Training courses

Kernel and Embedded Linux

Bootlin training courses

Embedded Linux, kernel,
Yocto Project, Buildroot, real-time,
graphics, boot time, debugging...

Bootlin logo

Elixir Cross Referencer

  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
/* Implementations of operations between mpfr and mpz/mpq data

Copyright 2001, 2003-2023 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

/* TODO: for functions with mpz_srcptr, check whether mpz_fits_slong_p
   is really useful in all cases. For instance, concerning the addition,
   one now has mpz_t -> long -> unsigned long -> mpfr_t then mpfr_add
   instead of mpz_t -> mpfr_t then mpfr_add. */

/* Init and set a mpfr_t with enough precision to store a mpz.
   This function should be called in the extended exponent range. */
static void
init_set_z (mpfr_ptr t, mpz_srcptr z)
{
  mpfr_prec_t p;
  int i;

  if (mpz_size (z) <= 1)
    p = GMP_NUMB_BITS;
  else
    MPFR_MPZ_SIZEINBASE2 (p, z);
  mpfr_init2 (t, p);
  i = mpfr_set_z (t, z, MPFR_RNDN);
  /* Possible assertion failure in case of overflow. Such cases,
     which imply that z is huge (if the function is called in
     the extended exponent range), are currently not supported,
     just like precisions around MPFR_PREC_MAX. */
  MPFR_ASSERTN (i == 0);  (void) i; /* use i to avoid a warning */
}

/* Init, set a mpfr_t with enough precision to store a mpz_t without round,
   call the function, and clear the allocated mpfr_t  */
static int
foo (mpfr_ptr x, mpfr_srcptr y, mpz_srcptr z, mpfr_rnd_t r,
     int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
{
  mpfr_t t;
  int i;
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_SAVE_EXPO_MARK (expo);
  init_set_z (t, z);  /* There should be no exceptions. */
  i = (*f) (x, y, t, r);
  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
  mpfr_clear (t);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (x, i, r);
}

static int
foo2 (mpfr_ptr x, mpz_srcptr y, mpfr_srcptr z, mpfr_rnd_t r,
     int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
{
  mpfr_t t;
  int i;
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_SAVE_EXPO_MARK (expo);
  init_set_z (t, y);  /* There should be no exceptions. */
  i = (*f) (x, t, z, r);
  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
  mpfr_clear (t);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (x, i, r);
}

int
mpfr_mul_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
  if (mpz_fits_slong_p (z))
    return mpfr_mul_si (y, x, mpz_get_si (z), r);
  else
    return foo (y, x, z, r, mpfr_mul);
}

int
mpfr_div_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
  if (mpz_fits_slong_p (z))
    return mpfr_div_si (y, x, mpz_get_si (z), r);
  else
    return foo (y, x, z, r, mpfr_div);
}

int
mpfr_add_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
  if (mpz_fits_slong_p (z))
    return mpfr_add_si (y, x, mpz_get_si (z), r);
  else
    return foo (y, x, z, r, mpfr_add);
}

int
mpfr_sub_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
  if (mpz_fits_slong_p (z))
    return mpfr_sub_si (y, x, mpz_get_si (z), r);
  else
    return foo (y, x, z, r, mpfr_sub);
}

int
mpfr_z_sub (mpfr_ptr y, mpz_srcptr x, mpfr_srcptr z, mpfr_rnd_t r)
{
  if (mpz_fits_slong_p (x))
    return mpfr_si_sub (y, mpz_get_si (x), z, r);
  else
    return foo2 (y, x, z, r, mpfr_sub);
}

int
mpfr_cmp_z (mpfr_srcptr x, mpz_srcptr z)
{
  mpfr_t t;
  int res;
  mpfr_prec_t p;
  mpfr_flags_t flags;

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    return mpfr_cmp_si (x, mpz_sgn (z));

  if (mpz_fits_slong_p (z))
    return mpfr_cmp_si (x, mpz_get_si (z));

  if (mpz_size (z) <= 1)
    p = GMP_NUMB_BITS;
  else
    MPFR_MPZ_SIZEINBASE2 (p, z);
  mpfr_init2 (t, p);
  flags = __gmpfr_flags;
  if (mpfr_set_z (t, z, MPFR_RNDN))
    {
      /* overflow (t is an infinity) or underflow: z does not fit in the
         current exponent range.
         If overflow, then z is larger than the largest *integer* < +Inf
         (if z > 0), thus we get t = +Inf (or -Inf), and the value of
         mpfr_cmp (x, t) below is correct.
         If underflow, then z is smaller than the smallest number > 0,
         which is necessarily an integer, say xmin.
         If z > xmin/2, then t is xmin, and we divide t by 2 to ensure t
         is zero, and then the value of mpfr_cmp (x, t) below is correct. */
      mpfr_div_2ui (t, t, 2, MPFR_RNDZ);  /* if underflow, set t to zero */
      __gmpfr_flags = flags;  /* restore the flags */
      /* The real value of t (= z), which falls outside the exponent range,
         has been replaced by an equivalent value for the comparison: zero
         or an infinity. */
    }
  res = mpfr_cmp (x, t);
  mpfr_clear (t);
  return res;
}

#ifndef MPFR_USE_MINI_GMP
/* Compute y = RND(x*n/d), where n and d are mpz integers.
   An integer 0 is assumed to have a positive sign.
   This function is used by mpfr_mul_q and mpfr_div_q.
   Note: the status of the rational 0/(-1) is not clear (if there is
   a signed infinity, there should be a signed zero). But infinities
   are not currently supported/documented in GMP, and if the rational
   is canonicalized as it should be, the case 0/(-1) cannot occur. */
static int
mpfr_muldiv_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr n, mpz_srcptr d,
               mpfr_rnd_t rnd_mode)
{
  if (MPFR_UNLIKELY (mpz_sgn (n) == 0))
    {
      if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
        MPFR_SET_NAN (y);
      else
        {
          mpfr_mul_ui (y, x, 0, MPFR_RNDN);  /* exact: +0, -0 or NaN */
          if (MPFR_UNLIKELY (mpz_sgn (d) < 0))
            MPFR_CHANGE_SIGN (y);
        }
      return 0;
    }
  else if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
    {
      mpfr_div_ui (y, x, 0, MPFR_RNDN);  /* exact: +Inf, -Inf or NaN */
      if (MPFR_UNLIKELY (mpz_sgn (n) < 0))
        MPFR_CHANGE_SIGN (y);
      return 0;
    }
  else
    {
      mpfr_prec_t p;
      mpfr_t tmp;
      int inexact;
      MPFR_SAVE_EXPO_DECL (expo);

      MPFR_SAVE_EXPO_MARK (expo);

      /* With the current MPFR code, using mpfr_mul_z and mpfr_div_z
         for the general case should be faster than doing everything
         in mpn, mpz and/or mpq. MPFR_SAVE_EXPO_MARK could be avoided
         here, but it would be more difficult to handle corner cases. */
      MPFR_MPZ_SIZEINBASE2 (p, n);
      mpfr_init2 (tmp, MPFR_PREC (x) + p);
      inexact = mpfr_mul_z (tmp, x, n, MPFR_RNDN);
      /* Since |n| >= 1, an underflow is not possible. And the precision of
         tmp has been chosen so that inexact != 0 iff there's an overflow. */
      if (MPFR_UNLIKELY (inexact != 0))
        {
          mpfr_t x0;
          mpfr_exp_t ex;
          MPFR_BLOCK_DECL (flags);

          /* intermediate overflow case */
          MPFR_ASSERTD (mpfr_inf_p (tmp));
          ex = MPFR_GET_EXP (x);  /* x is a pure FP number */
          MPFR_ALIAS (x0, x, MPFR_SIGN(x), 0);  /* x0 = x / 2^ex */
          MPFR_BLOCK (flags,
                      inexact = mpfr_mul_z (tmp, x0, n, MPFR_RNDN);
                      MPFR_ASSERTD (inexact == 0);
                      inexact = mpfr_div_z (y, tmp, d, rnd_mode);
                      /* Just in case the division underflows
                         (highly unlikely, not supported)... */
                      MPFR_ASSERTN (!MPFR_BLOCK_EXCEP));
          MPFR_EXP (y) += ex;
          /* Detect highly unlikely, not supported corner cases... */
          MPFR_ASSERTN (MPFR_EXP (y) >= __gmpfr_emin);
          MPFR_ASSERTN (! MPFR_IS_SINGULAR (y));
          /* The potential overflow will be detected by mpfr_check_range. */
        }
      else
        inexact = mpfr_div_z (y, tmp, d, rnd_mode);

      mpfr_clear (tmp);

      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_check_range (y, inexact, rnd_mode);
    }
}

int
mpfr_mul_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
  return mpfr_muldiv_z (y, x, mpq_numref (z), mpq_denref (z), rnd_mode);
}

int
mpfr_div_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
  return mpfr_muldiv_z (y, x, mpq_denref (z), mpq_numref (z), rnd_mode);
}

int
mpfr_add_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
  mpfr_t      t,q;
  mpfr_prec_t p;
  mpfr_exp_t  err;
  int res;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN (x))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF (x))
        {
          if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
                             MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
                                             MPFR_SIGN (x)) <= 0))
            {
              MPFR_SET_NAN (y);
              MPFR_RET_NAN;
            }
          MPFR_SET_INF (y);
          MPFR_SET_SAME_SIGN (y, x);
          MPFR_RET (0);
        }
      else
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (x));
          if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
            return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
          else
            return mpfr_set_q (y, z, rnd_mode);
        }
    }

  MPFR_SAVE_EXPO_MARK (expo);

  p = MPFR_PREC (y) + 10;
  mpfr_init2 (t, p);
  mpfr_init2 (q, p);

  MPFR_ZIV_INIT (loop, p);
  for (;;)
    {
      MPFR_BLOCK_DECL (flags);

      res = mpfr_set_q (q, z, MPFR_RNDN);  /* Error <= 1/2 ulp(q) */
      /* If z if @INF@ (1/0), res = 0, so it quits immediately */
      if (MPFR_UNLIKELY (res == 0))
        /* Result is exact so we can add it directly! */
        {
          res = mpfr_add (y, x, q, rnd_mode);
          break;
        }
      MPFR_BLOCK (flags, mpfr_add (t, x, q, MPFR_RNDN));
      /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
         but such an exception is very unlikely as it would be possible
         only if q has a huge numerator or denominator. Not supported! */
      MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
      /* Error / ulp(t)      <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
         If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
                             <= 2^(EXP(q)-EXP(t))
         If EXP(q)-EXP(t)<0, <= 2^0 */
      /* We can get 0, but we can't round since q is inexact */
      if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
        {
          err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
          if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode)))
            {
              res = mpfr_set (y, t, rnd_mode);
              break;
            }
        }
      MPFR_ZIV_NEXT (loop, p);
      mpfr_set_prec (t, p);
      mpfr_set_prec (q, p);
    }
  MPFR_ZIV_FREE (loop);
  mpfr_clear (t);
  mpfr_clear (q);

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, res, rnd_mode);
}

int
mpfr_sub_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z,mpfr_rnd_t rnd_mode)
{
  mpfr_t t,q;
  mpfr_prec_t p;
  int res;
  mpfr_exp_t err;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN (x))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF (x))
        {
          if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
                             MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
                                             MPFR_SIGN (x)) >= 0))
            {
              MPFR_SET_NAN (y);
              MPFR_RET_NAN;
            }
          MPFR_SET_INF (y);
          MPFR_SET_SAME_SIGN (y, x);
          MPFR_RET (0);
        }
      else
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (x));

          if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
            return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
          else
            {
              res =  mpfr_set_q (y, z, MPFR_INVERT_RND (rnd_mode));
              MPFR_CHANGE_SIGN (y);
              return -res;
            }
        }
    }

  MPFR_SAVE_EXPO_MARK (expo);

  p = MPFR_PREC (y) + 10;
  mpfr_init2 (t, p);
  mpfr_init2 (q, p);

  MPFR_ZIV_INIT (loop, p);
  for(;;)
    {
      MPFR_BLOCK_DECL (flags);

      res = mpfr_set_q(q, z, MPFR_RNDN);  /* Error <= 1/2 ulp(q) */
      /* If z if @INF@ (1/0), res = 0, so it quits immediately */
      if (MPFR_UNLIKELY (res == 0))
        /* Result is exact so we can add it directly!*/
        {
          res = mpfr_sub (y, x, q, rnd_mode);
          break;
        }
      MPFR_BLOCK (flags, mpfr_sub (t, x, q, MPFR_RNDN));
      /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
         but such an exception is very unlikely as it would be possible
         only if q has a huge numerator or denominator. Not supported! */
      MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
      /* Error / ulp(t)      <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
         If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
                             <= 2^(EXP(q)-EXP(t))
                             If EXP(q)-EXP(t)<0, <= 2^0 */
      /* We can get 0, but we can't round since q is inexact */
      if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
        {
          err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
          res = MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode);
          if (MPFR_LIKELY (res != 0))  /* We can round! */
            {
              res = mpfr_set (y, t, rnd_mode);
              break;
            }
        }
      MPFR_ZIV_NEXT (loop, p);
      mpfr_set_prec (t, p);
      mpfr_set_prec (q, p);
    }
  MPFR_ZIV_FREE (loop);
  mpfr_clear (t);
  mpfr_clear (q);

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, res, rnd_mode);
}

int
mpfr_cmp_q (mpfr_srcptr x, mpq_srcptr q)
{
  mpfr_t t;
  int res;
  mpfr_prec_t p;
  MPFR_SAVE_EXPO_DECL (expo);

  /* GMP allows the user to set the denominator to 0. This is interpreted
     by MPFR as the value being an infinity or NaN (probably better than
     an assertion failure). */
  if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (q)) == 0))
    {
      /* q is an infinity or NaN */
      mpfr_flags_t old_flags;

      mpfr_init2 (t, MPFR_PREC_MIN);
      old_flags = __gmpfr_flags;
      mpfr_set_q (t, q, MPFR_RNDN);
      __gmpfr_flags = old_flags;
      res = mpfr_cmp (x, t);
      mpfr_clear (t);
      return res;
    }

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    return mpfr_cmp_si (x, mpq_sgn (q));

  MPFR_SAVE_EXPO_MARK (expo);

  /* x < a/b ? <=> x*b < a */
  MPFR_MPZ_SIZEINBASE2 (p, mpq_denref (q));
  mpfr_init2 (t, MPFR_PREC(x) + p);
  res = mpfr_mul_z (t, x, mpq_denref (q), MPFR_RNDN);
  MPFR_ASSERTD (res == 0);
  res = mpfr_cmp_z (t, mpq_numref (q));
  mpfr_clear (t);

  MPFR_SAVE_EXPO_FREE (expo);
  return res;
}
#endif

#ifndef MPFR_USE_MINI_GMP
int
mpfr_cmp_f (mpfr_srcptr x, mpf_srcptr z)
{
  mpfr_t t;
  int res;
  MPFR_SAVE_EXPO_DECL (expo);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    return mpfr_cmp_si (x, mpf_sgn (z));

  MPFR_SAVE_EXPO_MARK (expo);

  mpfr_init2 (t, MPFR_PREC_MIN + ABSIZ(z) * GMP_NUMB_BITS);
  res = mpfr_set_f (t, z, MPFR_RNDN);
  MPFR_ASSERTD (res == 0);
  res = mpfr_cmp (x, t);
  mpfr_clear (t);

  MPFR_SAVE_EXPO_FREE (expo);
  return res;
}
#endif