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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  f= new gmp_float( 0 );
142  }
143  else
144  {
145  f= new gmp_float( gmp_float(1) / (*(gmp_float*)a) );
146  }
147  return (number)f;
148 }
149 
150 /*2
151 * u:= a + b
152 */
153 static number ngfAdd (number a, number b, const coeffs R)
154 {
155  assume( getCoeffType(R) == n_long_R );
156 
157  gmp_float* r= new gmp_float( (*(gmp_float*)a) + (*(gmp_float*)b) );
158  return (number)r;
159 }
160 
161 /*2
162 * u:= a - b
163 */
164 static number ngfSub (number a, number b, const coeffs R)
165 {
166  assume( getCoeffType(R) == n_long_R );
167 
168  gmp_float* r= new gmp_float( (*(gmp_float*)a) - (*(gmp_float*)b) );
169  return (number)r;
170 }
171 
172 /*2
173 * u := a * b
174 */
175 static number ngfMult (number a, number b, const coeffs R)
176 {
177  assume( getCoeffType(R) == n_long_R );
178 
179  gmp_float* r= new gmp_float( (*(gmp_float*)a) * (*(gmp_float*)b) );
180  return (number)r;
181 }
182 
183 /*2
184 * u := a / b
185 */
186 static number ngfDiv (number a, number b, const coeffs r)
187 {
188  assume( getCoeffType(r) == n_long_R );
189 
190  gmp_float* f;
191  if ( ((gmp_float*)b)->isZero() )
192  {
193  // a/0 = error
194  WerrorS(nDivBy0);
195  f= new gmp_float( 0 );
196  }
197  else
198  {
199  f= new gmp_float( (*(gmp_float*)a) / (*(gmp_float*)b) );
200  }
201  return (number)f;
202 }
203 
204 /*2
205 * u:= x ^ exp
206 */
207 static number ngfPower (number x, int exp, const coeffs r)
208 {
209  assume( getCoeffType(r) == n_long_R );
210 
211  if ( exp == 0 )
212  {
213  gmp_float* n = new gmp_float(1);
214  return (number)n;
215  }
216  else if ( ngfIsZero(x, r) ) // 0^e, e>0
217  {
218  return ngfInit(0, r);
219  }
220  else if ( exp == 1 )
221  {
222  return ngfCopy(x,r);
223  }
224  return (number) ( new gmp_float( (*(gmp_float*)x)^exp ) );
225 }
226 
227 /* kept for compatibility reasons, to be deleted */
228 static void ngfPower ( number x, int exp, number * u, const coeffs r )
229 {
230  *u = ngfPower(x, exp, r);
231 }
232 
233 /*2
234 * za > 0 ?
235 */
236 static BOOLEAN ngfGreaterZero (number a, const coeffs r)
237 {
238  assume( getCoeffType(r) == n_long_R );
239 
240  return (((gmp_float*)a)->sign() > 0);
241 }
242 
243 /*2
244 * a > b ?
245 */
246 static BOOLEAN ngfGreater (number a, number b, const coeffs r)
247 {
248  assume( getCoeffType(r) == n_long_R );
249 
250  return ( (*(gmp_float*)a) > (*(gmp_float*)b) );
251 }
252 
253 /*2
254 * a = b ?
255 */
256 static BOOLEAN ngfEqual (number a, number b, const coeffs r)
257 {
258  assume( getCoeffType(r) == n_long_R );
259 
260  return ( (*(gmp_float*)a) == (*(gmp_float*)b) );
261 }
262 
263 /*2
264 * a == 1 ?
265 */
266 static BOOLEAN ngfIsOne (number a, const coeffs r)
267 {
268  assume( getCoeffType(r) == n_long_R );
269 
270  return ((gmp_float*)a)->isOne();
271 }
272 
273 /*2
274 * a == -1 ?
275 */
276 static BOOLEAN ngfIsMOne (number a, const coeffs r)
277 {
278  assume( getCoeffType(r) == n_long_R );
279 
280  return ((gmp_float*)a)->isMOne();
281 }
282 
283 static char * ngfEatFloatNExp(char * s )
284 {
285  char *start= s;
286 
287  // eat floats (mantissa) like:
288  // 0.394394993, 102.203003008, .300303032, pssibly starting with -
289  if (*s == '-') s++;
290  while ((*s >= '0' && *s <= '9')||(*s == '.')) s++;
291 
292  // eat the exponent, starts with 'e' followed by '+', '-'
293  // and digits, like:
294  // e-202, e+393, accept also E7
295  if ( (s != start) && ((*s == 'e')||(*s=='E')))
296  {
297  if (*s=='E') *s='e';
298  s++; // skip 'e'/'E'
299  if ((*s == '+') || (*s == '-')) s++;
300  while ((*s >= '0' && *s <= '9')) s++;
301  }
302 
303  return s;
304 }
305 
306 /*2
307 * extracts the number a from s, returns the rest
308 *
309 * This is also called to print components of complex coefficients.
310 * Handle with care!
311 */
312 const char * ngfRead (const char * start, number * a, const coeffs r)
313 {
315 
316  char *s= (char *)start;
317 
318  //Print("%s\n",s);
319 
320  s= ngfEatFloatNExp( s );
321 
322  if (*s=='\0') // 0
323  {
324  if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float();
325  (*(gmp_float**)a)->setFromStr(start);
326  }
327  else if (s==start) // 1
328  {
329  if ( *(gmp_float**)a != NULL ) delete (*(gmp_float**)a);
330  (*(gmp_float**)a)= new gmp_float(1);
331  }
332  else
333  {
334  gmp_float divisor(1.0);
335  char *start2=s;
336  if ( *s == '/' )
337  {
338  s++;
339  s= ngfEatFloatNExp( (char *)s );
340  if (s!= start2+1)
341  {
342  char tmp_c=*s;
343  *s='\0';
344  divisor.setFromStr(start2+1);
345  *s=tmp_c;
346  }
347  else
348  {
349  Werror("wrong long real format: %s",start2);
350  }
351  }
352  char c=*start2;
353  *start2='\0';
354  if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float();
355  (*(gmp_float**)a)->setFromStr(start);
356  *start2=c;
357  if (divisor.isZero())
358  {
359  WerrorS(nDivBy0);
360  }
361  else
362  (**(gmp_float**)a) /= divisor;
363  }
364 
365  return s;
366 }
367 
368 /*2
369 * write a floating point number
370 */
371 static void ngfWrite (number a, const coeffs r)
372 {
373  assume( getCoeffType(r) == n_long_R );
374 
375  char *out;
376  if ( a != NULL )
377  {
378  out= floatToStr(*(gmp_float*)a, r->float_len);
379  StringAppendS(out);
380  //omFreeSize((void *)out, (strlen(out)+1)* sizeof(char) );
381  omFree( (void *)out );
382  }
383  else
384  {
385  StringAppendS("0");
386  }
387 }
388 
389 static BOOLEAN ngfCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter)
390 {
391  if (n==n_long_R)
392  {
393  LongComplexInfo* p = (LongComplexInfo *)(parameter);
394  if ((p!=NULL)
395  && (p->float_len == r->float_len)
396  && (p->float_len2 == r->float_len2))
397  return TRUE;
398  }
399  return FALSE;
400 }
401 
402 static void ngfSetChar(const coeffs r)
403 {
404  setGMPFloatDigits(r->float_len, r->float_len2);
405 }
406 
407 static char* ngfCoeffName(const coeffs r)
408 {
409  STATIC_VAR char ngfCoeffName_buf[30];
410  snprintf(ngfCoeffName_buf,30,"Float(%d,%d)",r->float_len,r->float_len2);
411  return ngfCoeffName_buf;
412 }
413 
414 static number ngfMapQ(number from, const coeffs src, const coeffs dst)
415 {
416  assume( getCoeffType(dst) == n_long_R );
417  assume( src->rep == n_rep_gap_rat );
418 
420  return (number)res;
421 }
422 static number ngfMapZ(number from, const coeffs aRing, const coeffs r)
423 {
424  assume( getCoeffType(r) == n_long_R );
425  assume( aRing->rep == n_rep_gap_gmp);
426 
427  if ( from != NULL )
428  {
429  if (SR_HDL(from) & SR_INT)
430  {
431  gmp_float f_i= gmp_float(SR_TO_INT(from));
432  gmp_float *res=new gmp_float(f_i);
433  return (number)res;
434  }
435  gmp_float f_i=(mpz_ptr)from;
436  gmp_float *res=new gmp_float(f_i);
437  return (number)res;
438  }
439  else
440  return NULL;
441 }
442 
443 static number ngfMapR(number from, const coeffs src, const coeffs dst)
444 {
445  assume( getCoeffType(dst) == n_long_R );
446  assume( getCoeffType(src) == n_R );
447 
448  gmp_float *res=new gmp_float((double)nf(from).F());
449  return (number)res;
450 }
451 
452 static number ngfMapP(number from, const coeffs src, const coeffs dst)
453 {
454  assume( getCoeffType(dst) == n_long_R );
455  assume( getCoeffType(src) == n_Zp );
456 
457  return ngfInit(npInt(from,src), dst); // FIXME? TODO? // extern int npInt (number &n, const coeffs r);
458 }
459 
460 static number ngfMapC(number from, const coeffs src, const coeffs dst)
461 {
462  assume( getCoeffType(dst) == n_long_R );
463  assume( getCoeffType(src) == n_long_C );
464 
465  gmp_float *res=new gmp_float(((gmp_complex*)from)->real());
466  return (number)res;
467 }
468 
469 static number ngfInitMPZ(mpz_t m, const coeffs)
470 {
471  gmp_float *res=new gmp_float(m);
472  return (number)res;
473 }
474 
475 static nMapFunc ngfSetMap(const coeffs src, const coeffs dst)
476 {
477  assume( getCoeffType(dst) == n_long_R );
478 
479  if (src->rep==n_rep_gap_rat) /*Q, Z*/
480  {
481  return ngfMapQ;
482  }
483  if (src->rep==n_rep_gap_gmp) /*Q, Z*/
484  {
485  return ngfMapZ;
486  }
487  if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src))
488  {
489  return ndCopyMap; //ngfCopyMap;
490  }
491  if ((src->rep==n_rep_float) && nCoeff_is_R(src))
492  {
493  return ngfMapR;
494  }
495  if ((src->rep==n_rep_gmp_complex) && nCoeff_is_long_C(src))
496  {
497  return ngfMapC;
498  }
499  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src))
500  {
501  return ngfMapP;
502  }
503  return NULL;
504 }
505 
506 BOOLEAN ngfInitChar(coeffs n, void *parameter)
507 {
508  assume( getCoeffType(n) == n_long_R );
509 
510  n->is_field=TRUE;
511  n->is_domain=TRUE;
512  n->rep=n_rep_gmp_float;
513 
514  //n->cfKillChar = ndKillChar; /* dummy */
515 
516  n->cfSetChar = ngfSetChar;
517  n->ch = 0;
518  n->cfCoeffName=ngfCoeffName;
519 
520  n->cfDelete = ngfDelete;
521  //n->cfNormalize=ndNormalize;
522  n->cfInit = ngfInit;
523  n->cfInitMPZ = ngfInitMPZ;
524  n->cfInt = ngfInt;
525  n->cfAdd = ngfAdd;
526  n->cfSub = ngfSub;
527  n->cfMult = ngfMult;
528  n->cfDiv = ngfDiv;
529  n->cfExactDiv= ngfDiv;
530  n->cfInpNeg = ngfNeg;
531  n->cfInvers = ngfInvers;
532  n->cfCopy = ngfCopy;
533  n->cfGreater = ngfGreater;
534  n->cfEqual = ngfEqual;
535  n->cfIsZero = ngfIsZero;
536  n->cfIsOne = ngfIsOne;
537  n->cfIsMOne = ngfIsMOne;
538  n->cfGreaterZero = ngfGreaterZero;
539  n->cfWriteLong = ngfWrite;
540  n->cfRead = ngfRead;
541  n->cfPower = ngfPower;
542  n->cfSetMap = ngfSetMap;
543 #ifdef LDEBUG
544  //n->cfDBTest = ndDBTest; // not yet implemented: ngfDBTest
545 #endif
546 
547  n->nCoeffIsEqual = ngfCoeffIsEqual;
548 
549  if( parameter != NULL)
550  {
551  LongComplexInfo* p = (LongComplexInfo*)parameter;
552 
553  n->float_len = p->float_len;
554  n->float_len2 = p->float_len2;
555  } else // default values, just for testing!
556  {
557  n->float_len = SHORT_REAL_LENGTH;
558  n->float_len2 = SHORT_REAL_LENGTH;
559  }
560 
561  assume( n->float_len2 >= SHORT_REAL_LENGTH );
562 
563  assume( n_NumberOfParameters(n) == 0 );
564  assume( n_ParameterNames(n) == NULL );
565 
566  return FALSE;
567 }
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 m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
Variable x
Definition: cfModGcd.cc:4084
int p
Definition: cfModGcd.cc:4080
CanonicalForm b
Definition: cfModGcd.cc:4105
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.
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition: numbers.cc:259
static FORCE_INLINE BOOLEAN nCoeff_is_long_R(const coeffs r)
Definition: coeffs.h:915
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:802
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:798
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:824
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:112
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:113
@ n_rep_float
(float), see shortfl.h
Definition: coeffs.h:117
@ n_rep_int
(int), see modulop.h
Definition: coeffs.h:111
@ n_rep_gmp_float
(gmp_float), see
Definition: coeffs.h:118
@ n_rep_gmp_complex
(gmp_complex), see gnumpc.h
Definition: coeffs.h:119
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:74
static FORCE_INLINE BOOLEAN nCoeff_is_R(const coeffs r)
Definition: coeffs.h:860
static FORCE_INLINE BOOLEAN nCoeff_is_long_C(const coeffs r)
Definition: coeffs.h:918
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
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:460
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:246
static void ngfSetChar(const coeffs r)
Definition: gnumpfl.cc:402
static number ngfMapZ(number from, const coeffs aRing, const coeffs r)
Definition: gnumpfl.cc:422
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 number ngfInitMPZ(mpz_t m, const coeffs)
Definition: gnumpfl.cc:469
static number ngfDiv(number a, number b, const coeffs r)
Definition: gnumpfl.cc:186
static number ngfAdd(number a, number b, const coeffs R)
Definition: gnumpfl.cc:153
static char * ngfEatFloatNExp(char *s)
Definition: gnumpfl.cc:283
static number ngfMapP(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:452
static BOOLEAN ngfGreaterZero(number a, const coeffs r)
Definition: gnumpfl.cc:236
static BOOLEAN ngfIsMOne(number a, const coeffs r)
Definition: gnumpfl.cc:276
static BOOLEAN ngfIsZero(number a, const coeffs r)
Definition: gnumpfl.cc:61
static void ngfWrite(number a, const coeffs r)
Definition: gnumpfl.cc:371
static number ngfPower(number x, int exp, const coeffs r)
Definition: gnumpfl.cc:207
static BOOLEAN ngfEqual(number a, number b, const coeffs r)
Definition: gnumpfl.cc:256
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:414
const char * ngfRead(const char *s, number *a, const coeffs r)
Definition: gnumpfl.cc:312
static BOOLEAN ngfCoeffIsEqual(const coeffs r, n_coeffType n, void *parameter)
Definition: gnumpfl.cc:389
static number ngfNeg(number a, const coeffs r)
Definition: gnumpfl.cc:122
static BOOLEAN ngfIsOne(number a, const coeffs r)
Definition: gnumpfl.cc:266
static number ngfMult(number a, number b, const coeffs R)
Definition: gnumpfl.cc:175
static nMapFunc ngfSetMap(const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:475
BOOLEAN ngfInitChar(coeffs n, void *parameter)
Initialize r.
Definition: gnumpfl.cc:506
static number ngfSub(number a, number b, const coeffs R)
Definition: gnumpfl.cc:164
static number ngfMapR(number from, const coeffs src, const coeffs dst)
Definition: gnumpfl.cc:443
static char * ngfCoeffName(const coeffs r)
Definition: gnumpfl.cc:407
#define SR_INT
Definition: longrat.h:67
#define SR_TO_INT(SR)
Definition: longrat.h:69
#define assume(x)
Definition: mod2.h:387
long npInt(number &n, const coeffs r)
Definition: modulop.cc:85
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.
const char *const nDivBy0
Definition: numbers.h:87
#define SHORT_REAL_LENGTH
Definition: numbers.h:57
#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:3377
#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