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gnumpfl.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: computations with GMP floating-point numbers
6 *
7 * ngf == number gnu floats
8 */
9 
10 #include "misc/auxiliary.h"
11 
12 #include "reporter/reporter.h"
13 
14 #include "coeffs/coeffs.h"
15 #include "coeffs/numbers.h"
16 #include "coeffs/mpr_complex.h"
17 
18 #include "coeffs/longrat.h"
19 #include "coeffs/shortfl.h"
20 #include "coeffs/gnumpfl.h"
21 #include "coeffs/gnumpc.h"
22 #include "coeffs/modulop.h"
23 
24 const char * ngfRead (const char *s, number *a, const coeffs r);
25 
26 union nf
27 {
29  number _n;
30  nf(SI_FLOAT f) {_f = f;}
31  nf(number n) {_n = n;}
32  SI_FLOAT F() const {return _f;}
33  number N() const {return _n;}
34 };
35 
36 /*2
37 * n := i
38 */
39 static number ngfInit (long i, const coeffs r)
40 {
41  assume( getCoeffType(r) == n_long_R );
42 
43  gmp_float* n= new gmp_float( (double)i );
44  return (number)n;
45 }
46 
47 /*2
48 * convert number to int
49 */
50 static long ngfInt(number &i, const coeffs r)
51 {
52  assume( getCoeffType(r) == n_long_R );
53 
54  double d=(double)*(gmp_float*)i;
55  if (d<0.0)
56  return (long)(d-0.5);
57  else
58  return (long)(d+0.5);
59 }
60 
61 static BOOLEAN ngfIsZero (number a, const coeffs r)
62 {
63  assume( getCoeffType(r) == n_long_R );
64 
65  return ( ((gmp_float*)a)->isZero() );
66 }
67 
68 static int ngfSize(number n, const coeffs r)
69 {
70  long i = ngfInt(n, r);
71  /* basically return the largest integer in n;
72  only if this happens to be zero although n != 0,
73  return 1;
74  (this code ensures that zero has the size zero) */
75  if ((i == 0) && (ngfIsZero(n,r) == FALSE)) i = 1;
76  return ABS(i);
77 }
78 
79 /*2
80 * delete a
81 */
82 static void ngfDelete (number * a, const coeffs r)
83 {
84  assume( getCoeffType(r) == n_long_R );
85 
86  if ( *a != NULL )
87  {
88  delete *(gmp_float**)a;
89  *a=NULL;
90  }
91 }
92 
93 /*2
94 * copy a to b
95 */
96 static number ngfCopy(number a, const coeffs r)
97 {
98  assume( getCoeffType(r) == n_long_R );
99 
100  gmp_float* b= new gmp_float( *(gmp_float*)a );
101  return (number)b;
102 }
103 
104 #if 0
105 static number ngfCopyMap(number a, const coeffs r1, const coeffs r2)
106 {
107  assume( getCoeffType(r1) == n_long_R );
108  assume( getCoeffType(r2) == n_long_R );
109 
110  gmp_float* b= NULL;
111  if ( a != NULL )
112  {
113  b= new gmp_float( *(gmp_float*)a );
114  }
115  return (number)b;
116 }
117 #endif
118 
119 /*2
120 * za:= - za
121 */
122 static number ngfNeg (number a, const coeffs r)
123 {
124  assume( getCoeffType(r) == n_long_R );
125 
126  *(gmp_float*)a= -(*(gmp_float*)a);
127  return (number)a;
128 }
129 
130 /*
131 * 1/a
132 */
133 static number ngfInvers(number a, const coeffs r)
134 {
135  assume( getCoeffType(r) == n_long_R );
136 
137  gmp_float* f= NULL;
138  if (((gmp_float*)a)->isZero() )
139  {
140  WerrorS(nDivBy0);
141  }
142  else
143  {
144  f= new gmp_float( gmp_float(1) / (*(gmp_float*)a) );
145  }
146  return (number)f;
147 }
148 
149 /*2
150 * u:= a + b
151 */
152 static number ngfAdd (number a, number b, const coeffs R)
153 {
154  assume( getCoeffType(R) == n_long_R );
155 
156  gmp_float* r= new gmp_float( (*(gmp_float*)a) + (*(gmp_float*)b) );
157  return (number)r;
158 }
159 
160 /*2
161 * u:= a - b
162 */
163 static number ngfSub (number a, number b, const coeffs R)
164 {
165  assume( getCoeffType(R) == n_long_R );
166 
167  gmp_float* r= new gmp_float( (*(gmp_float*)a) - (*(gmp_float*)b) );
168  return (number)r;
169 }
170 
171 /*2
172 * u := a * b
173 */
174 static number ngfMult (number a, number b, const coeffs R)
175 {
176  assume( getCoeffType(R) == n_long_R );
177 
178  gmp_float* r= new gmp_float( (*(gmp_float*)a) * (*(gmp_float*)b) );
179  return (number)r;
180 }
181 
182 /*2
183 * u := a / b
184 */
185 static number ngfDiv (number a, number b, const coeffs r)
186 {
187  assume( getCoeffType(r) == n_long_R );
188 
189  if ( ((gmp_float*)b)->isZero() )
190  {
191  // a/0 = error
192  WerrorS(nDivBy0);
193  return NULL;
194  }
195  gmp_float* f= new gmp_float( (*(gmp_float*)a) / (*(gmp_float*)b) );
196  return (number)f;
197 }
198 
199 /*2
200 * u:= x ^ exp
201 */
202 static number ngfPower (number x, int exp, const coeffs r)
203 {
204  assume( getCoeffType(r) == n_long_R );
205 
206  if ( exp == 0 )
207  {
208  gmp_float* n = new gmp_float(1);
209  return (number)n;
210  }
211  else if ( ngfIsZero(x, r) ) // 0^e, e>0
212  {
213  return ngfInit(0, r);
214  }
215  else if ( exp == 1 )
216  {
217  return ngfCopy(x,r);
218  }
219  return (number) ( new gmp_float( (*(gmp_float*)x)^exp ) );
220 }
221 
222 /* kept for compatibility reasons, to be deleted */
223 static void ngfPower ( number x, int exp, number * u, const coeffs r )
224 {
225  *u = ngfPower(x, exp, r);
226 }
227 
228 /*2
229 * za > 0 ?
230 */
231 static BOOLEAN ngfGreaterZero (number a, const coeffs r)
232 {
233  assume( getCoeffType(r) == n_long_R );
234 
235  return (((gmp_float*)a)->sign() > 0);
236 }
237 
238 /*2
239 * a > b ?
240 */
241 static BOOLEAN ngfGreater (number a, number b, const coeffs r)
242 {
243  assume( getCoeffType(r) == n_long_R );
244 
245  return ( (*(gmp_float*)a) > (*(gmp_float*)b) );
246 }
247 
248 /*2
249 * a = b ?
250 */
251 static BOOLEAN ngfEqual (number a, number b, const coeffs r)
252 {
253  assume( getCoeffType(r) == n_long_R );
254 
255  return ( (*(gmp_float*)a) == (*(gmp_float*)b) );
256 }
257 
258 /*2
259 * a == 1 ?
260 */
261 static BOOLEAN ngfIsOne (number a, const coeffs r)
262 {
263  assume( getCoeffType(r) == n_long_R );
264 
265  return ((gmp_float*)a)->isOne();
266 }
267 
268 /*2
269 * a == -1 ?
270 */
271 static BOOLEAN ngfIsMOne (number a, const coeffs r)
272 {
273  assume( getCoeffType(r) == n_long_R );
274 
275  return ((gmp_float*)a)->isMOne();
276 }
277 
278 static char * ngfEatFloatNExp(char * s )
279 {
280  char *start= s;
281 
282  // eat floats (mantissa) like:
283  // 0.394394993, 102.203003008, .300303032, pssibly starting with -
284  if (*s == '-') s++;
285  while ((*s >= '0' && *s <= '9')||(*s == '.')) s++;
286 
287  // eat the exponent, starts with 'e' followed by '+', '-'
288  // and digits, like:
289  // e-202, e+393, accept also E7
290  if ( (s != start) && ((*s == 'e')||(*s=='E')))
291  {
292  if (*s=='E') *s='e';
293  s++; // skip 'e'/'E'
294  if ((*s == '+') || (*s == '-')) s++;
295  while ((*s >= '0' && *s <= '9')) s++;
296  }
297 
298  return s;
299 }
300 
301 /*2
302 * extracts the number a from s, returns the rest
303 *
304 * This is also called to print components of complex coefficients.
305 * Handle with care!
306 */
307 const char * ngfRead (const char * start, number * a, const coeffs r)
308 {
310 
311  char *s= (char *)start;
312 
313  //Print("%s\n",s);
314 
315  s= ngfEatFloatNExp( s );
316 
317  if (*s=='\0') // 0
318  {
319  if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float();
320  (*(gmp_float**)a)->setFromStr(start);
321  }
322  else if (s==start) // 1
323  {
324  if ( *(gmp_float**)a != NULL ) delete (*(gmp_float**)a);
325  (*(gmp_float**)a)= new gmp_float(1);
326  }
327  else
328  {
329  gmp_float divisor(1.0);
330  char *start2=s;
331  if ( *s == '/' )
332  {
333  s++;
334  s= ngfEatFloatNExp( (char *)s );
335  if (s!= start2+1)
336  {
337  char tmp_c=*s;
338  *s='\0';
339  divisor.setFromStr(start2+1);
340  *s=tmp_c;
341  }
342  else
343  {
344  Werror("wrong long real format: %s",start2);
345  }
346  }
347  char c=*start2;
348  *start2='\0';
349  if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float();
350  (*(gmp_float**)a)->setFromStr(start);
351  *start2=c;
352  if (divisor.isZero())
353  {
354  WerrorS(nDivBy0);
355  }
356  else
357  (**(gmp_float**)a) /= divisor;
358  }
359 
360  return s;
361 }
362 
363 /*2
364 * write a floating point number
365 */
366 static void ngfWrite (number a, const coeffs r)
367 {
368  assume( getCoeffType(r) == n_long_R );
369 
370  char *out;
371  if ( a != NULL )
372  {
373  out= floatToStr(*(gmp_float*)a, r->float_len);
374  StringAppendS(out);
375  //omFreeSize((void *)out, (strlen(out)+1)* sizeof(char) );
376  omFree( (void *)out );
377  }
378  else
379  {
380  StringAppendS("0");
381  }
382 }
383 
384 static BOOLEAN ngfCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter)
385 {
386  if (n==n_long_R)
387  {
388  LongComplexInfo* p = (LongComplexInfo *)(parameter);
389  if ((p!=NULL)
390  && (p->float_len == r->float_len)
391  && (p->float_len2 == r->float_len2))
392  return TRUE;
393  }
394  return FALSE;
395 }
396 
397 static void ngfSetChar(const coeffs r)
398 {
399  setGMPFloatDigits(r->float_len, r->float_len2);
400 }
401 
402 static char* ngfCoeffString(const coeffs r)
403 {
404  char *s=(char*)omAlloc(30);
405  snprintf(s,30,"Float(%d,%d)",r->float_len,r->float_len2);
406  return s;
407 }
408 
409 static char* ngfCoeffName(const coeffs r)
410 {
411  STATIC_VAR char ngfCoeffName_buf[30];
412  snprintf(ngfCoeffName_buf,30,"Float(%d,%d)",r->float_len,r->float_len2);
413  return ngfCoeffName_buf;
414 }
415 
416 static number ngfMapQ(number from, const coeffs src, const coeffs dst)
417 {
418  assume( getCoeffType(dst) == n_long_R );
419  assume( src->rep == n_rep_gap_rat );
420 
422  return (number)res;
423 }
424 static number ngfMapZ(number from, const coeffs aRing, const coeffs r)
425 {
426  assume( getCoeffType(r) == n_long_R );
427  assume( aRing->rep == n_rep_gap_gmp);
428 
429  if ( from != NULL )
430  {
431  if (SR_HDL(from) & SR_INT)
432  {
433  gmp_float f_i= gmp_float(SR_TO_INT(from));
434  gmp_float *res=new gmp_float(f_i);
435  return (number)res;
436  }
437  gmp_float f_i=(mpz_ptr)from;
438  gmp_float *res=new gmp_float(f_i);
439  return (number)res;
440  }
441  else
442  return NULL;
443 }
444 
445 static number ngfMapR(number from, const coeffs src, const coeffs dst)
446 {
447  assume( getCoeffType(dst) == n_long_R );
448  assume( getCoeffType(src) == n_R );
449 
450  gmp_float *res=new gmp_float((double)nf(from).F());
451  return (number)res;
452 }
453 
454 static number ngfMapP(number from, const coeffs src, const coeffs dst)
455 {
456  assume( getCoeffType(dst) == n_long_R );
457  assume( getCoeffType(src) == n_Zp );
458 
459  return ngfInit(npInt(from,src), dst); // FIXME? TODO? // extern int npInt (number &n, const coeffs r);
460 }
461 
462 static number ngfMapC(number from, const coeffs src, const coeffs dst)
463 {
464  assume( getCoeffType(dst) == n_long_R );
465  assume( getCoeffType(src) == n_long_C );
466 
467  gmp_float *res=new gmp_float(((gmp_complex*)from)->real());
468  return (number)res;
469 }
470 
471 static nMapFunc ngfSetMap(const coeffs src, const coeffs dst)
472 {
473  assume( getCoeffType(dst) == n_long_R );
474 
475  if (src->rep==n_rep_gap_rat) /*Q, Z*/
476  {
477  return ngfMapQ;
478  }
479  if (src->rep==n_rep_gap_gmp) /*Q, Z*/
480  {
481  return ngfMapZ;
482  }
483  if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src))
484  {
485  return ndCopyMap; //ngfCopyMap;
486  }
487  if ((src->rep==n_rep_float) && nCoeff_is_R(src))
488  {
489  return ngfMapR;
490  }
491  if ((src->rep==n_rep_gmp_complex) && nCoeff_is_long_C(src))
492  {
493  return ngfMapC;
494  }
495  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src))
496  {
497  return ngfMapP;
498  }
499  return NULL;
500 }
501 
502 static void ngfCoeffWrite (const coeffs r, BOOLEAN /*details*/)
503 {
504  Print("Float(%d,%d)", r->float_len,r->float_len2); /* long R */
505 }
506 
507 BOOLEAN ngfInitChar(coeffs n, void *parameter)
508 {
509  assume( getCoeffType(n) == n_long_R );
510 
511  n->is_field=TRUE;
512  n->is_domain=TRUE;
513  n->rep=n_rep_gmp_float;
514 
515  //n->cfKillChar = ndKillChar; /* dummy */
516 
517  n->cfSetChar = ngfSetChar;
518  n->ch = 0;
519  n->cfCoeffString=ngfCoeffString;
520  n->cfCoeffName=ngfCoeffName;
521 
522  n->cfDelete = ngfDelete;
523  //n->cfNormalize=ndNormalize;
524  n->cfInit = ngfInit;
525  n->cfInt = ngfInt;
526  n->cfAdd = ngfAdd;
527  n->cfSub = ngfSub;
528  n->cfMult = ngfMult;
529  n->cfDiv = ngfDiv;
530  n->cfExactDiv= ngfDiv;
531  n->cfInpNeg = ngfNeg;
532  n->cfInvers = ngfInvers;
533  n->cfCopy = ngfCopy;
534  n->cfGreater = ngfGreater;
535  n->cfEqual = ngfEqual;
536  n->cfIsZero = ngfIsZero;
537  n->cfIsOne = ngfIsOne;
538  n->cfIsMOne = ngfIsMOne;
539  n->cfGreaterZero = ngfGreaterZero;
540  n->cfWriteLong = ngfWrite;
541  n->cfRead = ngfRead;
542  n->cfPower = ngfPower;
543  n->cfSetMap = ngfSetMap;
544  n->cfCoeffWrite = ngfCoeffWrite;
545 #ifdef LDEBUG
546  //n->cfDBTest = ndDBTest; // not yet implemented: ngfDBTest
547 #endif
548 
549  n->nCoeffIsEqual = ngfCoeffIsEqual;
550 
551  if( parameter != NULL)
552  {
553  LongComplexInfo* p = (LongComplexInfo*)parameter;
554 
555  n->float_len = p->float_len;
556  n->float_len2 = p->float_len2;
557  } else // default values, just for testing!
558  {
559  n->float_len = SHORT_REAL_LENGTH;
560  n->float_len2 = SHORT_REAL_LENGTH;
561  }
562 
563  assume( n->float_len2 >= SHORT_REAL_LENGTH );
564 
565  assume( n_NumberOfParameters(n) == 0 );
566  assume( n_ParameterNames(n) == NULL );
567 
568  return FALSE;
569 }
All the auxiliary stuff.
static int ABS(int v)
Definition: auxiliary.h:112
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
int i
Definition: cfEzgcd.cc:125
Variable x
Definition: cfModGcd.cc:4023
int p
Definition: cfModGcd.cc:4019
CanonicalForm b
Definition: cfModGcd.cc:4044
FILE * f
Definition: checklibs.c:9
gmp_complex numbers based on
Definition: mpr_complex.h:179
void setFromStr(const char *in)
Definition: mpr_complex.cc:78
bool isZero() const
Definition: mpr_complex.cc:252
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE BOOLEAN nCoeff_is_long_R(const coeffs r)
Definition: coeffs.h:913
n_coeffType
Definition: coeffs.h:28
@ n_R
single prescision (6,6) real numbers
Definition: coeffs.h:32
@ n_long_R
real floating point (GMP) numbers
Definition: coeffs.h:34
@ n_Zp
\F{p < 2^31}
Definition: coeffs.h:30
@ n_long_C
complex floating point (GMP) numbers
Definition: coeffs.h:42
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
Definition: coeffs.h:800
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:421
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:796
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:822
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:111
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:112
@ n_rep_float
(float), see shortfl.h
Definition: coeffs.h:116
@ n_rep_int
(int), see modulop.h
Definition: coeffs.h:110
@ n_rep_gmp_float
(gmp_float), see
Definition: coeffs.h:117
@ n_rep_gmp_complex
(gmp_complex), see gnumpc.h
Definition: coeffs.h:118
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
static FORCE_INLINE BOOLEAN nCoeff_is_R(const coeffs r)
Definition: coeffs.h:858
static FORCE_INLINE BOOLEAN nCoeff_is_long_C(const coeffs r)
Definition: coeffs.h:916
#define Print
Definition: emacs.cc:80
const CanonicalForm int s
Definition: facAbsFact.cc:55
CanonicalForm res
Definition: facAbsFact.cc:64
bool isZero(const CFArray &A)
checks if entries of A are zero
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define STATIC_VAR
Definition: globaldefs.h:7
static number ngfInit(long i, const coeffs r)
Definition: gnumpfl.cc:39
static number ngfMapC(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:462
static number ngfCopy(number a, const coeffs r)
Definition: gnumpfl.cc:96
static BOOLEAN ngfGreater(number a, number b, const coeffs r)
Definition: gnumpfl.cc:241
static void ngfSetChar(const coeffs r)
Definition: gnumpfl.cc:397
static void ngfCoeffWrite(const coeffs r, BOOLEAN)
Definition: gnumpfl.cc:502
static number ngfMapZ(number from, const coeffs aRing, const coeffs r)
Definition: gnumpfl.cc:424
static number ngfInvers(number a, const coeffs r)
Definition: gnumpfl.cc:133
static long ngfInt(number &i, const coeffs r)
Definition: gnumpfl.cc:50
static char * ngfCoeffString(const coeffs r)
Definition: gnumpfl.cc:402
static number ngfDiv(number a, number b, const coeffs r)
Definition: gnumpfl.cc:185
static number ngfAdd(number a, number b, const coeffs R)
Definition: gnumpfl.cc:152
static char * ngfEatFloatNExp(char *s)
Definition: gnumpfl.cc:278
static number ngfMapP(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:454
static BOOLEAN ngfGreaterZero(number a, const coeffs r)
Definition: gnumpfl.cc:231
static BOOLEAN ngfIsMOne(number a, const coeffs r)
Definition: gnumpfl.cc:271
static BOOLEAN ngfIsZero(number a, const coeffs r)
Definition: gnumpfl.cc:61
static void ngfWrite(number a, const coeffs r)
Definition: gnumpfl.cc:366
static number ngfPower(number x, int exp, const coeffs r)
Definition: gnumpfl.cc:202
static BOOLEAN ngfEqual(number a, number b, const coeffs r)
Definition: gnumpfl.cc:251
static int ngfSize(number n, const coeffs r)
Definition: gnumpfl.cc:68
static void ngfDelete(number *a, const coeffs r)
Definition: gnumpfl.cc:82
static number ngfMapQ(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:416
const char * ngfRead(const char *s, number *a, const coeffs r)
Definition: gnumpfl.cc:307
static BOOLEAN ngfCoeffIsEqual(const coeffs r, n_coeffType n, void *parameter)
Definition: gnumpfl.cc:384
static number ngfNeg(number a, const coeffs r)
Definition: gnumpfl.cc:122
static BOOLEAN ngfIsOne(number a, const coeffs r)
Definition: gnumpfl.cc:261
static number ngfMult(number a, number b, const coeffs R)
Definition: gnumpfl.cc:174
static nMapFunc ngfSetMap(const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:471
BOOLEAN ngfInitChar(coeffs n, void *parameter)
Initialize r.
Definition: gnumpfl.cc:507
static number ngfSub(number a, number b, const coeffs R)
Definition: gnumpfl.cc:163
static number ngfMapR(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:445
static char * ngfCoeffName(const coeffs r)
Definition: gnumpfl.cc:409
#define SR_INT
Definition: longrat.h:66
#define SR_TO_INT(SR)
Definition: longrat.h:68
#define assume(x)
Definition: mod2.h:390
long npInt(number &n, const coeffs r)
Definition: modulop.cc:127
char * floatToStr(const gmp_float &r, const unsigned int oprec)
Definition: mpr_complex.cc:578
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
gmp_float numberFieldToFloat(number num, int cf)
Definition: mpr_complex.cc:438
void setGMPFloatDigits(size_t digits, size_t rest)
Set size of mantissa digits - the number of output digits (basis 10) the size of mantissa consists of...
Definition: mpr_complex.cc:60
#define QTOF
Definition: mpr_complex.h:19
The main handler for Singular numbers which are suitable for Singular polynomials.
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:251
const char *const nDivBy0
Definition: numbers.h:88
#define SHORT_REAL_LENGTH
Definition: numbers.h:57
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omFree(addr)
Definition: omAllocDecl.h:261
#define NULL
Definition: omList.c:12
void StringAppendS(const char *st)
Definition: reporter.cc:107
void Werror(const char *fmt,...)
Definition: reporter.cc:189
static int sign(int x)
Definition: ring.cc:3375
#define SI_FLOAT
Definition: shortfl.h:15
#define R
Definition: sirandom.c:27
#define SR_HDL(A)
Definition: tgb.cc:35
Definition: gnumpfl.cc:27
nf(number n)
Definition: gnumpfl.cc:31
nf(SI_FLOAT f)
Definition: gnumpfl.cc:30
SI_FLOAT _f
Definition: gnumpfl.cc:28
number _n
Definition: gnumpfl.cc:29
SI_FLOAT F() const
Definition: gnumpfl.cc:32
number N() const
Definition: gnumpfl.cc:33