1/* Test file for mpfr_sub1sp.
2
3Copyright 2003-2023 Free Software Foundation, Inc.
4Contributed by the AriC and Caramba projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23#include "mpfr-test.h"
24
25static void check_special (void);
26static void check_random (mpfr_prec_t p);
27static void check_underflow (mpfr_prec_t p);
28static void check_corner (mpfr_prec_t p);
29
30static void
31bug20170109 (void)
32{
33  mpfr_t a, b, c;
34
35  mpfr_init2 (a, 111);
36  mpfr_init2 (b, 111);
37  mpfr_init2 (c, 111);
38  mpfr_set_str_binary (b, "0.110010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000001101110E1");
39  mpfr_set_str_binary (c, "0.111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111E-63");
40  mpfr_sub (a, b, c, MPFR_RNDN);
41  mpfr_set_str_binary (b, "0.110010010000111111011010101000100010000101101000110000100011001111000100110001100110001010001011100000001101110E1");
42  MPFR_ASSERTN(mpfr_equal_p (a, b));
43  mpfr_clear (a);
44  mpfr_clear (b);
45  mpfr_clear (c);
46}
47
48/* check mpfr_sub1sp1 when:
49   (1) p = GMP_NUMB_BITS-1, d = GMP_NUMB_BITS and bp[0] = MPFR_LIMB_HIGHBIT
50   (2) p = 2*GMP_NUMB_BITS-1, d = 2*GMP_NUMB_BITS and b = 1000...000
51   (3) p = 3*GMP_NUMB_BITS-1, d = 3*GMP_NUMB_BITS and b = 1000...000
52*/
53static void
54test20170208 (void)
55{
56  mpfr_t a, b, c;
57  int inex;
58
59  mpfr_inits2 (GMP_NUMB_BITS - 1, a, b, c, (mpfr_ptr) 0);
60
61  /* test (1) */
62  mpfr_set_ui_2exp (b, 1, GMP_NUMB_BITS, MPFR_RNDN);
63  mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
64  inex = mpfr_sub (a, b, c, MPFR_RNDN);
65  /* b-c = 2^GMP_NUMB_BITS-1 which has GMP_NUMB_BITS bits, thus we should
66     round to 2^GMP_NUMB_BITS (even rule) */
67  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, GMP_NUMB_BITS) == 0);
68  MPFR_ASSERTN(inex > 0);
69  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
70  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, GMP_NUMB_BITS) == 0);
71  MPFR_ASSERTN(inex > 0);
72
73  mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
74  mpfr_nextbelow (c);
75  /* now c = 2 - 2^(1-GMP_NUMB_BITS) */
76  inex = mpfr_sub (a, b, c, MPFR_RNDN);
77  /* b-c = 2^GMP_NUMB_BITS-2+2^(1-GMP_NUMB_BITS), which should
78     round to 2^GMP_NUMB_BITS-2. We check by directly inspecting the bit
79     field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
80     than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
81     to construct the expected result. */
82  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
83  MPFR_ASSERTN(MPFR_EXP(a) == GMP_NUMB_BITS);
84  MPFR_ASSERTN(inex < 0);
85  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
86  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
87  MPFR_ASSERTN(MPFR_EXP(a) == GMP_NUMB_BITS);
88  MPFR_ASSERTN(inex < 0);
89
90  /* test (2) */
91  mpfr_set_prec (a, 2 * GMP_NUMB_BITS - 1);
92  mpfr_set_prec (b, 2 * GMP_NUMB_BITS - 1);
93  mpfr_set_prec (c, 2 * GMP_NUMB_BITS - 1);
94  mpfr_set_ui_2exp (b, 1, 2 * GMP_NUMB_BITS, MPFR_RNDN);
95  mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
96  inex = mpfr_sub (a, b, c, MPFR_RNDN);
97  /* b-c = 2^(2*GMP_NUMB_BITS)-1 which has 2*GMP_NUMB_BITS bits, thus we should
98     round to 2^(2*GMP_NUMB_BITS) (even rule) */
99  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 2 * GMP_NUMB_BITS) == 0);
100  MPFR_ASSERTN(inex > 0);
101  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
102  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 2 * GMP_NUMB_BITS) == 0);
103  MPFR_ASSERTN(inex > 0);
104
105  mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
106  mpfr_nextbelow (c);
107  /* now c = 2 - 2^(1-2*GMP_NUMB_BITS) */
108  inex = mpfr_sub (a, b, c, MPFR_RNDN);
109  /* b-c = 2^(2*GMP_NUMB_BITS)-2+2^(1-2*GMP_NUMB_BITS), which should
110     round to 2^(2*GMP_NUMB_BITS)-2. We check by directly inspecting the bit
111     field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
112     than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
113     to construct the expected result. */
114  MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
115  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
116  MPFR_ASSERTN(MPFR_EXP(a) == 2 * GMP_NUMB_BITS);
117  MPFR_ASSERTN(inex < 0);
118  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
119  MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
120  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
121  MPFR_ASSERTN(MPFR_EXP(a) == 2 * GMP_NUMB_BITS);
122  MPFR_ASSERTN(inex < 0);
123
124  /* test (3) */
125  mpfr_set_prec (a, 3 * GMP_NUMB_BITS - 1);
126  mpfr_set_prec (b, 3 * GMP_NUMB_BITS - 1);
127  mpfr_set_prec (c, 3 * GMP_NUMB_BITS - 1);
128  mpfr_set_ui_2exp (b, 1, 3 * GMP_NUMB_BITS, MPFR_RNDN);
129  mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
130  inex = mpfr_sub (a, b, c, MPFR_RNDN);
131  /* b-c = 2^(3*GMP_NUMB_BITS)-1 which has 3*GMP_NUMB_BITS bits, thus we should
132     round to 3^(2*GMP_NUMB_BITS) (even rule) */
133  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 3 * GMP_NUMB_BITS) == 0);
134  MPFR_ASSERTN(inex > 0);
135  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
136  MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, 3 * GMP_NUMB_BITS) == 0);
137  MPFR_ASSERTN(inex > 0);
138
139  mpfr_set_ui_2exp (c, 2, 0, MPFR_RNDN);
140  mpfr_nextbelow (c);
141  /* now c = 2 - 2^(1-3*GMP_NUMB_BITS) */
142  inex = mpfr_sub (a, b, c, MPFR_RNDN);
143  /* b-c = 2^(3*GMP_NUMB_BITS)-2+2^(1-3*GMP_NUMB_BITS), which should
144     round to 2^(3*GMP_NUMB_BITS)-2. We check by directly inspecting the bit
145     field of a, since mpfr_cmp_ui might not work if unsigned long is shorter
146     than mp_limb_t, and we don't want to use mpfr_add_ui or mpfr_sub_ui
147     to construct the expected result. */
148  MPFR_ASSERTN(MPFR_MANT(a)[2] == (mp_limb_t) -1);
149  MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
150  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
151  MPFR_ASSERTN(MPFR_EXP(a) == 3 * GMP_NUMB_BITS);
152  MPFR_ASSERTN(inex < 0);
153  inex = mpfr_sub1sp (a, b, c, MPFR_RNDN);
154  MPFR_ASSERTN(MPFR_MANT(a)[2] == (mp_limb_t) -1);
155  MPFR_ASSERTN(MPFR_MANT(a)[1] == (mp_limb_t) -1);
156  MPFR_ASSERTN(MPFR_MANT(a)[0] == (mp_limb_t) -2);
157  MPFR_ASSERTN(MPFR_EXP(a) == 3 * GMP_NUMB_BITS);
158  MPFR_ASSERTN(inex < 0);
159
160  mpfr_clears (a, b, c, (mpfr_ptr) 0);
161}
162
163static void
164compare_sub_sub1sp (void)
165{
166  mpfr_t a, b, c, a_ref;
167  mpfr_prec_t p;
168  unsigned long d;
169  int i, inex_ref, inex;
170  int r;
171
172  for (p = 1; p <= 3*GMP_NUMB_BITS; p++)
173    {
174      mpfr_inits2 (p, a, b, c, a_ref, (mpfr_ptr) 0);
175      for (d = 0; d <= p + 2; d++)
176        {
177          /* EXP(b) - EXP(c) = d */
178          for (i = 0; i < 4; i++)
179            {
180              /* for i even, b is the smallest number, for b odd the largest */
181              mpfr_set_ui_2exp (b, 1, d, MPFR_RNDN);
182              if (i & 1)
183                {
184                  mpfr_mul_2ui (b, b, 1, MPFR_RNDN);
185                  mpfr_nextbelow (b);
186                }
187              mpfr_set_ui_2exp (c, 1, 0, MPFR_RNDN);
188              if (i & 2)
189                {
190                  mpfr_mul_2ui (c, c, 1, MPFR_RNDN);
191                  mpfr_nextbelow (c);
192                }
193              RND_LOOP_NO_RNDF (r)
194                {
195                  /* increase the precision of b to ensure sub1sp is not used */
196                  mpfr_prec_round (b, p + 1, MPFR_RNDN);
197                  inex_ref = mpfr_sub (a_ref, b, c, (mpfr_rnd_t) r);
198                  inex = mpfr_prec_round (b, p, MPFR_RNDN);
199                  MPFR_ASSERTN(inex == 0);
200                  inex = mpfr_sub1sp (a, b, c, (mpfr_rnd_t) r);
201                  if (inex != inex_ref)
202                    {
203                      printf ("mpfr_sub and mpfr_sub1sp differ for r=%s\n",
204                              mpfr_print_rnd_mode ((mpfr_rnd_t) r));
205                      printf ("b="); mpfr_dump (b);
206                      printf ("c="); mpfr_dump (c);
207                      printf ("expected inex=%d and ", inex_ref);
208                      mpfr_dump (a_ref);
209                      printf ("got      inex=%d and ", inex);
210                      mpfr_dump (a);
211                      exit (1);
212                    }
213                  MPFR_ASSERTN(mpfr_equal_p (a, a_ref));
214                }
215            }
216        }
217      mpfr_clears (a, b, c, a_ref, (mpfr_ptr) 0);
218    }
219}
220
221static void
222bug20171213 (void)
223{
224  mpfr_t a, b, c;
225
226  mpfr_init2 (a, 127);
227  mpfr_init2 (b, 127);
228  mpfr_init2 (c, 127);
229  mpfr_set_str_binary (b, "0.1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E1");
230  mpfr_set_str_binary (c, "0.1000011010111101100101100110101111111001011001010000110000000000000000000000000000000000000000000000000000000000000000000000000E-74");
231  mpfr_sub (a, b, c, MPFR_RNDN);
232  mpfr_set_str_binary (b, "0.1111111111111111111111111111111111111111111111111111111111111111111111111101111001010000100110100110010100000001101001101011110E0");
233  MPFR_ASSERTN(mpfr_equal_p (a, b));
234  mpfr_clear (a);
235  mpfr_clear (b);
236  mpfr_clear (c);
237}
238
239/* generic test for bug20171213:
240   b = 1.0 with precision p
241   c = 0.1xxx110...0E-e with precision p, with e >= 1, such that the part 1xxx1 has
242       exactly p+1-e bits, thus b-c = 0.111..01... is exact on p+1 bits.
243   Due to the round-to-even rule, b-c should be rounded to 0.111..0.
244*/
245static void
246bug20171213_gen (mpfr_prec_t pmax)
247{
248  mpfr_prec_t p;
249  mpfr_exp_t e;
250  mpfr_t a, b, c, d;
251
252  for (p = MPFR_PREC_MIN; p <= pmax; p++)
253    {
254      for (e = 1; e < p; e++)
255        {
256          mpfr_init2 (a, p);
257          mpfr_init2 (b, p);
258          mpfr_init2 (c, p);
259          mpfr_init2 (d, p);
260          mpfr_set_ui (b, 1, MPFR_RNDN);
261          mpfr_set_ui_2exp (c, 1, p + 1 - e, MPFR_RNDN); /* c = 2^(p + 1 - e) */
262          mpfr_sub_ui (c, c, 1, MPFR_RNDN); /* c = 2^(p + 1 - e) - 1 */
263          mpfr_div_2ui (c, c, p + 1, MPFR_RNDN); /* c = 2^(-e) - 2^(-p-1) */
264          /* the exact difference is 1 - 2^(-e) + 2^(-p-1) */
265          mpfr_sub (a, b, c, MPFR_RNDN);
266          /* check that a = 1 - 2^(-e) */
267          mpfr_set_ui_2exp (d, 1, e, MPFR_RNDN); /* b = 2^e */
268          mpfr_sub_ui (d, d, 1, MPFR_RNDN);      /* b = 2^e - 1 */
269          mpfr_div_2ui (d, d, e, MPFR_RNDN);    /* b = 1 - 2^(-e) */
270          if (! mpfr_equal_p (a, d))
271            {
272              printf ("bug20171213_gen failed for p=%ld, e=%ld\n",
273                      (long) p, (long) e);
274              printf ("b="); mpfr_dump (b);
275              printf ("c="); mpfr_dump (c);
276              printf ("got      a="); mpfr_dump (a);
277              printf ("expected d="); mpfr_dump (d);
278              exit (1);
279            }
280          mpfr_clear (a);
281          mpfr_clear (b);
282          mpfr_clear (c);
283          mpfr_clear (d);
284        }
285    }
286}
287
288static void
289coverage (void)
290{
291  mpfr_t a, b, c, d, u;
292  int inex;
293
294  /* coverage test in mpfr_sub1sp: case d=1, limb > MPFR_LIMB_HIGHBIT, RNDF
295     and also RNDZ */
296  mpfr_init2 (a, 3 * GMP_NUMB_BITS);
297  mpfr_init2 (b, 3 * GMP_NUMB_BITS);
298  mpfr_init2 (c, 3 * GMP_NUMB_BITS);
299  mpfr_init2 (d, 3 * GMP_NUMB_BITS);
300  mpfr_init2 (u, 3 * GMP_NUMB_BITS);
301  mpfr_set_ui (b, 1, MPFR_RNDN);
302  mpfr_nextbelow (b); /* b = 1 - 2^(-p) */
303  mpfr_set_prec (c, GMP_NUMB_BITS);
304  mpfr_set_ui_2exp (c, 1, -1, MPFR_RNDN);
305  mpfr_nextbelow (c);
306  mpfr_nextbelow (c); /* c = 1/2 - 2*2^(-GMP_NUMB_BITS-1) */
307  mpfr_prec_round (c, 3 * GMP_NUMB_BITS, MPFR_RNDN);
308  mpfr_nextbelow (c); /* c = 1/2 - 2*2^(-GMP_NUMB_BITS-1) - 2^(-p-1) */
309  /* b-c = c */
310  mpfr_sub (a, b, c, MPFR_RNDF);
311  mpfr_sub (d, b, c, MPFR_RNDD);
312  mpfr_sub (u, b, c, MPFR_RNDU);
313  /* check a = d or u */
314  MPFR_ASSERTN(mpfr_equal_p (a, d) || mpfr_equal_p (a, u));
315
316  /* coverage test in mpfr_sub1sp: case d=p, RNDN, sb = 0, significand of b
317     is even but b<>2^e, (case 1e) */
318  mpfr_set_prec (a, 3 * GMP_NUMB_BITS);
319  mpfr_set_prec (b, 3 * GMP_NUMB_BITS);
320  mpfr_set_prec (c, 3 * GMP_NUMB_BITS);
321  mpfr_set_ui (b, 1, MPFR_RNDN);
322  mpfr_nextabove (b);
323  mpfr_nextabove (b);
324  mpfr_set_ui_2exp (c, 1, -3 * GMP_NUMB_BITS, MPFR_RNDN);
325  inex = mpfr_sub (a, b, c, MPFR_RNDN);
326  MPFR_ASSERTN(inex > 0);
327  MPFR_ASSERTN(mpfr_equal_p (a, b));
328
329  mpfr_clear (a);
330  mpfr_clear (b);
331  mpfr_clear (c);
332  mpfr_clear (d);
333  mpfr_clear (u);
334}
335
336/* bug in mpfr_sub1sp1n, made generic */
337static void
338bug20180217 (mpfr_prec_t pmax)
339{
340  mpfr_t a, b, c;
341  int inex;
342  mpfr_prec_t p;
343
344  for (p = MPFR_PREC_MIN; p <= pmax; p++)
345    {
346      mpfr_init2 (a, p);
347      mpfr_init2 (b, p);
348      mpfr_init2 (c, p);
349      mpfr_set_ui (b, 1, MPFR_RNDN); /* b = 1 */
350      mpfr_set_ui_2exp (c, 1, -p-1, MPFR_RNDN); /* c = 2^(-p-1) */
351      /* a - b = 1 - 2^(-p-1) and should be rounded to 1 (case 2f of
352         mpfr_sub1sp) */
353      inex = mpfr_sub (a, b, c, MPFR_RNDN);
354      MPFR_ASSERTN(inex > 0);
355      MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
356      /* check also when a=b */
357      mpfr_set_ui (a, 1, MPFR_RNDN);
358      inex = mpfr_sub (a, a, c, MPFR_RNDN);
359      MPFR_ASSERTN(inex > 0);
360      MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
361      /* and when a=c */
362      mpfr_set_ui (b, 1, MPFR_RNDN); /* b = 1 */
363      mpfr_set_ui_2exp (a, 1, -p-1, MPFR_RNDN);
364      inex = mpfr_sub (a, b, a, MPFR_RNDN);
365      MPFR_ASSERTN(inex > 0);
366      MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0);
367      mpfr_clear (a);
368      mpfr_clear (b);
369      mpfr_clear (c);
370    }
371}
372
373/* bug in revision 12985 with tlog and GMP_CHECK_RANDOMIZE=1534111552615050
374   (introduced in revision 12242, does not affect the 4.0 branch) */
375static void
376bug20180813 (void)
377{
378  mpfr_t a, b, c;
379
380  mpfr_init2 (a, 194);
381  mpfr_init2 (b, 194);
382  mpfr_init2 (c, 194);
383  mpfr_set_str_binary (b, "0.10000111101000100000010000100010110111011100110100000101100111000010101000110110010101011101101011110110001000111001000010110010111010010100011011010100001010001110000101000010101110100110001000E7");
384  mpfr_set_str_binary (c, "0.10000000000000000100001111010001000000100001000101101110111001101000001011001110000101010001101100101010111011010111101100010001110010000101100101110100101000110110101000010100011100001010000101E24");
385  mpfr_sub (a, b, c, MPFR_RNDN);
386  mpfr_set_str_binary (b, "-0.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111E23");
387  MPFR_ASSERTN(mpfr_equal_p (a, b));
388  mpfr_clear (a);
389  mpfr_clear (b);
390  mpfr_clear (c);
391}
392
393/* bug in revision 13599 with tatan and GMP_CHECK_RANDOMIZE=1567609230659336:
394   the values are equal, but the ternary value differs between sub1 and sub1sp
395   (bug introduced with mpfr_sub1sp2n, does not affect the 4.0 branch) */
396static void
397bug20190904 (void)
398{
399  mpfr_t a, b, c;
400  int ret;
401
402  mpfr_init2 (a, 128);
403  mpfr_init2 (b, 128);
404  mpfr_init2 (c, 128);
405  mpfr_set_str_binary (b, "0.11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001E1");
406  mpfr_set_str_binary (c, "0.10010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010010000000000000000000000E-102");
407  ret = mpfr_sub (a, b, c, MPFR_RNDN);
408  mpfr_set_str_binary (b, "0.11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101101111111101111000001110011010001E1");
409  MPFR_ASSERTN(mpfr_equal_p (a, b));
410  MPFR_ASSERTN(ret > 0);
411  mpfr_clear (a);
412  mpfr_clear (b);
413  mpfr_clear (c);
414}
415
416int
417main (void)
418{
419  mpfr_prec_t p;
420
421  tests_start_mpfr ();
422
423  bug20190904 ();
424  bug20180813 ();
425  bug20180217 (1024);
426  coverage ();
427  compare_sub_sub1sp ();
428  test20170208 ();
429  bug20170109 ();
430  bug20171213 ();
431  bug20171213_gen (256);
432  check_special ();
433  for (p = MPFR_PREC_MIN ; p < 200 ; p++)
434    {
435      check_underflow (p);
436      check_random (p);
437      check_corner (p);
438    }
439
440  tests_end_mpfr ();
441  return 0;
442}
443
444#define STD_ERROR                                                       \
445  do                                                                    \
446    {                                                                   \
447      printf("ERROR: for %s and p=%lu and i=%d:\nY=",                   \
448             mpfr_print_rnd_mode ((mpfr_rnd_t) r), (unsigned long) p, i); \
449      mpfr_dump (y);                                                    \
450      printf ("Z="); mpfr_dump (z);                                     \
451      printf ("Expected: "); mpfr_dump (x2);                            \
452      printf ("Got :     "); mpfr_dump (x);                             \
453      abort();                                                          \
454    }                                                                   \
455 while (0)
456
457#define STD_ERROR2                                                      \
458  do                                                                    \
459    {                                                                   \
460      printf("ERROR: for %s and p=%lu and i=%d:\nY=",                   \
461             mpfr_print_rnd_mode ((mpfr_rnd_t) r), (unsigned long) p, i); \
462      mpfr_dump (y);                                                    \
463      printf ("Z="); mpfr_dump (z);                                     \
464      printf ("Expected: "); mpfr_dump (x2);                            \
465      printf ("Got :     "); mpfr_dump (x);                             \
466      printf ("Wrong inexact flag. Expected %d. Got %d\n",              \
467              inexact1, inexact2);                                      \
468      exit(1);                                                          \
469    }                                                                   \
470 while (0)
471
472static void
473check_random (mpfr_prec_t p)
474{
475  mpfr_t x,y,z,x2;
476  int r;
477  int i, inexact1, inexact2;
478
479  mpfr_inits2 (p, x, y, z, x2, (mpfr_ptr) 0);
480
481  for (i = 0 ; i < 500 ; i++)
482    {
483      mpfr_urandomb (y, RANDS);
484      mpfr_urandomb (z, RANDS);
485      if (MPFR_IS_PURE_FP(y) && MPFR_IS_PURE_FP(z))
486        RND_LOOP (r)
487          {
488            if (r == MPFR_RNDF)
489              continue; /* mpfr_sub1 and mpfr_sub1sp could differ,
490                           and inexact makes no sense */
491            inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
492            inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
493            if (mpfr_cmp(x, x2))
494              STD_ERROR;
495            if (inexact1 != inexact2)
496              STD_ERROR2;
497          }
498    }
499
500  mpfr_clears (x, y, z, x2, (mpfr_ptr) 0);
501}
502
503static void
504check_special (void)
505{
506  mpfr_t x,y,z,x2;
507  int r;
508  mpfr_prec_t p;
509  int i = -1, inexact1, inexact2;
510  mpfr_exp_t es;
511
512  mpfr_inits (x, y, z, x2, (mpfr_ptr) 0);
513
514  RND_LOOP (r)
515    {
516      if (r == MPFR_RNDF)
517        continue; /* comparison between sub1 and sub1sp makes no sense here */
518
519      p = 53;
520      mpfr_set_prec(x, 53);
521      mpfr_set_prec(x2, 53);
522      mpfr_set_prec(y, 53);
523      mpfr_set_prec(z, 53);
524
525      mpfr_set_str_binary (y,
526       "0.10110111101101110010010010011011000001101101011011001E31");
527
528      mpfr_sub1sp (x, y, y, (mpfr_rnd_t) r);
529      if (mpfr_cmp_ui(x, 0))
530        {
531          printf("Error for x-x with p=%lu. Expected 0. Got:",
532                 (unsigned long) p);
533          mpfr_dump (x);
534          exit(1);
535        }
536
537      mpfr_set(z, y, (mpfr_rnd_t) r);
538      mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
539      if (mpfr_cmp_ui(x, 0))
540        {
541          printf("Error for x-y with y=x and p=%lu. Expected 0. Got:",
542                 (unsigned long) p);
543          mpfr_dump (x);
544          exit(1);
545        }
546      /* diff = 0 */
547      mpfr_set_str_binary (y,
548       "0.10110111101101110010010010011011001001101101011011001E31");
549      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
550      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
551      if (mpfr_cmp(x, x2))
552        STD_ERROR;
553      if (inexact1 != inexact2)
554        STD_ERROR2;
555
556      /* Diff = 1 */
557      mpfr_set_str_binary (y,
558       "0.10110111101101110010010010011011000001101101011011001E30");
559      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
560      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
561      if (mpfr_cmp(x, x2))
562        STD_ERROR;
563      if (inexact1 != inexact2)
564        STD_ERROR2;
565
566      /* Diff = 2 */
567      mpfr_set_str_binary (y,
568       "0.10110111101101110010010010011011000101101101011011001E32");
569      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
570      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
571      if (mpfr_cmp(x, x2))
572        STD_ERROR;
573      if (inexact1 != inexact2)
574        STD_ERROR2;
575
576      /* Diff = 32 */
577      mpfr_set_str_binary (y,
578       "0.10110111101101110010010010011011000001101101011011001E63");
579      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
580      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
581      if (mpfr_cmp(x, x2))
582        STD_ERROR;
583      if (inexact1 != inexact2)
584        STD_ERROR2;
585
586      /* Diff = 52 */
587      mpfr_set_str_binary (y,
588       "0.10110111101101110010010010011011010001101101011011001E83");
589      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
590      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
591      if (mpfr_cmp(x, x2))
592        STD_ERROR;
593      if (inexact1 != inexact2)
594        STD_ERROR2;
595
596      /* Diff = 53 */
597      mpfr_set_str_binary (y,
598       "0.10110111101101110010010010011111000001101101011011001E31");
599      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
600      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
601      if (mpfr_cmp(x, x2))
602        STD_ERROR;
603      if (inexact1 != inexact2)
604        STD_ERROR2;
605
606      /* Diff > 200 */
607      mpfr_set_str_binary (y,
608       "0.10110111101101110010010010011011000001101101011011001E331");
609      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
610      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
611      if (mpfr_cmp(x, x2))
612        STD_ERROR;
613      if (inexact1 != inexact2)
614        STD_ERROR2;
615
616      mpfr_set_str_binary (y,
617       "0.10000000000000000000000000000000000000000000000000000E31");
618      mpfr_set_str_binary (z,
619       "0.11111111111111111111111111111111111111111111111111111E30");
620      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
621      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
622      if (mpfr_cmp(x, x2))
623        STD_ERROR;
624      if (inexact1 != inexact2)
625        STD_ERROR2;
626
627      mpfr_set_str_binary (y,
628       "0.10000000000000000000000000000000000000000000000000000E31");
629      mpfr_set_str_binary (z,
630       "0.11111111111111111111111111111111111111111111111111111E29");
631      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
632      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
633      if (mpfr_cmp(x, x2))
634        STD_ERROR;
635      if (inexact1 != inexact2)
636        STD_ERROR2;
637
638      mpfr_set_str_binary (y,
639       "0.10000000000000000000000000000000000000000000000000000E52");
640      mpfr_set_str_binary (z,
641       "0.10000000000010000000000000000000000000000000000000000E00");
642      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
643      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
644      if (mpfr_cmp(x, x2))
645        STD_ERROR;
646      if (inexact1 != inexact2)
647        STD_ERROR2;
648
649      mpfr_set_str_binary (y,
650        "0.11100000000000000000000000000000000000000000000000000E53");
651      mpfr_set_str_binary (z,
652        "0.10000000000000000000000000000000000000000000000000000E00");
653      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
654      inexact2 = mpfr_sub1sp(z, y, z, (mpfr_rnd_t) r);
655      mpfr_set(x, z, (mpfr_rnd_t) r);
656      if (mpfr_cmp(x, x2))
657        STD_ERROR;
658      if (inexact1 != inexact2)
659        STD_ERROR2;
660
661      mpfr_set_str_binary (y,
662       "0.10000000000000000000000000000000000000000000000000000E53");
663      mpfr_set_str_binary (z,
664       "0.10100000000000000000000000000000000000000000000000000E00");
665      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
666      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
667      if (mpfr_cmp(x, x2))
668        STD_ERROR;
669      if (inexact1 != inexact2)
670        STD_ERROR2;
671
672      mpfr_set_str_binary (y,
673        "0.10000000000000000000000000000000000000000000000000000E54");
674      mpfr_set_str_binary (z,
675        "0.10100000000000000000000000000000000000000000000000000E00");
676      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
677      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
678      if (mpfr_cmp(x, x2))
679        STD_ERROR;
680      if (inexact1 != inexact2)
681        STD_ERROR2;
682
683      p = 63;
684      mpfr_set_prec(x, p);
685      mpfr_set_prec(x2, p);
686      mpfr_set_prec(y, p);
687      mpfr_set_prec(z, p);
688      mpfr_set_str_binary (y,
689      "0.100000000000000000000000000000000000000000000000000000000000000E62");
690      mpfr_set_str_binary (z,
691      "0.110000000000000000000000000000000000000000000000000000000000000E00");
692      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
693      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
694      if (mpfr_cmp(x, x2))
695        STD_ERROR;
696      if (inexact1 != inexact2)
697        STD_ERROR2;
698
699      p = 64;
700      mpfr_set_prec(x, 64);
701      mpfr_set_prec(x2, 64);
702      mpfr_set_prec(y, 64);
703      mpfr_set_prec(z, 64);
704
705      mpfr_set_str_binary (y,
706      "0.1100000000000000000000000000000000000000000000000000000000000000E31");
707      mpfr_set_str_binary (z,
708      "0.1111111111111111111111111110000000000000000000000000011111111111E29");
709      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
710      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
711      if (mpfr_cmp(x, x2))
712        STD_ERROR;
713      if (inexact1 != inexact2)
714        STD_ERROR2;
715
716      mpfr_set_str_binary (y,
717      "0.1000000000000000000000000000000000000000000000000000000000000000E63");
718      mpfr_set_str_binary (z,
719      "0.1011000000000000000000000000000000000000000000000000000000000000E00");
720      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
721      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
722      if (mpfr_cmp(x, x2))
723        STD_ERROR;
724      if (inexact1 != inexact2)
725        STD_ERROR2;
726
727      mpfr_set_str_binary (y,
728      "0.1000000000000000000000000000000000000000000000000000000000000000E63");
729      mpfr_set_str_binary (z,
730      "0.1110000000000000000000000000000000000000000000000000000000000000E00");
731      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
732      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
733      if (mpfr_cmp(x, x2))
734        STD_ERROR;
735      if (inexact1 != inexact2)
736        STD_ERROR2;
737
738      mpfr_set_str_binary (y,
739        "0.10000000000000000000000000000000000000000000000000000000000000E63");
740      mpfr_set_str_binary (z,
741        "0.10000000000000000000000000000000000000000000000000000000000000E00");
742      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
743      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
744      if (mpfr_cmp(x, x2))
745        STD_ERROR;
746      if (inexact1 != inexact2)
747        STD_ERROR2;
748
749      mpfr_set_str_binary (y,
750      "0.1000000000000000000000000000000000000000000000000000000000000000E64");
751      mpfr_set_str_binary (z,
752      "0.1010000000000000000000000000000000000000000000000000000000000000E00");
753      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
754      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
755      if (mpfr_cmp(x, x2))
756        STD_ERROR;
757      if (inexact1 != inexact2)
758        STD_ERROR2;
759
760      MPFR_SET_NAN(x);
761      MPFR_SET_NAN(x2);
762      mpfr_set_str_binary (y,
763      "0.1000000000000000000000000000000000000000000000000000000000000000"
764                          "E-1073741823");
765      mpfr_set_str_binary (z,
766      "0.1100000000000000000000000000000000000000000000000000000000000000"
767                          "E-1073741823");
768      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
769      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
770      if (mpfr_cmp(x, x2))
771        STD_ERROR;
772      if (inexact1 != inexact2)
773        STD_ERROR2;
774
775      p = 9;
776      mpfr_set_prec(x, p);
777      mpfr_set_prec(x2, p);
778      mpfr_set_prec(y, p);
779      mpfr_set_prec(z, p);
780
781      mpfr_set_str_binary (y, "0.100000000E1");
782      mpfr_set_str_binary (z, "0.100000000E-8");
783      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
784      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
785      if (mpfr_cmp(x, x2))
786        STD_ERROR;
787      if (inexact1 != inexact2)
788        STD_ERROR2;
789
790      p = 34;
791      mpfr_set_prec(x, p);
792      mpfr_set_prec(x2, p);
793      mpfr_set_prec(y, p);
794      mpfr_set_prec(z, p);
795
796      mpfr_set_str_binary (y, "-0.1011110000111100010111011100110100E-18");
797      mpfr_set_str_binary (z, "0.1000101010110011010101011110000000E-14");
798      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
799      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
800      if (mpfr_cmp(x, x2))
801        STD_ERROR;
802      if (inexact1 != inexact2)
803        STD_ERROR2;
804
805      p = 124;
806      mpfr_set_prec(x, p);
807      mpfr_set_prec(x2, p);
808      mpfr_set_prec(y, p);
809      mpfr_set_prec(z, p);
810
811      mpfr_set_str_binary (y,
812"0.1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E1");
813      mpfr_set_str_binary (z,
814"0.1011111000100111000011001000011101010101101100101010101001000001110100001101110110001110111010000011101001100010111110001100E-31");
815      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
816      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
817      if (mpfr_cmp(x, x2))
818        STD_ERROR;
819      if (inexact1 != inexact2)
820        STD_ERROR2;
821
822      p = 288;
823      mpfr_set_prec(x, p);
824      mpfr_set_prec(x2, p);
825      mpfr_set_prec(y, p);
826      mpfr_set_prec(z, p);
827
828      mpfr_set_str_binary (y,
829     "0.111000110011000001000111101010111011110011101001101111111110000011100101000001001010110010101010011001010100000001110011110001010101101010001011101110100100001011110100110000101101100011010001001011011010101010000010001101001000110010010111111011110001111101001000101101001100101100101000E80");
830      mpfr_set_str_binary (z,
831     "-0.100001111111101001011010001100110010100111001110000110011101001011010100001000000100111011010110110010000000000010101101011000010000110001110010100001100101011100100100001011000100011110000001010101000100011101001000010111100000111000111011001000100100011000100000010010111000000100100111E-258");
832      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
833      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
834      if (mpfr_cmp(x, x2))
835        STD_ERROR;
836      if (inexact1 != inexact2)
837        STD_ERROR2;
838
839      p = 85;
840      mpfr_set_prec(x, p);
841      mpfr_set_prec(x2, p);
842      mpfr_set_prec(y, p);
843      mpfr_set_prec(z, p);
844
845      mpfr_set_str_binary (y,
846"0.1111101110100110110110100010101011101001100010100011110110110010010011101100101111100E-4");
847      mpfr_set_str_binary (z,
848"0.1111101110100110110110100010101001001000011000111000011101100101110100001110101010110E-4");
849      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
850      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
851      if (mpfr_cmp(x, x2))
852        STD_ERROR;
853      if (inexact1 != inexact2)
854        STD_ERROR2;
855
856      p = 64;
857      mpfr_set_prec(x, p); mpfr_set_prec(x2, p);
858      mpfr_set_prec(y, p); mpfr_set_prec(z, p);
859
860      mpfr_set_str_binary (y,
861                          "0.11000000000000000000000000000000"
862                          "00000000000000000000000000000000E1");
863      mpfr_set_str_binary (z,
864                          "0.10000000000000000000000000000000"
865                          "00000000000000000000000000000001E0");
866      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
867      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
868      if (mpfr_cmp(x, x2))
869        STD_ERROR;
870      if (inexact1 != inexact2)
871        STD_ERROR2;
872
873      mpfr_set_str_binary (y,
874                          "0.11000000000000000000000000000000"
875                          "000000000000000000000000000001E1");
876      mpfr_set_str_binary (z,
877                          "0.10000000000000000000000000000000"
878                          "00000000000000000000000000000001E0");
879      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
880      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
881      if (mpfr_cmp(x, x2))
882        STD_ERROR;
883      if (inexact1 != inexact2)
884        STD_ERROR2;
885
886      es = mpfr_get_emin ();
887      set_emin (-1024);
888
889      mpfr_set_str_binary (y,
890                          "0.10000000000000000000000000000000"
891                          "000000000000000000000000000000E-1023");
892      mpfr_set_str_binary (z,
893                          "0.10000000000000000000000000000000"
894                          "00000000000000000000000000000001E-1023");
895      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
896      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
897      if (mpfr_cmp(x, x2))
898        STD_ERROR;
899      if (inexact1 != inexact2)
900        STD_ERROR2;
901
902      mpfr_set_str_binary (y,
903                           "0.10000000000000000000000000000000"
904                           "000000000000000000000000000000E-1023");
905      mpfr_set_str_binary (z,
906                           "0.1000000000000000000000000000000"
907                           "000000000000000000000000000000E-1023");
908      inexact1 = mpfr_sub1(x2, y, z, (mpfr_rnd_t) r);
909      inexact2 = mpfr_sub1sp(x, y, z, (mpfr_rnd_t) r);
910      if (mpfr_cmp(x, x2))
911        STD_ERROR;
912      if (inexact1 != inexact2)
913        STD_ERROR2;
914
915      set_emin (es);
916    }
917
918  mpfr_clears (x, y, z, x2, (mpfr_ptr) 0);
919}
920
921static void
922check_underflow (mpfr_prec_t p)
923{
924  mpfr_t x, y, z;
925  int inexact;
926
927  mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
928
929  if (p >= 2) /* we need p >= 2 so that 3 is exact */
930    {
931      mpfr_set_ui_2exp (y, 4, mpfr_get_emin () - 2, MPFR_RNDN);
932      mpfr_set_ui_2exp (z, 3, mpfr_get_emin () - 2, MPFR_RNDN);
933      inexact = mpfr_sub (x, y, z, MPFR_RNDN);
934      if (inexact >= 0 || (mpfr_cmp_ui (x, 0) != 0))
935        {
936          printf ("4*2^(emin-2) - 3*2^(emin-2) with RNDN failed for p=%ld\n",
937                  (long) p);
938          printf ("Expected inexact < 0 with x=0\n");
939          printf ("Got inexact=%d with x=", inexact);
940          mpfr_dump (x);
941          exit (1);
942        }
943    }
944
945  if (p >= 3) /* we need p >= 3 so that 5 is exact */
946    {
947      mpfr_set_ui_2exp (y, 5, mpfr_get_emin () - 2, MPFR_RNDN);
948      mpfr_set_ui_2exp (z, 4, mpfr_get_emin () - 2, MPFR_RNDN);
949      inexact = mpfr_sub (x, y, z, MPFR_RNDN);
950      if (inexact >= 0 || (mpfr_cmp_ui (x, 0) != 0))
951        {
952          printf ("5*2^(emin-2) - 4*2^(emin-2) with RNDN failed for p=%ld\n",
953                  (long) p);
954          printf ("Expected inexact < 0 with x=0\n");
955          printf ("Got inexact=%d with x=", inexact);
956          mpfr_dump (x);
957          exit (1);
958        }
959    }
960
961  mpfr_clears (x, y, z, (mpfr_ptr) 0);
962}
963
964/* check corner cases of mpfr_sub1sp in case d = 1 and limb = MPFR_LIMB_HIGHBIT */
965static void
966check_corner (mpfr_prec_t p)
967{
968  mpfr_t x, y, z;
969  mpfr_exp_t e;
970  int inex, odd;
971
972  if (p < 4) /* ensures that the initial value of z is > 1 below */
973    return;
974
975  mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0);
976  mpfr_const_pi (y, MPFR_RNDN);
977  mpfr_set_ui (z, 2, MPFR_RNDN);
978  inex = mpfr_sub (z, y, z, MPFR_RNDN); /* z is near pi-2, thus y-z is near 2 */
979  MPFR_ASSERTN(inex == 0);
980  for (e = 0; e < p; e++)
981    {
982      /* add 2^(-e) to z */
983      mpfr_mul_2ui (z, z, e, MPFR_RNDN);
984      inex = mpfr_add_ui (z, z, 1, MPFR_RNDN);
985      MPFR_ASSERTN(inex == 0);
986      mpfr_div_2ui (z, z, e, MPFR_RNDN);
987
988      /* compute x = y - z which should be exact, near 2-2^(-e) */
989      inex = mpfr_sub (x, y, z, MPFR_RNDN);
990      MPFR_ASSERTN(inex == 0);
991      MPFR_ASSERTN(mpfr_get_exp (x) == 1);
992
993      /* restore initial z */
994      mpfr_mul_2ui (z, z, e, MPFR_RNDN);
995      inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN);
996      MPFR_ASSERTN(inex == 0);
997      mpfr_div_2ui (z, z, e, MPFR_RNDN);
998
999      /* subtract 2^(-e) to z */
1000      mpfr_mul_2ui (z, z, e, MPFR_RNDN);
1001      inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN);
1002      MPFR_ASSERTN(inex == 0);
1003      mpfr_div_2ui (z, z, e, MPFR_RNDN);
1004
1005      /* ensure last significant bit of z is 0 so that y-z is exact */
1006      odd = mpfr_min_prec (z) == p;
1007      if (odd) /* add one ulp to z */
1008        mpfr_nextabove (z);
1009
1010      /* compute x = y - z which should be exact, near 2+2^(-e) */
1011      inex = mpfr_sub (x, y, z, MPFR_RNDN);
1012      MPFR_ASSERTN(inex == 0);
1013      MPFR_ASSERTN(mpfr_get_exp (x) == 2);
1014
1015      /* restore initial z */
1016      if (odd)
1017        mpfr_nextbelow (z);
1018      mpfr_mul_2ui (z, z, e, MPFR_RNDN);
1019      inex = mpfr_add_ui (z, z, 1, MPFR_RNDN);
1020      MPFR_ASSERTN(inex == 0);
1021      mpfr_div_2ui (z, z, e, MPFR_RNDN);
1022    }
1023  mpfr_clears (x, y, z, (mpfr_ptr) 0);
1024}
1025