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MathExtras.h
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1 //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // This file contains some functions that are useful for math stuff.
10 //
11 //===----------------------------------------------------------------------===//
12 
13 #ifndef LLVM_SUPPORT_MATHEXTRAS_H
14 #define LLVM_SUPPORT_MATHEXTRAS_H
15 
16 #include "llvm/Support/Compiler.h"
17 #include <cassert>
18 #include <climits>
19 #include <cmath>
20 #include <cstdint>
21 #include <cstring>
22 #include <limits>
23 #include <type_traits>
24 
25 #ifdef __ANDROID_NDK__
26 #include <android/api-level.h>
27 #endif
28 
29 #ifdef _MSC_VER
30 // Declare these intrinsics manually rather including intrin.h. It's very
31 // expensive, and MathExtras.h is popular.
32 // #include <intrin.h>
33 extern "C" {
34 unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
35 unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
36 unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
37 unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
38 }
39 #endif
40 
41 namespace llvm {
42 
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 /// Mathematical constants.
54 namespace numbers {
55 // TODO: Track C++20 std::numbers.
56 // TODO: Favor using the hexadecimal FP constants (requires C++17).
57 constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
58  egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
59  ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
60  ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
61  log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0)
62  log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
63  pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
64  inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
65  sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
66  inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
67  sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
68  inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
69  sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
70  inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1)
71  phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
72 constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
73  egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
74  ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
75  ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
76  log2ef = 1.44269504F, // (0x1.715476P+0)
77  log10ef = .434294482F, // (0x1.bcb7b2P-2)
78  pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
79  inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
80  sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
81  inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
82  sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
83  inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1)
84  sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
85  inv_sqrt3f = .577350269F, // (0x1.279a74P-1)
86  phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
87 } // namespace numbers
88 
89 namespace detail {
90 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
91  static unsigned count(T Val, ZeroBehavior) {
92  if (!Val)
93  return std::numeric_limits<T>::digits;
94  if (Val & 0x1)
95  return 0;
96 
97  // Bisection method.
98  unsigned ZeroBits = 0;
99  T Shift = std::numeric_limits<T>::digits >> 1;
101  while (Shift) {
102  if ((Val & Mask) == 0) {
103  Val >>= Shift;
104  ZeroBits |= Shift;
105  }
106  Shift >>= 1;
107  Mask >>= Shift;
108  }
109  return ZeroBits;
110  }
111 };
112 
113 #if defined(__GNUC__) || defined(_MSC_VER)
114 template <typename T> struct TrailingZerosCounter<T, 4> {
115  static unsigned count(T Val, ZeroBehavior ZB) {
116  if (ZB != ZB_Undefined && Val == 0)
117  return 32;
118 
119 #if __has_builtin(__builtin_ctz) || defined(__GNUC__)
120  return __builtin_ctz(Val);
121 #elif defined(_MSC_VER)
122  unsigned long Index;
123  _BitScanForward(&Index, Val);
124  return Index;
125 #endif
126  }
127 };
128 
129 #if !defined(_MSC_VER) || defined(_M_X64)
130 template <typename T> struct TrailingZerosCounter<T, 8> {
131  static unsigned count(T Val, ZeroBehavior ZB) {
132  if (ZB != ZB_Undefined && Val == 0)
133  return 64;
134 
135 #if __has_builtin(__builtin_ctzll) || defined(__GNUC__)
136  return __builtin_ctzll(Val);
137 #elif defined(_MSC_VER)
138  unsigned long Index;
139  _BitScanForward64(&Index, Val);
140  return Index;
141 #endif
142  }
143 };
144 #endif
145 #endif
146 } // namespace detail
147 
148 /// Count number of 0's from the least significant bit to the most
149 /// stopping at the first 1.
150 ///
151 /// Only unsigned integral types are allowed.
152 ///
153 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
154 /// valid arguments.
155 template <typename T>
156 unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
157  static_assert(std::numeric_limits<T>::is_integer &&
158  !std::numeric_limits<T>::is_signed,
159  "Only unsigned integral types are allowed.");
160  return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
161 }
162 
163 namespace detail {
164 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
165  static unsigned count(T Val, ZeroBehavior) {
166  if (!Val)
167  return std::numeric_limits<T>::digits;
168 
169  // Bisection method.
170  unsigned ZeroBits = 0;
171  for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
172  T Tmp = Val >> Shift;
173  if (Tmp)
174  Val = Tmp;
175  else
176  ZeroBits |= Shift;
177  }
178  return ZeroBits;
179  }
180 };
181 
182 #if defined(__GNUC__) || defined(_MSC_VER)
183 template <typename T> struct LeadingZerosCounter<T, 4> {
184  static unsigned count(T Val, ZeroBehavior ZB) {
185  if (ZB != ZB_Undefined && Val == 0)
186  return 32;
187 
188 #if __has_builtin(__builtin_clz) || defined(__GNUC__)
189  return __builtin_clz(Val);
190 #elif defined(_MSC_VER)
191  unsigned long Index;
192  _BitScanReverse(&Index, Val);
193  return Index ^ 31;
194 #endif
195  }
196 };
197 
198 #if !defined(_MSC_VER) || defined(_M_X64)
199 template <typename T> struct LeadingZerosCounter<T, 8> {
200  static unsigned count(T Val, ZeroBehavior ZB) {
201  if (ZB != ZB_Undefined && Val == 0)
202  return 64;
203 
204 #if __has_builtin(__builtin_clzll) || defined(__GNUC__)
205  return __builtin_clzll(Val);
206 #elif defined(_MSC_VER)
207  unsigned long Index;
208  _BitScanReverse64(&Index, Val);
209  return Index ^ 63;
210 #endif
211  }
212 };
213 #endif
214 #endif
215 } // namespace detail
216 
217 /// Count number of 0's from the most significant bit to the least
218 /// stopping at the first 1.
219 ///
220 /// Only unsigned integral types are allowed.
221 ///
222 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
223 /// valid arguments.
224 template <typename T>
225 unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
226  static_assert(std::numeric_limits<T>::is_integer &&
227  !std::numeric_limits<T>::is_signed,
228  "Only unsigned integral types are allowed.");
229  return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
230 }
231 
232 /// Get the index of the first set bit starting from the least
233 /// significant bit.
234 ///
235 /// Only unsigned integral types are allowed.
236 ///
237 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
238 /// valid arguments.
239 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
240  if (ZB == ZB_Max && Val == 0)
242 
243  return countTrailingZeros(Val, ZB_Undefined);
244 }
245 
246 /// Create a bitmask with the N right-most bits set to 1, and all other
247 /// bits set to 0. Only unsigned types are allowed.
248 template <typename T> T maskTrailingOnes(unsigned N) {
249  static_assert(std::is_unsigned<T>::value, "Invalid type!");
250  const unsigned Bits = CHAR_BIT * sizeof(T);
251  assert(N <= Bits && "Invalid bit index");
252  return N == 0 ? 0 : (T(-1) >> (Bits - N));
253 }
254 
255 /// Create a bitmask with the N left-most bits set to 1, and all other
256 /// bits set to 0. Only unsigned types are allowed.
257 template <typename T> T maskLeadingOnes(unsigned N) {
258  return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
259 }
260 
261 /// Create a bitmask with the N right-most bits set to 0, and all other
262 /// bits set to 1. Only unsigned types are allowed.
263 template <typename T> T maskTrailingZeros(unsigned N) {
264  return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
265 }
266 
267 /// Create a bitmask with the N left-most bits set to 0, and all other
268 /// bits set to 1. Only unsigned types are allowed.
269 template <typename T> T maskLeadingZeros(unsigned N) {
270  return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
271 }
272 
273 /// Get the index of the last set bit starting from the least
274 /// significant bit.
275 ///
276 /// Only unsigned integral types are allowed.
277 ///
278 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
279 /// valid arguments.
280 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
281  if (ZB == ZB_Max && Val == 0)
283 
284  // Use ^ instead of - because both gcc and llvm can remove the associated ^
285  // in the __builtin_clz intrinsic on x86.
286  return countLeadingZeros(Val, ZB_Undefined) ^
287  (std::numeric_limits<T>::digits - 1);
288 }
289 
290 /// Macro compressed bit reversal table for 256 bits.
291 ///
292 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
293 static const unsigned char BitReverseTable256[256] = {
294 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
295 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
296 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
297  R6(0), R6(2), R6(1), R6(3)
298 #undef R2
299 #undef R4
300 #undef R6
301 };
302 
303 /// Reverse the bits in \p Val.
304 template <typename T>
305 T reverseBits(T Val) {
306  unsigned char in[sizeof(Val)];
307  unsigned char out[sizeof(Val)];
308  std::memcpy(in, &Val, sizeof(Val));
309  for (unsigned i = 0; i < sizeof(Val); ++i)
310  out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
311  std::memcpy(&Val, out, sizeof(Val));
312  return Val;
313 }
314 
315 #if __has_builtin(__builtin_bitreverse8)
316 template<>
317 inline uint8_t reverseBits<uint8_t>(uint8_t Val) {
318  return __builtin_bitreverse8(Val);
319 }
320 #endif
321 
322 #if __has_builtin(__builtin_bitreverse16)
323 template<>
324 inline uint16_t reverseBits<uint16_t>(uint16_t Val) {
325  return __builtin_bitreverse16(Val);
326 }
327 #endif
328 
329 #if __has_builtin(__builtin_bitreverse32)
330 template<>
331 inline uint32_t reverseBits<uint32_t>(uint32_t Val) {
332  return __builtin_bitreverse32(Val);
333 }
334 #endif
335 
336 #if __has_builtin(__builtin_bitreverse64)
337 template<>
338 inline uint64_t reverseBits<uint64_t>(uint64_t Val) {
339  return __builtin_bitreverse64(Val);
340 }
341 #endif
342 
343 // NOTE: The following support functions use the _32/_64 extensions instead of
344 // type overloading so that signed and unsigned integers can be used without
345 // ambiguity.
346 
347 /// Return the high 32 bits of a 64 bit value.
348 constexpr inline uint32_t Hi_32(uint64_t Value) {
349  return static_cast<uint32_t>(Value >> 32);
350 }
351 
352 /// Return the low 32 bits of a 64 bit value.
353 constexpr inline uint32_t Lo_32(uint64_t Value) {
354  return static_cast<uint32_t>(Value);
355 }
356 
357 /// Make a 64-bit integer from a high / low pair of 32-bit integers.
358 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
359  return ((uint64_t)High << 32) | (uint64_t)Low;
360 }
361 
362 /// Checks if an integer fits into the given bit width.
363 template <unsigned N> constexpr inline bool isInt(int64_t x) {
364  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
365 }
366 // Template specializations to get better code for common cases.
367 template <> constexpr inline bool isInt<8>(int64_t x) {
368  return static_cast<int8_t>(x) == x;
369 }
370 template <> constexpr inline bool isInt<16>(int64_t x) {
371  return static_cast<int16_t>(x) == x;
372 }
373 template <> constexpr inline bool isInt<32>(int64_t x) {
374  return static_cast<int32_t>(x) == x;
375 }
376 
377 /// Checks if a signed integer is an N bit number shifted left by S.
378 template <unsigned N, unsigned S>
379 constexpr inline bool isShiftedInt(int64_t x) {
380  static_assert(
381  N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
382  static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
383  return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
384 }
385 
386 /// Checks if an unsigned integer fits into the given bit width.
387 ///
388 /// This is written as two functions rather than as simply
389 ///
390 /// return N >= 64 || X < (UINT64_C(1) << N);
391 ///
392 /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
393 /// left too many places.
394 template <unsigned N>
395 constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) {
396  static_assert(N > 0, "isUInt<0> doesn't make sense");
397  return X < (UINT64_C(1) << (N));
398 }
399 template <unsigned N>
400 constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) {
401  return true;
402 }
403 
404 // Template specializations to get better code for common cases.
405 template <> constexpr inline bool isUInt<8>(uint64_t x) {
406  return static_cast<uint8_t>(x) == x;
407 }
408 template <> constexpr inline bool isUInt<16>(uint64_t x) {
409  return static_cast<uint16_t>(x) == x;
410 }
411 template <> constexpr inline bool isUInt<32>(uint64_t x) {
412  return static_cast<uint32_t>(x) == x;
413 }
414 
415 /// Checks if a unsigned integer is an N bit number shifted left by S.
416 template <unsigned N, unsigned S>
417 constexpr inline bool isShiftedUInt(uint64_t x) {
418  static_assert(
419  N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
420  static_assert(N + S <= 64,
421  "isShiftedUInt<N, S> with N + S > 64 is too wide.");
422  // Per the two static_asserts above, S must be strictly less than 64. So
423  // 1 << S is not undefined behavior.
424  return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
425 }
426 
427 /// Gets the maximum value for a N-bit unsigned integer.
429  assert(N > 0 && N <= 64 && "integer width out of range");
430 
431  // uint64_t(1) << 64 is undefined behavior, so we can't do
432  // (uint64_t(1) << N) - 1
433  // without checking first that N != 64. But this works and doesn't have a
434  // branch.
435  return UINT64_MAX >> (64 - N);
436 }
437 
438 /// Gets the minimum value for a N-bit signed integer.
439 inline int64_t minIntN(int64_t N) {
440  assert(N > 0 && N <= 64 && "integer width out of range");
441 
442  return UINT64_C(1) + ~(UINT64_C(1) << (N - 1));
443 }
444 
445 /// Gets the maximum value for a N-bit signed integer.
446 inline int64_t maxIntN(int64_t N) {
447  assert(N > 0 && N <= 64 && "integer width out of range");
448 
449  // This relies on two's complement wraparound when N == 64, so we convert to
450  // int64_t only at the very end to avoid UB.
451  return (UINT64_C(1) << (N - 1)) - 1;
452 }
453 
454 /// Checks if an unsigned integer fits into the given (dynamic) bit width.
455 inline bool isUIntN(unsigned N, uint64_t x) {
456  return N >= 64 || x <= maxUIntN(N);
457 }
458 
459 /// Checks if an signed integer fits into the given (dynamic) bit width.
460 inline bool isIntN(unsigned N, int64_t x) {
461  return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
462 }
463 
464 /// Return true if the argument is a non-empty sequence of ones starting at the
465 /// least significant bit with the remainder zero (32 bit version).
466 /// Ex. isMask_32(0x0000FFFFU) == true.
467 constexpr inline bool isMask_32(uint32_t Value) {
468  return Value && ((Value + 1) & Value) == 0;
469 }
470 
471 /// Return true if the argument is a non-empty sequence of ones starting at the
472 /// least significant bit with the remainder zero (64 bit version).
473 constexpr inline bool isMask_64(uint64_t Value) {
474  return Value && ((Value + 1) & Value) == 0;
475 }
476 
477 /// Return true if the argument contains a non-empty sequence of ones with the
478 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
479 constexpr inline bool isShiftedMask_32(uint32_t Value) {
480  return Value && isMask_32((Value - 1) | Value);
481 }
482 
483 /// Return true if the argument contains a non-empty sequence of ones with the
484 /// remainder zero (64 bit version.)
485 constexpr inline bool isShiftedMask_64(uint64_t Value) {
486  return Value && isMask_64((Value - 1) | Value);
487 }
488 
489 /// Return true if the argument is a power of two > 0.
490 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
491 constexpr inline bool isPowerOf2_32(uint32_t Value) {
492  return Value && !(Value & (Value - 1));
493 }
494 
495 /// Return true if the argument is a power of two > 0 (64 bit edition.)
496 constexpr inline bool isPowerOf2_64(uint64_t Value) {
497  return Value && !(Value & (Value - 1));
498 }
499 
500 /// Count the number of ones from the most significant bit to the first
501 /// zero bit.
502 ///
503 /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
504 /// Only unsigned integral types are allowed.
505 ///
506 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
507 /// ZB_Undefined are valid arguments.
508 template <typename T>
510  static_assert(std::numeric_limits<T>::is_integer &&
511  !std::numeric_limits<T>::is_signed,
512  "Only unsigned integral types are allowed.");
513  return countLeadingZeros<T>(~Value, ZB);
514 }
515 
516 /// Count the number of ones from the least significant bit to the first
517 /// zero bit.
518 ///
519 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
520 /// Only unsigned integral types are allowed.
521 ///
522 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
523 /// ZB_Undefined are valid arguments.
524 template <typename T>
526  static_assert(std::numeric_limits<T>::is_integer &&
527  !std::numeric_limits<T>::is_signed,
528  "Only unsigned integral types are allowed.");
529  return countTrailingZeros<T>(~Value, ZB);
530 }
531 
532 namespace detail {
533 template <typename T, std::size_t SizeOfT> struct PopulationCounter {
534  static unsigned count(T Value) {
535  // Generic version, forward to 32 bits.
536  static_assert(SizeOfT <= 4, "Not implemented!");
537 #if defined(__GNUC__)
538  return __builtin_popcount(Value);
539 #else
540  uint32_t v = Value;
541  v = v - ((v >> 1) & 0x55555555);
542  v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
543  return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
544 #endif
545  }
546 };
547 
548 template <typename T> struct PopulationCounter<T, 8> {
549  static unsigned count(T Value) {
550 #if defined(__GNUC__)
551  return __builtin_popcountll(Value);
552 #else
553  uint64_t v = Value;
554  v = v - ((v >> 1) & 0x5555555555555555ULL);
555  v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
556  v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
557  return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
558 #endif
559  }
560 };
561 } // namespace detail
562 
563 /// Count the number of set bits in a value.
564 /// Ex. countPopulation(0xF000F000) = 8
565 /// Returns 0 if the word is zero.
566 template <typename T>
567 inline unsigned countPopulation(T Value) {
568  static_assert(std::numeric_limits<T>::is_integer &&
569  !std::numeric_limits<T>::is_signed,
570  "Only unsigned integral types are allowed.");
571  return detail::PopulationCounter<T, sizeof(T)>::count(Value);
572 }
573 
574 /// Compile time Log2.
575 /// Valid only for positive powers of two.
576 template <size_t kValue> constexpr inline size_t CTLog2() {
577  static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
578  "Value is not a valid power of 2");
579  return 1 + CTLog2<kValue / 2>();
580 }
581 
582 template <> constexpr inline size_t CTLog2<1>() { return 0; }
583 
584 /// Return the log base 2 of the specified value.
585 inline double Log2(double Value) {
586 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
587  return __builtin_log(Value) / __builtin_log(2.0);
588 #else
589  return log2(Value);
590 #endif
591 }
592 
593 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
594 /// (32 bit edition.)
595 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
596 inline unsigned Log2_32(uint32_t Value) {
597  return 31 - countLeadingZeros(Value);
598 }
599 
600 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
601 /// (64 bit edition.)
602 inline unsigned Log2_64(uint64_t Value) {
603  return 63 - countLeadingZeros(Value);
604 }
605 
606 /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
607 /// (32 bit edition).
608 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
609 inline unsigned Log2_32_Ceil(uint32_t Value) {
610  return 32 - countLeadingZeros(Value - 1);
611 }
612 
613 /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
614 /// (64 bit edition.)
615 inline unsigned Log2_64_Ceil(uint64_t Value) {
616  return 64 - countLeadingZeros(Value - 1);
617 }
618 
619 /// Return the greatest common divisor of the values using Euclid's algorithm.
620 template <typename T>
621 inline T greatestCommonDivisor(T A, T B) {
622  while (B) {
623  T Tmp = B;
624  B = A % B;
625  A = Tmp;
626  }
627  return A;
628 }
629 
631  return greatestCommonDivisor<uint64_t>(A, B);
632 }
633 
634 /// This function takes a 64-bit integer and returns the bit equivalent double.
635 inline double BitsToDouble(uint64_t Bits) {
636  double D;
637  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
638  memcpy(&D, &Bits, sizeof(Bits));
639  return D;
640 }
641 
642 /// This function takes a 32-bit integer and returns the bit equivalent float.
643 inline float BitsToFloat(uint32_t Bits) {
644  float F;
645  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
646  memcpy(&F, &Bits, sizeof(Bits));
647  return F;
648 }
649 
650 /// This function takes a double and returns the bit equivalent 64-bit integer.
651 /// Note that copying doubles around changes the bits of NaNs on some hosts,
652 /// notably x86, so this routine cannot be used if these bits are needed.
653 inline uint64_t DoubleToBits(double Double) {
654  uint64_t Bits;
655  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
656  memcpy(&Bits, &Double, sizeof(Double));
657  return Bits;
658 }
659 
660 /// This function takes a float and returns the bit equivalent 32-bit integer.
661 /// Note that copying floats around changes the bits of NaNs on some hosts,
662 /// notably x86, so this routine cannot be used if these bits are needed.
663 inline uint32_t FloatToBits(float Float) {
664  uint32_t Bits;
665  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
666  memcpy(&Bits, &Float, sizeof(Float));
667  return Bits;
668 }
669 
670 /// A and B are either alignments or offsets. Return the minimum alignment that
671 /// may be assumed after adding the two together.
672 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
673  // The largest power of 2 that divides both A and B.
674  //
675  // Replace "-Value" by "1+~Value" in the following commented code to avoid
676  // MSVC warning C4146
677  // return (A | B) & -(A | B);
678  return (A | B) & (1 + ~(A | B));
679 }
680 
681 /// Returns the next power of two (in 64-bits) that is strictly greater than A.
682 /// Returns zero on overflow.
684  A |= (A >> 1);
685  A |= (A >> 2);
686  A |= (A >> 4);
687  A |= (A >> 8);
688  A |= (A >> 16);
689  A |= (A >> 32);
690  return A + 1;
691 }
692 
693 /// Returns the power of two which is less than or equal to the given value.
694 /// Essentially, it is a floor operation across the domain of powers of two.
696  if (!A) return 0;
697  return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
698 }
699 
700 /// Returns the power of two which is greater than or equal to the given value.
701 /// Essentially, it is a ceil operation across the domain of powers of two.
703  if (!A)
704  return 0;
705  return NextPowerOf2(A - 1);
706 }
707 
708 /// Returns the next integer (mod 2**64) that is greater than or equal to
709 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
710 ///
711 /// If non-zero \p Skew is specified, the return value will be a minimal
712 /// integer that is greater than or equal to \p Value and equal to
713 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
714 /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
715 ///
716 /// Examples:
717 /// \code
718 /// alignTo(5, 8) = 8
719 /// alignTo(17, 8) = 24
720 /// alignTo(~0LL, 8) = 0
721 /// alignTo(321, 255) = 510
722 ///
723 /// alignTo(5, 8, 7) = 7
724 /// alignTo(17, 8, 1) = 17
725 /// alignTo(~0LL, 8, 3) = 3
726 /// alignTo(321, 255, 42) = 552
727 /// \endcode
729  assert(Align != 0u && "Align can't be 0.");
730  Skew %= Align;
731  return (Value + Align - 1 - Skew) / Align * Align + Skew;
732 }
733 
734 /// Returns the next integer (mod 2**64) that is greater than or equal to
735 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
736 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
737  static_assert(Align != 0u, "Align must be non-zero");
738  return (Value + Align - 1) / Align * Align;
739 }
740 
741 /// Returns the integer ceil(Numerator / Denominator).
742 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
743  return alignTo(Numerator, Denominator) / Denominator;
744 }
745 
746 /// Returns the integer nearest(Numerator / Denominator).
747 inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
748  return (Numerator + (Denominator / 2)) / Denominator;
749 }
750 
751 /// Returns the largest uint64_t less than or equal to \p Value and is
752 /// \p Skew mod \p Align. \p Align must be non-zero
754  assert(Align != 0u && "Align can't be 0.");
755  Skew %= Align;
756  return (Value - Skew) / Align * Align + Skew;
757 }
758 
759 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
760 /// Requires 0 < B <= 32.
761 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
762  static_assert(B > 0, "Bit width can't be 0.");
763  static_assert(B <= 32, "Bit width out of range.");
764  return int32_t(X << (32 - B)) >> (32 - B);
765 }
766 
767 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
768 /// Requires 0 < B <= 32.
769 inline int32_t SignExtend32(uint32_t X, unsigned B) {
770  assert(B > 0 && "Bit width can't be 0.");
771  assert(B <= 32 && "Bit width out of range.");
772  return int32_t(X << (32 - B)) >> (32 - B);
773 }
774 
775 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
776 /// Requires 0 < B <= 64.
777 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
778  static_assert(B > 0, "Bit width can't be 0.");
779  static_assert(B <= 64, "Bit width out of range.");
780  return int64_t(x << (64 - B)) >> (64 - B);
781 }
782 
783 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
784 /// Requires 0 < B <= 64.
785 inline int64_t SignExtend64(uint64_t X, unsigned B) {
786  assert(B > 0 && "Bit width can't be 0.");
787  assert(B <= 64 && "Bit width out of range.");
788  return int64_t(X << (64 - B)) >> (64 - B);
789 }
790 
791 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
792 /// value of the result.
793 template <typename T>
794 std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
795  return X > Y ? (X - Y) : (Y - X);
796 }
797 
798 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
799 /// maximum representable value of T on overflow. ResultOverflowed indicates if
800 /// the result is larger than the maximum representable value of type T.
801 template <typename T>
802 std::enable_if_t<std::is_unsigned<T>::value, T>
803 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
804  bool Dummy;
805  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
806  // Hacker's Delight, p. 29
807  T Z = X + Y;
808  Overflowed = (Z < X || Z < Y);
809  if (Overflowed)
811  else
812  return Z;
813 }
814 
815 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
816 /// maximum representable value of T on overflow. ResultOverflowed indicates if
817 /// the result is larger than the maximum representable value of type T.
818 template <typename T>
819 std::enable_if_t<std::is_unsigned<T>::value, T>
820 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
821  bool Dummy;
822  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
823 
824  // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
825  // because it fails for uint16_t (where multiplication can have undefined
826  // behavior due to promotion to int), and requires a division in addition
827  // to the multiplication.
828 
829  Overflowed = false;
830 
831  // Log2(Z) would be either Log2Z or Log2Z + 1.
832  // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
833  // will necessarily be less than Log2Max as desired.
834  int Log2Z = Log2_64(X) + Log2_64(Y);
835  const T Max = std::numeric_limits<T>::max();
836  int Log2Max = Log2_64(Max);
837  if (Log2Z < Log2Max) {
838  return X * Y;
839  }
840  if (Log2Z > Log2Max) {
841  Overflowed = true;
842  return Max;
843  }
844 
845  // We're going to use the top bit, and maybe overflow one
846  // bit past it. Multiply all but the bottom bit then add
847  // that on at the end.
848  T Z = (X >> 1) * Y;
849  if (Z & ~(Max >> 1)) {
850  Overflowed = true;
851  return Max;
852  }
853  Z <<= 1;
854  if (X & 1)
855  return SaturatingAdd(Z, Y, ResultOverflowed);
856 
857  return Z;
858 }
859 
860 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
861 /// the product. Clamp the result to the maximum representable value of T on
862 /// overflow. ResultOverflowed indicates if the result is larger than the
863 /// maximum representable value of type T.
864 template <typename T>
865 std::enable_if_t<std::is_unsigned<T>::value, T>
866 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
867  bool Dummy;
868  bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
869 
870  T Product = SaturatingMultiply(X, Y, &Overflowed);
871  if (Overflowed)
872  return Product;
873 
874  return SaturatingAdd(A, Product, &Overflowed);
875 }
876 
877 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
878 extern const float huge_valf;
879 
880 
881 /// Add two signed integers, computing the two's complement truncated result,
882 /// returning true if overflow occured.
883 template <typename T>
884 std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
885 #if __has_builtin(__builtin_add_overflow)
886  return __builtin_add_overflow(X, Y, &Result);
887 #else
888  // Perform the unsigned addition.
889  using U = std::make_unsigned_t<T>;
890  const U UX = static_cast<U>(X);
891  const U UY = static_cast<U>(Y);
892  const U UResult = UX + UY;
893 
894  // Convert to signed.
895  Result = static_cast<T>(UResult);
896 
897  // Adding two positive numbers should result in a positive number.
898  if (X > 0 && Y > 0)
899  return Result <= 0;
900  // Adding two negatives should result in a negative number.
901  if (X < 0 && Y < 0)
902  return Result >= 0;
903  return false;
904 #endif
905 }
906 
907 /// Subtract two signed integers, computing the two's complement truncated
908 /// result, returning true if an overflow ocurred.
909 template <typename T>
910 std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
911 #if __has_builtin(__builtin_sub_overflow)
912  return __builtin_sub_overflow(X, Y, &Result);
913 #else
914  // Perform the unsigned addition.
915  using U = std::make_unsigned_t<T>;
916  const U UX = static_cast<U>(X);
917  const U UY = static_cast<U>(Y);
918  const U UResult = UX - UY;
919 
920  // Convert to signed.
921  Result = static_cast<T>(UResult);
922 
923  // Subtracting a positive number from a negative results in a negative number.
924  if (X <= 0 && Y > 0)
925  return Result >= 0;
926  // Subtracting a negative number from a positive results in a positive number.
927  if (X >= 0 && Y < 0)
928  return Result <= 0;
929  return false;
930 #endif
931 }
932 
933 /// Multiply two signed integers, computing the two's complement truncated
934 /// result, returning true if an overflow ocurred.
935 template <typename T>
936 std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
937  // Perform the unsigned multiplication on absolute values.
938  using U = std::make_unsigned_t<T>;
939  const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
940  const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
941  const U UResult = UX * UY;
942 
943  // Convert to signed.
944  const bool IsNegative = (X < 0) ^ (Y < 0);
945  Result = IsNegative ? (0 - UResult) : UResult;
946 
947  // If any of the args was 0, result is 0 and no overflow occurs.
948  if (UX == 0 || UY == 0)
949  return false;
950 
951  // UX and UY are in [1, 2^n], where n is the number of digits.
952  // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
953  // positive) divided by an argument compares to the other.
954  if (IsNegative)
955  return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
956  else
957  return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
958 }
959 
960 } // End llvm namespace
961 
962 #endif
llvm::SaturatingMultiply
std::enable_if_t< std::is_unsigned< T >::value, T > SaturatingMultiply(T X, T Y, bool *ResultOverflowed=nullptr)
Multiply two unsigned integers, X and Y, of type T.
Definition: MathExtras.h:820
i
i
Definition: README.txt:29
llvm::NextPowerOf2
uint64_t NextPowerOf2(uint64_t A)
Returns the next power of two (in 64-bits) that is strictly greater than A.
Definition: MathExtras.h:683
llvm::alignTo
uint64_t alignTo(uint64_t Size, Align A)
Returns a multiple of A needed to store Size bytes.
Definition: Alignment.h:148
llvm::findFirstSet
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:239
llvm::numbers::sqrt3f
constexpr float sqrt3f
Definition: MathExtras.h:84
llvm::CTLog2< 1 >
constexpr size_t CTLog2< 1 >()
Definition: MathExtras.h:582
llvm
---------------------— PointerInfo ------------------------------------—
Definition: AllocatorList.h:23
llvm::detail::LeadingZerosCounter::count
static unsigned count(T Val, ZeroBehavior)
Definition: MathExtras.h:165
llvm::SaturatingAdd
std::enable_if_t< std::is_unsigned< T >::value, T > SaturatingAdd(T X, T Y, bool *ResultOverflowed=nullptr)
Add two unsigned integers, X and Y, of type T.
Definition: MathExtras.h:803
llvm::maskTrailingOnes
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:248
llvm::numbers::sqrt3
constexpr double sqrt3
Definition: MathExtras.h:69
llvm::maskTrailingZeros
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:263
llvm::reverseBits
T reverseBits(T Val)
Reverse the bits in Val.
Definition: MathExtras.h:305
llvm::detail::TrailingZerosCounter::count
static unsigned count(T Val, ZeroBehavior)
Definition: MathExtras.h:91
llvm::detail::PopulationCounter
Definition: MathExtras.h:533
llvm::greatestCommonDivisor
T greatestCommonDivisor(T A, T B)
Return the greatest common divisor of the values using Euclid's algorithm.
Definition: MathExtras.h:621
llvm::CTLog2
constexpr size_t CTLog2()
Compile time Log2.
Definition: MathExtras.h:576
High
uint64_t High
Definition: NVVMIntrRange.cpp:61
llvm::huge_valf
const float huge_valf
Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
Definition: MathExtras.cpp:28
llvm::detail::TrailingZerosCounter
Definition: MathExtras.h:90
llvm::isShiftedMask_32
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:479
Shift
bool Shift
Definition: README.txt:468
llvm::tgtok::Bits
@ Bits
Definition: TGLexer.h:50
llvm::FloatToBits
uint32_t FloatToBits(float Float)
This function takes a float and returns the bit equivalent 32-bit integer.
Definition: MathExtras.h:663
llvm::maxIntN
int64_t maxIntN(int64_t N)
Gets the maximum value for a N-bit signed integer.
Definition: MathExtras.h:446
llvm::GreatestCommonDivisor64
uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B)
Definition: MathExtras.h:630
T
#define T
Definition: Mips16ISelLowering.cpp:341
llvm::numbers::log10e
constexpr double log10e
Definition: MathExtras.h:62
llvm::detail::LeadingZerosCounter
Definition: MathExtras.h:164
llvm::PowerOf2Ceil
uint64_t PowerOf2Ceil(uint64_t A)
Returns the power of two which is greater than or equal to the given value.
Definition: MathExtras.h:702
llvm::ZB_Width
@ ZB_Width
The returned value is numeric_limits<T>::digits.
Definition: MathExtras.h:50
llvm::isPowerOf2_32
constexpr bool isPowerOf2_32(uint32_t Value)
Return true if the argument is a power of two > 0.
Definition: MathExtras.h:491
llvm::countLeadingOnes
unsigned 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:509
llvm::isInt
constexpr bool isInt(int64_t x)
Checks if an integer fits into the given bit width.
Definition: MathExtras.h:363
llvm::Lo_32
constexpr uint32_t Lo_32(uint64_t Value)
Return the low 32 bits of a 64 bit value.
Definition: MathExtras.h:353
llvm::numbers::log10ef
constexpr float log10ef
Definition: MathExtras.h:77
llvm::BitmaskEnumDetail::Mask
std::underlying_type_t< E > Mask()
Get a bitmask with 1s in all places up to the high-order bit of E's largest value.
Definition: BitmaskEnum.h:80
llvm::ZB_Undefined
@ ZB_Undefined
The returned value is undefined.
Definition: MathExtras.h:46
F
#define F(x, y, z)
Definition: MD5.cpp:56
llvm::detail::PopulationCounter< T, 8 >::count
static unsigned count(T Value)
Definition: MathExtras.h:549
llvm::MinAlign
constexpr uint64_t MinAlign(uint64_t A, uint64_t B)
A and B are either alignments or offsets.
Definition: MathExtras.h:672
llvm::numbers::egammaf
constexpr float egammaf
Definition: MathExtras.h:73
llvm::Log2_64
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:602
llvm::numbers::inv_sqrt2
constexpr double inv_sqrt2
Definition: MathExtras.h:68
llvm::PowerOf2Floor
uint64_t PowerOf2Floor(uint64_t A)
Returns the power of two which is less than or equal to the given value.
Definition: MathExtras.h:695
llvm::Log2
unsigned Log2(Align A)
Returns the log2 of the alignment.
Definition: Alignment.h:207
llvm::isShiftedMask_64
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:485
Y
static GCMetadataPrinterRegistry::Add< OcamlGCMetadataPrinter > Y("ocaml", "ocaml 3.10-compatible collector")
llvm::DoubleToBits
uint64_t DoubleToBits(double Double)
This function takes a double and returns the bit equivalent 64-bit integer.
Definition: MathExtras.h:653
UINT64_MAX
#define UINT64_MAX
Definition: DataTypes.h:77
llvm::numbers::log2ef
constexpr float log2ef
Definition: MathExtras.h:76
llvm::alignDown
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:753
llvm::Log2_32
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:596
llvm::numbers::ln10f
constexpr float ln10f
Definition: MathExtras.h:75
B
static GCRegistry::Add< OcamlGC > B("ocaml", "ocaml 3.10-compatible GC")
llvm::isUIntN
bool isUIntN(unsigned N, uint64_t x)
Checks if an unsigned integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:455
in
The object format emitted by the WebAssembly backed is documented in
Definition: README.txt:11
llvm::AddOverflow
std::enable_if_t< std::is_signed< T >::value, T > AddOverflow(T X, T Y, T &Result)
Add two signed integers, computing the two's complement truncated result, returning true if overflow ...
Definition: MathExtras.h:884
llvm::numbers::inv_sqrt3f
constexpr float inv_sqrt3f
Definition: MathExtras.h:85
llvm::numbers::sqrt2
constexpr double sqrt2
Definition: MathExtras.h:67
Align
uint64_t Align
Definition: ELFObjHandler.cpp:83
llvm::Align
This struct is a compact representation of a valid (non-zero power of two) alignment.
Definition: Alignment.h:39
llvm::numbers::inv_sqrt2f
constexpr float inv_sqrt2f
Definition: MathExtras.h:83
llvm::isIntN
bool isIntN(unsigned N, int64_t x)
Checks if an signed integer fits into the given (dynamic) bit width.
Definition: MathExtras.h:460
X
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
llvm::Log2_32_Ceil
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:609
llvm::Hi_32
constexpr uint32_t Hi_32(uint64_t Value)
Return the high 32 bits of a 64 bit value.
Definition: MathExtras.h:348
llvm::isInt< 8 >
constexpr bool isInt< 8 >(int64_t x)
Definition: MathExtras.h:367
llvm::Make_64
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:358
llvm::detail::PopulationCounter::count
static unsigned count(T Value)
Definition: MathExtras.h:534
llvm::SignExtend32
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:761
llvm::divideCeil
uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator)
Returns the integer ceil(Numerator / Denominator).
Definition: MathExtras.h:742
llvm::countPopulation
unsigned countPopulation(T Value)
Count the number of set bits in a value.
Definition: MathExtras.h:567
llvm::isInt< 32 >
constexpr bool isInt< 32 >(int64_t x)
Definition: MathExtras.h:373
llvm::minIntN
int64_t minIntN(int64_t N)
Gets the minimum value for a N-bit signed integer.
Definition: MathExtras.h:439
llvm::isUInt< 16 >
constexpr bool isUInt< 16 >(uint64_t x)
Definition: MathExtras.h:408
llvm::count
auto count(R &&Range, const E &Element)
Wrapper function around std::count to count the number of times an element Element occurs in the give...
Definition: STLExtras.h:1630
Index
uint32_t Index
Definition: ELFObjHandler.cpp:84
uint64_t
D
static GCRegistry::Add< StatepointGC > D("statepoint-example", "an example strategy for statepoint")
llvm::numbers::egamma
constexpr double egamma
Definition: MathExtras.h:58
llvm::numbers::e
constexpr double e
Definition: MathExtras.h:57
llvm::numbers::inv_sqrt3
constexpr double inv_sqrt3
Definition: MathExtras.h:70
llvm::ZB_Max
@ ZB_Max
The returned value is numeric_limits<T>::max()
Definition: MathExtras.h:48
llvm::SaturatingMultiplyAdd
std::enable_if_t< std::is_unsigned< T >::value, T > 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:866
llvm::countTrailingOnes
unsigned 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:525
llvm::maskLeadingZeros
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:269
llvm::numbers::log2e
constexpr double log2e
Definition: MathExtras.h:61
llvm::Log2_64_Ceil
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:615
numbers
SSE has instructions for doing operations on complex numbers
Definition: README-SSE.txt:22
llvm::isUInt< 32 >
constexpr bool isUInt< 32 >(uint64_t x)
Definition: MathExtras.h:411
assert
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
llvm::isUInt< 8 >
constexpr bool isUInt< 8 >(uint64_t x)
Definition: MathExtras.h:405
llvm::numbers::inv_pif
constexpr float inv_pif
Definition: MathExtras.h:79
memcpy
<%struct.s * > cast struct s *S to sbyte *< sbyte * > sbyte uint cast struct s *agg result to sbyte *< sbyte * > sbyte uint cast struct s *memtmp to sbyte *< sbyte * > sbyte uint ret void llc ends up issuing two memcpy or custom lower memcpy(of small size) to be ldmia/stmia. I think option 2 is better but the current register allocator cannot allocate a chunk of registers at a time. A feasible temporary solution is to use specific physical registers at the lowering time for small(<
llvm::isShiftedUInt
constexpr bool isShiftedUInt(uint64_t x)
Checks if a unsigned integer is an N bit number shifted left by S.
Definition: MathExtras.h:417
llvm::findLastSet
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:280
llvm::numbers::inv_sqrtpi
constexpr double inv_sqrtpi
Definition: MathExtras.h:66
R6
#define R6(n)
llvm::isMask_32
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:467
llvm::NVPTXISD::Dummy
@ Dummy
Definition: NVPTXISelLowering.h:60
llvm::countTrailingZeros
unsigned countTrailingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0's from the least significant bit to the most stopping at the first 1.
Definition: MathExtras.h:156
llvm::BitReverseTable256
static const unsigned char BitReverseTable256[256]
Macro compressed bit reversal table for 256 bits.
Definition: MathExtras.h:293
uint32_t
Compiler.h
S
add sub stmia L5 ldr r0 bl L_printf $stub Instead of a and a wouldn t it be better to do three moves *Return an aggregate type is even return S
Definition: README.txt:210
llvm::BitsToFloat
float BitsToFloat(uint32_t Bits)
This function takes a 32-bit integer and returns the bit equivalent float.
Definition: MathExtras.h:643
llvm::SignExtend64
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:777
llvm::ZeroBehavior
ZeroBehavior
The behavior an operation has on an input of 0.
Definition: MathExtras.h:44
llvm::isInt< 16 >
constexpr bool isInt< 16 >(int64_t x)
Definition: MathExtras.h:370
llvm::numbers::inv_pi
constexpr double inv_pi
Definition: MathExtras.h:64
llvm::numbers::ef
constexpr float ef
Definition: MathExtras.h:72
uint16_t
llvm::numbers::inv_sqrtpif
constexpr float inv_sqrtpif
Definition: MathExtras.h:81
llvm::maskLeadingOnes
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:257
llvm::MulOverflow
std::enable_if_t< std::is_signed< T >::value, T > MulOverflow(T X, T Y, T &Result)
Multiply two signed integers, computing the two's complement truncated result, returning true if an o...
Definition: MathExtras.h:936
llvm::TargetStackID::Value
Value
Definition: TargetFrameLowering.h:27
llvm::isShiftedInt
constexpr bool isShiftedInt(int64_t x)
Checks if a signed integer is an N bit number shifted left by S.
Definition: MathExtras.h:379
x
TODO unsigned x
Definition: README.txt:10
llvm::numbers::phif
constexpr float phif
Definition: MathExtras.h:86
llvm::log2
static double log2(double V)
Definition: AMDGPULibCalls.cpp:842
llvm::countLeadingZeros
unsigned countLeadingZeros(T Val, ZeroBehavior ZB=ZB_Width)
Count number of 0's from the most significant bit to the least stopping at the first 1.
Definition: MathExtras.h:225
llvm::SubOverflow
std::enable_if_t< std::is_signed< T >::value, T > SubOverflow(T X, T Y, T &Result)
Subtract two signed integers, computing the two's complement truncated result, returning true if an o...
Definition: MathExtras.h:910
llvm::numbers::sqrtpi
constexpr double sqrtpi
Definition: MathExtras.h:65
llvm::BitsToDouble
double BitsToDouble(uint64_t Bits)
This function takes a 64-bit integer and returns the bit equivalent double.
Definition: MathExtras.h:635
llvm::numbers::ln2
constexpr double ln2
Definition: MathExtras.h:59
llvm::numbers::phi
constexpr double phi
Definition: MathExtras.h:71
llvm::numbers::pi
constexpr double pi
Definition: MathExtras.h:63
llvm::numbers::sqrt2f
constexpr float sqrt2f
Definition: MathExtras.h:82
N
#define N
llvm::max
Align max(MaybeAlign Lhs, Align Rhs)
Definition: Alignment.h:340
llvm::numbers::sqrtpif
constexpr float sqrtpif
Definition: MathExtras.h:80
llvm::numbers::pif
constexpr float pif
Definition: MathExtras.h:78
llvm::maxUIntN
uint64_t maxUIntN(uint64_t N)
Gets the maximum value for a N-bit unsigned integer.
Definition: MathExtras.h:428
llvm::isMask_64
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:473
llvm::isUInt
constexpr std::enable_if_t<(N< 64), bool > isUInt(uint64_t X)
Checks if an unsigned integer fits into the given bit width.
Definition: MathExtras.h:395
llvm::isPowerOf2_64
constexpr bool isPowerOf2_64(uint64_t Value)
Return true if the argument is a power of two > 0 (64 bit edition.)
Definition: MathExtras.h:496
llvm::numbers::ln2f
constexpr float ln2f
Definition: MathExtras.h:74
llvm::divideNearest
uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator)
Returns the integer nearest(Numerator / Denominator).
Definition: MathExtras.h:747
llvm::Value
LLVM Value Representation.
Definition: Value.h:75
llvm::numbers::ln10
constexpr double ln10
Definition: MathExtras.h:60
llvm::AbsoluteDifference
std::enable_if_t< std::is_unsigned< T >::value, T > 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:794