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1 734 jeremybenn
/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
2
 
3
This file is part of GCC.
4
 
5
GCC is free software; you can redistribute it and/or modify it under
6
the terms of the GNU General Public License as published by the Free
7
Software Foundation; either version 3, or (at your option) any later
8
version.
9
 
10
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
11
WARRANTY; without even the implied warranty of MERCHANTABILITY or
12
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
13
for more details.
14
 
15
Under Section 7 of GPL version 3, you are granted additional
16
permissions described in the GCC Runtime Library Exception, version
17
3.1, as published by the Free Software Foundation.
18
 
19
You should have received a copy of the GNU General Public License and
20
a copy of the GCC Runtime Library Exception along with this program;
21
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
22
<http://www.gnu.org/licenses/>.  */
23
 
24
#define BID_128RES
25
#include "bid_internal.h"
26
#include "bid_sqrt_macros.h"
27
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
28
#include <fenv.h>
29
 
30
#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
31
#endif
32
 
33
BID128_FUNCTION_ARG1 (bid128_sqrt, x)
34
 
35
     UINT256 M256, C256, C4, C8;
36
     UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
37
     UINT64 sign_x, Carry;
38
     SINT64 D;
39
     int_float fx, f64;
40
     int exponent_x, bin_expon_cx;
41
     int digits, scale, exponent_q;
42
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
43
     fexcept_t binaryflags = 0;
44
#endif
45
 
46
  // unpack arguments, check for NaN or Infinity
47
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
48
res.w[1] = CX.w[1];
49
res.w[0] = CX.w[0];
50
    // NaN ?
51
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
52
#ifdef SET_STATUS_FLAGS
53
  if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull)        // sNaN
54
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
55
#endif
56
  res.w[1] = CX.w[1] & QUIET_MASK64;
57
  BID_RETURN (res);
58
}
59
    // x is Infinity?
60
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
61
  res.w[1] = CX.w[1];
62
  if (sign_x) {
63
    // -Inf, return NaN
64
    res.w[1] = 0x7c00000000000000ull;
65
#ifdef SET_STATUS_FLAGS
66
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
67
#endif
68
  }
69
  BID_RETURN (res);
70
}
71
    // x is 0 otherwise
72
 
73
res.w[1] =
74
  sign_x |
75
  ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) << 49);
76
res.w[0] = 0;
77
BID_RETURN (res);
78
}
79
if (sign_x) {
80
  res.w[1] = 0x7c00000000000000ull;
81
  res.w[0] = 0;
82
#ifdef SET_STATUS_FLAGS
83
  __set_status_flags (pfpsf, INVALID_EXCEPTION);
84
#endif
85
  BID_RETURN (res);
86
}
87
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
88
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
89
#endif
90
  // 2^64
91
f64.i = 0x5f800000;
92
 
93
  // fx ~ CX
94
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
95
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
96
digits = estimate_decimal_digits[bin_expon_cx];
97
 
98
A10 = CX;
99
if (exponent_x & 1) {
100
  A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
101
  A10.w[0] = CX.w[0] << 3;
102
  CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
103
  CX2.w[0] = CX.w[0] << 1;
104
  __add_128_128 (A10, A10, CX2);
105
}
106
 
107
CS.w[0] = short_sqrt128 (A10);
108
CS.w[1] = 0;
109
  // check for exact result
110
if (CS.w[0] * CS.w[0] == A10.w[0]) {
111
  __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
112
  if (S2.w[1] == A10.w[1])      // && S2.w[0]==A10.w[0])
113
  {
114
    get_BID128_very_fast (&res, 0,
115
                          (exponent_x +
116
                           DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
117
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
118
    (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
119
#endif
120
    BID_RETURN (res);
121
  }
122
}
123
  // get number of digits in CX
124
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
125
if (D > 0
126
    || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
127
  digits++;
128
 
129
  // if exponent is odd, scale coefficient by 10
130
scale = 67 - digits;
131
exponent_q = exponent_x - scale;
132
scale += (exponent_q & 1);      // exp. bias is even
133
 
134
if (scale > 38) {
135
  T128 = power10_table_128[scale - 37];
136
  __mul_128x128_low (CX1, CX, T128);
137
 
138
  TP128 = power10_table_128[37];
139
  __mul_128x128_to_256 (C256, CX1, TP128);
140
} else {
141
  T128 = power10_table_128[scale];
142
  __mul_128x128_to_256 (C256, CX, T128);
143
}
144
 
145
 
146
  // 4*C256
147
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
148
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
149
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
150
C4.w[0] = C256.w[0] << 2;
151
 
152
long_sqrt128 (&CS, C256);
153
 
154
#ifndef IEEE_ROUND_NEAREST
155
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
156
if (!((rnd_mode) & 3)) {
157
#endif
158
#endif
159
  // compare to midpoints
160
  CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
161
  CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
162
  // CSM^2
163
  //__mul_128x128_to_256(M256, CSM, CSM);
164
  __sqr128_to_256 (M256, CSM);
165
 
166
  if (C4.w[3] > M256.w[3]
167
      || (C4.w[3] == M256.w[3]
168
          && (C4.w[2] > M256.w[2]
169
              || (C4.w[2] == M256.w[2]
170
                  && (C4.w[1] > M256.w[1]
171
                      || (C4.w[1] == M256.w[1]
172
                          && C4.w[0] > M256.w[0])))))) {
173
    // round up
174
    CS.w[0]++;
175
    if (!CS.w[0])
176
      CS.w[1]++;
177
  } else {
178
    C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
179
    C8.w[0] = CS.w[0] << 3;
180
    // M256 - 8*CSM
181
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
182
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
183
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
184
    M256.w[3] = M256.w[3] - Carry;
185
 
186
    // if CSM' > C256, round up
187
    if (M256.w[3] > C4.w[3]
188
        || (M256.w[3] == C4.w[3]
189
            && (M256.w[2] > C4.w[2]
190
                || (M256.w[2] == C4.w[2]
191
                    && (M256.w[1] > C4.w[1]
192
                        || (M256.w[1] == C4.w[1]
193
                            && M256.w[0] > C4.w[0])))))) {
194
      // round down
195
      if (!CS.w[0])
196
        CS.w[1]--;
197
      CS.w[0]--;
198
    }
199
  }
200
#ifndef IEEE_ROUND_NEAREST
201
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
202
} else {
203
  __sqr128_to_256 (M256, CS);
204
  C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
205
  C8.w[0] = CS.w[0] << 1;
206
  if (M256.w[3] > C256.w[3]
207
      || (M256.w[3] == C256.w[3]
208
          && (M256.w[2] > C256.w[2]
209
              || (M256.w[2] == C256.w[2]
210
                  && (M256.w[1] > C256.w[1]
211
                      || (M256.w[1] == C256.w[1]
212
                          && M256.w[0] > C256.w[0])))))) {
213
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
214
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
215
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
216
    M256.w[3] = M256.w[3] - Carry;
217
    M256.w[0]++;
218
    if (!M256.w[0]) {
219
      M256.w[1]++;
220
      if (!M256.w[1]) {
221
        M256.w[2]++;
222
        if (!M256.w[2])
223
          M256.w[3]++;
224
      }
225
    }
226
 
227
    if (!CS.w[0])
228
      CS.w[1]--;
229
    CS.w[0]--;
230
 
231
    if (M256.w[3] > C256.w[3]
232
        || (M256.w[3] == C256.w[3]
233
            && (M256.w[2] > C256.w[2]
234
                || (M256.w[2] == C256.w[2]
235
                    && (M256.w[1] > C256.w[1]
236
                        || (M256.w[1] == C256.w[1]
237
                            && M256.w[0] > C256.w[0])))))) {
238
 
239
      if (!CS.w[0])
240
        CS.w[1]--;
241
      CS.w[0]--;
242
    }
243
  }
244
 
245
  else {
246
    __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
247
    __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
248
    __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
249
    M256.w[3] = M256.w[3] + Carry;
250
    M256.w[0]++;
251
    if (!M256.w[0]) {
252
      M256.w[1]++;
253
      if (!M256.w[1]) {
254
        M256.w[2]++;
255
        if (!M256.w[2])
256
          M256.w[3]++;
257
      }
258
    }
259
    if (M256.w[3] < C256.w[3]
260
        || (M256.w[3] == C256.w[3]
261
            && (M256.w[2] < C256.w[2]
262
                || (M256.w[2] == C256.w[2]
263
                    && (M256.w[1] < C256.w[1]
264
                        || (M256.w[1] == C256.w[1]
265
                            && M256.w[0] <= C256.w[0])))))) {
266
 
267
      CS.w[0]++;
268
      if (!CS.w[0])
269
        CS.w[1]++;
270
    }
271
  }
272
  // RU?
273
  if ((rnd_mode) == ROUNDING_UP) {
274
    CS.w[0]++;
275
    if (!CS.w[0])
276
      CS.w[1]++;
277
  }
278
 
279
}
280
#endif
281
#endif
282
 
283
#ifdef SET_STATUS_FLAGS
284
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
285
#endif
286
get_BID128_fast (&res, 0,
287
                 (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
288
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
289
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
290
#endif
291
BID_RETURN (res);
292
}
293
 
294
 
295
 
296
BID128_FUNCTION_ARGTYPE1 (bid128d_sqrt, UINT64, x)
297
 
298
     UINT256 M256, C256, C4, C8;
299
     UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
300
     UINT64 sign_x, Carry;
301
     SINT64 D;
302
     int_float fx, f64;
303
     int exponent_x, bin_expon_cx;
304
     int digits, scale, exponent_q;
305
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
306
     fexcept_t binaryflags = 0;
307
#endif
308
 
309
        // unpack arguments, check for NaN or Infinity
310
   // unpack arguments, check for NaN or Infinity
311
CX.w[1] = 0;
312
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) {
313
res.w[1] = CX.w[0];
314
res.w[0] = 0;
315
           // NaN ?
316
if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
317
#ifdef SET_STATUS_FLAGS
318
  if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
319
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
320
#endif
321
  res.w[0] = (CX.w[0] & 0x0003ffffffffffffull);
322
  __mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
323
  res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull);
324
  BID_RETURN (res);
325
}
326
           // x is Infinity?
327
if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
328
  if (sign_x) {
329
    // -Inf, return NaN
330
    res.w[1] = 0x7c00000000000000ull;
331
#ifdef SET_STATUS_FLAGS
332
    __set_status_flags (pfpsf, INVALID_EXCEPTION);
333
#endif
334
  }
335
  BID_RETURN (res);
336
}
337
           // x is 0 otherwise
338
 
339
exponent_x =
340
  exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
341
res.w[1] =
342
  sign_x | ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1)
343
            << 49);
344
res.w[0] = 0;
345
BID_RETURN (res);
346
}
347
if (sign_x) {
348
  res.w[1] = 0x7c00000000000000ull;
349
  res.w[0] = 0;
350
#ifdef SET_STATUS_FLAGS
351
  __set_status_flags (pfpsf, INVALID_EXCEPTION);
352
#endif
353
  BID_RETURN (res);
354
}
355
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
356
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
357
#endif
358
exponent_x =
359
  exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
360
 
361
           // 2^64
362
f64.i = 0x5f800000;
363
 
364
           // fx ~ CX
365
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
366
bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
367
digits = estimate_decimal_digits[bin_expon_cx];
368
 
369
A10 = CX;
370
if (exponent_x & 1) {
371
  A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
372
  A10.w[0] = CX.w[0] << 3;
373
  CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
374
  CX2.w[0] = CX.w[0] << 1;
375
  __add_128_128 (A10, A10, CX2);
376
}
377
 
378
CS.w[0] = short_sqrt128 (A10);
379
CS.w[1] = 0;
380
           // check for exact result
381
if (CS.w[0] * CS.w[0] == A10.w[0]) {
382
  __mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
383
  if (S2.w[1] == A10.w[1]) {
384
    get_BID128_very_fast (&res, 0,
385
                          (exponent_x + DECIMAL_EXPONENT_BIAS_128) >> 1,
386
                          CS);
387
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
388
    (void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
389
#endif
390
    BID_RETURN (res);
391
  }
392
}
393
           // get number of digits in CX
394
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
395
if (D > 0
396
    || (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
397
  digits++;
398
 
399
                // if exponent is odd, scale coefficient by 10
400
scale = 67 - digits;
401
exponent_q = exponent_x - scale;
402
scale += (exponent_q & 1);      // exp. bias is even
403
 
404
if (scale > 38) {
405
  T128 = power10_table_128[scale - 37];
406
  __mul_128x128_low (CX1, CX, T128);
407
 
408
  TP128 = power10_table_128[37];
409
  __mul_128x128_to_256 (C256, CX1, TP128);
410
} else {
411
  T128 = power10_table_128[scale];
412
  __mul_128x128_to_256 (C256, CX, T128);
413
}
414
 
415
 
416
           // 4*C256
417
C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
418
C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
419
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
420
C4.w[0] = C256.w[0] << 2;
421
 
422
long_sqrt128 (&CS, C256);
423
 
424
#ifndef IEEE_ROUND_NEAREST
425
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
426
if (!((rnd_mode) & 3)) {
427
#endif
428
#endif
429
  // compare to midpoints
430
  CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
431
  CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
432
  // CSM^2
433
  //__mul_128x128_to_256(M256, CSM, CSM);
434
  __sqr128_to_256 (M256, CSM);
435
 
436
  if (C4.w[3] > M256.w[3]
437
      || (C4.w[3] == M256.w[3]
438
          && (C4.w[2] > M256.w[2]
439
              || (C4.w[2] == M256.w[2]
440
                  && (C4.w[1] > M256.w[1]
441
                      || (C4.w[1] == M256.w[1]
442
                          && C4.w[0] > M256.w[0])))))) {
443
    // round up
444
    CS.w[0]++;
445
    if (!CS.w[0])
446
      CS.w[1]++;
447
  } else {
448
    C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
449
    C8.w[0] = CS.w[0] << 3;
450
    // M256 - 8*CSM
451
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
452
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
453
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
454
    M256.w[3] = M256.w[3] - Carry;
455
 
456
    // if CSM' > C256, round up
457
    if (M256.w[3] > C4.w[3]
458
        || (M256.w[3] == C4.w[3]
459
            && (M256.w[2] > C4.w[2]
460
                || (M256.w[2] == C4.w[2]
461
                    && (M256.w[1] > C4.w[1]
462
                        || (M256.w[1] == C4.w[1]
463
                            && M256.w[0] > C4.w[0])))))) {
464
      // round down
465
      if (!CS.w[0])
466
        CS.w[1]--;
467
      CS.w[0]--;
468
    }
469
  }
470
#ifndef IEEE_ROUND_NEAREST
471
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
472
} else {
473
  __sqr128_to_256 (M256, CS);
474
  C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
475
  C8.w[0] = CS.w[0] << 1;
476
  if (M256.w[3] > C256.w[3]
477
      || (M256.w[3] == C256.w[3]
478
          && (M256.w[2] > C256.w[2]
479
              || (M256.w[2] == C256.w[2]
480
                  && (M256.w[1] > C256.w[1]
481
                      || (M256.w[1] == C256.w[1]
482
                          && M256.w[0] > C256.w[0])))))) {
483
    __sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
484
    __sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
485
    __sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
486
    M256.w[3] = M256.w[3] - Carry;
487
    M256.w[0]++;
488
    if (!M256.w[0]) {
489
      M256.w[1]++;
490
      if (!M256.w[1]) {
491
        M256.w[2]++;
492
        if (!M256.w[2])
493
          M256.w[3]++;
494
      }
495
    }
496
 
497
    if (!CS.w[0])
498
      CS.w[1]--;
499
    CS.w[0]--;
500
 
501
    if (M256.w[3] > C256.w[3]
502
        || (M256.w[3] == C256.w[3]
503
            && (M256.w[2] > C256.w[2]
504
                || (M256.w[2] == C256.w[2]
505
                    && (M256.w[1] > C256.w[1]
506
                        || (M256.w[1] == C256.w[1]
507
                            && M256.w[0] > C256.w[0])))))) {
508
 
509
      if (!CS.w[0])
510
        CS.w[1]--;
511
      CS.w[0]--;
512
    }
513
  }
514
 
515
  else {
516
    __add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
517
    __add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
518
    __add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
519
    M256.w[3] = M256.w[3] + Carry;
520
    M256.w[0]++;
521
    if (!M256.w[0]) {
522
      M256.w[1]++;
523
      if (!M256.w[1]) {
524
        M256.w[2]++;
525
        if (!M256.w[2])
526
          M256.w[3]++;
527
      }
528
    }
529
    if (M256.w[3] < C256.w[3]
530
        || (M256.w[3] == C256.w[3]
531
            && (M256.w[2] < C256.w[2]
532
                || (M256.w[2] == C256.w[2]
533
                    && (M256.w[1] < C256.w[1]
534
                        || (M256.w[1] == C256.w[1]
535
                            && M256.w[0] <= C256.w[0])))))) {
536
 
537
      CS.w[0]++;
538
      if (!CS.w[0])
539
        CS.w[1]++;
540
    }
541
  }
542
  // RU?
543
  if ((rnd_mode) == ROUNDING_UP) {
544
    CS.w[0]++;
545
    if (!CS.w[0])
546
      CS.w[1]++;
547
  }
548
 
549
}
550
#endif
551
#endif
552
 
553
#ifdef SET_STATUS_FLAGS
554
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
555
#endif
556
get_BID128_fast (&res, 0, (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1,
557
                 CS);
558
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
559
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
560
#endif
561
BID_RETURN (res);
562
 
563
 
564
}

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