // reference count
_G_uint16_t s[1]; // start of ushort array represention
};
public:
typedef void (*PEH)(Rep*);
private:
Rep* rep;
Fix(Rep*);
Fix(int, const Rep*);
void unique();
static const _G_uint16_t min_length = 1;
static const _G_uint16_t max_length = 65535;
static const double min_value = -1.0;
static const double max_value = 1.0;
static _G_uint16_t default_length;
static int default_print_width;
static Rep Rep_0;
static Rep Rep_m1;
static Rep Rep_quotient_bump;
// internal class functions
static void mask(Rep*);
static int compare(const Rep*, const Rep* = &Rep_0);
static Rep* new_Fix(_G_uint16_t);
static Rep* new_Fix(_G_uint16_t, const Rep*);
static Rep* new_Fix(_G_uint16_t, double);
static Rep* copy(const Rep*, Rep*);
static Rep* negate(const Rep*, Rep* = NULL);
static Rep* add(const Rep*, const Rep*, Rep* = NULL);
static Rep* subtract(const Rep*, const Rep*, Rep* = NULL);
static Rep* multiply(const Rep*, const Rep*, Rep* = NULL);
static Rep* multiply(const Rep*, int, Rep* = NULL);
static Rep* divide(const Rep*, const Rep*, Rep* = NULL,
Rep* = NULL);
static Rep* shift(const Rep*, int, Rep* = NULL);
static one_arg_error_handler_t error_handler;
static one_arg_error_handler_t range_error_handler;
static PEH overflow_handler;
public:
Fix();
Fix(const Fix&);
Fix(double);
Fix(int);
Fix(int, const Fix&);
Fix(int, double);
~Fix();
Fix operator = (const Fix&);
Fix operator = (double);
friend int operator == (const Fix&, const Fix&);
friend int operator != (const Fix&, const Fix&);
friend int operator < (const Fix&, const Fix&);
friend int operator <= (const Fix&, const Fix&);
friend int operator > (const Fix&, const Fix&);
friend int operator >= (const Fix&, const Fix&);
Fix& operator + ();
Fix operator - ();
friend Fix operator + (const Fix&, const Fix&);
friend Fix operator - (const Fix&, const Fix&);
friend Fix operator * (const Fix&, const Fix&);
friend Fix operator / (const Fix&, const Fix&);
friend Fix operator * (const Fix&, int);
friend Fix operator * (int, const Fix&);
friend Fix operator % (const Fix&, int);
friend Fix operator << (const Fix&, int);
friend Fix operator >> (const Fix&, int);
#if defined (__GNUG__) && ! defined (__STRICT_ANSI__)
friend Fix operator <? (const Fix&, const Fix&); // min
friend Fix operator >? (const Fix&, const Fix&); // max
#endif
Fix operator += (const Fix&);
Fix operator -= (const Fix&);
Fix operator *= (const Fix&);
Fix operator /= (const Fix&);
Fix operator *= (int);
Fix operator %= (int);
Fix operator <<=(int);
Fix operator >>=(int);
friend char* Ftoa(const Fix&, int width = default_print_width);
void printon(ostream&, int width = default_print_width) const;
friend Fix atoF(const char*, int len = default_length);
friend istream& operator >> (istream&, Fix&);
friend ostream& operator << (ostream&, const Fix&);
// built-in functions
friend Fix abs(Fix); // absolute value
friend int sgn(const Fix&); // -1, 0, +1
friend Integer mantissa(const Fix&); // integer representation
friend double value(const Fix&); // double value
friend int length(const Fix&); // field length
friend void show(const Fix&); // show contents
// error handlers
static void error(const char* msg); // error handler
static void range_error(const char* msg); // range error handler
static one_arg_error_handler_t set_error_handler(one_arg_error_handler_t f);
static one_arg_error_handler_t
set_range_error_handler(one_arg_error_handler_t f);
static void default_error_handler (const char *);
static void default_range_error_handler (const char *);
// non-operator versions for user
friend void negate(const Fix& x, Fix& r);
friend void add(const Fix& x, const Fix& y, Fix& r);
friend void subtract(const Fix& x, const Fix& y, Fix& r);
friend void multiply(const Fix& x, const Fix& y, Fix& r);
friend void divide(const Fix& x, const Fix& y, Fix& q, Fix& r);
friend void shift(const Fix& x, int y, Fix& r);
// overflow handlers
static void overflow_saturate(Fix::Rep*);
static void overflow_wrap(Fix::Rep*);
static void overflow_warning_saturate(Fix::Rep*);
static void overflow_warning(Fix::Rep*);
static void overflow_error(Fix::Rep*);
static PEH set_overflow_handler(PEH);
static int set_default_length(int);
};
// function definitions
inline void
Fix::unique()
{
if ( rep->ref > 1 )
{
rep->ref--;
rep = new_Fix(rep->len,rep);
}
}
inline void
Fix::mask (Fix::Rep* x)
{
int n = x->len & 0x0f;
if ( n )
x->s[x->siz - 1] &= 0xffff0000 >> n;
}
inline Fix::Rep*
Fix::copy(const Fix::Rep* from, Fix::Rep* to)
{
_G_uint16_t *ts = to->s;
const _G_uint16_t *fs = from->s;
int ilim = to->siz < from->siz ? to->siz : from->siz;
for ( int i=0; i < ilim; i++ )
*ts++ = *fs++;
for ( ; i < to->siz; i++ )
*ts++ = 0;
mask(to);
return to;
}
inline
Fix::Fix(Rep* f)
{
rep = f;
}
inline
Fix::Fix()
{
rep = new_Fix(default_length);
}
inline
Fix::Fix(int len)
{
if ( len < min_length || len > max_length )
error("illegal length in declaration");
rep = new_Fix((_G_uint16_t) len);
}
inline
Fix::Fix(double d)
{
rep = new_Fix(default_length,d);
}
inline
Fix::Fix(const Fix& y)
{
rep = y.rep; rep->ref++;
}
inline
Fix::Fix(int len, const Fix& y)
{
if ( len < Fix::min_length || len > Fix::max_length )
error("illegal length in declaration");
rep = new_Fix((_G_uint16_t) len,y.rep);
}
inline
Fix::Fix(int len, const Rep* fr)
{
if ( len < Fix::min_length || len > Fix::max_length )
error("illegal length in declaration");
rep = new_Fix((_G_uint16_t) len,fr);
}
inline
Fix::Fix(int len, double d)
{
if ( len < Fix::min_length || len > Fix::max_length )
error("illegal length in declaration");
rep = new_Fix((_G_uint16_t) len,d);
}
inline
Fix::~Fix()
{
if ( --rep->ref <= 0 ) delete rep;
}
inline Fix
Fix::operator = (const Fix& y)
{
if ( rep->len == y.rep->len ) {
++y.rep->ref;
if ( --rep->ref <= 0 ) delete rep;
rep = y.rep;
}
else {
unique();
copy(y.rep,rep);
}
return *this;
}
inline Fix
Fix::operator = (double d)
{
int oldlen = rep->len;
if ( --rep->ref <= 0 ) delete rep;
rep = new_Fix(oldlen,d);
return *this;
}
inline int
operator == (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) == 0;
}
inline int
operator != (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) != 0;
}
inline int
operator < (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) < 0;
}
inline int
operator <= (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) <= 0;
}
inline int
operator > (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) > 0;
}
inline int
operator >= (const Fix& x, const Fix& y)
{
return Fix::compare(x.rep, y.rep) >= 0;
}
inline Fix&
Fix::operator + ()
{
return *this;
}
inline Fix
Fix::operator - ()
{
Rep* r = negate(rep); return r;
}
inline Fix
operator + (const Fix& x, const Fix& y)
{
Fix::Rep* r = Fix::add(x.rep, y.rep); return r;
}
inline Fix
operator - (const Fix& x, const Fix& y)
{
Fix::Rep* r = Fix::subtract(x.rep, y.rep); return r;
}
inline Fix
operator * (const Fix& x, const Fix& y)
{
Fix::Rep* r = Fix::multiply(x.rep, y.rep); return r;
}
inline Fix
operator * (const Fix& x, int y)
{
Fix::Rep* r = Fix::multiply(x.rep, y); return r;
}
inline Fix
operator * (int y, const Fix& x)
{
Fix::Rep* r = Fix::multiply(x.rep, y); return r;
}
inline Fix
operator / (const Fix& x, const Fix& y)
{
Fix::Rep* r = Fix::divide(x.rep, y.rep); return r;
}
inline Fix
Fix::operator += (const Fix& y)
{
unique(); Fix::add(rep, y.rep, rep); return *this;
}
inline Fix
Fix::operator -= (const Fix& y)
{
unique(); Fix::subtract(rep, y.rep, rep); return *this;
}
inline Fix
Fix::operator *= (const Fix& y)
{
unique(); Fix::multiply(rep, y.rep, rep); return *this;
}
inline Fix
Fix::operator *= (int y)
{
unique(); Fix::multiply(rep, y, rep); return *this;
}
inline Fix
Fix::operator /= (const Fix& y)
{
unique(); Fix::divide(rep, y.rep, rep); return *this;
}
inline Fix
operator % (const Fix& x, int y)
{
Fix r((int) x.rep->len + y, x); return r;
}
inline Fix
operator << (const Fix& x, int y)
{
Fix::Rep* rep = Fix::shift(x.rep, y); return rep;
}
inline Fix
operator >> (const Fix& x, int y)
{
Fix::Rep* rep = Fix::shift(x.rep, -y); return rep;
}
inline Fix
Fix::operator <<= (int y)
{
unique(); Fix::shift(rep, y, rep); return *this;
}
inline Fix
Fix::operator >>= (int y)
{
unique(); Fix::shift(rep, -y, rep); return *this;
}
#if defined (__GNUG__) && ! defined (__STRICT_ANSI__)
inline Fix
operator <? (const Fix& x, const Fix& y)
{
if ( Fix::compare(x.rep, y.rep) <= 0 ) return x; else return y;
}
inline Fix
operator >? (const Fix& x, const Fix& y)
{
if ( Fix::compare(x.rep, y.rep) >= 0 ) return x; else return y;
}
#endif
inline Fix
abs(Fix x)
{
Fix::Rep* r = (Fix::compare(x.rep) >= 0 ? Fix::new_Fix(x.rep->len,x.rep) :
Fix::negate(x.rep));
return r;
}
inline int
sgn(const Fix& x)
{
int a = Fix::compare(x.rep);
return a == 0 ? 0 : (a > 0 ? 1 : -1);
}
inline int
length(const Fix& x)
{
return x.rep->len;
}
inline ostream&
operator << (ostream& s, const Fix& y)
{
if (s.opfx())
y.printon(s);
return s;
}
inline void
negate (const Fix& x, Fix& r)
{
Fix::negate(x.rep, r.rep);
}
inline void
add (const Fix& x, const Fix& y, Fix& r)
{
Fix::add(x.rep, y.rep, r.rep);
}
inline void
subtract (const Fix& x, const Fix& y, Fix& r)
{
Fix::subtract(x.rep, y.rep, r.rep);
}
inline void
multiply (const Fix& x, const Fix& y, Fix& r)
{
Fix::multiply(x.rep, y.rep, r.rep);
}
inline void
divide (const Fix& x, const Fix& y, Fix& q, Fix& r)
{
Fix::divide(x.rep, y.rep, q.rep, r.rep);
}
inline void
shift (const Fix& x, int y, Fix& r)
{
Fix::shift(x.rep, y, r.rep);
}
#endif
|
