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MathExtras.h
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1 //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
2 //
3 // The LLVM Compiler Infrastructure
4 //
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // This file contains some functions that are useful for math stuff.
11 //
12 //===----------------------------------------------------------------------===//
13 
14 #ifndef LLVM_SUPPORT_MATHEXTRAS_H
15 #define LLVM_SUPPORT_MATHEXTRAS_H
16 
17 #include "llvm/Support/Compiler.h"
19 #include <algorithm>
20 #include <cassert>
21 #include <climits>
22 #include <cstring>
23 #include <limits>
24 #include <type_traits>
25 
26 #ifdef _MSC_VER
27 #include <intrin.h>
28 #endif
29 
30 #ifdef __ANDROID_NDK__
31 #include <android/api-level.h>
32 #endif
33 
34 namespace llvm {
35 /// \brief The behavior an operation has on an input of 0.
37  /// \brief The returned value is undefined.
39  /// \brief The returned value is numeric_limits<T>::max()
41  /// \brief The returned value is numeric_limits<T>::digits
43 };
44 
45 namespace detail {
46 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
47  static std::size_t count(T Val, ZeroBehavior) {
48  if (!Val)
49  return std::numeric_limits<T>::digits;
50  if (Val & 0x1)
51  return 0;
52 
53  // Bisection method.
54  std::size_t ZeroBits = 0;
55  T Shift = std::numeric_limits<T>::digits >> 1;
56  T Mask = std::numeric_limits<T>::max() >> Shift;
57  while (Shift) {
58  if ((Val & Mask) == 0) {
59  Val >>= Shift;
60  ZeroBits |= Shift;
61  }
62  Shift >>= 1;
63  Mask >>= Shift;
64  }
65  return ZeroBits;
66  }
67 };
68 
69 #if __GNUC__ >= 4 || defined(_MSC_VER)
70 template <typename T> struct TrailingZerosCounter<T, 4> {
71  static std::size_t count(T Val, ZeroBehavior ZB) {
72  if (ZB != ZB_Undefined && Val == 0)
73  return 32;
74 
75 #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
76  return __builtin_ctz(Val);
77 #elif defined(_MSC_VER)
78  unsigned long Index;
79  _BitScanForward(&Index, Val);
80  return Index;
81 #endif
82  }
83 };
84 
85 #if !defined(_MSC_VER) || defined(_M_X64)
86 template <typename T> struct TrailingZerosCounter<T, 8> {
87  static std::size_t count(T Val, ZeroBehavior ZB) {
88  if (ZB != ZB_Undefined && Val == 0)
89  return 64;
90 
91 #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
92  return __builtin_ctzll(Val);
93 #elif defined(_MSC_VER)
94  unsigned long Index;
95  _BitScanForward64(&Index, Val);
96  return Index;
97 #endif
98  }
99 };
100 #endif
101 #endif
102 } // namespace detail
103 
104 /// \brief Count number of 0's from the least significant bit to the most
105 /// stopping at the first 1.
106 ///
107 /// Only unsigned integral types are allowed.
108 ///
109 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
110 /// valid arguments.
111 template <typename T>
112 std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
113  static_assert(std::numeric_limits<T>::is_integer &&
114  !std::numeric_limits<T>::is_signed,
115  "Only unsigned integral types are allowed.");
117 }
118 
119 namespace detail {
120 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
121  static std::size_t count(T Val, ZeroBehavior) {
122  if (!Val)
123  return std::numeric_limits<T>::digits;
124 
125  // Bisection method.
126  std::size_t ZeroBits = 0;
127  for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
128  T Tmp = Val >> Shift;
129  if (Tmp)
130  Val = Tmp;
131  else
132  ZeroBits |= Shift;
133  }
134  return ZeroBits;
135  }
136 };
137 
138 #if __GNUC__ >= 4 || defined(_MSC_VER)
139 template <typename T> struct LeadingZerosCounter<T, 4> {
140  static std::size_t count(T Val, ZeroBehavior ZB) {
141  if (ZB != ZB_Undefined && Val == 0)
142  return 32;
143 
144 #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
145  return __builtin_clz(Val);
146 #elif defined(_MSC_VER)
147  unsigned long Index;
148  _BitScanReverse(&Index, Val);
149  return Index ^ 31;
150 #endif
151  }
152 };
153 
154 #if !defined(_MSC_VER) || defined(_M_X64)
155 template <typename T> struct LeadingZerosCounter<T, 8> {
156  static std::size_t count(T Val, ZeroBehavior ZB) {
157  if (ZB != ZB_Undefined && Val == 0)
158  return 64;
159 
160 #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
161  return __builtin_clzll(Val);
162 #elif defined(_MSC_VER)
163  unsigned long Index;
164  _BitScanReverse64(&Index, Val);
165  return Index ^ 63;
166 #endif
167  }
168 };
169 #endif
170 #endif
171 } // namespace detail
172 
173 /// \brief Count number of 0's from the most significant bit to the least
174 /// stopping at the first 1.
175 ///
176 /// Only unsigned integral types are allowed.
177 ///
178 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
179 /// valid arguments.
180 template <typename T>
181 std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
182  static_assert(std::numeric_limits<T>::is_integer &&
183  !std::numeric_limits<T>::is_signed,
184  "Only unsigned integral types are allowed.");
186 }
187 
188 /// \brief Get the index of the first set bit starting from the least
189 /// significant bit.
190 ///
191 /// Only unsigned integral types are allowed.
192 ///
193 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
194 /// valid arguments.
195 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
196  if (ZB == ZB_Max && Val == 0)
198 
199  return countTrailingZeros(Val, ZB_Undefined);
200 }
201 
202 /// \brief Create a bitmask with the N right-most bits set to 1, and all other
203 /// bits set to 0. Only unsigned types are allowed.
204 template <typename T> T maskTrailingOnes(unsigned N) {
205  static_assert(std::is_unsigned<T>::value, "Invalid type!");
206  const unsigned Bits = CHAR_BIT * sizeof(T);
207  assert(N <= Bits && "Invalid bit index");
208  return N == 0 ? 0 : (T(-1) >> (Bits - N));
209 }
210 
211 /// \brief Create a bitmask with the N left-most bits set to 1, and all other
212 /// bits set to 0. Only unsigned types are allowed.
213 template <typename T> T maskLeadingOnes(unsigned N) {
214  return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
215 }
216 
217 /// \brief Create a bitmask with the N right-most bits set to 0, and all other
218 /// bits set to 1. Only unsigned types are allowed.
219 template <typename T> T maskTrailingZeros(unsigned N) {
220  return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
221 }
222 
223 /// \brief Create a bitmask with the N left-most bits set to 0, and all other
224 /// bits set to 1. Only unsigned types are allowed.
225 template <typename T> T maskLeadingZeros(unsigned N) {
226  return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
227 }
228 
229 /// \brief Get the index of the last set bit starting from the least
230 /// significant bit.
231 ///
232 /// Only unsigned integral types are allowed.
233 ///
234 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
235 /// valid arguments.
236 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
237  if (ZB == ZB_Max && Val == 0)
239 
240  // Use ^ instead of - because both gcc and llvm can remove the associated ^
241  // in the __builtin_clz intrinsic on x86.
242  return countLeadingZeros(Val, ZB_Undefined) ^
243  (std::numeric_limits<T>::digits - 1);
244 }
245 
246 /// \brief Macro compressed bit reversal table for 256 bits.
247 ///
248 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
249 static const unsigned char BitReverseTable256[256] = {
250 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
251 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
252 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
253  R6(0), R6(2), R6(1), R6(3)
254 #undef R2
255 #undef R4
256 #undef R6
257 };
258 
259 /// \brief Reverse the bits in \p Val.
260 template <typename T>
262  unsigned char in[sizeof(Val)];
263  unsigned char out[sizeof(Val)];
264  std::memcpy(in, &Val, sizeof(Val));
265  for (unsigned i = 0; i < sizeof(Val); ++i)
266  out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
267  std::memcpy(&Val, out, sizeof(Val));
268  return Val;
269 }
270 
271 // NOTE: The following support functions use the _32/_64 extensions instead of
272 // type overloading so that signed and unsigned integers can be used without
273 // ambiguity.
274 
275 /// Return the high 32 bits of a 64 bit value.
276 constexpr inline uint32_t Hi_32(uint64_t Value) {
277  return static_cast<uint32_t>(Value >> 32);
278 }
279 
280 /// Return the low 32 bits of a 64 bit value.
281 constexpr inline uint32_t Lo_32(uint64_t Value) {
282  return static_cast<uint32_t>(Value);
283 }
284 
285 /// Make a 64-bit integer from a high / low pair of 32-bit integers.
286 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
287  return ((uint64_t)High << 32) | (uint64_t)Low;
288 }
289 
290 /// Checks if an integer fits into the given bit width.
291 template <unsigned N> constexpr inline bool isInt(int64_t x) {
292  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
293 }
294 // Template specializations to get better code for common cases.
295 template <> constexpr inline bool isInt<8>(int64_t x) {
296  return static_cast<int8_t>(x) == x;
297 }
298 template <> constexpr inline bool isInt<16>(int64_t x) {
299  return static_cast<int16_t>(x) == x;
300 }
301 template <> constexpr inline bool isInt<32>(int64_t x) {
302  return static_cast<int32_t>(x) == x;
303 }
304 
305 /// Checks if a signed integer is an N bit number shifted left by S.
306 template <unsigned N, unsigned S>
307 constexpr inline bool isShiftedInt(int64_t x) {
308  static_assert(
309  N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
310  static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
311  return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
312 }
313 
314 /// Checks if an unsigned integer fits into the given bit width.
315 ///
316 /// This is written as two functions rather than as simply
317 ///
318 /// return N >= 64 || X < (UINT64_C(1) << N);
319 ///
320 /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
321 /// left too many places.
322 template <unsigned N>
323 constexpr inline typename std::enable_if<(N < 64), bool>::type
324 isUInt(uint64_t X) {
325  static_assert(N > 0, "isUInt<0> doesn't make sense");
326  return X < (UINT64_C(1) << (N));
327 }
328 template <unsigned N>
329 constexpr inline typename std::enable_if<N >= 64, bool>::type
330 isUInt(uint64_t X) {
331  return true;
332 }
333 
334 // Template specializations to get better code for common cases.
335 template <> constexpr inline bool isUInt<8>(uint64_t x) {
336  return static_cast<uint8_t>(x) == x;
337 }
338 template <> constexpr inline bool isUInt<16>(uint64_t x) {
339  return static_cast<uint16_t>(x) == x;
340 }
341 template <> constexpr inline bool isUInt<32>(uint64_t x) {
342  return static_cast<uint32_t>(x) == x;
343 }
344 
345 /// Checks if a unsigned integer is an N bit number shifted left by S.
346 template <unsigned N, unsigned S>
347 constexpr inline bool isShiftedUInt(uint64_t x) {
348  static_assert(
349  N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
350  static_assert(N + S <= 64,
351  "isShiftedUInt<N, S> with N + S > 64 is too wide.");
352  // Per the two static_asserts above, S must be strictly less than 64. So
353  // 1 << S is not undefined behavior.
354  return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
355 }
356 
357 /// Gets the maximum value for a N-bit unsigned integer.
358 inline uint64_t maxUIntN(uint64_t N) {
359  assert(N > 0 && N <= 64 && "integer width out of range");
360 
361  // uint64_t(1) << 64 is undefined behavior, so we can't do
362  // (uint64_t(1) << N) - 1
363  // without checking first that N != 64. But this works and doesn't have a
364  // branch.
365  return UINT64_MAX >> (64 - N);
366 }
367 
368 /// Gets the minimum value for a N-bit signed integer.
369 inline int64_t minIntN(int64_t N) {
370  assert(N > 0 && N <= 64 && "integer width out of range");
371 
372  return -(UINT64_C(1)<<(N-1));
373 }
374 
375 /// Gets the maximum value for a N-bit signed integer.
376 inline int64_t maxIntN(int64_t N) {
377  assert(N > 0 && N <= 64 && "integer width out of range");
378 
379  // This relies on two's complement wraparound when N == 64, so we convert to
380  // int64_t only at the very end to avoid UB.
381  return (UINT64_C(1) << (N - 1)) - 1;
382 }
383 
384 /// Checks if an unsigned integer fits into the given (dynamic) bit width.
385 inline bool isUIntN(unsigned N, uint64_t x) {
386  return N >= 64 || x <= maxUIntN(N);
387 }
388 
389 /// Checks if an signed integer fits into the given (dynamic) bit width.
390 inline bool isIntN(unsigned N, int64_t x) {
391  return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
392 }
393 
394 /// Return true if the argument is a non-empty sequence of ones starting at the
395 /// least significant bit with the remainder zero (32 bit version).
396 /// Ex. isMask_32(0x0000FFFFU) == true.
397 constexpr inline bool isMask_32(uint32_t Value) {
398  return Value && ((Value + 1) & Value) == 0;
399 }
400 
401 /// Return true if the argument is a non-empty sequence of ones starting at the
402 /// least significant bit with the remainder zero (64 bit version).
403 constexpr inline bool isMask_64(uint64_t Value) {
404  return Value && ((Value + 1) & Value) == 0;
405 }
406 
407 /// Return true if the argument contains a non-empty sequence of ones with the
408 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
409 constexpr inline bool isShiftedMask_32(uint32_t Value) {
410  return Value && isMask_32((Value - 1) | Value);
411 }
412 
413 /// Return true if the argument contains a non-empty sequence of ones with the
414 /// remainder zero (64 bit version.)
415 constexpr inline bool isShiftedMask_64(uint64_t Value) {
416  return Value && isMask_64((Value - 1) | Value);
417 }
418 
419 /// Return true if the argument is a power of two > 0.
420 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
421 constexpr inline bool isPowerOf2_32(uint32_t Value) {
422  return Value && !(Value & (Value - 1));
423 }
424 
425 /// Return true if the argument is a power of two > 0 (64 bit edition.)
426 constexpr inline bool isPowerOf2_64(uint64_t Value) {
427  return Value && !(Value & (Value - int64_t(1L)));
428 }
429 
430 /// Return a byte-swapped representation of the 16-bit argument.
431 inline uint16_t ByteSwap_16(uint16_t Value) {
432  return sys::SwapByteOrder_16(Value);
433 }
434 
435 /// Return a byte-swapped representation of the 32-bit argument.
437  return sys::SwapByteOrder_32(Value);
438 }
439 
440 /// Return a byte-swapped representation of the 64-bit argument.
441 inline uint64_t ByteSwap_64(uint64_t Value) {
442  return sys::SwapByteOrder_64(Value);
443 }
444 
445 /// \brief Count the number of ones from the most significant bit to the first
446 /// zero bit.
447 ///
448 /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
449 /// Only unsigned integral types are allowed.
450 ///
451 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
452 /// ZB_Undefined are valid arguments.
453 template <typename T>
455  static_assert(std::numeric_limits<T>::is_integer &&
456  !std::numeric_limits<T>::is_signed,
457  "Only unsigned integral types are allowed.");
458  return countLeadingZeros(~Value, ZB);
459 }
460 
461 /// \brief Count the number of ones from the least significant bit to the first
462 /// zero bit.
463 ///
464 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
465 /// Only unsigned integral types are allowed.
466 ///
467 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
468 /// ZB_Undefined are valid arguments.
469 template <typename T>
471  static_assert(std::numeric_limits<T>::is_integer &&
472  !std::numeric_limits<T>::is_signed,
473  "Only unsigned integral types are allowed.");
474  return countTrailingZeros(~Value, ZB);
475 }
476 
477 namespace detail {
478 template <typename T, std::size_t SizeOfT> struct PopulationCounter {
479  static unsigned count(T Value) {
480  // Generic version, forward to 32 bits.
481  static_assert(SizeOfT <= 4, "Not implemented!");
482 #if __GNUC__ >= 4
483  return __builtin_popcount(Value);
484 #else
485  uint32_t v = Value;
486  v = v - ((v >> 1) & 0x55555555);
487  v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
488  return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
489 #endif
490  }
491 };
492 
493 template <typename T> struct PopulationCounter<T, 8> {
494  static unsigned count(T Value) {
495 #if __GNUC__ >= 4
496  return __builtin_popcountll(Value);
497 #else
498  uint64_t v = Value;
499  v = v - ((v >> 1) & 0x5555555555555555ULL);
500  v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
501  v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
502  return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
503 #endif
504  }
505 };
506 } // namespace detail
507 
508 /// \brief Count the number of set bits in a value.
509 /// Ex. countPopulation(0xF000F000) = 8
510 /// Returns 0 if the word is zero.
511 template <typename T>
512 inline unsigned countPopulation(T Value) {
513  static_assert(std::numeric_limits<T>::is_integer &&
514  !std::numeric_limits<T>::is_signed,
515  "Only unsigned integral types are allowed.");
517 }
518 
519 /// Return the log base 2 of the specified value.
520 inline double Log2(double Value) {
521 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
522  return __builtin_log(Value) / __builtin_log(2.0);
523 #else
524  return log2(Value);
525 #endif
526 }
527 
528 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
529 /// (32 bit edition.)
530 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
531 inline unsigned Log2_32(uint32_t Value) {
532  return 31 - countLeadingZeros(Value);
533 }
534 
535 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
536 /// (64 bit edition.)
537 inline unsigned Log2_64(uint64_t Value) {
538  return 63 - countLeadingZeros(Value);
539 }
540 
541 /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
542 /// (32 bit edition).
543 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
544 inline unsigned Log2_32_Ceil(uint32_t Value) {
545  return 32 - countLeadingZeros(Value - 1);
546 }
547 
548 /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
549 /// (64 bit edition.)
550 inline unsigned Log2_64_Ceil(uint64_t Value) {
551  return 64 - countLeadingZeros(Value - 1);
552 }
553 
554 /// Return the greatest common divisor of the values using Euclid's algorithm.
555 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
556  while (B) {
557  uint64_t T = B;
558  B = A % B;
559  A = T;
560  }
561  return A;
562 }
563 
564 /// This function takes a 64-bit integer and returns the bit equivalent double.
565 inline double BitsToDouble(uint64_t Bits) {
566  double D;
567  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
568  memcpy(&D, &Bits, sizeof(Bits));
569  return D;
570 }
571 
572 /// This function takes a 32-bit integer and returns the bit equivalent float.
573 inline float BitsToFloat(uint32_t Bits) {
574  float F;
575  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
576  memcpy(&F, &Bits, sizeof(Bits));
577  return F;
578 }
579 
580 /// This function takes a double and returns the bit equivalent 64-bit integer.
581 /// Note that copying doubles around changes the bits of NaNs on some hosts,
582 /// notably x86, so this routine cannot be used if these bits are needed.
583 inline uint64_t DoubleToBits(double Double) {
584  uint64_t Bits;
585  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
586  memcpy(&Bits, &Double, sizeof(Double));
587  return Bits;
588 }
589 
590 /// This function takes a float and returns the bit equivalent 32-bit integer.
591 /// Note that copying floats around changes the bits of NaNs on some hosts,
592 /// notably x86, so this routine cannot be used if these bits are needed.
593 inline uint32_t FloatToBits(float Float) {
594  uint32_t Bits;
595  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
596  memcpy(&Bits, &Float, sizeof(Float));
597  return Bits;
598 }
599 
600 /// A and B are either alignments or offsets. Return the minimum alignment that
601 /// may be assumed after adding the two together.
602 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
603  // The largest power of 2 that divides both A and B.
604  //
605  // Replace "-Value" by "1+~Value" in the following commented code to avoid
606  // MSVC warning C4146
607  // return (A | B) & -(A | B);
608  return (A | B) & (1 + ~(A | B));
609 }
610 
611 /// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
612 ///
613 /// Alignment should be a power of two. This method rounds up, so
614 /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
615 inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
616  assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
617  "Alignment is not a power of two!");
618 
619  assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
620 
621  return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
622 }
623 
624 /// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
625 /// bytes, rounding up.
626 inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
627  return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
628 }
629 
630 /// Returns the next power of two (in 64-bits) that is strictly greater than A.
631 /// Returns zero on overflow.
632 inline uint64_t NextPowerOf2(uint64_t A) {
633  A |= (A >> 1);
634  A |= (A >> 2);
635  A |= (A >> 4);
636  A |= (A >> 8);
637  A |= (A >> 16);
638  A |= (A >> 32);
639  return A + 1;
640 }
641 
642 /// Returns the power of two which is less than or equal to the given value.
643 /// Essentially, it is a floor operation across the domain of powers of two.
644 inline uint64_t PowerOf2Floor(uint64_t A) {
645  if (!A) return 0;
646  return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
647 }
648 
649 /// Returns the power of two which is greater than or equal to the given value.
650 /// Essentially, it is a ceil operation across the domain of powers of two.
651 inline uint64_t PowerOf2Ceil(uint64_t A) {
652  if (!A)
653  return 0;
654  return NextPowerOf2(A - 1);
655 }
656 
657 /// Returns the next integer (mod 2**64) that is greater than or equal to
658 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
659 ///
660 /// If non-zero \p Skew is specified, the return value will be a minimal
661 /// integer that is greater than or equal to \p Value and equal to
662 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
663 /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
664 ///
665 /// Examples:
666 /// \code
667 /// alignTo(5, 8) = 8
668 /// alignTo(17, 8) = 24
669 /// alignTo(~0LL, 8) = 0
670 /// alignTo(321, 255) = 510
671 ///
672 /// alignTo(5, 8, 7) = 7
673 /// alignTo(17, 8, 1) = 17
674 /// alignTo(~0LL, 8, 3) = 3
675 /// alignTo(321, 255, 42) = 552
676 /// \endcode
677 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
678  assert(Align != 0u && "Align can't be 0.");
679  Skew %= Align;
680  return (Value + Align - 1 - Skew) / Align * Align + Skew;
681 }
682 
683 /// Returns the next integer (mod 2**64) that is greater than or equal to
684 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
685 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
686  static_assert(Align != 0u, "Align must be non-zero");
687  return (Value + Align - 1) / Align * Align;
688 }
689 
690 /// \c alignTo for contexts where a constant expression is required.
691 /// \sa alignTo
692 ///
693 /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
694 template <uint64_t Align>
695 struct AlignTo {
696  static_assert(Align != 0u, "Align must be non-zero");
697  template <uint64_t Value>
698  struct from_value {
699  static const uint64_t value = (Value + Align - 1) / Align * Align;
700  };
701 };
702 
703 /// Returns the largest uint64_t less than or equal to \p Value and is
704 /// \p Skew mod \p Align. \p Align must be non-zero
705 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
706  assert(Align != 0u && "Align can't be 0.");
707  Skew %= Align;
708  return (Value - Skew) / Align * Align + Skew;
709 }
710 
711 /// Returns the offset to the next integer (mod 2**64) that is greater than
712 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
713 /// non-zero.
714 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
715  return alignTo(Value, Align) - Value;
716 }
717 
718 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
719 /// Requires 0 < B <= 32.
720 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
721  static_assert(B > 0, "Bit width can't be 0.");
722  static_assert(B <= 32, "Bit width out of range.");
723  return int32_t(X << (32 - B)) >> (32 - B);
724 }
725 
726 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
727 /// Requires 0 < B < 32.
728 inline int32_t SignExtend32(uint32_t X, unsigned B) {
729  assert(B > 0 && "Bit width can't be 0.");
730  assert(B <= 32 && "Bit width out of range.");
731  return int32_t(X << (32 - B)) >> (32 - B);
732 }
733 
734 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
735 /// Requires 0 < B < 64.
736 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
737  static_assert(B > 0, "Bit width can't be 0.");
738  static_assert(B <= 64, "Bit width out of range.");
739  return int64_t(x << (64 - B)) >> (64 - B);
740 }
741 
742 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
743 /// Requires 0 < B < 64.
744 inline int64_t SignExtend64(uint64_t X, unsigned B) {
745  assert(B > 0 && "Bit width can't be 0.");
746  assert(B <= 64 && "Bit width out of range.");
747  return int64_t(X << (64 - B)) >> (64 - B);
748 }
749 
750 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
751 /// value of the result.
752 template <typename T>
753 typename std::enable_if<std::is_unsigned<T>::value, T>::type
755  return std::max(X, Y) - std::min(X, Y);
756 }
757 
758 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
759 /// maximum representable value of T on overflow. ResultOverflowed indicates if
760 /// the result is larger than the maximum representable value of type T.
761 template <typename T>
762 typename std::enable_if<std::is_unsigned<T>::value, T>::type
763 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
764  bool Dummy;
765  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
766  // Hacker's Delight, p. 29
767  T Z = X + Y;
768  Overflowed = (Z < X || Z < Y);
769  if (Overflowed)
771  else
772  return Z;
773 }
774 
775 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
776 /// maximum representable value of T on overflow. ResultOverflowed indicates if
777 /// the result is larger than the maximum representable value of type T.
778 template <typename T>
779 typename std::enable_if<std::is_unsigned<T>::value, T>::type
780 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
781  bool Dummy;
782  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
783 
784  // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
785  // because it fails for uint16_t (where multiplication can have undefined
786  // behavior due to promotion to int), and requires a division in addition
787  // to the multiplication.
788 
789  Overflowed = false;
790 
791  // Log2(Z) would be either Log2Z or Log2Z + 1.
792  // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
793  // will necessarily be less than Log2Max as desired.
794  int Log2Z = Log2_64(X) + Log2_64(Y);
795  const T Max = std::numeric_limits<T>::max();
796  int Log2Max = Log2_64(Max);
797  if (Log2Z < Log2Max) {
798  return X * Y;
799  }
800  if (Log2Z > Log2Max) {
801  Overflowed = true;
802  return Max;
803  }
804 
805  // We're going to use the top bit, and maybe overflow one
806  // bit past it. Multiply all but the bottom bit then add
807  // that on at the end.
808  T Z = (X >> 1) * Y;
809  if (Z & ~(Max >> 1)) {
810  Overflowed = true;
811  return Max;
812  }
813  Z <<= 1;
814  if (X & 1)
815  return SaturatingAdd(Z, Y, ResultOverflowed);
816 
817  return Z;
818 }
819 
820 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
821 /// the product. Clamp the result to the maximum representable value of T on
822 /// overflow. ResultOverflowed indicates if the result is larger than the
823 /// maximum representable value of type T.
824 template <typename T>
825 typename std::enable_if<std::is_unsigned<T>::value, T>::type
826 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
827  bool Dummy;
828  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
829 
830  T Product = SaturatingMultiply(X, Y, &Overflowed);
831  if (Overflowed)
832  return Product;
833 
834  return SaturatingAdd(A, Product, &Overflowed);
835 }
836 
837 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
838 extern const float huge_valf;
839 } // End llvm namespace
840 
841 #endif
constexpr bool isUInt< 32 >(uint64_t x)
Definition: MathExtras.h:341
unsigned Log2_32_Ceil(uint32_t Value)
Return the ceil log base 2 of the specified value, 32 if the value is zero.
Definition: MathExtras.h:544
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
T findLastSet(T Val, ZeroBehavior ZB=ZB_Max)
Get the index of the last set bit starting from the least significant bit.
Definition: MathExtras.h:236
GCNRegPressure max(const GCNRegPressure &P1, const GCNRegPressure &P2)
uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B)
Return the greatest common divisor of the values using Euclid&#39;s algorithm.
Definition: MathExtras.h:555
Compute iterated dominance frontiers using a linear time algorithm.
Definition: AllocatorList.h:24
constexpr uint32_t Lo_32(uint64_t Value)
Return the low 32 bits of a 64 bit value.
Definition: MathExtras.h:281
static unsigned count(T Value)
Definition: MathExtras.h:479
float BitsToFloat(uint32_t Bits)
This function takes a 32-bit integer and returns the bit equivalent float.
Definition: MathExtras.h:573
constexpr bool isInt< 8 >(int64_t x)
Definition: MathExtras.h:295
ZeroBehavior
The behavior an operation has on an input of 0.
Definition: MathExtras.h:36
constexpr bool isInt< 16 >(int64_t x)
Definition: MathExtras.h:298
uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew=0)
Returns the next integer (mod 2**64) that is greater than or equal to Value and is a multiple of Alig...
Definition: MathExtras.h:677
std::size_t countLeadingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0&#39;s from the most significant bit to the least stopping at the first 1...
Definition: MathExtras.h:181
std::enable_if< std::is_unsigned< T >::value, T >::type SaturatingMultiply(T X, T Y, bool *ResultOverflowed=nullptr)
Multiply two unsigned integers, X and Y, of type T.
Definition: MathExtras.h:780
uint64_t High
constexpr bool isMask_32(uint32_t Value)
Return true if the argument is a non-empty sequence of ones starting at the least significant bit wit...
Definition: MathExtras.h:397
std::enable_if< std::is_unsigned< T >::value, T >::type SaturatingAdd(T X, T Y, bool *ResultOverflowed=nullptr)
Add two unsigned integers, X and Y, of type T.
Definition: MathExtras.h:763
T maskTrailingOnes(unsigned N)
Create a bitmask with the N right-most bits set to 1, and all other bits set to 0.
Definition: MathExtras.h:204
static GCMetadataPrinterRegistry::Add< OcamlGCMetadataPrinter > Y("ocaml", "ocaml 3.10-compatible collector")
uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew=0)
Returns the largest uint64_t less than or equal to Value and is Skew mod Align.
Definition: MathExtras.h:705
uint32_t SwapByteOrder_32(uint32_t value)
SwapByteOrder_32 - This function returns a byte-swapped representation of the 32-bit argument...
Definition: SwapByteOrder.h:44
The returned value is numeric_limits<T>::digits.
Definition: MathExtras.h:42
std::size_t countTrailingOnes(T Value, ZeroBehavior ZB=ZB_Width)
Count the number of ones from the least significant bit to the first zero bit.
Definition: MathExtras.h:470
The returned value is undefined.
Definition: MathExtras.h:38
static unsigned count(T Value)
Definition: MathExtras.h:494
uint32_t ByteSwap_32(uint32_t Value)
Return a byte-swapped representation of the 32-bit argument.
Definition: MathExtras.h:436
zlib-gnu style compression
int64_t maxIntN(int64_t N)
Gets the maximum value for a N-bit signed integer.
Definition: MathExtras.h:376
static const unsigned char BitReverseTable256[256]
Macro compressed bit reversal table for 256 bits.
Definition: MathExtras.h:249
#define F(x, y, z)
Definition: MD5.cpp:55
constexpr bool isMask_64(uint64_t Value)
Return true if the argument is a non-empty sequence of ones starting at the least significant bit wit...
Definition: MathExtras.h:403
uint16_t ByteSwap_16(uint16_t Value)
Return a byte-swapped representation of the 16-bit argument.
Definition: MathExtras.h:431
#define T
constexpr bool isShiftedUInt(uint64_t x)
Checks if a unsigned integer is an N bit number shifted left by S.
Definition: MathExtras.h:347
int64_t minIntN(int64_t N)
Gets the minimum value for a N-bit signed integer.
Definition: MathExtras.h:369
const float huge_valf
Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
Definition: MathExtras.cpp:29
T maskTrailingZeros(unsigned N)
Create a bitmask with the N right-most bits set to 0, and all other bits set to 1.
Definition: MathExtras.h:219
uint32_t FloatToBits(float Float)
This function takes a float and returns the bit equivalent 32-bit integer.
Definition: MathExtras.h:593
uint16_t SwapByteOrder_16(uint16_t value)
SwapByteOrder_16 - This function returns a byte-swapped representation of the 16-bit argument...
Definition: SwapByteOrder.h:30
constexpr uint64_t MinAlign(uint64_t A, uint64_t B)
A and B are either alignments or offsets.
Definition: MathExtras.h:602
constexpr bool isUInt< 8 >(uint64_t x)
Definition: MathExtras.h:335
std::size_t countTrailingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0&#39;s from the least significant bit to the most stopping at the first 1...
Definition: MathExtras.h:112
constexpr bool isShiftedInt(int64_t x)
Checks if a signed integer is an N bit number shifted left by S.
Definition: MathExtras.h:307
constexpr bool isPowerOf2_32(uint32_t Value)
Return true if the argument is a power of two > 0.
Definition: MathExtras.h:421
constexpr bool isInt(int64_t x)
Checks if an integer fits into the given bit width.
Definition: MathExtras.h:291
size_t alignmentAdjustment(const void *Ptr, size_t Alignment)
Returns the necessary adjustment for aligning Ptr to Alignment bytes, rounding up.
Definition: MathExtras.h:626
#define A
Definition: LargeTest.cpp:12
constexpr bool isPowerOf2_64(uint64_t Value)
Return true if the argument is a power of two > 0 (64 bit edition.)
Definition: MathExtras.h:426
The returned value is numeric_limits<T>::max()
Definition: MathExtras.h:40
bool isIntN(unsigned N, int64_t x)
Checks if an signed integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:390
uint64_t NextPowerOf2(uint64_t A)
Returns the next power of two (in 64-bits) that is strictly greater than A.
Definition: MathExtras.h:632
T findFirstSet(T Val, ZeroBehavior ZB=ZB_Max)
Get the index of the first set bit starting from the least significant bit.
Definition: MathExtras.h:195
uint64_t SwapByteOrder_64(uint64_t value)
SwapByteOrder_64 - This function returns a byte-swapped representation of the 64-bit argument...
Definition: SwapByteOrder.h:60
std::enable_if< std::is_unsigned< T >::value, T >::type SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed=nullptr)
Multiply two unsigned integers, X and Y, and add the unsigned integer, A to the product.
Definition: MathExtras.h:826
unsigned countPopulation(T Value)
Count the number of set bits in a value.
Definition: MathExtras.h:512
constexpr std::enable_if<(N< 64), bool >::type isUInt(uint64_t X)
Checks if an unsigned integer fits into the given bit width.
Definition: MathExtras.h:324
#define R6(n)
constexpr bool isInt< 32 >(int64_t x)
Definition: MathExtras.h:301
#define B
Definition: LargeTest.cpp:24
double Log2(double Value)
Return the log base 2 of the specified value.
Definition: MathExtras.h:520
const size_t N
uint64_t DoubleToBits(double Double)
This function takes a double and returns the bit equivalent 64-bit integer.
Definition: MathExtras.h:583
double BitsToDouble(uint64_t Bits)
This function takes a 64-bit integer and returns the bit equivalent double.
Definition: MathExtras.h:565
static std::size_t count(T Val, ZeroBehavior)
Definition: MathExtras.h:121
unsigned Log2_64_Ceil(uint64_t Value)
Return the ceil log base 2 of the specified value, 64 if the value is zero.
Definition: MathExtras.h:550
unsigned Log2_32(uint32_t Value)
Return the floor log base 2 of the specified value, -1 if the value is zero.
Definition: MathExtras.h:531
alignTo for contexts where a constant expression is required.
Definition: MathExtras.h:695
uintptr_t alignAddr(const void *Addr, size_t Alignment)
Aligns Addr to Alignment bytes, rounding up.
Definition: MathExtras.h:615
static std::size_t count(T Val, ZeroBehavior)
Definition: MathExtras.h:47
constexpr bool isShiftedMask_64(uint64_t Value)
Return true if the argument contains a non-empty sequence of ones with the remainder zero (64 bit ver...
Definition: MathExtras.h:415
uint64_t maxUIntN(uint64_t N)
Gets the maximum value for a N-bit unsigned integer.
Definition: MathExtras.h:358
T maskLeadingZeros(unsigned N)
Create a bitmask with the N left-most bits set to 0, and all other bits set to 1. ...
Definition: MathExtras.h:225
uint64_t ByteSwap_64(uint64_t Value)
Return a byte-swapped representation of the 64-bit argument.
Definition: MathExtras.h:441
std::enable_if< std::is_unsigned< T >::value, T >::type AbsoluteDifference(T X, T Y)
Subtract two unsigned integers, X and Y, of type T and return the absolute value of the result...
Definition: MathExtras.h:754
constexpr char Align[]
Key for Kernel::Arg::Metadata::mAlign.
constexpr int32_t SignExtend32(uint32_t X)
Sign-extend the number in the bottom B bits of X to a 32-bit integer.
Definition: MathExtras.h:720
constexpr bool isUInt< 16 >(uint64_t x)
Definition: MathExtras.h:338
constexpr int64_t SignExtend64(uint64_t x)
Sign-extend the number in the bottom B bits of X to a 64-bit integer.
Definition: MathExtras.h:736
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
uint64_t PowerOf2Floor(uint64_t A)
Returns the power of two which is less than or equal to the given value.
Definition: MathExtras.h:644
constexpr uint32_t Hi_32(uint64_t Value)
Return the high 32 bits of a 64 bit value.
Definition: MathExtras.h:276
LLVM Value Representation.
Definition: Value.h:73
std::underlying_type< E >::type Mask()
Get a bitmask with 1s in all places up to the high-order bit of E&#39;s largest value.
Definition: BitmaskEnum.h:81
uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align)
Returns the offset to the next integer (mod 2**64) that is greater than or equal to Value and is a mu...
Definition: MathExtras.h:714
constexpr uint64_t Make_64(uint32_t High, uint32_t Low)
Make a 64-bit integer from a high / low pair of 32-bit integers.
Definition: MathExtras.h:286
constexpr bool isShiftedMask_32(uint32_t Value)
Return true if the argument contains a non-empty sequence of ones with the remainder zero (32 bit ver...
Definition: MathExtras.h:409
int * Ptr
bool isUIntN(unsigned N, uint64_t x)
Checks if an unsigned integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:385
T reverseBits(T Val)
Reverse the bits in Val.
Definition: MathExtras.h:261
std::size_t countLeadingOnes(T Value, ZeroBehavior ZB=ZB_Width)
Count the number of ones from the most significant bit to the first zero bit.
Definition: MathExtras.h:454
unsigned Log2_64(uint64_t Value)
Return the floor log base 2 of the specified value, -1 if the value is zero.
Definition: MathExtras.h:537
#define D
Definition: LargeTest.cpp:26
uint64_t PowerOf2Ceil(uint64_t A)
Returns the power of two which is greater than or equal to the given value.
Definition: MathExtras.h:651
T maskLeadingOnes(unsigned N)
Create a bitmask with the N left-most bits set to 1, and all other bits set to 0. ...
Definition: MathExtras.h:213