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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"
18 #include "llvm/Support/SwapByteOrder.h"
19 #include <algorithm>
20 #include <cassert>
21 #include <cstring>
22 #include <type_traits>
23 #include <limits>
24 
25 #ifdef _MSC_VER
26 #include <intrin.h>
27 #endif
28 
29 #ifdef __ANDROID_NDK__
30 #include <android/api-level.h>
31 #endif
32 
33 namespace llvm {
34 /// \brief The behavior an operation has on an input of 0.
35 enum ZeroBehavior {
36   /// \brief The returned value is undefined.
37   ZB_Undefined,
38   /// \brief The returned value is numeric_limits<T>::max()
39   ZB_Max,
40   /// \brief The returned value is numeric_limits<T>::digits
41   ZB_Width
42 };
43 
44 namespace detail {
45 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
countTrailingZerosCounter46   static std::size_t count(T Val, ZeroBehavior) {
47     if (!Val)
48       return std::numeric_limits<T>::digits;
49     if (Val & 0x1)
50       return 0;
51 
52     // Bisection method.
53     std::size_t ZeroBits = 0;
54     T Shift = std::numeric_limits<T>::digits >> 1;
55     T Mask = std::numeric_limits<T>::max() >> Shift;
56     while (Shift) {
57       if ((Val & Mask) == 0) {
58         Val >>= Shift;
59         ZeroBits |= Shift;
60       }
61       Shift >>= 1;
62       Mask >>= Shift;
63     }
64     return ZeroBits;
65   }
66 };
67 
68 #if __GNUC__ >= 4 || defined(_MSC_VER)
69 template <typename T> struct TrailingZerosCounter<T, 4> {
70   static std::size_t count(T Val, ZeroBehavior ZB) {
71     if (ZB != ZB_Undefined && Val == 0)
72       return 32;
73 
74 #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
75     return __builtin_ctz(Val);
76 #elif defined(_MSC_VER)
77     unsigned long Index;
78     _BitScanForward(&Index, Val);
79     return Index;
80 #endif
81   }
82 };
83 
84 #if !defined(_MSC_VER) || defined(_M_X64)
85 template <typename T> struct TrailingZerosCounter<T, 8> {
86   static std::size_t count(T Val, ZeroBehavior ZB) {
87     if (ZB != ZB_Undefined && Val == 0)
88       return 64;
89 
90 #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
91     return __builtin_ctzll(Val);
92 #elif defined(_MSC_VER)
93     unsigned long Index;
94     _BitScanForward64(&Index, Val);
95     return Index;
96 #endif
97   }
98 };
99 #endif
100 #endif
101 } // namespace detail
102 
103 /// \brief Count number of 0's from the least significant bit to the most
104 ///   stopping at the first 1.
105 ///
106 /// Only unsigned integral types are allowed.
107 ///
108 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
109 ///   valid arguments.
110 template <typename T>
111 std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
112   static_assert(std::numeric_limits<T>::is_integer &&
113                     !std::numeric_limits<T>::is_signed,
114                 "Only unsigned integral types are allowed.");
115   return detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
116 }
117 
118 namespace detail {
119 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
120   static std::size_t count(T Val, ZeroBehavior) {
121     if (!Val)
122       return std::numeric_limits<T>::digits;
123 
124     // Bisection method.
125     std::size_t ZeroBits = 0;
126     for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
127       T Tmp = Val >> Shift;
128       if (Tmp)
129         Val = Tmp;
130       else
131         ZeroBits |= Shift;
132     }
133     return ZeroBits;
134   }
135 };
136 
137 #if __GNUC__ >= 4 || defined(_MSC_VER)
138 template <typename T> struct LeadingZerosCounter<T, 4> {
139   static std::size_t count(T Val, ZeroBehavior ZB) {
140     if (ZB != ZB_Undefined && Val == 0)
141       return 32;
142 
143 #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
144     return __builtin_clz(Val);
145 #elif defined(_MSC_VER)
146     unsigned long Index;
147     _BitScanReverse(&Index, Val);
148     return Index ^ 31;
149 #endif
150   }
151 };
152 
153 #if !defined(_MSC_VER) || defined(_M_X64)
154 template <typename T> struct LeadingZerosCounter<T, 8> {
155   static std::size_t count(T Val, ZeroBehavior ZB) {
156     if (ZB != ZB_Undefined && Val == 0)
157       return 64;
158 
159 #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
160     return __builtin_clzll(Val);
161 #elif defined(_MSC_VER)
162     unsigned long Index;
163     _BitScanReverse64(&Index, Val);
164     return Index ^ 63;
165 #endif
166   }
167 };
168 #endif
169 #endif
170 } // namespace detail
171 
172 /// \brief Count number of 0's from the most significant bit to the least
173 ///   stopping at the first 1.
174 ///
175 /// Only unsigned integral types are allowed.
176 ///
177 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
178 ///   valid arguments.
179 template <typename T>
180 std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
181   static_assert(std::numeric_limits<T>::is_integer &&
182                     !std::numeric_limits<T>::is_signed,
183                 "Only unsigned integral types are allowed.");
184   return detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
185 }
186 
187 /// \brief Get the index of the first set bit starting from the least
188 ///   significant bit.
189 ///
190 /// Only unsigned integral types are allowed.
191 ///
192 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
193 ///   valid arguments.
194 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
195   if (ZB == ZB_Max && Val == 0)
196     return std::numeric_limits<T>::max();
197 
198   return countTrailingZeros(Val, ZB_Undefined);
199 }
200 
201 /// \brief Get the index of the last set bit starting from the least
202 ///   significant bit.
203 ///
204 /// Only unsigned integral types are allowed.
205 ///
206 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
207 ///   valid arguments.
208 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
209   if (ZB == ZB_Max && Val == 0)
210     return std::numeric_limits<T>::max();
211 
212   // Use ^ instead of - because both gcc and llvm can remove the associated ^
213   // in the __builtin_clz intrinsic on x86.
214   return countLeadingZeros(Val, ZB_Undefined) ^
215          (std::numeric_limits<T>::digits - 1);
216 }
217 
218 /// \brief Macro compressed bit reversal table for 256 bits.
219 ///
220 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
221 static const unsigned char BitReverseTable256[256] = {
222 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
223 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
224 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
225   R6(0), R6(2), R6(1), R6(3)
226 #undef R2
227 #undef R4
228 #undef R6
229 };
230 
231 /// \brief Reverse the bits in \p Val.
232 template <typename T>
233 T reverseBits(T Val) {
234   unsigned char in[sizeof(Val)];
235   unsigned char out[sizeof(Val)];
236   std::memcpy(in, &Val, sizeof(Val));
237   for (unsigned i = 0; i < sizeof(Val); ++i)
238     out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
239   std::memcpy(&Val, out, sizeof(Val));
240   return Val;
241 }
242 
243 // NOTE: The following support functions use the _32/_64 extensions instead of
244 // type overloading so that signed and unsigned integers can be used without
245 // ambiguity.
246 
247 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
248 inline uint32_t Hi_32(uint64_t Value) {
249   return static_cast<uint32_t>(Value >> 32);
250 }
251 
252 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
253 inline uint32_t Lo_32(uint64_t Value) {
254   return static_cast<uint32_t>(Value);
255 }
256 
257 /// Make_64 - This functions makes a 64-bit integer from a high / low pair of
258 ///           32-bit integers.
259 inline uint64_t Make_64(uint32_t High, uint32_t Low) {
260   return ((uint64_t)High << 32) | (uint64_t)Low;
261 }
262 
263 /// isInt - Checks if an integer fits into the given bit width.
264 template<unsigned N>
265 inline bool isInt(int64_t x) {
266   return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
267 }
268 // Template specializations to get better code for common cases.
269 template<>
270 inline bool isInt<8>(int64_t x) {
271   return static_cast<int8_t>(x) == x;
272 }
273 template<>
274 inline bool isInt<16>(int64_t x) {
275   return static_cast<int16_t>(x) == x;
276 }
277 template<>
278 inline bool isInt<32>(int64_t x) {
279   return static_cast<int32_t>(x) == x;
280 }
281 
282 /// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
283 ///                     left by S.
284 template<unsigned N, unsigned S>
285 inline bool isShiftedInt(int64_t x) {
286   return isInt<N+S>(x) && (x % (1<<S) == 0);
287 }
288 
289 /// isUInt - Checks if an unsigned integer fits into the given bit width.
290 template<unsigned N>
291 inline bool isUInt(uint64_t x) {
292   return N >= 64 || x < (UINT64_C(1)<<(N));
293 }
294 // Template specializations to get better code for common cases.
295 template<>
296 inline bool isUInt<8>(uint64_t x) {
297   return static_cast<uint8_t>(x) == x;
298 }
299 template<>
300 inline bool isUInt<16>(uint64_t x) {
301   return static_cast<uint16_t>(x) == x;
302 }
303 template<>
304 inline bool isUInt<32>(uint64_t x) {
305   return static_cast<uint32_t>(x) == x;
306 }
307 
308 /// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
309 ///                     left by S.
310 template<unsigned N, unsigned S>
311 inline bool isShiftedUInt(uint64_t x) {
312   return isUInt<N+S>(x) && (x % (1<<S) == 0);
313 }
314 
315 /// Gets the maximum value for a N-bit unsigned integer.
316 inline uint64_t maxUIntN(uint64_t N) {
317   assert(N > 0 && N <= 64 && "integer width out of range");
318 
319   return (UINT64_C(1) << N) - 1;
320 }
321 
322 /// Gets the minimum value for a N-bit signed integer.
323 inline int64_t minIntN(int64_t N) {
324   assert(N > 0 && N <= 64 && "integer width out of range");
325 
326   return -(INT64_C(1)<<(N-1));
327 }
328 
329 /// Gets the maximum value for a N-bit signed integer.
330 inline int64_t maxIntN(int64_t N) {
331   assert(N > 0 && N <= 64 && "integer width out of range");
332 
333   return (INT64_C(1)<<(N-1)) - 1;
334 }
335 
336 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
337 /// bit width.
338 inline bool isUIntN(unsigned N, uint64_t x) {
339   return N >= 64 || x <= maxUIntN(N);
340 }
341 
342 /// isIntN - Checks if an signed integer fits into the given (dynamic)
343 /// bit width.
344 inline bool isIntN(unsigned N, int64_t x) {
345   return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
346 }
347 
348 /// isMask_32 - This function returns true if the argument is a non-empty
349 /// sequence of ones starting at the least significant bit with the remainder
350 /// zero (32 bit version).  Ex. isMask_32(0x0000FFFFU) == true.
351 inline bool isMask_32(uint32_t Value) {
352   return Value && ((Value + 1) & Value) == 0;
353 }
354 
355 /// isMask_64 - This function returns true if the argument is a non-empty
356 /// sequence of ones starting at the least significant bit with the remainder
357 /// zero (64 bit version).
358 inline bool isMask_64(uint64_t Value) {
359   return Value && ((Value + 1) & Value) == 0;
360 }
361 
362 /// isShiftedMask_32 - This function returns true if the argument contains a
363 /// non-empty sequence of ones with the remainder zero (32 bit version.)
364 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
365 inline bool isShiftedMask_32(uint32_t Value) {
366   return Value && isMask_32((Value - 1) | Value);
367 }
368 
369 /// isShiftedMask_64 - This function returns true if the argument contains a
370 /// non-empty sequence of ones with the remainder zero (64 bit version.)
371 inline bool isShiftedMask_64(uint64_t Value) {
372   return Value && isMask_64((Value - 1) | Value);
373 }
374 
375 /// isPowerOf2_32 - This function returns true if the argument is a power of
376 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
377 inline bool isPowerOf2_32(uint32_t Value) {
378   return Value && !(Value & (Value - 1));
379 }
380 
381 /// isPowerOf2_64 - This function returns true if the argument is a power of two
382 /// > 0 (64 bit edition.)
383 inline bool isPowerOf2_64(uint64_t Value) {
384   return Value && !(Value & (Value - int64_t(1L)));
385 }
386 
387 /// ByteSwap_16 - This function returns a byte-swapped representation of the
388 /// 16-bit argument, Value.
389 inline uint16_t ByteSwap_16(uint16_t Value) {
390   return sys::SwapByteOrder_16(Value);
391 }
392 
393 /// ByteSwap_32 - This function returns a byte-swapped representation of the
394 /// 32-bit argument, Value.
395 inline uint32_t ByteSwap_32(uint32_t Value) {
396   return sys::SwapByteOrder_32(Value);
397 }
398 
399 /// ByteSwap_64 - This function returns a byte-swapped representation of the
400 /// 64-bit argument, Value.
401 inline uint64_t ByteSwap_64(uint64_t Value) {
402   return sys::SwapByteOrder_64(Value);
403 }
404 
405 /// \brief Count the number of ones from the most significant bit to the first
406 /// zero bit.
407 ///
408 /// Ex. CountLeadingOnes(0xFF0FFF00) == 8.
409 /// Only unsigned integral types are allowed.
410 ///
411 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
412 /// ZB_Undefined are valid arguments.
413 template <typename T>
414 std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
415   static_assert(std::numeric_limits<T>::is_integer &&
416                     !std::numeric_limits<T>::is_signed,
417                 "Only unsigned integral types are allowed.");
418   return countLeadingZeros(~Value, ZB);
419 }
420 
421 /// \brief Count the number of ones from the least significant bit to the first
422 /// zero bit.
423 ///
424 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
425 /// Only unsigned integral types are allowed.
426 ///
427 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
428 /// ZB_Undefined are valid arguments.
429 template <typename T>
430 std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
431   static_assert(std::numeric_limits<T>::is_integer &&
432                     !std::numeric_limits<T>::is_signed,
433                 "Only unsigned integral types are allowed.");
434   return countTrailingZeros(~Value, ZB);
435 }
436 
437 namespace detail {
438 template <typename T, std::size_t SizeOfT> struct PopulationCounter {
439   static unsigned count(T Value) {
440     // Generic version, forward to 32 bits.
441     static_assert(SizeOfT <= 4, "Not implemented!");
442 #if __GNUC__ >= 4
443     return __builtin_popcount(Value);
444 #else
445     uint32_t v = Value;
446     v = v - ((v >> 1) & 0x55555555);
447     v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
448     return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
449 #endif
450   }
451 };
452 
453 template <typename T> struct PopulationCounter<T, 8> {
454   static unsigned count(T Value) {
455 #if __GNUC__ >= 4
456     return __builtin_popcountll(Value);
457 #else
458     uint64_t v = Value;
459     v = v - ((v >> 1) & 0x5555555555555555ULL);
460     v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
461     v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
462     return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
463 #endif
464   }
465 };
466 } // namespace detail
467 
468 /// \brief Count the number of set bits in a value.
469 /// Ex. countPopulation(0xF000F000) = 8
470 /// Returns 0 if the word is zero.
471 template <typename T>
472 inline unsigned countPopulation(T Value) {
473   static_assert(std::numeric_limits<T>::is_integer &&
474                     !std::numeric_limits<T>::is_signed,
475                 "Only unsigned integral types are allowed.");
476   return detail::PopulationCounter<T, sizeof(T)>::count(Value);
477 }
478 
479 /// Log2 - This function returns the log base 2 of the specified value
480 inline double Log2(double Value) {
481 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
482   return __builtin_log(Value) / __builtin_log(2.0);
483 #else
484   return log2(Value);
485 #endif
486 }
487 
488 /// Log2_32 - This function returns the floor log base 2 of the specified value,
489 /// -1 if the value is zero. (32 bit edition.)
490 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
491 inline unsigned Log2_32(uint32_t Value) {
492   return 31 - countLeadingZeros(Value);
493 }
494 
495 /// Log2_64 - This function returns the floor log base 2 of the specified value,
496 /// -1 if the value is zero. (64 bit edition.)
497 inline unsigned Log2_64(uint64_t Value) {
498   return 63 - countLeadingZeros(Value);
499 }
500 
501 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
502 /// value, 32 if the value is zero. (32 bit edition).
503 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
504 inline unsigned Log2_32_Ceil(uint32_t Value) {
505   return 32 - countLeadingZeros(Value - 1);
506 }
507 
508 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
509 /// value, 64 if the value is zero. (64 bit edition.)
510 inline unsigned Log2_64_Ceil(uint64_t Value) {
511   return 64 - countLeadingZeros(Value - 1);
512 }
513 
514 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
515 /// values using Euclid's algorithm.
516 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
517   while (B) {
518     uint64_t T = B;
519     B = A % B;
520     A = T;
521   }
522   return A;
523 }
524 
525 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
526 /// equivalent double.
527 inline double BitsToDouble(uint64_t Bits) {
528   union {
529     uint64_t L;
530     double D;
531   } T;
532   T.L = Bits;
533   return T.D;
534 }
535 
536 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
537 /// equivalent float.
538 inline float BitsToFloat(uint32_t Bits) {
539   union {
540     uint32_t I;
541     float F;
542   } T;
543   T.I = Bits;
544   return T.F;
545 }
546 
547 /// DoubleToBits - This function takes a double and returns the bit
548 /// equivalent 64-bit integer.  Note that copying doubles around
549 /// changes the bits of NaNs on some hosts, notably x86, so this
550 /// routine cannot be used if these bits are needed.
551 inline uint64_t DoubleToBits(double Double) {
552   union {
553     uint64_t L;
554     double D;
555   } T;
556   T.D = Double;
557   return T.L;
558 }
559 
560 /// FloatToBits - This function takes a float and returns the bit
561 /// equivalent 32-bit integer.  Note that copying floats around
562 /// changes the bits of NaNs on some hosts, notably x86, so this
563 /// routine cannot be used if these bits are needed.
564 inline uint32_t FloatToBits(float Float) {
565   union {
566     uint32_t I;
567     float F;
568   } T;
569   T.F = Float;
570   return T.I;
571 }
572 
573 /// MinAlign - A and B are either alignments or offsets.  Return the minimum
574 /// alignment that may be assumed after adding the two together.
575 inline uint64_t MinAlign(uint64_t A, uint64_t B) {
576   // The largest power of 2 that divides both A and B.
577   //
578   // Replace "-Value" by "1+~Value" in the following commented code to avoid
579   // MSVC warning C4146
580   //    return (A | B) & -(A | B);
581   return (A | B) & (1 + ~(A | B));
582 }
583 
584 /// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
585 ///
586 /// Alignment should be a power of two.  This method rounds up, so
587 /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
588 inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
589   assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
590          "Alignment is not a power of two!");
591 
592   assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
593 
594   return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
595 }
596 
597 /// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
598 /// bytes, rounding up.
599 inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
600   return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
601 }
602 
603 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
604 /// that is strictly greater than A.  Returns zero on overflow.
605 inline uint64_t NextPowerOf2(uint64_t A) {
606   A |= (A >> 1);
607   A |= (A >> 2);
608   A |= (A >> 4);
609   A |= (A >> 8);
610   A |= (A >> 16);
611   A |= (A >> 32);
612   return A + 1;
613 }
614 
615 /// Returns the power of two which is less than or equal to the given value.
616 /// Essentially, it is a floor operation across the domain of powers of two.
617 inline uint64_t PowerOf2Floor(uint64_t A) {
618   if (!A) return 0;
619   return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
620 }
621 
622 /// Returns the next integer (mod 2**64) that is greater than or equal to
623 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
624 ///
625 /// If non-zero \p Skew is specified, the return value will be a minimal
626 /// integer that is greater than or equal to \p Value and equal to
627 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
628 /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
629 ///
630 /// Examples:
631 /// \code
632 ///   alignTo(5, 8) = 8
633 ///   alignTo(17, 8) = 24
634 ///   alignTo(~0LL, 8) = 0
635 ///   alignTo(321, 255) = 510
636 ///
637 ///   alignTo(5, 8, 7) = 7
638 ///   alignTo(17, 8, 1) = 17
639 ///   alignTo(~0LL, 8, 3) = 3
640 ///   alignTo(321, 255, 42) = 552
641 /// \endcode
642 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
643   Skew %= Align;
644   return (Value + Align - 1 - Skew) / Align * Align + Skew;
645 }
646 
647 /// Returns the largest uint64_t less than or equal to \p Value and is
648 /// \p Skew mod \p Align. \p Align must be non-zero
649 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
650   Skew %= Align;
651   return (Value - Skew) / Align * Align + Skew;
652 }
653 
654 /// Returns the offset to the next integer (mod 2**64) that is greater than
655 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
656 /// non-zero.
657 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
658   return alignTo(Value, Align) - Value;
659 }
660 
661 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
662 /// Usage int32_t r = SignExtend32<5>(x);
663 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
664   return int32_t(x << (32 - B)) >> (32 - B);
665 }
666 
667 /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
668 /// Requires 0 < B <= 32.
669 inline int32_t SignExtend32(uint32_t X, unsigned B) {
670   return int32_t(X << (32 - B)) >> (32 - B);
671 }
672 
673 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
674 /// Usage int64_t r = SignExtend64<5>(x);
675 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
676   return int64_t(x << (64 - B)) >> (64 - B);
677 }
678 
679 /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
680 /// Requires 0 < B <= 64.
681 inline int64_t SignExtend64(uint64_t X, unsigned B) {
682   return int64_t(X << (64 - B)) >> (64 - B);
683 }
684 
685 /// \brief Subtract two unsigned integers, X and Y, of type T and return their
686 /// absolute value.
687 template <typename T>
688 typename std::enable_if<std::is_unsigned<T>::value, T>::type
689 AbsoluteDifference(T X, T Y) {
690   return std::max(X, Y) - std::min(X, Y);
691 }
692 
693 /// \brief Add two unsigned integers, X and Y, of type T.
694 /// Clamp the result to the maximum representable value of T on overflow.
695 /// ResultOverflowed indicates if the result is larger than the maximum
696 /// representable value of type T.
697 template <typename T>
698 typename std::enable_if<std::is_unsigned<T>::value, T>::type
699 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
700   bool Dummy;
701   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
702   // Hacker's Delight, p. 29
703   T Z = X + Y;
704   Overflowed = (Z < X || Z < Y);
705   if (Overflowed)
706     return std::numeric_limits<T>::max();
707   else
708     return Z;
709 }
710 
711 /// \brief Multiply two unsigned integers, X and Y, of type T.
712 /// Clamp the result to the maximum representable value of T on overflow.
713 /// ResultOverflowed indicates if the result is larger than the maximum
714 /// representable value of type T.
715 template <typename T>
716 typename std::enable_if<std::is_unsigned<T>::value, T>::type
717 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
718   bool Dummy;
719   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
720 
721   // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
722   // because it fails for uint16_t (where multiplication can have undefined
723   // behavior due to promotion to int), and requires a division in addition
724   // to the multiplication.
725 
726   Overflowed = false;
727 
728   // Log2(Z) would be either Log2Z or Log2Z + 1.
729   // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
730   // will necessarily be less than Log2Max as desired.
731   int Log2Z = Log2_64(X) + Log2_64(Y);
732   const T Max = std::numeric_limits<T>::max();
733   int Log2Max = Log2_64(Max);
734   if (Log2Z < Log2Max) {
735     return X * Y;
736   }
737   if (Log2Z > Log2Max) {
738     Overflowed = true;
739     return Max;
740   }
741 
742   // We're going to use the top bit, and maybe overflow one
743   // bit past it. Multiply all but the bottom bit then add
744   // that on at the end.
745   T Z = (X >> 1) * Y;
746   if (Z & ~(Max >> 1)) {
747     Overflowed = true;
748     return Max;
749   }
750   Z <<= 1;
751   if (X & 1)
752     return SaturatingAdd(Z, Y, ResultOverflowed);
753 
754   return Z;
755 }
756 
757 /// \brief Multiply two unsigned integers, X and Y, and add the unsigned
758 /// integer, A to the product. Clamp the result to the maximum representable
759 /// value of T on overflow. ResultOverflowed indicates if the result is larger
760 /// than the maximum representable value of type T.
761 /// Note that this is purely a convenience function as there is no distinction
762 /// where overflow occurred in a 'fused' multiply-add for unsigned numbers.
763 template <typename T>
764 typename std::enable_if<std::is_unsigned<T>::value, T>::type
765 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
766   bool Dummy;
767   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
768 
769   T Product = SaturatingMultiply(X, Y, &Overflowed);
770   if (Overflowed)
771     return Product;
772 
773   return SaturatingAdd(A, Product, &Overflowed);
774 }
775 
776 extern const float huge_valf;
777 } // End llvm namespace
778 
779 #endif
780