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/ADT/bit.h"
17 #include "llvm/Support/Compiler.h"
18 #include <cassert>
19 #include <climits>
20 #include <cstdint>
21 #include <cstring>
22 #include <limits>
23 #include <type_traits>
24 
25 namespace llvm {
26 
27 /// The behavior an operation has on an input of 0.
28 enum ZeroBehavior {
29   /// The returned value is undefined.
30   ZB_Undefined,
31   /// The returned value is numeric_limits<T>::max()
32   ZB_Max
33 };
34 
35 /// Mathematical constants.
36 namespace numbers {
37 // TODO: Track C++20 std::numbers.
38 // TODO: Favor using the hexadecimal FP constants (requires C++17).
39 constexpr double e          = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
40                  egamma     = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
41                  ln2        = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
42                  ln10       = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
43                  log2e      = 1.4426950408889634074, // (0x1.71547652b82feP+0)
44                  log10e     = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
45                  pi         = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
46                  inv_pi     = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
47                  sqrtpi     = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
48                  inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
49                  sqrt2      = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
50                  inv_sqrt2  = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
51                  sqrt3      = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
52                  inv_sqrt3  = .57735026918962576451, // (0x1.279a74590331cP-1)
53                  phi        = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
54 constexpr float ef          = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
55                 egammaf     = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
56                 ln2f        = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
57                 ln10f       = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
58                 log2ef      = 1.44269504F, // (0x1.715476P+0)
59                 log10ef     = .434294482F, // (0x1.bcb7b2P-2)
60                 pif         = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
61                 inv_pif     = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
62                 sqrtpif     = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
63                 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
64                 sqrt2f      = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
65                 inv_sqrt2f  = .707106781F, // (0x1.6a09e6P-1)
66                 sqrt3f      = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
67                 inv_sqrt3f  = .577350269F, // (0x1.279a74P-1)
68                 phif        = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
69 } // namespace numbers
70 
71 /// Count number of 0's from the least significant bit to the most
72 ///   stopping at the first 1.
73 ///
74 /// Only unsigned integral types are allowed.
75 ///
76 /// Returns std::numeric_limits<T>::digits on an input of 0.
countTrailingZeros(T Val)77 template <typename T> unsigned countTrailingZeros(T Val) {
78   static_assert(std::is_unsigned_v<T>,
79                 "Only unsigned integral types are allowed.");
80   return llvm::countr_zero(Val);
81 }
82 
83 /// Count number of 0's from the most significant bit to the least
84 ///   stopping at the first 1.
85 ///
86 /// Only unsigned integral types are allowed.
87 ///
88 /// Returns std::numeric_limits<T>::digits on an input of 0.
countLeadingZeros(T Val)89 template <typename T> unsigned countLeadingZeros(T Val) {
90   static_assert(std::is_unsigned_v<T>,
91                 "Only unsigned integral types are allowed.");
92   return llvm::countl_zero(Val);
93 }
94 
95 /// Get the index of the first set bit starting from the least
96 ///   significant bit.
97 ///
98 /// Only unsigned integral types are allowed.
99 ///
100 /// \param ZB the behavior on an input of 0.
101 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
102   if (ZB == ZB_Max && Val == 0)
103     return std::numeric_limits<T>::max();
104 
105   return llvm::countr_zero(Val);
106 }
107 
108 /// Create a bitmask with the N right-most bits set to 1, and all other
109 /// bits set to 0.  Only unsigned types are allowed.
maskTrailingOnes(unsigned N)110 template <typename T> T maskTrailingOnes(unsigned N) {
111   static_assert(std::is_unsigned<T>::value, "Invalid type!");
112   const unsigned Bits = CHAR_BIT * sizeof(T);
113   assert(N <= Bits && "Invalid bit index");
114   return N == 0 ? 0 : (T(-1) >> (Bits - N));
115 }
116 
117 /// Create a bitmask with the N left-most bits set to 1, and all other
118 /// bits set to 0.  Only unsigned types are allowed.
maskLeadingOnes(unsigned N)119 template <typename T> T maskLeadingOnes(unsigned N) {
120   return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
121 }
122 
123 /// Create a bitmask with the N right-most bits set to 0, and all other
124 /// bits set to 1.  Only unsigned types are allowed.
maskTrailingZeros(unsigned N)125 template <typename T> T maskTrailingZeros(unsigned N) {
126   return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
127 }
128 
129 /// Create a bitmask with the N left-most bits set to 0, and all other
130 /// bits set to 1.  Only unsigned types are allowed.
maskLeadingZeros(unsigned N)131 template <typename T> T maskLeadingZeros(unsigned N) {
132   return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
133 }
134 
135 /// Get the index of the last set bit starting from the least
136 ///   significant bit.
137 ///
138 /// Only unsigned integral types are allowed.
139 ///
140 /// \param ZB the behavior on an input of 0.
141 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
142   if (ZB == ZB_Max && Val == 0)
143     return std::numeric_limits<T>::max();
144 
145   // Use ^ instead of - because both gcc and llvm can remove the associated ^
146   // in the __builtin_clz intrinsic on x86.
147   return llvm::countl_zero(Val) ^ (std::numeric_limits<T>::digits - 1);
148 }
149 
150 /// Macro compressed bit reversal table for 256 bits.
151 ///
152 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
153 static const unsigned char BitReverseTable256[256] = {
154 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
155 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
156 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
157   R6(0), R6(2), R6(1), R6(3)
158 #undef R2
159 #undef R4
160 #undef R6
161 };
162 
163 /// Reverse the bits in \p Val.
reverseBits(T Val)164 template <typename T> T reverseBits(T Val) {
165 #if __has_builtin(__builtin_bitreverse8)
166   if constexpr (std::is_same_v<T, uint8_t>)
167     return __builtin_bitreverse8(Val);
168 #endif
169 #if __has_builtin(__builtin_bitreverse16)
170   if constexpr (std::is_same_v<T, uint16_t>)
171     return __builtin_bitreverse16(Val);
172 #endif
173 #if __has_builtin(__builtin_bitreverse32)
174   if constexpr (std::is_same_v<T, uint32_t>)
175     return __builtin_bitreverse32(Val);
176 #endif
177 #if __has_builtin(__builtin_bitreverse64)
178   if constexpr (std::is_same_v<T, uint64_t>)
179     return __builtin_bitreverse64(Val);
180 #endif
181 
182   unsigned char in[sizeof(Val)];
183   unsigned char out[sizeof(Val)];
184   std::memcpy(in, &Val, sizeof(Val));
185   for (unsigned i = 0; i < sizeof(Val); ++i)
186     out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
187   std::memcpy(&Val, out, sizeof(Val));
188   return Val;
189 }
190 
191 // NOTE: The following support functions use the _32/_64 extensions instead of
192 // type overloading so that signed and unsigned integers can be used without
193 // ambiguity.
194 
195 /// Return the high 32 bits of a 64 bit value.
Hi_32(uint64_t Value)196 constexpr inline uint32_t Hi_32(uint64_t Value) {
197   return static_cast<uint32_t>(Value >> 32);
198 }
199 
200 /// Return the low 32 bits of a 64 bit value.
Lo_32(uint64_t Value)201 constexpr inline uint32_t Lo_32(uint64_t Value) {
202   return static_cast<uint32_t>(Value);
203 }
204 
205 /// Make a 64-bit integer from a high / low pair of 32-bit integers.
Make_64(uint32_t High,uint32_t Low)206 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
207   return ((uint64_t)High << 32) | (uint64_t)Low;
208 }
209 
210 /// Checks if an integer fits into the given bit width.
isInt(int64_t x)211 template <unsigned N> constexpr inline bool isInt(int64_t x) {
212   if constexpr (N == 8)
213     return static_cast<int8_t>(x) == x;
214   if constexpr (N == 16)
215     return static_cast<int16_t>(x) == x;
216   if constexpr (N == 32)
217     return static_cast<int32_t>(x) == x;
218   if constexpr (N < 64)
219     return -(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1));
220   (void)x; // MSVC v19.25 warns that x is unused.
221   return true;
222 }
223 
224 /// Checks if a signed integer is an N bit number shifted left by S.
225 template <unsigned N, unsigned S>
isShiftedInt(int64_t x)226 constexpr inline bool isShiftedInt(int64_t x) {
227   static_assert(
228       N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
229   static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
230   return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
231 }
232 
233 /// Checks if an unsigned integer fits into the given bit width.
isUInt(uint64_t x)234 template <unsigned N> constexpr inline bool isUInt(uint64_t x) {
235   static_assert(N > 0, "isUInt<0> doesn't make sense");
236   if constexpr (N == 8)
237     return static_cast<uint8_t>(x) == x;
238   if constexpr (N == 16)
239     return static_cast<uint16_t>(x) == x;
240   if constexpr (N == 32)
241     return static_cast<uint32_t>(x) == x;
242   if constexpr (N < 64)
243     return x < (UINT64_C(1) << (N));
244   (void)x; // MSVC v19.25 warns that x is unused.
245   return true;
246 }
247 
248 /// Checks if a unsigned integer is an N bit number shifted left by S.
249 template <unsigned N, unsigned S>
isShiftedUInt(uint64_t x)250 constexpr inline bool isShiftedUInt(uint64_t x) {
251   static_assert(
252       N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
253   static_assert(N + S <= 64,
254                 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
255   // Per the two static_asserts above, S must be strictly less than 64.  So
256   // 1 << S is not undefined behavior.
257   return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
258 }
259 
260 /// Gets the maximum value for a N-bit unsigned integer.
maxUIntN(uint64_t N)261 inline uint64_t maxUIntN(uint64_t N) {
262   assert(N > 0 && N <= 64 && "integer width out of range");
263 
264   // uint64_t(1) << 64 is undefined behavior, so we can't do
265   //   (uint64_t(1) << N) - 1
266   // without checking first that N != 64.  But this works and doesn't have a
267   // branch.
268   return UINT64_MAX >> (64 - N);
269 }
270 
271 /// Gets the minimum value for a N-bit signed integer.
minIntN(int64_t N)272 inline int64_t minIntN(int64_t N) {
273   assert(N > 0 && N <= 64 && "integer width out of range");
274 
275   return UINT64_C(1) + ~(UINT64_C(1) << (N - 1));
276 }
277 
278 /// Gets the maximum value for a N-bit signed integer.
maxIntN(int64_t N)279 inline int64_t maxIntN(int64_t N) {
280   assert(N > 0 && N <= 64 && "integer width out of range");
281 
282   // This relies on two's complement wraparound when N == 64, so we convert to
283   // int64_t only at the very end to avoid UB.
284   return (UINT64_C(1) << (N - 1)) - 1;
285 }
286 
287 /// Checks if an unsigned integer fits into the given (dynamic) bit width.
isUIntN(unsigned N,uint64_t x)288 inline bool isUIntN(unsigned N, uint64_t x) {
289   return N >= 64 || x <= maxUIntN(N);
290 }
291 
292 /// Checks if an signed integer fits into the given (dynamic) bit width.
isIntN(unsigned N,int64_t x)293 inline bool isIntN(unsigned N, int64_t x) {
294   return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
295 }
296 
297 /// Return true if the argument is a non-empty sequence of ones starting at the
298 /// least significant bit with the remainder zero (32 bit version).
299 /// Ex. isMask_32(0x0000FFFFU) == true.
isMask_32(uint32_t Value)300 constexpr inline bool isMask_32(uint32_t Value) {
301   return Value && ((Value + 1) & Value) == 0;
302 }
303 
304 /// Return true if the argument is a non-empty sequence of ones starting at the
305 /// least significant bit with the remainder zero (64 bit version).
isMask_64(uint64_t Value)306 constexpr inline bool isMask_64(uint64_t Value) {
307   return Value && ((Value + 1) & Value) == 0;
308 }
309 
310 /// Return true if the argument contains a non-empty sequence of ones with the
311 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
isShiftedMask_32(uint32_t Value)312 constexpr inline bool isShiftedMask_32(uint32_t Value) {
313   return Value && isMask_32((Value - 1) | Value);
314 }
315 
316 /// Return true if the argument contains a non-empty sequence of ones with the
317 /// remainder zero (64 bit version.)
isShiftedMask_64(uint64_t Value)318 constexpr inline bool isShiftedMask_64(uint64_t Value) {
319   return Value && isMask_64((Value - 1) | Value);
320 }
321 
322 /// Return true if the argument is a power of two > 0.
323 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
isPowerOf2_32(uint32_t Value)324 constexpr inline bool isPowerOf2_32(uint32_t Value) {
325   return llvm::has_single_bit(Value);
326 }
327 
328 /// Return true if the argument is a power of two > 0 (64 bit edition.)
isPowerOf2_64(uint64_t Value)329 constexpr inline bool isPowerOf2_64(uint64_t Value) {
330   return llvm::has_single_bit(Value);
331 }
332 
333 /// Count the number of ones from the most significant bit to the first
334 /// zero bit.
335 ///
336 /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
337 /// Only unsigned integral types are allowed.
338 ///
339 /// Returns std::numeric_limits<T>::digits on an input of all ones.
countLeadingOnes(T Value)340 template <typename T> unsigned countLeadingOnes(T Value) {
341   static_assert(std::is_unsigned_v<T>,
342                 "Only unsigned integral types are allowed.");
343   return llvm::countl_one<T>(Value);
344 }
345 
346 /// Count the number of ones from the least significant bit to the first
347 /// zero bit.
348 ///
349 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
350 /// Only unsigned integral types are allowed.
351 ///
352 /// Returns std::numeric_limits<T>::digits on an input of all ones.
countTrailingOnes(T Value)353 template <typename T> unsigned countTrailingOnes(T Value) {
354   static_assert(std::is_unsigned_v<T>,
355                 "Only unsigned integral types are allowed.");
356   return llvm::countr_one<T>(Value);
357 }
358 
359 /// Count the number of set bits in a value.
360 /// Ex. countPopulation(0xF000F000) = 8
361 /// Returns 0 if the word is zero.
362 template <typename T>
countPopulation(T Value)363 inline unsigned countPopulation(T Value) {
364   static_assert(std::is_unsigned_v<T>,
365                 "Only unsigned integral types are allowed.");
366   return (unsigned)llvm::popcount(Value);
367 }
368 
369 /// Return true if the argument contains a non-empty sequence of ones with the
370 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
371 /// If true, \p MaskIdx will specify the index of the lowest set bit and \p
372 /// MaskLen is updated to specify the length of the mask, else neither are
373 /// updated.
isShiftedMask_32(uint32_t Value,unsigned & MaskIdx,unsigned & MaskLen)374 inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx,
375                              unsigned &MaskLen) {
376   if (!isShiftedMask_32(Value))
377     return false;
378   MaskIdx = llvm::countr_zero(Value);
379   MaskLen = llvm::popcount(Value);
380   return true;
381 }
382 
383 /// Return true if the argument contains a non-empty sequence of ones with the
384 /// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index
385 /// of the lowest set bit and \p MaskLen is updated to specify the length of the
386 /// mask, else neither are updated.
isShiftedMask_64(uint64_t Value,unsigned & MaskIdx,unsigned & MaskLen)387 inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx,
388                              unsigned &MaskLen) {
389   if (!isShiftedMask_64(Value))
390     return false;
391   MaskIdx = llvm::countr_zero(Value);
392   MaskLen = llvm::popcount(Value);
393   return true;
394 }
395 
396 /// Compile time Log2.
397 /// Valid only for positive powers of two.
CTLog2()398 template <size_t kValue> constexpr inline size_t CTLog2() {
399   static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
400                 "Value is not a valid power of 2");
401   return 1 + CTLog2<kValue / 2>();
402 }
403 
404 template <> constexpr inline size_t CTLog2<1>() { return 0; }
405 
406 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
407 /// (32 bit edition.)
408 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
Log2_32(uint32_t Value)409 inline unsigned Log2_32(uint32_t Value) {
410   return 31 - llvm::countl_zero(Value);
411 }
412 
413 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
414 /// (64 bit edition.)
Log2_64(uint64_t Value)415 inline unsigned Log2_64(uint64_t Value) {
416   return 63 - llvm::countl_zero(Value);
417 }
418 
419 /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
420 /// (32 bit edition).
421 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
Log2_32_Ceil(uint32_t Value)422 inline unsigned Log2_32_Ceil(uint32_t Value) {
423   return 32 - llvm::countl_zero(Value - 1);
424 }
425 
426 /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
427 /// (64 bit edition.)
Log2_64_Ceil(uint64_t Value)428 inline unsigned Log2_64_Ceil(uint64_t Value) {
429   return 64 - llvm::countl_zero(Value - 1);
430 }
431 
432 /// This function takes a 64-bit integer and returns the bit equivalent double.
BitsToDouble(uint64_t Bits)433 inline double BitsToDouble(uint64_t Bits) {
434   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
435   return llvm::bit_cast<double>(Bits);
436 }
437 
438 /// This function takes a 32-bit integer and returns the bit equivalent float.
BitsToFloat(uint32_t Bits)439 inline float BitsToFloat(uint32_t Bits) {
440   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
441   return llvm::bit_cast<float>(Bits);
442 }
443 
444 /// This function takes a double and returns the bit equivalent 64-bit integer.
445 /// Note that copying doubles around changes the bits of NaNs on some hosts,
446 /// notably x86, so this routine cannot be used if these bits are needed.
DoubleToBits(double Double)447 inline uint64_t DoubleToBits(double Double) {
448   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
449   return llvm::bit_cast<uint64_t>(Double);
450 }
451 
452 /// This function takes a float and returns the bit equivalent 32-bit integer.
453 /// Note that copying floats around changes the bits of NaNs on some hosts,
454 /// notably x86, so this routine cannot be used if these bits are needed.
FloatToBits(float Float)455 inline uint32_t FloatToBits(float Float) {
456   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
457   return llvm::bit_cast<uint32_t>(Float);
458 }
459 
460 /// A and B are either alignments or offsets. Return the minimum alignment that
461 /// may be assumed after adding the two together.
MinAlign(uint64_t A,uint64_t B)462 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
463   // The largest power of 2 that divides both A and B.
464   //
465   // Replace "-Value" by "1+~Value" in the following commented code to avoid
466   // MSVC warning C4146
467   //    return (A | B) & -(A | B);
468   return (A | B) & (1 + ~(A | B));
469 }
470 
471 /// Returns the next power of two (in 64-bits) that is strictly greater than A.
472 /// Returns zero on overflow.
NextPowerOf2(uint64_t A)473 constexpr inline uint64_t NextPowerOf2(uint64_t A) {
474   A |= (A >> 1);
475   A |= (A >> 2);
476   A |= (A >> 4);
477   A |= (A >> 8);
478   A |= (A >> 16);
479   A |= (A >> 32);
480   return A + 1;
481 }
482 
483 /// Returns the power of two which is less than or equal to the given value.
484 /// Essentially, it is a floor operation across the domain of powers of two.
PowerOf2Floor(uint64_t A)485 inline uint64_t PowerOf2Floor(uint64_t A) {
486   return llvm::bit_floor(A);
487 }
488 
489 /// Returns the power of two which is greater than or equal to the given value.
490 /// Essentially, it is a ceil operation across the domain of powers of two.
PowerOf2Ceil(uint64_t A)491 inline uint64_t PowerOf2Ceil(uint64_t A) {
492   if (!A)
493     return 0;
494   return NextPowerOf2(A - 1);
495 }
496 
497 /// Returns the next integer (mod 2**64) that is greater than or equal to
498 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
499 ///
500 /// Examples:
501 /// \code
502 ///   alignTo(5, 8) = 8
503 ///   alignTo(17, 8) = 24
504 ///   alignTo(~0LL, 8) = 0
505 ///   alignTo(321, 255) = 510
506 /// \endcode
alignTo(uint64_t Value,uint64_t Align)507 inline uint64_t alignTo(uint64_t Value, uint64_t Align) {
508   assert(Align != 0u && "Align can't be 0.");
509   return (Value + Align - 1) / Align * Align;
510 }
511 
alignToPowerOf2(uint64_t Value,uint64_t Align)512 inline uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) {
513   assert(Align != 0 && (Align & (Align - 1)) == 0 &&
514          "Align must be a power of 2");
515   return (Value + Align - 1) & -Align;
516 }
517 
518 /// If non-zero \p Skew is specified, the return value will be a minimal integer
519 /// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
520 /// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
521 /// Skew mod \p A'. \p Align must be non-zero.
522 ///
523 /// Examples:
524 /// \code
525 ///   alignTo(5, 8, 7) = 7
526 ///   alignTo(17, 8, 1) = 17
527 ///   alignTo(~0LL, 8, 3) = 3
528 ///   alignTo(321, 255, 42) = 552
529 /// \endcode
alignTo(uint64_t Value,uint64_t Align,uint64_t Skew)530 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew) {
531   assert(Align != 0u && "Align can't be 0.");
532   Skew %= Align;
533   return alignTo(Value - Skew, Align) + Skew;
534 }
535 
536 /// Returns the next integer (mod 2**64) that is greater than or equal to
537 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
alignTo(uint64_t Value)538 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
539   static_assert(Align != 0u, "Align must be non-zero");
540   return (Value + Align - 1) / Align * Align;
541 }
542 
543 /// Returns the integer ceil(Numerator / Denominator).
divideCeil(uint64_t Numerator,uint64_t Denominator)544 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
545   return alignTo(Numerator, Denominator) / Denominator;
546 }
547 
548 /// Returns the integer nearest(Numerator / Denominator).
divideNearest(uint64_t Numerator,uint64_t Denominator)549 inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
550   return (Numerator + (Denominator / 2)) / Denominator;
551 }
552 
553 /// Returns the largest uint64_t less than or equal to \p Value and is
554 /// \p Skew mod \p Align. \p Align must be non-zero
555 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
556   assert(Align != 0u && "Align can't be 0.");
557   Skew %= Align;
558   return (Value - Skew) / Align * Align + Skew;
559 }
560 
561 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
562 /// Requires 0 < B <= 32.
SignExtend32(uint32_t X)563 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
564   static_assert(B > 0, "Bit width can't be 0.");
565   static_assert(B <= 32, "Bit width out of range.");
566   return int32_t(X << (32 - B)) >> (32 - B);
567 }
568 
569 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
570 /// Requires 0 < B <= 32.
SignExtend32(uint32_t X,unsigned B)571 inline int32_t SignExtend32(uint32_t X, unsigned B) {
572   assert(B > 0 && "Bit width can't be 0.");
573   assert(B <= 32 && "Bit width out of range.");
574   return int32_t(X << (32 - B)) >> (32 - B);
575 }
576 
577 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
578 /// Requires 0 < B <= 64.
SignExtend64(uint64_t x)579 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
580   static_assert(B > 0, "Bit width can't be 0.");
581   static_assert(B <= 64, "Bit width out of range.");
582   return int64_t(x << (64 - B)) >> (64 - B);
583 }
584 
585 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
586 /// Requires 0 < B <= 64.
SignExtend64(uint64_t X,unsigned B)587 inline int64_t SignExtend64(uint64_t X, unsigned B) {
588   assert(B > 0 && "Bit width can't be 0.");
589   assert(B <= 64 && "Bit width out of range.");
590   return int64_t(X << (64 - B)) >> (64 - B);
591 }
592 
593 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
594 /// value of the result.
595 template <typename T>
AbsoluteDifference(T X,T Y)596 std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
597   return X > Y ? (X - Y) : (Y - X);
598 }
599 
600 /// Add two unsigned integers, X and Y, of type T.  Clamp the result to the
601 /// maximum representable value of T on overflow.  ResultOverflowed indicates if
602 /// the result is larger than the maximum representable value of type T.
603 template <typename T>
604 std::enable_if_t<std::is_unsigned<T>::value, T>
605 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
606   bool Dummy;
607   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
608   // Hacker's Delight, p. 29
609   T Z = X + Y;
610   Overflowed = (Z < X || Z < Y);
611   if (Overflowed)
612     return std::numeric_limits<T>::max();
613   else
614     return Z;
615 }
616 
617 /// Add multiple unsigned integers of type T.  Clamp the result to the
618 /// maximum representable value of T on overflow.
619 template <class T, class... Ts>
SaturatingAdd(T X,T Y,T Z,Ts...Args)620 std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z,
621                                                          Ts... Args) {
622   bool Overflowed = false;
623   T XY = SaturatingAdd(X, Y, &Overflowed);
624   if (Overflowed)
625     return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...);
626   return SaturatingAdd(XY, Z, Args...);
627 }
628 
629 /// Multiply two unsigned integers, X and Y, of type T.  Clamp the result to the
630 /// maximum representable value of T on overflow.  ResultOverflowed indicates if
631 /// the result is larger than the maximum representable value of type T.
632 template <typename T>
633 std::enable_if_t<std::is_unsigned<T>::value, T>
634 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
635   bool Dummy;
636   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
637 
638   // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
639   // because it fails for uint16_t (where multiplication can have undefined
640   // behavior due to promotion to int), and requires a division in addition
641   // to the multiplication.
642 
643   Overflowed = false;
644 
645   // Log2(Z) would be either Log2Z or Log2Z + 1.
646   // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
647   // will necessarily be less than Log2Max as desired.
648   int Log2Z = Log2_64(X) + Log2_64(Y);
649   const T Max = std::numeric_limits<T>::max();
650   int Log2Max = Log2_64(Max);
651   if (Log2Z < Log2Max) {
652     return X * Y;
653   }
654   if (Log2Z > Log2Max) {
655     Overflowed = true;
656     return Max;
657   }
658 
659   // We're going to use the top bit, and maybe overflow one
660   // bit past it. Multiply all but the bottom bit then add
661   // that on at the end.
662   T Z = (X >> 1) * Y;
663   if (Z & ~(Max >> 1)) {
664     Overflowed = true;
665     return Max;
666   }
667   Z <<= 1;
668   if (X & 1)
669     return SaturatingAdd(Z, Y, ResultOverflowed);
670 
671   return Z;
672 }
673 
674 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
675 /// the product. Clamp the result to the maximum representable value of T on
676 /// overflow. ResultOverflowed indicates if the result is larger than the
677 /// maximum representable value of type T.
678 template <typename T>
679 std::enable_if_t<std::is_unsigned<T>::value, T>
680 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
681   bool Dummy;
682   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
683 
684   T Product = SaturatingMultiply(X, Y, &Overflowed);
685   if (Overflowed)
686     return Product;
687 
688   return SaturatingAdd(A, Product, &Overflowed);
689 }
690 
691 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
692 extern const float huge_valf;
693 
694 
695 /// Add two signed integers, computing the two's complement truncated result,
696 /// returning true if overflow occurred.
697 template <typename T>
AddOverflow(T X,T Y,T & Result)698 std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
699 #if __has_builtin(__builtin_add_overflow)
700   return __builtin_add_overflow(X, Y, &Result);
701 #else
702   // Perform the unsigned addition.
703   using U = std::make_unsigned_t<T>;
704   const U UX = static_cast<U>(X);
705   const U UY = static_cast<U>(Y);
706   const U UResult = UX + UY;
707 
708   // Convert to signed.
709   Result = static_cast<T>(UResult);
710 
711   // Adding two positive numbers should result in a positive number.
712   if (X > 0 && Y > 0)
713     return Result <= 0;
714   // Adding two negatives should result in a negative number.
715   if (X < 0 && Y < 0)
716     return Result >= 0;
717   return false;
718 #endif
719 }
720 
721 /// Subtract two signed integers, computing the two's complement truncated
722 /// result, returning true if an overflow ocurred.
723 template <typename T>
SubOverflow(T X,T Y,T & Result)724 std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
725 #if __has_builtin(__builtin_sub_overflow)
726   return __builtin_sub_overflow(X, Y, &Result);
727 #else
728   // Perform the unsigned addition.
729   using U = std::make_unsigned_t<T>;
730   const U UX = static_cast<U>(X);
731   const U UY = static_cast<U>(Y);
732   const U UResult = UX - UY;
733 
734   // Convert to signed.
735   Result = static_cast<T>(UResult);
736 
737   // Subtracting a positive number from a negative results in a negative number.
738   if (X <= 0 && Y > 0)
739     return Result >= 0;
740   // Subtracting a negative number from a positive results in a positive number.
741   if (X >= 0 && Y < 0)
742     return Result <= 0;
743   return false;
744 #endif
745 }
746 
747 /// Multiply two signed integers, computing the two's complement truncated
748 /// result, returning true if an overflow ocurred.
749 template <typename T>
MulOverflow(T X,T Y,T & Result)750 std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
751   // Perform the unsigned multiplication on absolute values.
752   using U = std::make_unsigned_t<T>;
753   const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
754   const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
755   const U UResult = UX * UY;
756 
757   // Convert to signed.
758   const bool IsNegative = (X < 0) ^ (Y < 0);
759   Result = IsNegative ? (0 - UResult) : UResult;
760 
761   // If any of the args was 0, result is 0 and no overflow occurs.
762   if (UX == 0 || UY == 0)
763     return false;
764 
765   // UX and UY are in [1, 2^n], where n is the number of digits.
766   // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
767   // positive) divided by an argument compares to the other.
768   if (IsNegative)
769     return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
770   else
771     return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
772 }
773 
774 } // End llvm namespace
775 
776 #endif
777