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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 __ANDROID_NDK__
27 #include <android/api-level.h>
28 #endif
29 
30 #ifdef _MSC_VER
31 // Declare these intrinsics manually rather including intrin.h. It's very
32 // expensive, and MathExtras.h is popular.
33 // #include <intrin.h>
34 extern "C" {
35 unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
36 unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
37 unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
38 unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
39 }
40 #endif
41 
42 namespace llvm {
43 /// The behavior an operation has on an input of 0.
45  /// The returned value is undefined.
47  /// The returned value is numeric_limits<T>::max()
49  /// The returned value is numeric_limits<T>::digits
51 };
52 
53 namespace detail {
54 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
55  static std::size_t count(T Val, ZeroBehavior) {
56  if (!Val)
57  return std::numeric_limits<T>::digits;
58  if (Val & 0x1)
59  return 0;
60 
61  // Bisection method.
62  std::size_t ZeroBits = 0;
63  T Shift = std::numeric_limits<T>::digits >> 1;
64  T Mask = std::numeric_limits<T>::max() >> Shift;
65  while (Shift) {
66  if ((Val & Mask) == 0) {
67  Val >>= Shift;
68  ZeroBits |= Shift;
69  }
70  Shift >>= 1;
71  Mask >>= Shift;
72  }
73  return ZeroBits;
74  }
75 };
76 
77 #if __GNUC__ >= 4 || defined(_MSC_VER)
78 template <typename T> struct TrailingZerosCounter<T, 4> {
79  static std::size_t count(T Val, ZeroBehavior ZB) {
80  if (ZB != ZB_Undefined && Val == 0)
81  return 32;
82 
83 #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
84  return __builtin_ctz(Val);
85 #elif defined(_MSC_VER)
86  unsigned long Index;
87  _BitScanForward(&Index, Val);
88  return Index;
89 #endif
90  }
91 };
92 
93 #if !defined(_MSC_VER) || defined(_M_X64)
94 template <typename T> struct TrailingZerosCounter<T, 8> {
95  static std::size_t count(T Val, ZeroBehavior ZB) {
96  if (ZB != ZB_Undefined && Val == 0)
97  return 64;
98 
99 #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
100  return __builtin_ctzll(Val);
101 #elif defined(_MSC_VER)
102  unsigned long Index;
103  _BitScanForward64(&Index, Val);
104  return Index;
105 #endif
106  }
107 };
108 #endif
109 #endif
110 } // namespace detail
111 
112 /// Count number of 0's from the least significant bit to the most
113 /// stopping at the first 1.
114 ///
115 /// Only unsigned integral types are allowed.
116 ///
117 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
118 /// valid arguments.
119 template <typename T>
120 std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
121  static_assert(std::numeric_limits<T>::is_integer &&
122  !std::numeric_limits<T>::is_signed,
123  "Only unsigned integral types are allowed.");
125 }
126 
127 namespace detail {
128 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
129  static std::size_t count(T Val, ZeroBehavior) {
130  if (!Val)
131  return std::numeric_limits<T>::digits;
132 
133  // Bisection method.
134  std::size_t ZeroBits = 0;
135  for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
136  T Tmp = Val >> Shift;
137  if (Tmp)
138  Val = Tmp;
139  else
140  ZeroBits |= Shift;
141  }
142  return ZeroBits;
143  }
144 };
145 
146 #if __GNUC__ >= 4 || defined(_MSC_VER)
147 template <typename T> struct LeadingZerosCounter<T, 4> {
148  static std::size_t count(T Val, ZeroBehavior ZB) {
149  if (ZB != ZB_Undefined && Val == 0)
150  return 32;
151 
152 #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
153  return __builtin_clz(Val);
154 #elif defined(_MSC_VER)
155  unsigned long Index;
156  _BitScanReverse(&Index, Val);
157  return Index ^ 31;
158 #endif
159  }
160 };
161 
162 #if !defined(_MSC_VER) || defined(_M_X64)
163 template <typename T> struct LeadingZerosCounter<T, 8> {
164  static std::size_t count(T Val, ZeroBehavior ZB) {
165  if (ZB != ZB_Undefined && Val == 0)
166  return 64;
167 
168 #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
169  return __builtin_clzll(Val);
170 #elif defined(_MSC_VER)
171  unsigned long Index;
172  _BitScanReverse64(&Index, Val);
173  return Index ^ 63;
174 #endif
175  }
176 };
177 #endif
178 #endif
179 } // namespace detail
180 
181 /// Count number of 0's from the most significant bit to the least
182 /// stopping at the first 1.
183 ///
184 /// Only unsigned integral types are allowed.
185 ///
186 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
187 /// valid arguments.
188 template <typename T>
189 std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
190  static_assert(std::numeric_limits<T>::is_integer &&
191  !std::numeric_limits<T>::is_signed,
192  "Only unsigned integral types are allowed.");
194 }
195 
196 /// Get the index of the first set bit starting from the least
197 /// significant bit.
198 ///
199 /// Only unsigned integral types are allowed.
200 ///
201 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
202 /// valid arguments.
203 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
204  if (ZB == ZB_Max && Val == 0)
206 
207  return countTrailingZeros(Val, ZB_Undefined);
208 }
209 
210 /// Create a bitmask with the N right-most bits set to 1, and all other
211 /// bits set to 0. Only unsigned types are allowed.
212 template <typename T> T maskTrailingOnes(unsigned N) {
213  static_assert(std::is_unsigned<T>::value, "Invalid type!");
214  const unsigned Bits = CHAR_BIT * sizeof(T);
215  assert(N <= Bits && "Invalid bit index");
216  return N == 0 ? 0 : (T(-1) >> (Bits - N));
217 }
218 
219 /// Create a bitmask with the N left-most bits set to 1, and all other
220 /// bits set to 0. Only unsigned types are allowed.
221 template <typename T> T maskLeadingOnes(unsigned N) {
222  return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
223 }
224 
225 /// Create a bitmask with the N right-most bits set to 0, and all other
226 /// bits set to 1. Only unsigned types are allowed.
227 template <typename T> T maskTrailingZeros(unsigned N) {
228  return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
229 }
230 
231 /// Create a bitmask with the N left-most bits set to 0, and all other
232 /// bits set to 1. Only unsigned types are allowed.
233 template <typename T> T maskLeadingZeros(unsigned N) {
234  return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
235 }
236 
237 /// Get the index of the last set bit starting from the least
238 /// significant bit.
239 ///
240 /// Only unsigned integral types are allowed.
241 ///
242 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
243 /// valid arguments.
244 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
245  if (ZB == ZB_Max && Val == 0)
247 
248  // Use ^ instead of - because both gcc and llvm can remove the associated ^
249  // in the __builtin_clz intrinsic on x86.
250  return countLeadingZeros(Val, ZB_Undefined) ^
251  (std::numeric_limits<T>::digits - 1);
252 }
253 
254 /// Macro compressed bit reversal table for 256 bits.
255 ///
256 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
257 static const unsigned char BitReverseTable256[256] = {
258 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
259 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
260 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
261  R6(0), R6(2), R6(1), R6(3)
262 #undef R2
263 #undef R4
264 #undef R6
265 };
266 
267 /// Reverse the bits in \p Val.
268 template <typename T>
270  unsigned char in[sizeof(Val)];
271  unsigned char out[sizeof(Val)];
272  std::memcpy(in, &Val, sizeof(Val));
273  for (unsigned i = 0; i < sizeof(Val); ++i)
274  out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
275  std::memcpy(&Val, out, sizeof(Val));
276  return Val;
277 }
278 
279 // NOTE: The following support functions use the _32/_64 extensions instead of
280 // type overloading so that signed and unsigned integers can be used without
281 // ambiguity.
282 
283 /// Return the high 32 bits of a 64 bit value.
284 constexpr inline uint32_t Hi_32(uint64_t Value) {
285  return static_cast<uint32_t>(Value >> 32);
286 }
287 
288 /// Return the low 32 bits of a 64 bit value.
289 constexpr inline uint32_t Lo_32(uint64_t Value) {
290  return static_cast<uint32_t>(Value);
291 }
292 
293 /// Make a 64-bit integer from a high / low pair of 32-bit integers.
294 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
295  return ((uint64_t)High << 32) | (uint64_t)Low;
296 }
297 
298 /// Checks if an integer fits into the given bit width.
299 template <unsigned N> constexpr inline bool isInt(int64_t x) {
300  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
301 }
302 // Template specializations to get better code for common cases.
303 template <> constexpr inline bool isInt<8>(int64_t x) {
304  return static_cast<int8_t>(x) == x;
305 }
306 template <> constexpr inline bool isInt<16>(int64_t x) {
307  return static_cast<int16_t>(x) == x;
308 }
309 template <> constexpr inline bool isInt<32>(int64_t x) {
310  return static_cast<int32_t>(x) == x;
311 }
312 
313 /// Checks if a signed integer is an N bit number shifted left by S.
314 template <unsigned N, unsigned S>
315 constexpr inline bool isShiftedInt(int64_t x) {
316  static_assert(
317  N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
318  static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
319  return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
320 }
321 
322 /// Checks if an unsigned integer fits into the given bit width.
323 ///
324 /// This is written as two functions rather than as simply
325 ///
326 /// return N >= 64 || X < (UINT64_C(1) << N);
327 ///
328 /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
329 /// left too many places.
330 template <unsigned N>
331 constexpr inline typename std::enable_if<(N < 64), bool>::type
332 isUInt(uint64_t X) {
333  static_assert(N > 0, "isUInt<0> doesn't make sense");
334  return X < (UINT64_C(1) << (N));
335 }
336 template <unsigned N>
337 constexpr inline typename std::enable_if<N >= 64, bool>::type
338 isUInt(uint64_t X) {
339  return true;
340 }
341 
342 // Template specializations to get better code for common cases.
343 template <> constexpr inline bool isUInt<8>(uint64_t x) {
344  return static_cast<uint8_t>(x) == x;
345 }
346 template <> constexpr inline bool isUInt<16>(uint64_t x) {
347  return static_cast<uint16_t>(x) == x;
348 }
349 template <> constexpr inline bool isUInt<32>(uint64_t x) {
350  return static_cast<uint32_t>(x) == x;
351 }
352 
353 /// Checks if a unsigned integer is an N bit number shifted left by S.
354 template <unsigned N, unsigned S>
355 constexpr inline bool isShiftedUInt(uint64_t x) {
356  static_assert(
357  N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
358  static_assert(N + S <= 64,
359  "isShiftedUInt<N, S> with N + S > 64 is too wide.");
360  // Per the two static_asserts above, S must be strictly less than 64. So
361  // 1 << S is not undefined behavior.
362  return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
363 }
364 
365 /// Gets the maximum value for a N-bit unsigned integer.
366 inline uint64_t maxUIntN(uint64_t N) {
367  assert(N > 0 && N <= 64 && "integer width out of range");
368 
369  // uint64_t(1) << 64 is undefined behavior, so we can't do
370  // (uint64_t(1) << N) - 1
371  // without checking first that N != 64. But this works and doesn't have a
372  // branch.
373  return UINT64_MAX >> (64 - N);
374 }
375 
376 /// Gets the minimum value for a N-bit signed integer.
377 inline int64_t minIntN(int64_t N) {
378  assert(N > 0 && N <= 64 && "integer width out of range");
379 
380  return -(UINT64_C(1)<<(N-1));
381 }
382 
383 /// Gets the maximum value for a N-bit signed integer.
384 inline int64_t maxIntN(int64_t N) {
385  assert(N > 0 && N <= 64 && "integer width out of range");
386 
387  // This relies on two's complement wraparound when N == 64, so we convert to
388  // int64_t only at the very end to avoid UB.
389  return (UINT64_C(1) << (N - 1)) - 1;
390 }
391 
392 /// Checks if an unsigned integer fits into the given (dynamic) bit width.
393 inline bool isUIntN(unsigned N, uint64_t x) {
394  return N >= 64 || x <= maxUIntN(N);
395 }
396 
397 /// Checks if an signed integer fits into the given (dynamic) bit width.
398 inline bool isIntN(unsigned N, int64_t x) {
399  return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
400 }
401 
402 /// Return true if the argument is a non-empty sequence of ones starting at the
403 /// least significant bit with the remainder zero (32 bit version).
404 /// Ex. isMask_32(0x0000FFFFU) == true.
405 constexpr inline bool isMask_32(uint32_t Value) {
406  return Value && ((Value + 1) & Value) == 0;
407 }
408 
409 /// Return true if the argument is a non-empty sequence of ones starting at the
410 /// least significant bit with the remainder zero (64 bit version).
411 constexpr inline bool isMask_64(uint64_t Value) {
412  return Value && ((Value + 1) & Value) == 0;
413 }
414 
415 /// Return true if the argument contains a non-empty sequence of ones with the
416 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
417 constexpr inline bool isShiftedMask_32(uint32_t Value) {
418  return Value && isMask_32((Value - 1) | Value);
419 }
420 
421 /// Return true if the argument contains a non-empty sequence of ones with the
422 /// remainder zero (64 bit version.)
423 constexpr inline bool isShiftedMask_64(uint64_t Value) {
424  return Value && isMask_64((Value - 1) | Value);
425 }
426 
427 /// Return true if the argument is a power of two > 0.
428 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
429 constexpr inline bool isPowerOf2_32(uint32_t Value) {
430  return Value && !(Value & (Value - 1));
431 }
432 
433 /// Return true if the argument is a power of two > 0 (64 bit edition.)
434 constexpr inline bool isPowerOf2_64(uint64_t Value) {
435  return Value && !(Value & (Value - 1));
436 }
437 
438 /// Return a byte-swapped representation of the 16-bit argument.
439 inline uint16_t ByteSwap_16(uint16_t Value) {
440  return sys::SwapByteOrder_16(Value);
441 }
442 
443 /// Return a byte-swapped representation of the 32-bit argument.
445  return sys::SwapByteOrder_32(Value);
446 }
447 
448 /// Return a byte-swapped representation of the 64-bit argument.
449 inline uint64_t ByteSwap_64(uint64_t Value) {
450  return sys::SwapByteOrder_64(Value);
451 }
452 
453 /// Count the number of ones from the most significant bit to the first
454 /// zero bit.
455 ///
456 /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
457 /// Only unsigned integral types are allowed.
458 ///
459 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
460 /// ZB_Undefined are valid arguments.
461 template <typename T>
463  static_assert(std::numeric_limits<T>::is_integer &&
464  !std::numeric_limits<T>::is_signed,
465  "Only unsigned integral types are allowed.");
466  return countLeadingZeros<T>(~Value, ZB);
467 }
468 
469 /// Count the number of ones from the least significant bit to the first
470 /// zero bit.
471 ///
472 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
473 /// Only unsigned integral types are allowed.
474 ///
475 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
476 /// ZB_Undefined are valid arguments.
477 template <typename T>
479  static_assert(std::numeric_limits<T>::is_integer &&
480  !std::numeric_limits<T>::is_signed,
481  "Only unsigned integral types are allowed.");
482  return countTrailingZeros<T>(~Value, ZB);
483 }
484 
485 namespace detail {
486 template <typename T, std::size_t SizeOfT> struct PopulationCounter {
487  static unsigned count(T Value) {
488  // Generic version, forward to 32 bits.
489  static_assert(SizeOfT <= 4, "Not implemented!");
490 #if __GNUC__ >= 4
491  return __builtin_popcount(Value);
492 #else
493  uint32_t v = Value;
494  v = v - ((v >> 1) & 0x55555555);
495  v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
496  return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
497 #endif
498  }
499 };
500 
501 template <typename T> struct PopulationCounter<T, 8> {
502  static unsigned count(T Value) {
503 #if __GNUC__ >= 4
504  return __builtin_popcountll(Value);
505 #else
506  uint64_t v = Value;
507  v = v - ((v >> 1) & 0x5555555555555555ULL);
508  v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
509  v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
510  return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
511 #endif
512  }
513 };
514 } // namespace detail
515 
516 /// Count the number of set bits in a value.
517 /// Ex. countPopulation(0xF000F000) = 8
518 /// Returns 0 if the word is zero.
519 template <typename T>
520 inline unsigned countPopulation(T Value) {
521  static_assert(std::numeric_limits<T>::is_integer &&
522  !std::numeric_limits<T>::is_signed,
523  "Only unsigned integral types are allowed.");
525 }
526 
527 /// Return the log base 2 of the specified value.
528 inline double Log2(double Value) {
529 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
530  return __builtin_log(Value) / __builtin_log(2.0);
531 #else
532  return log2(Value);
533 #endif
534 }
535 
536 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
537 /// (32 bit edition.)
538 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
539 inline unsigned Log2_32(uint32_t Value) {
540  return 31 - countLeadingZeros(Value);
541 }
542 
543 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
544 /// (64 bit edition.)
545 inline unsigned Log2_64(uint64_t Value) {
546  return 63 - countLeadingZeros(Value);
547 }
548 
549 /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
550 /// (32 bit edition).
551 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
552 inline unsigned Log2_32_Ceil(uint32_t Value) {
553  return 32 - countLeadingZeros(Value - 1);
554 }
555 
556 /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
557 /// (64 bit edition.)
558 inline unsigned Log2_64_Ceil(uint64_t Value) {
559  return 64 - countLeadingZeros(Value - 1);
560 }
561 
562 /// Return the greatest common divisor of the values using Euclid's algorithm.
563 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
564  while (B) {
565  uint64_t T = B;
566  B = A % B;
567  A = T;
568  }
569  return A;
570 }
571 
572 /// This function takes a 64-bit integer and returns the bit equivalent double.
573 inline double BitsToDouble(uint64_t Bits) {
574  double D;
575  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
576  memcpy(&D, &Bits, sizeof(Bits));
577  return D;
578 }
579 
580 /// This function takes a 32-bit integer and returns the bit equivalent float.
581 inline float BitsToFloat(uint32_t Bits) {
582  float F;
583  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
584  memcpy(&F, &Bits, sizeof(Bits));
585  return F;
586 }
587 
588 /// This function takes a double and returns the bit equivalent 64-bit integer.
589 /// Note that copying doubles around changes the bits of NaNs on some hosts,
590 /// notably x86, so this routine cannot be used if these bits are needed.
591 inline uint64_t DoubleToBits(double Double) {
592  uint64_t Bits;
593  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
594  memcpy(&Bits, &Double, sizeof(Double));
595  return Bits;
596 }
597 
598 /// This function takes a float and returns the bit equivalent 32-bit integer.
599 /// Note that copying floats around changes the bits of NaNs on some hosts,
600 /// notably x86, so this routine cannot be used if these bits are needed.
601 inline uint32_t FloatToBits(float Float) {
602  uint32_t Bits;
603  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
604  memcpy(&Bits, &Float, sizeof(Float));
605  return Bits;
606 }
607 
608 /// A and B are either alignments or offsets. Return the minimum alignment that
609 /// may be assumed after adding the two together.
610 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
611  // The largest power of 2 that divides both A and B.
612  //
613  // Replace "-Value" by "1+~Value" in the following commented code to avoid
614  // MSVC warning C4146
615  // return (A | B) & -(A | B);
616  return (A | B) & (1 + ~(A | B));
617 }
618 
619 /// Aligns \c Addr to \c Alignment bytes, rounding up.
620 ///
621 /// Alignment should be a power of two. This method rounds up, so
622 /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
623 inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
624  assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
625  "Alignment is not a power of two!");
626 
627  assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
628 
629  return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
630 }
631 
632 /// Returns the necessary adjustment for aligning \c Ptr to \c Alignment
633 /// bytes, rounding up.
634 inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
635  return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
636 }
637 
638 /// Returns the next power of two (in 64-bits) that is strictly greater than A.
639 /// Returns zero on overflow.
640 inline uint64_t NextPowerOf2(uint64_t A) {
641  A |= (A >> 1);
642  A |= (A >> 2);
643  A |= (A >> 4);
644  A |= (A >> 8);
645  A |= (A >> 16);
646  A |= (A >> 32);
647  return A + 1;
648 }
649 
650 /// Returns the power of two which is less than or equal to the given value.
651 /// Essentially, it is a floor operation across the domain of powers of two.
652 inline uint64_t PowerOf2Floor(uint64_t A) {
653  if (!A) return 0;
654  return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
655 }
656 
657 /// Returns the power of two which is greater than or equal to the given value.
658 /// Essentially, it is a ceil operation across the domain of powers of two.
659 inline uint64_t PowerOf2Ceil(uint64_t A) {
660  if (!A)
661  return 0;
662  return NextPowerOf2(A - 1);
663 }
664 
665 /// Returns the next integer (mod 2**64) that is greater than or equal to
666 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
667 ///
668 /// If non-zero \p Skew is specified, the return value will be a minimal
669 /// integer that is greater than or equal to \p Value and equal to
670 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
671 /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
672 ///
673 /// Examples:
674 /// \code
675 /// alignTo(5, 8) = 8
676 /// alignTo(17, 8) = 24
677 /// alignTo(~0LL, 8) = 0
678 /// alignTo(321, 255) = 510
679 ///
680 /// alignTo(5, 8, 7) = 7
681 /// alignTo(17, 8, 1) = 17
682 /// alignTo(~0LL, 8, 3) = 3
683 /// alignTo(321, 255, 42) = 552
684 /// \endcode
685 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
686  assert(Align != 0u && "Align can't be 0.");
687  Skew %= Align;
688  return (Value + Align - 1 - Skew) / Align * Align + Skew;
689 }
690 
691 /// Returns the next integer (mod 2**64) that is greater than or equal to
692 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
693 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
694  static_assert(Align != 0u, "Align must be non-zero");
695  return (Value + Align - 1) / Align * Align;
696 }
697 
698 /// Returns the integer ceil(Numerator / Denominator).
699 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
700  return alignTo(Numerator, Denominator) / Denominator;
701 }
702 
703 /// \c alignTo for contexts where a constant expression is required.
704 /// \sa alignTo
705 ///
706 /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
707 template <uint64_t Align>
708 struct AlignTo {
709  static_assert(Align != 0u, "Align must be non-zero");
710  template <uint64_t Value>
711  struct from_value {
712  static const uint64_t value = (Value + Align - 1) / Align * Align;
713  };
714 };
715 
716 /// Returns the largest uint64_t less than or equal to \p Value and is
717 /// \p Skew mod \p Align. \p Align must be non-zero
718 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
719  assert(Align != 0u && "Align can't be 0.");
720  Skew %= Align;
721  return (Value - Skew) / Align * Align + Skew;
722 }
723 
724 /// Returns the offset to the next integer (mod 2**64) that is greater than
725 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
726 /// non-zero.
727 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
728  return alignTo(Value, Align) - Value;
729 }
730 
731 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
732 /// Requires 0 < B <= 32.
733 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
734  static_assert(B > 0, "Bit width can't be 0.");
735  static_assert(B <= 32, "Bit width out of range.");
736  return int32_t(X << (32 - B)) >> (32 - B);
737 }
738 
739 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
740 /// Requires 0 < B < 32.
741 inline int32_t SignExtend32(uint32_t X, unsigned B) {
742  assert(B > 0 && "Bit width can't be 0.");
743  assert(B <= 32 && "Bit width out of range.");
744  return int32_t(X << (32 - B)) >> (32 - B);
745 }
746 
747 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
748 /// Requires 0 < B < 64.
749 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
750  static_assert(B > 0, "Bit width can't be 0.");
751  static_assert(B <= 64, "Bit width out of range.");
752  return int64_t(x << (64 - B)) >> (64 - B);
753 }
754 
755 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
756 /// Requires 0 < B < 64.
757 inline int64_t SignExtend64(uint64_t X, unsigned B) {
758  assert(B > 0 && "Bit width can't be 0.");
759  assert(B <= 64 && "Bit width out of range.");
760  return int64_t(X << (64 - B)) >> (64 - B);
761 }
762 
763 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
764 /// value of the result.
765 template <typename T>
766 typename std::enable_if<std::is_unsigned<T>::value, T>::type
768  return std::max(X, Y) - std::min(X, Y);
769 }
770 
771 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
772 /// maximum representable value of T on overflow. ResultOverflowed indicates if
773 /// the result is larger than the maximum representable value of type T.
774 template <typename T>
775 typename std::enable_if<std::is_unsigned<T>::value, T>::type
776 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
777  bool Dummy;
778  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
779  // Hacker's Delight, p. 29
780  T Z = X + Y;
781  Overflowed = (Z < X || Z < Y);
782  if (Overflowed)
784  else
785  return Z;
786 }
787 
788 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
789 /// maximum representable value of T on overflow. ResultOverflowed indicates if
790 /// the result is larger than the maximum representable value of type T.
791 template <typename T>
792 typename std::enable_if<std::is_unsigned<T>::value, T>::type
793 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
794  bool Dummy;
795  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
796 
797  // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
798  // because it fails for uint16_t (where multiplication can have undefined
799  // behavior due to promotion to int), and requires a division in addition
800  // to the multiplication.
801 
802  Overflowed = false;
803 
804  // Log2(Z) would be either Log2Z or Log2Z + 1.
805  // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
806  // will necessarily be less than Log2Max as desired.
807  int Log2Z = Log2_64(X) + Log2_64(Y);
808  const T Max = std::numeric_limits<T>::max();
809  int Log2Max = Log2_64(Max);
810  if (Log2Z < Log2Max) {
811  return X * Y;
812  }
813  if (Log2Z > Log2Max) {
814  Overflowed = true;
815  return Max;
816  }
817 
818  // We're going to use the top bit, and maybe overflow one
819  // bit past it. Multiply all but the bottom bit then add
820  // that on at the end.
821  T Z = (X >> 1) * Y;
822  if (Z & ~(Max >> 1)) {
823  Overflowed = true;
824  return Max;
825  }
826  Z <<= 1;
827  if (X & 1)
828  return SaturatingAdd(Z, Y, ResultOverflowed);
829 
830  return Z;
831 }
832 
833 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
834 /// the product. Clamp the result to the maximum representable value of T on
835 /// overflow. ResultOverflowed indicates if the result is larger than the
836 /// maximum representable value of type T.
837 template <typename T>
838 typename std::enable_if<std::is_unsigned<T>::value, T>::type
839 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
840  bool Dummy;
841  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
842 
843  T Product = SaturatingMultiply(X, Y, &Overflowed);
844  if (Overflowed)
845  return Product;
846 
847  return SaturatingAdd(A, Product, &Overflowed);
848 }
849 
850 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
851 extern const float huge_valf;
852 } // End llvm namespace
853 
854 #endif
constexpr bool isUInt< 32 >(uint64_t x)
Definition: MathExtras.h:349
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:552
constexpr char Align[]
Key for Kernel::Arg::Metadata::mAlign.
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:244
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:563
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:289
static unsigned count(T Value)
Definition: MathExtras.h:487
float BitsToFloat(uint32_t Bits)
This function takes a 32-bit integer and returns the bit equivalent float.
Definition: MathExtras.h:581
constexpr bool isInt< 8 >(int64_t x)
Definition: MathExtras.h:303
ZeroBehavior
The behavior an operation has on an input of 0.
Definition: MathExtras.h:44
constexpr bool isInt< 16 >(int64_t x)
Definition: MathExtras.h:306
F(f)
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:685
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:189
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:793
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:405
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:776
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:212
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:718
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:50
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:478
The returned value is undefined.
Definition: MathExtras.h:46
static unsigned count(T Value)
Definition: MathExtras.h:502
uint32_t ByteSwap_32(uint32_t Value)
Return a byte-swapped representation of the 32-bit argument.
Definition: MathExtras.h:444
int64_t maxIntN(int64_t N)
Gets the maximum value for a N-bit signed integer.
Definition: MathExtras.h:384
static const unsigned char BitReverseTable256[256]
Macro compressed bit reversal table for 256 bits.
Definition: MathExtras.h:257
#define UINT64_MAX
Definition: DataTypes.h:83
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:411
uint16_t ByteSwap_16(uint16_t Value)
Return a byte-swapped representation of the 16-bit argument.
Definition: MathExtras.h:439
#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:355
int64_t minIntN(int64_t N)
Gets the minimum value for a N-bit signed integer.
Definition: MathExtras.h:377
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:227
uint32_t FloatToBits(float Float)
This function takes a float and returns the bit equivalent 32-bit integer.
Definition: MathExtras.h:601
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:610
static GCRegistry::Add< OcamlGC > B("ocaml", "ocaml 3.10-compatible GC")
constexpr bool isUInt< 8 >(uint64_t x)
Definition: MathExtras.h:343
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:120
constexpr bool isShiftedInt(int64_t x)
Checks if a signed integer is an N bit number shifted left by S.
Definition: MathExtras.h:315
constexpr bool isPowerOf2_32(uint32_t Value)
Return true if the argument is a power of two > 0.
Definition: MathExtras.h:429
constexpr bool isInt(int64_t x)
Checks if an integer fits into the given bit width.
Definition: MathExtras.h:299
size_t alignmentAdjustment(const void *Ptr, size_t Alignment)
Returns the necessary adjustment for aligning Ptr to Alignment bytes, rounding up.
Definition: MathExtras.h:634
constexpr bool isPowerOf2_64(uint64_t Value)
Return true if the argument is a power of two > 0 (64 bit edition.)
Definition: MathExtras.h:434
The returned value is numeric_limits<T>::max()
Definition: MathExtras.h:48
static double log2(double V)
bool isIntN(unsigned N, int64_t x)
Checks if an signed integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:398
uint64_t NextPowerOf2(uint64_t A)
Returns the next power of two (in 64-bits) that is strictly greater than A.
Definition: MathExtras.h:640
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:203
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:839
unsigned countPopulation(T Value)
Count the number of set bits in a value.
Definition: MathExtras.h:520
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:332
#define R6(n)
constexpr bool isInt< 32 >(int64_t x)
Definition: MathExtras.h:309
double Log2(double Value)
Return the log base 2 of the specified value.
Definition: MathExtras.h:528
static GCRegistry::Add< StatepointGC > D("statepoint-example", "an example strategy for statepoint")
uint64_t DoubleToBits(double Double)
This function takes a double and returns the bit equivalent 64-bit integer.
Definition: MathExtras.h:591
double BitsToDouble(uint64_t Bits)
This function takes a 64-bit integer and returns the bit equivalent double.
Definition: MathExtras.h:573
static std::size_t count(T Val, ZeroBehavior)
Definition: MathExtras.h:129
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:558
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:539
alignTo for contexts where a constant expression is required.
Definition: MathExtras.h:708
uintptr_t alignAddr(const void *Addr, size_t Alignment)
Aligns Addr to Alignment bytes, rounding up.
Definition: MathExtras.h:623
static std::size_t count(T Val, ZeroBehavior)
Definition: MathExtras.h:55
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:423
uint64_t maxUIntN(uint64_t N)
Gets the maximum value for a N-bit unsigned integer.
Definition: MathExtras.h:366
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:233
uint64_t ByteSwap_64(uint64_t Value)
Return a byte-swapped representation of the 64-bit argument.
Definition: MathExtras.h:449
#define N
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:767
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:733
uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator)
Returns the integer ceil(Numerator / Denominator).
Definition: MathExtras.h:699
constexpr bool isUInt< 16 >(uint64_t x)
Definition: MathExtras.h:346
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:749
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:652
constexpr uint32_t Hi_32(uint64_t Value)
Return the high 32 bits of a 64 bit value.
Definition: MathExtras.h:284
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:727
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:294
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:417
bool isUIntN(unsigned N, uint64_t x)
Checks if an unsigned integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:393
T reverseBits(T Val)
Reverse the bits in Val.
Definition: MathExtras.h:269
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:462
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:545
uint64_t PowerOf2Ceil(uint64_t A)
Returns the power of two which is greater than or equal to the given value.
Definition: MathExtras.h:659
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:221