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1 272 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
#ifndef _DIV_MACROS_H_
25
#define _DIV_MACROS_H_
26
 
27
#include "bid_internal.h"
28
 
29
#define FENCE __fence
30
//#define FENCE 
31
 
32
//#define DOUBLE_EXTENDED_ON
33
 
34
#if DOUBLE_EXTENDED_ON
35
 
36
 
37
__BID_INLINE__ void
38
__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX, UINT128 CY) {
39
  UINT128 CB, CB2, CB4, CB8, CQB, CA;
40
  int_double d64, dm64, ds;
41
  int_float t64;
42
  double dx, dq, dqh;
43
  BINARY80 lq, lx, ly;
44
  UINT64 Rh, R, B2, B4, Ph, Ql, Ql2, carry, Qh;
45
 
46
  if (!CY.w[1]) {
47
    pCR->w[1] = 0;
48
 
49
    if (!CX.w[1]) {
50
      pCQ->w[0] = CX.w[0] / CY.w[0];
51
      pCQ->w[1] = 0;
52
      pCR->w[1] = 0;
53
      pCR->w[0] = CX.w[0] - pCQ->w[0] * CY.w[0];
54
    } else {
55
 
56
      // This path works for CX<2^116 only 
57
 
58
      // 2^64
59
      d64.i = 0x43f0000000000000;
60
      // 2^64
61
      dm64.i = 0x3bf0000000000000;
62
      // 1.5*2^(-52)
63
      ds.i = 0x3cb8000000000000;
64
      dx = (BINARY80) CX.w[1] * d64.d + (BINARY80) CX.w[0];
65
      dq = dx / (BINARY80) CY.w[0];
66
      dq -= dq * (ds.d);
67
      dqh = dq * dm64.d;
68
      Qh = (UINT64) dqh;
69
      Ql = (UINT64) (dq - ((double) Qh) * d64.d);
70
 
71
      Rh = CX.w[0] - Ql * CY.w[0];
72
      Ql2 = Rh / CY.w[0];
73
      pCR->w[0] = Rh - Ql2 * CY.w[0];
74
      __add_carry_out ((pCQ->w[0]), carry, Ql, Ql2);
75
      pCQ->w[1] = Qh + carry;
76
 
77
    }
78
    return;
79
  }
80
  // now CY.w[1] > 0
81
 
82
  // 2^64
83
  t64.i = 0x5f800000;
84
  lx = (BINARY80) CX.w[1] * (BINARY80) t64.d + (BINARY80) CX.w[0];
85
  ly = (BINARY80) CY.w[1] * (BINARY80) t64.d + (BINARY80) CY.w[0];
86
  lq = lx / ly;
87
  pCQ->w[0] = (UINT64) lq;
88
 
89
  pCQ->w[1] = 0;
90
 
91
  if (!pCQ->w[0]) {
92
    /*if(__unsigned_compare_ge_128(CX,CY))
93
       {
94
       pCQ->w[0] = 1;
95
       __sub_128_128((*pCR), CX, CY);
96
       }
97
       else */
98
    {
99
      pCR->w[1] = CX.w[1];
100
      pCR->w[0] = CX.w[0];
101
    }
102
    return;
103
  }
104
 
105
  if (CY.w[1] >= 16 || pCQ->w[0] <= 0x1000000000000000ull) {
106
    pCQ->w[0] = (UINT64) lq - 1;
107
    __mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY);
108
    __sub_128_128 (CA, CX, CQB);
109
    if (__unsigned_compare_ge_128 (CA, CY)) {
110
      __sub_128_128 (CA, CA, CY);
111
      pCQ->w[0]++;
112
      if (__unsigned_compare_ge_128 (CA, CY)) {
113
        __sub_128_128 (CA, CA, CY);
114
        pCQ->w[0]++;
115
      }
116
    }
117
    pCR->w[1] = CA.w[1];
118
    pCR->w[0] = CA.w[0];
119
  } else {
120
    pCQ->w[0] = (UINT64) lq - 6;
121
 
122
    __mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY);
123
    __sub_128_128 (CA, CX, CQB);
124
 
125
    CB8.w[1] = (CY.w[1] << 3) | (CY.w[0] >> 61);
126
    CB8.w[0] = CY.w[0] << 3;
127
    CB4.w[1] = (CY.w[1] << 2) | (CY.w[0] >> 62);
128
    CB4.w[0] = CY.w[0] << 2;
129
    CB2.w[1] = (CY.w[1] << 1) | (CY.w[0] >> 63);
130
    CB2.w[0] = CY.w[0] << 1;
131
 
132
    if (__unsigned_compare_ge_128 (CA, CB8)) {
133
      pCQ->w[0] += 8;
134
      __sub_128_128 (CA, CA, CB8);
135
    }
136
    if (__unsigned_compare_ge_128 (CA, CB4)) {
137
      pCQ->w[0] += 4;
138
      __sub_128_128 (CA, CA, CB4);
139
    }
140
    if (__unsigned_compare_ge_128 (CA, CB2)) {
141
      pCQ->w[0] += 2;
142
      __sub_128_128 (CA, CA, CB2);
143
    }
144
    if (__unsigned_compare_ge_128 (CA, CY)) {
145
      pCQ->w[0] += 1;
146
      __sub_128_128 (CA, CA, CY);
147
    }
148
 
149
    pCR->w[1] = CA.w[1];
150
    pCR->w[0] = CA.w[0];
151
  }
152
}
153
 
154
 
155
 
156
 
157
 
158
 
159
__BID_INLINE__ void
160
__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) {
161
  UINT256 CQ2Y;
162
  UINT128 CQ2, CQ3Y;
163
  UINT64 Q3, carry64;
164
  int_double d64;
165
  BINARY80 lx, ly, lq, l64, l128;
166
 
167
  // 2^64
168
  d64.i = 0x43f0000000000000ull;
169
  l64 = (BINARY80) d64.d;
170
  // 2^128
171
  l128 = l64 * l64;
172
 
173
  lx =
174
    ((BINARY80) (*pCA4).w[3] * l64 +
175
     (BINARY80) (*pCA4).w[2]) * l128 +
176
    (BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0];
177
  ly = (BINARY80) CY.w[1] * l128 + (BINARY80) CY.w[0] * l64;
178
 
179
  lq = lx / ly;
180
  CQ2.w[1] = (UINT64) lq;
181
  lq = (lq - CQ2.w[1]) * l64;
182
  CQ2.w[0] = (UINT64) lq;
183
 
184
  // CQ2*CY
185
  __mul_128x128_to_256 (CQ2Y, CY, CQ2);
186
 
187
  // CQ2Y <= (*pCA4) ?
188
  if (CQ2Y.w[3] < (*pCA4).w[3]
189
      || (CQ2Y.w[3] == (*pCA4).w[3]
190
          && (CQ2Y.w[2] < (*pCA4).w[2]
191
              || (CQ2Y.w[2] == (*pCA4).w[2]
192
                  && (CQ2Y.w[1] < (*pCA4).w[1]
193
                      || (CQ2Y.w[1] == (*pCA4).w[1]
194
                          && (CQ2Y.w[0] <= (*pCA4).w[0]))))))) {
195
 
196
    // (*pCA4) -CQ2Y, guaranteed below 5*2^49*CY < 5*2^(49+128)
197
    __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ2Y.w[0]);
198
    __sub_borrow_in_out ((*pCA4).w[1], carry64, (*pCA4).w[1], CQ2Y.w[1],
199
                         carry64);
200
    (*pCA4).w[2] = (*pCA4).w[2] - CQ2Y.w[2] - carry64;
201
 
202
    lx = ((BINARY80) (*pCA4).w[2] * l128 +
203
          ((BINARY80) (*pCA4).w[1] * l64 +
204
           (BINARY80) (*pCA4).w[0])) * l64;
205
    lq = lx / ly;
206
    Q3 = (UINT64) lq;
207
 
208
    if (Q3) {
209
      Q3--;
210
      __mul_64x128_short (CQ3Y, Q3, CY);
211
      __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ3Y.w[0]);
212
      (*pCA4).w[1] = (*pCA4).w[1] - CQ3Y.w[1] - carry64;
213
 
214
      if ((*pCA4).w[1] > CY.w[1]
215
          || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
216
        Q3++;
217
        __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
218
        (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
219
        if ((*pCA4).w[1] > CY.w[1]
220
            || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
221
          Q3++;
222
          __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0],
223
                            CY.w[0]);
224
          (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
225
        }
226
      }
227
      // add Q3 to Q2
228
      __add_carry_out (CQ2.w[0], carry64, Q3, CQ2.w[0]);
229
      CQ2.w[1] += carry64;
230
    }
231
  } else {
232
    // CQ2Y - (*pCA4), guaranteed below 5*2^(49+128)
233
    __sub_borrow_out ((*pCA4).w[0], carry64, CQ2Y.w[0], (*pCA4).w[0]);
234
    __sub_borrow_in_out ((*pCA4).w[1], carry64, CQ2Y.w[1], (*pCA4).w[1],
235
                         carry64);
236
    (*pCA4).w[2] = CQ2Y.w[2] - (*pCA4).w[2] - carry64;
237
 
238
    lx =
239
      ((BINARY80) (*pCA4).w[2] * l128 +
240
       (BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0]) * l64;
241
    lq = lx / ly;
242
    Q3 = 1 + (UINT64) lq;
243
 
244
    __mul_64x128_short (CQ3Y, Q3, CY);
245
    __sub_borrow_out ((*pCA4).w[0], carry64, CQ3Y.w[0], (*pCA4).w[0]);
246
    (*pCA4).w[1] = CQ3Y.w[1] - (*pCA4).w[1] - carry64;
247
 
248
    if ((SINT64) (*pCA4).w[1] > (SINT64) CY.w[1]
249
        || ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
250
      Q3--;
251
      __sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
252
      (*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
253
    } else if ((SINT64) (*pCA4).w[1] < 0) {
254
      Q3++;
255
      __add_carry_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
256
      (*pCA4).w[1] = (*pCA4).w[1] + CY.w[1] + carry64;
257
    }
258
    // subtract Q3 from Q2
259
    __sub_borrow_out (CQ2.w[0], carry64, CQ2.w[0], Q3);
260
    CQ2.w[1] -= carry64;
261
  }
262
 
263
  // (*pCQ) + CQ2 + carry
264
  __add_carry_out ((*pCQ).w[0], carry64, CQ2.w[0], (*pCQ).w[0]);
265
  (*pCQ).w[1] = (*pCQ).w[1] + CQ2.w[1] + carry64;
266
 
267
 
268
}
269
#else
270
 
271
__BID_INLINE__ void
272
__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX0, UINT128 CY) {
273
  UINT128 CY36, CY51, CQ, A2, CX, CQT;
274
  UINT64 Q;
275
  int_double t64, d49, d60;
276
  double lx, ly, lq;
277
 
278
  if (!CX0.w[1] && !CY.w[1]) {
279
    pCQ->w[0] = CX0.w[0] / CY.w[0];
280
    pCQ->w[1] = 0;
281
    pCR->w[1] = pCR->w[0] = 0;
282
    pCR->w[0] = CX0.w[0] - pCQ->w[0] * CY.w[0];
283
    return;
284
  }
285
 
286
  CX.w[1] = CX0.w[1];
287
  CX.w[0] = CX0.w[0];
288
 
289
  // 2^64
290
  t64.i = 0x43f0000000000000ull;
291
  lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
292
  ly = (double) CY.w[1] * t64.d + (double) CY.w[0];
293
  lq = lx / ly;
294
 
295
  CY36.w[1] = CY.w[0] >> (64 - 36);
296
  CY36.w[0] = CY.w[0] << 36;
297
 
298
  CQ.w[1] = CQ.w[0] = 0;
299
 
300
  // Q >= 2^100 ?
301
  if (!CY.w[1] && !CY36.w[1] && (CX.w[1] >= CY36.w[0])) {
302
    // then Q >= 2^100
303
 
304
    // 2^(-60)*CX/CY
305
    d60.i = 0x3c30000000000000ull;
306
    lq *= d60.d;
307
    Q = (UINT64) lq - 4ull;
308
 
309
    // Q*CY
310
    __mul_64x64_to_128 (A2, Q, CY.w[0]);
311
 
312
    // A2 <<= 60
313
    A2.w[1] = (A2.w[1] << 60) | (A2.w[0] >> (64 - 60));
314
    A2.w[0] <<= 60;
315
 
316
    __sub_128_128 (CX, CX, A2);
317
 
318
    lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
319
    lq = lx / ly;
320
 
321
    CQ.w[1] = Q >> (64 - 60);
322
    CQ.w[0] = Q << 60;
323
  }
324
 
325
 
326
  CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51));
327
  CY51.w[0] = CY.w[0] << 51;
328
 
329
  if (CY.w[1] < (UINT64) (1 << (64 - 51))
330
      && (__unsigned_compare_gt_128 (CX, CY51))) {
331
    // Q > 2^51 
332
 
333
    // 2^(-49)*CX/CY
334
    d49.i = 0x3ce0000000000000ull;
335
    lq *= d49.d;
336
 
337
    Q = (UINT64) lq - 1ull;
338
 
339
    // Q*CY
340
    __mul_64x64_to_128 (A2, Q, CY.w[0]);
341
    A2.w[1] += Q * CY.w[1];
342
 
343
    // A2 <<= 49
344
    A2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49));
345
    A2.w[0] <<= 49;
346
 
347
    __sub_128_128 (CX, CX, A2);
348
 
349
    CQT.w[1] = Q >> (64 - 49);
350
    CQT.w[0] = Q << 49;
351
    __add_128_128 (CQ, CQ, CQT);
352
 
353
    lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
354
    lq = lx / ly;
355
  }
356
 
357
  Q = (UINT64) lq;
358
 
359
  __mul_64x64_to_128 (A2, Q, CY.w[0]);
360
  A2.w[1] += Q * CY.w[1];
361
 
362
  __sub_128_128 (CX, CX, A2);
363
  if ((SINT64) CX.w[1] < 0) {
364
    Q--;
365
    CX.w[0] += CY.w[0];
366
    if (CX.w[0] < CY.w[0])
367
      CX.w[1]++;
368
    CX.w[1] += CY.w[1];
369
    if ((SINT64) CX.w[1] < 0) {
370
      Q--;
371
      CX.w[0] += CY.w[0];
372
      if (CX.w[0] < CY.w[0])
373
        CX.w[1]++;
374
      CX.w[1] += CY.w[1];
375
    }
376
  } else if (__unsigned_compare_ge_128 (CX, CY)) {
377
    Q++;
378
    __sub_128_128 (CX, CX, CY);
379
  }
380
 
381
  __add_128_64 (CQ, CQ, Q);
382
 
383
 
384
  pCQ->w[1] = CQ.w[1];
385
  pCQ->w[0] = CQ.w[0];
386
  pCR->w[1] = CX.w[1];
387
  pCR->w[0] = CX.w[0];
388
  return;
389
}
390
 
391
 
392
__BID_INLINE__ void
393
__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) {
394
  UINT256 CA4, CA2, CY51, CY36;
395
  UINT128 CQ, A2, A2h, CQT;
396
  UINT64 Q, carry64;
397
  int_double t64, d49, d60;
398
  double lx, ly, lq, d128, d192;
399
 
400
  // the quotient is assumed to be at most 113 bits, 
401
  // as needed by BID128 divide routines
402
 
403
  // initial dividend
404
  CA4.w[3] = (*pCA4).w[3];
405
  CA4.w[2] = (*pCA4).w[2];
406
  CA4.w[1] = (*pCA4).w[1];
407
  CA4.w[0] = (*pCA4).w[0];
408
  CQ.w[1] = (*pCQ).w[1];
409
  CQ.w[0] = (*pCQ).w[0];
410
 
411
  // 2^64
412
  t64.i = 0x43f0000000000000ull;
413
  d128 = t64.d * t64.d;
414
  d192 = d128 * t64.d;
415
  lx = (double) CA4.w[3] * d192 + ((double) CA4.w[2] * d128 +
416
                                   ((double) CA4.w[1] * t64.d +
417
                                    (double) CA4.w[0]));
418
  ly = (double) CY.w[1] * t64.d + (double) CY.w[0];
419
  lq = lx / ly;
420
 
421
  CY36.w[2] = CY.w[1] >> (64 - 36);
422
  CY36.w[1] = (CY.w[1] << 36) | (CY.w[0] >> (64 - 36));
423
  CY36.w[0] = CY.w[0] << 36;
424
 
425
  CQ.w[1] = (*pCQ).w[1];
426
  CQ.w[0] = (*pCQ).w[0];
427
 
428
  // Q >= 2^100 ?
429
  if (CA4.w[3] > CY36.w[2]
430
      || (CA4.w[3] == CY36.w[2]
431
          && (CA4.w[2] > CY36.w[1]
432
              || (CA4.w[2] == CY36.w[1] && CA4.w[1] >= CY36.w[0])))) {
433
    // 2^(-60)*CA4/CY
434
    d60.i = 0x3c30000000000000ull;
435
    lq *= d60.d;
436
    Q = (UINT64) lq - 4ull;
437
 
438
    // Q*CY
439
    __mul_64x128_to_192 (CA2, Q, CY);
440
 
441
    // CA2 <<= 60
442
    // CA2.w[3] = CA2.w[2] >> (64-60);
443
    CA2.w[2] = (CA2.w[2] << 60) | (CA2.w[1] >> (64 - 60));
444
    CA2.w[1] = (CA2.w[1] << 60) | (CA2.w[0] >> (64 - 60));
445
    CA2.w[0] <<= 60;
446
 
447
    // CA4 -= CA2
448
    __sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]);
449
    __sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1],
450
                         carry64);
451
    CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64;
452
 
453
    lx = ((double) CA4.w[2] * d128 +
454
          ((double) CA4.w[1] * t64.d + (double) CA4.w[0]));
455
    lq = lx / ly;
456
 
457
    CQT.w[1] = Q >> (64 - 60);
458
    CQT.w[0] = Q << 60;
459
    __add_128_128 (CQ, CQ, CQT);
460
  }
461
 
462
  CY51.w[2] = CY.w[1] >> (64 - 51);
463
  CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51));
464
  CY51.w[0] = CY.w[0] << 51;
465
 
466
  if (CA4.w[2] > CY51.w[2] || ((CA4.w[2] == CY51.w[2])
467
                               &&
468
                               (__unsigned_compare_gt_128 (CA4, CY51))))
469
  {
470
    // Q > 2^51 
471
 
472
    // 2^(-49)*CA4/CY
473
    d49.i = 0x3ce0000000000000ull;
474
    lq *= d49.d;
475
 
476
    Q = (UINT64) lq - 1ull;
477
 
478
    // Q*CY
479
    __mul_64x64_to_128 (A2, Q, CY.w[0]);
480
    __mul_64x64_to_128 (A2h, Q, CY.w[1]);
481
    A2.w[1] += A2h.w[0];
482
    if (A2.w[1] < A2h.w[0])
483
      A2h.w[1]++;
484
 
485
    // A2 <<= 49
486
    CA2.w[2] = (A2h.w[1] << 49) | (A2.w[1] >> (64 - 49));
487
    CA2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49));
488
    CA2.w[0] = A2.w[0] << 49;
489
 
490
    __sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]);
491
    __sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1],
492
                         carry64);
493
    CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64;
494
 
495
    CQT.w[1] = Q >> (64 - 49);
496
    CQT.w[0] = Q << 49;
497
    __add_128_128 (CQ, CQ, CQT);
498
 
499
    lx = ((double) CA4.w[2] * d128 +
500
          ((double) CA4.w[1] * t64.d + (double) CA4.w[0]));
501
    lq = lx / ly;
502
  }
503
 
504
  Q = (UINT64) lq;
505
  __mul_64x64_to_128 (A2, Q, CY.w[0]);
506
  A2.w[1] += Q * CY.w[1];
507
 
508
  __sub_128_128 (CA4, CA4, A2);
509
  if ((SINT64) CA4.w[1] < 0) {
510
    Q--;
511
    CA4.w[0] += CY.w[0];
512
    if (CA4.w[0] < CY.w[0])
513
      CA4.w[1]++;
514
    CA4.w[1] += CY.w[1];
515
    if ((SINT64) CA4.w[1] < 0) {
516
      Q--;
517
      CA4.w[0] += CY.w[0];
518
      if (CA4.w[0] < CY.w[0])
519
        CA4.w[1]++;
520
      CA4.w[1] += CY.w[1];
521
    }
522
  } else if (__unsigned_compare_ge_128 (CA4, CY)) {
523
    Q++;
524
    __sub_128_128 (CA4, CA4, CY);
525
  }
526
 
527
  __add_128_64 (CQ, CQ, Q);
528
 
529
  pCQ->w[1] = CQ.w[1];
530
  pCQ->w[0] = CQ.w[0];
531
  pCA4->w[1] = CA4.w[1];
532
  pCA4->w[0] = CA4.w[0];
533
  return;
534
 
535
 
536
 
537
}
538
 
539
#endif
540
#endif

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