xref: /openbmc/qemu/util/host-utils.c (revision a976a99a)
1  /*
2   * Utility compute operations used by translated code.
3   *
4   * Copyright (c) 2003 Fabrice Bellard
5   * Copyright (c) 2007 Aurelien Jarno
6   *
7   * Permission is hereby granted, free of charge, to any person obtaining a copy
8   * of this software and associated documentation files (the "Software"), to deal
9   * in the Software without restriction, including without limitation the rights
10   * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
11   * copies of the Software, and to permit persons to whom the Software is
12   * furnished to do so, subject to the following conditions:
13   *
14   * The above copyright notice and this permission notice shall be included in
15   * all copies or substantial portions of the Software.
16   *
17   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
18   * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
20   * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
21   * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
22   * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
23   * THE SOFTWARE.
24   */
25  
26  #include "qemu/osdep.h"
27  #include "qemu/host-utils.h"
28  
29  #ifndef CONFIG_INT128
30  /* Long integer helpers */
31  static inline void mul64(uint64_t *plow, uint64_t *phigh,
32                           uint64_t a, uint64_t b)
33  {
34      typedef union {
35          uint64_t ll;
36          struct {
37  #if HOST_BIG_ENDIAN
38              uint32_t high, low;
39  #else
40              uint32_t low, high;
41  #endif
42          } l;
43      } LL;
44      LL rl, rm, rn, rh, a0, b0;
45      uint64_t c;
46  
47      a0.ll = a;
48      b0.ll = b;
49  
50      rl.ll = (uint64_t)a0.l.low * b0.l.low;
51      rm.ll = (uint64_t)a0.l.low * b0.l.high;
52      rn.ll = (uint64_t)a0.l.high * b0.l.low;
53      rh.ll = (uint64_t)a0.l.high * b0.l.high;
54  
55      c = (uint64_t)rl.l.high + rm.l.low + rn.l.low;
56      rl.l.high = c;
57      c >>= 32;
58      c = c + rm.l.high + rn.l.high + rh.l.low;
59      rh.l.low = c;
60      rh.l.high += (uint32_t)(c >> 32);
61  
62      *plow = rl.ll;
63      *phigh = rh.ll;
64  }
65  
66  /* Unsigned 64x64 -> 128 multiplication */
67  void mulu64 (uint64_t *plow, uint64_t *phigh, uint64_t a, uint64_t b)
68  {
69      mul64(plow, phigh, a, b);
70  }
71  
72  /* Signed 64x64 -> 128 multiplication */
73  void muls64 (uint64_t *plow, uint64_t *phigh, int64_t a, int64_t b)
74  {
75      uint64_t rh;
76  
77      mul64(plow, &rh, a, b);
78  
79      /* Adjust for signs.  */
80      if (b < 0) {
81          rh -= a;
82      }
83      if (a < 0) {
84          rh -= b;
85      }
86      *phigh = rh;
87  }
88  
89  /*
90   * Unsigned 128-by-64 division.
91   * Returns the remainder.
92   * Returns quotient via plow and phigh.
93   * Also returns the remainder via the function return value.
94   */
95  uint64_t divu128(uint64_t *plow, uint64_t *phigh, uint64_t divisor)
96  {
97      uint64_t dhi = *phigh;
98      uint64_t dlo = *plow;
99      uint64_t rem, dhighest;
100      int sh;
101  
102      if (divisor == 0 || dhi == 0) {
103          *plow  = dlo / divisor;
104          *phigh = 0;
105          return dlo % divisor;
106      } else {
107          sh = clz64(divisor);
108  
109          if (dhi < divisor) {
110              if (sh != 0) {
111                  /* normalize the divisor, shifting the dividend accordingly */
112                  divisor <<= sh;
113                  dhi = (dhi << sh) | (dlo >> (64 - sh));
114                  dlo <<= sh;
115              }
116  
117              *phigh = 0;
118              *plow = udiv_qrnnd(&rem, dhi, dlo, divisor);
119          } else {
120              if (sh != 0) {
121                  /* normalize the divisor, shifting the dividend accordingly */
122                  divisor <<= sh;
123                  dhighest = dhi >> (64 - sh);
124                  dhi = (dhi << sh) | (dlo >> (64 - sh));
125                  dlo <<= sh;
126  
127                  *phigh = udiv_qrnnd(&dhi, dhighest, dhi, divisor);
128              } else {
129                  /**
130                   * dhi >= divisor
131                   * Since the MSB of divisor is set (sh == 0),
132                   * (dhi - divisor) < divisor
133                   *
134                   * Thus, the high part of the quotient is 1, and we can
135                   * calculate the low part with a single call to udiv_qrnnd
136                   * after subtracting divisor from dhi
137                   */
138                  dhi -= divisor;
139                  *phigh = 1;
140              }
141  
142              *plow = udiv_qrnnd(&rem, dhi, dlo, divisor);
143          }
144  
145          /*
146           * since the dividend/divisor might have been normalized,
147           * the remainder might also have to be shifted back
148           */
149          return rem >> sh;
150      }
151  }
152  
153  /*
154   * Signed 128-by-64 division.
155   * Returns quotient via plow and phigh.
156   * Also returns the remainder via the function return value.
157   */
158  int64_t divs128(uint64_t *plow, int64_t *phigh, int64_t divisor)
159  {
160      bool neg_quotient = false, neg_remainder = false;
161      uint64_t unsig_hi = *phigh, unsig_lo = *plow;
162      uint64_t rem;
163  
164      if (*phigh < 0) {
165          neg_quotient = !neg_quotient;
166          neg_remainder = !neg_remainder;
167  
168          if (unsig_lo == 0) {
169              unsig_hi = -unsig_hi;
170          } else {
171              unsig_hi = ~unsig_hi;
172              unsig_lo = -unsig_lo;
173          }
174      }
175  
176      if (divisor < 0) {
177          neg_quotient = !neg_quotient;
178  
179          divisor = -divisor;
180      }
181  
182      rem = divu128(&unsig_lo, &unsig_hi, (uint64_t)divisor);
183  
184      if (neg_quotient) {
185          if (unsig_lo == 0) {
186              *phigh = -unsig_hi;
187              *plow = 0;
188          } else {
189              *phigh = ~unsig_hi;
190              *plow = -unsig_lo;
191          }
192      } else {
193          *phigh = unsig_hi;
194          *plow = unsig_lo;
195      }
196  
197      if (neg_remainder) {
198          return -rem;
199      } else {
200          return rem;
201      }
202  }
203  #endif
204  
205  /**
206   * urshift - 128-bit Unsigned Right Shift.
207   * @plow: in/out - lower 64-bit integer.
208   * @phigh: in/out - higher 64-bit integer.
209   * @shift: in - bytes to shift, between 0 and 127.
210   *
211   * Result is zero-extended and stored in plow/phigh, which are
212   * input/output variables. Shift values outside the range will
213   * be mod to 128. In other words, the caller is responsible to
214   * verify/assert both the shift range and plow/phigh pointers.
215   */
216  void urshift(uint64_t *plow, uint64_t *phigh, int32_t shift)
217  {
218      shift &= 127;
219      if (shift == 0) {
220          return;
221      }
222  
223      uint64_t h = *phigh >> (shift & 63);
224      if (shift >= 64) {
225          *plow = h;
226          *phigh = 0;
227      } else {
228          *plow = (*plow >> (shift & 63)) | (*phigh << (64 - (shift & 63)));
229          *phigh = h;
230      }
231  }
232  
233  /**
234   * ulshift - 128-bit Unsigned Left Shift.
235   * @plow: in/out - lower 64-bit integer.
236   * @phigh: in/out - higher 64-bit integer.
237   * @shift: in - bytes to shift, between 0 and 127.
238   * @overflow: out - true if any 1-bit is shifted out.
239   *
240   * Result is zero-extended and stored in plow/phigh, which are
241   * input/output variables. Shift values outside the range will
242   * be mod to 128. In other words, the caller is responsible to
243   * verify/assert both the shift range and plow/phigh pointers.
244   */
245  void ulshift(uint64_t *plow, uint64_t *phigh, int32_t shift, bool *overflow)
246  {
247      uint64_t low = *plow;
248      uint64_t high = *phigh;
249  
250      shift &= 127;
251      if (shift == 0) {
252          return;
253      }
254  
255      /* check if any bit will be shifted out */
256      urshift(&low, &high, 128 - shift);
257      if (low | high) {
258          *overflow = true;
259      }
260  
261      if (shift >= 64) {
262          *phigh = *plow << (shift & 63);
263          *plow = 0;
264      } else {
265          *phigh = (*plow >> (64 - (shift & 63))) | (*phigh << (shift & 63));
266          *plow = *plow << shift;
267      }
268  }
269  
270  /*
271   * Unsigned 256-by-128 division.
272   * Returns the remainder via r.
273   * Returns lower 128 bit of quotient.
274   * Needs a normalized divisor (most significant bit set to 1).
275   *
276   * Adapted from include/qemu/host-utils.h udiv_qrnnd,
277   * from the GNU Multi Precision Library - longlong.h __udiv_qrnnd
278   * (https://gmplib.org/repo/gmp/file/tip/longlong.h)
279   *
280   * Licensed under the GPLv2/LGPLv3
281   */
282  static Int128 udiv256_qrnnd(Int128 *r, Int128 n1, Int128 n0, Int128 d)
283  {
284      Int128 d0, d1, q0, q1, r1, r0, m;
285      uint64_t mp0, mp1;
286  
287      d0 = int128_make64(int128_getlo(d));
288      d1 = int128_make64(int128_gethi(d));
289  
290      r1 = int128_remu(n1, d1);
291      q1 = int128_divu(n1, d1);
292      mp0 = int128_getlo(q1);
293      mp1 = int128_gethi(q1);
294      mulu128(&mp0, &mp1, int128_getlo(d0));
295      m = int128_make128(mp0, mp1);
296      r1 = int128_make128(int128_gethi(n0), int128_getlo(r1));
297      if (int128_ult(r1, m)) {
298          q1 = int128_sub(q1, int128_one());
299          r1 = int128_add(r1, d);
300          if (int128_uge(r1, d)) {
301              if (int128_ult(r1, m)) {
302                  q1 = int128_sub(q1, int128_one());
303                  r1 = int128_add(r1, d);
304              }
305          }
306      }
307      r1 = int128_sub(r1, m);
308  
309      r0 = int128_remu(r1, d1);
310      q0 = int128_divu(r1, d1);
311      mp0 = int128_getlo(q0);
312      mp1 = int128_gethi(q0);
313      mulu128(&mp0, &mp1, int128_getlo(d0));
314      m = int128_make128(mp0, mp1);
315      r0 = int128_make128(int128_getlo(n0), int128_getlo(r0));
316      if (int128_ult(r0, m)) {
317          q0 = int128_sub(q0, int128_one());
318          r0 = int128_add(r0, d);
319          if (int128_uge(r0, d)) {
320              if (int128_ult(r0, m)) {
321                  q0 = int128_sub(q0, int128_one());
322                  r0 = int128_add(r0, d);
323              }
324          }
325      }
326      r0 = int128_sub(r0, m);
327  
328      *r = r0;
329      return int128_or(int128_lshift(q1, 64), q0);
330  }
331  
332  /*
333   * Unsigned 256-by-128 division.
334   * Returns the remainder.
335   * Returns quotient via plow and phigh.
336   * Also returns the remainder via the function return value.
337   */
338  Int128 divu256(Int128 *plow, Int128 *phigh, Int128 divisor)
339  {
340      Int128 dhi = *phigh;
341      Int128 dlo = *plow;
342      Int128 rem, dhighest;
343      int sh;
344  
345      if (!int128_nz(divisor) || !int128_nz(dhi)) {
346          *plow  = int128_divu(dlo, divisor);
347          *phigh = int128_zero();
348          return int128_remu(dlo, divisor);
349      } else {
350          sh = clz128(divisor);
351  
352          if (int128_ult(dhi, divisor)) {
353              if (sh != 0) {
354                  /* normalize the divisor, shifting the dividend accordingly */
355                  divisor = int128_lshift(divisor, sh);
356                  dhi = int128_or(int128_lshift(dhi, sh),
357                                  int128_urshift(dlo, (128 - sh)));
358                  dlo = int128_lshift(dlo, sh);
359              }
360  
361              *phigh = int128_zero();
362              *plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
363          } else {
364              if (sh != 0) {
365                  /* normalize the divisor, shifting the dividend accordingly */
366                  divisor = int128_lshift(divisor, sh);
367                  dhighest = int128_rshift(dhi, (128 - sh));
368                  dhi = int128_or(int128_lshift(dhi, sh),
369                                  int128_urshift(dlo, (128 - sh)));
370                  dlo = int128_lshift(dlo, sh);
371  
372                  *phigh = udiv256_qrnnd(&dhi, dhighest, dhi, divisor);
373              } else {
374                  /*
375                   * dhi >= divisor
376                   * Since the MSB of divisor is set (sh == 0),
377                   * (dhi - divisor) < divisor
378                   *
379                   * Thus, the high part of the quotient is 1, and we can
380                   * calculate the low part with a single call to udiv_qrnnd
381                   * after subtracting divisor from dhi
382                   */
383                  dhi = int128_sub(dhi, divisor);
384                  *phigh = int128_one();
385              }
386  
387              *plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
388          }
389  
390          /*
391           * since the dividend/divisor might have been normalized,
392           * the remainder might also have to be shifted back
393           */
394          rem = int128_urshift(rem, sh);
395          return rem;
396      }
397  }
398  
399  /*
400   * Signed 256-by-128 division.
401   * Returns quotient via plow and phigh.
402   * Also returns the remainder via the function return value.
403   */
404  Int128 divs256(Int128 *plow, Int128 *phigh, Int128 divisor)
405  {
406      bool neg_quotient = false, neg_remainder = false;
407      Int128 unsig_hi = *phigh, unsig_lo = *plow;
408      Int128 rem;
409  
410      if (!int128_nonneg(*phigh)) {
411          neg_quotient = !neg_quotient;
412          neg_remainder = !neg_remainder;
413  
414          if (!int128_nz(unsig_lo)) {
415              unsig_hi = int128_neg(unsig_hi);
416          } else {
417              unsig_hi = int128_not(unsig_hi);
418              unsig_lo = int128_neg(unsig_lo);
419          }
420      }
421  
422      if (!int128_nonneg(divisor)) {
423          neg_quotient = !neg_quotient;
424  
425          divisor = int128_neg(divisor);
426      }
427  
428      rem = divu256(&unsig_lo, &unsig_hi, divisor);
429  
430      if (neg_quotient) {
431          if (!int128_nz(unsig_lo)) {
432              *phigh = int128_neg(unsig_hi);
433              *plow = int128_zero();
434          } else {
435              *phigh = int128_not(unsig_hi);
436              *plow = int128_neg(unsig_lo);
437          }
438      } else {
439          *phigh = unsig_hi;
440          *plow = unsig_lo;
441      }
442  
443      if (neg_remainder) {
444          return int128_neg(rem);
445      } else {
446          return rem;
447      }
448  }
449