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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 <climits>
22 : #include <cstring>
23 : #include <limits>
24 : #include <type_traits>
25 :
26 : #ifdef __ANDROID_NDK__
27 : #include <android/api-level.h>
28 : #endif
29 :
30 : #ifdef _MSC_VER
31 : // Declare these intrinsics manually rather including intrin.h. It's very
32 : // expensive, and MathExtras.h is popular.
33 : // #include <intrin.h>
34 : extern "C" {
35 : unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
36 : unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
37 : unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
38 : unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
39 : }
40 : #endif
41 :
42 : namespace llvm {
43 : /// The behavior an operation has on an input of 0.
44 : enum ZeroBehavior {
45 : /// The returned value is undefined.
46 : ZB_Undefined,
47 : /// The returned value is numeric_limits<T>::max()
48 : ZB_Max,
49 : /// The returned value is numeric_limits<T>::digits
50 : ZB_Width
51 : };
52 :
53 : namespace detail {
54 : template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
55 : static std::size_t count(T Val, ZeroBehavior) {
56 139 : if (!Val)
57 : return std::numeric_limits<T>::digits;
58 169 : if (Val & 0x1)
59 : return 0;
60 :
61 : // Bisection method.
62 : std::size_t ZeroBits = 0;
63 : T Shift = std::numeric_limits<T>::digits >> 1;
64 : T Mask = std::numeric_limits<T>::max() >> Shift;
65 554 : while (Shift) {
66 416 : if ((Val & Mask) == 0) {
67 216 : Val >>= Shift;
68 216 : ZeroBits |= Shift;
69 : }
70 416 : Shift >>= 1;
71 416 : Mask >>= Shift;
72 : }
73 : return ZeroBits;
74 : }
75 : };
76 :
77 : #if __GNUC__ >= 4 || defined(_MSC_VER)
78 : template <typename T> struct TrailingZerosCounter<T, 4> {
79 : static std::size_t count(T Val, ZeroBehavior ZB) {
80 721383 : if (ZB != ZB_Undefined && Val == 0)
81 : return 32;
82 :
83 : #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
84 86821562 : return __builtin_ctz(Val);
85 : #elif defined(_MSC_VER)
86 : unsigned long Index;
87 : _BitScanForward(&Index, Val);
88 : return Index;
89 : #endif
90 : }
91 : };
92 :
93 : #if !defined(_MSC_VER) || defined(_M_X64)
94 : template <typename T> struct TrailingZerosCounter<T, 8> {
95 : static std::size_t count(T Val, ZeroBehavior ZB) {
96 43100256 : if (ZB != ZB_Undefined && Val == 0)
97 : return 64;
98 :
99 : #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
100 239900158 : return __builtin_ctzll(Val);
101 : #elif defined(_MSC_VER)
102 : unsigned long Index;
103 : _BitScanForward64(&Index, Val);
104 : return Index;
105 : #endif
106 : }
107 : };
108 : #endif
109 : #endif
110 : } // namespace detail
111 :
112 : /// Count number of 0's from the least significant bit to the most
113 : /// stopping at the first 1.
114 : ///
115 : /// Only unsigned integral types are allowed.
116 : ///
117 : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
118 : /// valid arguments.
119 : template <typename T>
120 : std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
121 : static_assert(std::numeric_limits<T>::is_integer &&
122 : !std::numeric_limits<T>::is_signed,
123 : "Only unsigned integral types are allowed.");
124 : return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
125 : }
126 :
127 : namespace detail {
128 : template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
129 : static std::size_t count(T Val, ZeroBehavior) {
130 0 : if (!Val)
131 : return std::numeric_limits<T>::digits;
132 :
133 : // Bisection method.
134 : std::size_t ZeroBits = 0;
135 18 : for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
136 14 : T Tmp = Val >> Shift;
137 14 : if (Tmp)
138 : Val = Tmp;
139 : else
140 6 : ZeroBits |= Shift;
141 : }
142 : return ZeroBits;
143 : }
144 : };
145 :
146 : #if __GNUC__ >= 4 || defined(_MSC_VER)
147 : template <typename T> struct LeadingZerosCounter<T, 4> {
148 : static std::size_t count(T Val, ZeroBehavior ZB) {
149 89365250 : if (ZB != ZB_Undefined && Val == 0)
150 : return 32;
151 :
152 : #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
153 71592414 : return __builtin_clz(Val);
154 : #elif defined(_MSC_VER)
155 : unsigned long Index;
156 : _BitScanReverse(&Index, Val);
157 : return Index ^ 31;
158 : #endif
159 : }
160 : };
161 :
162 : #if !defined(_MSC_VER) || defined(_M_X64)
163 : template <typename T> struct LeadingZerosCounter<T, 8> {
164 : static std::size_t count(T Val, ZeroBehavior ZB) {
165 128315338 : if (ZB != ZB_Undefined && Val == 0)
166 : return 64;
167 :
168 : #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
169 186187222 : return __builtin_clzll(Val);
170 : #elif defined(_MSC_VER)
171 : unsigned long Index;
172 : _BitScanReverse64(&Index, Val);
173 : return Index ^ 63;
174 : #endif
175 : }
176 : };
177 : #endif
178 : #endif
179 : } // namespace detail
180 :
181 : /// Count number of 0's from the most significant bit to the least
182 : /// stopping at the first 1.
183 : ///
184 : /// Only unsigned integral types are allowed.
185 : ///
186 : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
187 : /// valid arguments.
188 : template <typename T>
189 : std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
190 : static_assert(std::numeric_limits<T>::is_integer &&
191 : !std::numeric_limits<T>::is_signed,
192 : "Only unsigned integral types are allowed.");
193 : return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
194 : }
195 :
196 : /// Get the index of the first set bit starting from the least
197 : /// significant bit.
198 : ///
199 : /// Only unsigned integral types are allowed.
200 : ///
201 : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
202 : /// valid arguments.
203 : template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
204 5082 : if (ZB == ZB_Max && Val == 0)
205 : return std::numeric_limits<T>::max();
206 :
207 2 : return countTrailingZeros(Val, ZB_Undefined);
208 : }
209 :
210 : /// Create a bitmask with the N right-most bits set to 1, and all other
211 : /// bits set to 0. Only unsigned types are allowed.
212 : template <typename T> T maskTrailingOnes(unsigned N) {
213 : static_assert(std::is_unsigned<T>::value, "Invalid type!");
214 : const unsigned Bits = CHAR_BIT * sizeof(T);
215 : assert(N <= Bits && "Invalid bit index");
216 57951571 : return N == 0 ? 0 : (T(-1) >> (Bits - N));
217 : }
218 :
219 : /// Create a bitmask with the N left-most bits set to 1, and all other
220 : /// bits set to 0. Only unsigned types are allowed.
221 : template <typename T> T maskLeadingOnes(unsigned N) {
222 222550936 : return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
223 : }
224 :
225 : /// Create a bitmask with the N right-most bits set to 0, and all other
226 : /// bits set to 1. Only unsigned types are allowed.
227 : template <typename T> T maskTrailingZeros(unsigned N) {
228 53066932 : return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
229 : }
230 :
231 : /// Create a bitmask with the N left-most bits set to 0, and all other
232 : /// bits set to 1. Only unsigned types are allowed.
233 : template <typename T> T maskLeadingZeros(unsigned N) {
234 : return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
235 : }
236 :
237 : /// Get the index of the last set bit starting from the least
238 : /// significant bit.
239 : ///
240 : /// Only unsigned integral types are allowed.
241 : ///
242 : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
243 : /// valid arguments.
244 : template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
245 15189 : if (ZB == ZB_Max && Val == 0)
246 : return std::numeric_limits<T>::max();
247 :
248 : // Use ^ instead of - because both gcc and llvm can remove the associated ^
249 : // in the __builtin_clz intrinsic on x86.
250 2 : return countLeadingZeros(Val, ZB_Undefined) ^
251 2090992 : (std::numeric_limits<T>::digits - 1);
252 : }
253 :
254 : /// Macro compressed bit reversal table for 256 bits.
255 : ///
256 : /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
257 : static const unsigned char BitReverseTable256[256] = {
258 : #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
259 : #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
260 : #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
261 : R6(0), R6(2), R6(1), R6(3)
262 : #undef R2
263 : #undef R4
264 : #undef R6
265 : };
266 :
267 : /// Reverse the bits in \p Val.
268 : template <typename T>
269 : T reverseBits(T Val) {
270 : unsigned char in[sizeof(Val)];
271 : unsigned char out[sizeof(Val)];
272 15205 : std::memcpy(in, &Val, sizeof(Val));
273 77243 : for (unsigned i = 0; i < sizeof(Val); ++i)
274 62242 : out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
275 15205 : std::memcpy(&Val, out, sizeof(Val));
276 : return Val;
277 : }
278 :
279 : // NOTE: The following support functions use the _32/_64 extensions instead of
280 : // type overloading so that signed and unsigned integers can be used without
281 : // ambiguity.
282 :
283 : /// Return the high 32 bits of a 64 bit value.
284 : constexpr inline uint32_t Hi_32(uint64_t Value) {
285 871811 : return static_cast<uint32_t>(Value >> 32);
286 : }
287 :
288 : /// Return the low 32 bits of a 64 bit value.
289 : constexpr inline uint32_t Lo_32(uint64_t Value) {
290 2281155 : return static_cast<uint32_t>(Value);
291 : }
292 :
293 : /// Make a 64-bit integer from a high / low pair of 32-bit integers.
294 : constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
295 1291544 : return ((uint64_t)High << 32) | (uint64_t)Low;
296 : }
297 :
298 : /// Checks if an integer fits into the given bit width.
299 0 : template <unsigned N> constexpr inline bool isInt(int64_t x) {
300 4053376 : return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
301 : }
302 : // Template specializations to get better code for common cases.
303 : template <> constexpr inline bool isInt<8>(int64_t x) {
304 2116616 : return static_cast<int8_t>(x) == x;
305 : }
306 : template <> constexpr inline bool isInt<16>(int64_t x) {
307 392823 : return static_cast<int16_t>(x) == x;
308 : }
309 : template <> constexpr inline bool isInt<32>(int64_t x) {
310 8681951 : return static_cast<int32_t>(x) == x;
311 : }
312 :
313 : /// Checks if a signed integer is an N bit number shifted left by S.
314 : template <unsigned N, unsigned S>
315 : constexpr inline bool isShiftedInt(int64_t x) {
316 : static_assert(
317 : N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
318 : static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
319 5580 : return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
320 : }
321 :
322 : /// Checks if an unsigned integer fits into the given bit width.
323 : ///
324 : /// This is written as two functions rather than as simply
325 : ///
326 : /// return N >= 64 || X < (UINT64_C(1) << N);
327 : ///
328 : /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
329 : /// left too many places.
330 : template <unsigned N>
331 : constexpr inline typename std::enable_if<(N < 64), bool>::type
332 : isUInt(uint64_t X) {
333 : static_assert(N > 0, "isUInt<0> doesn't make sense");
334 25095 : return X < (UINT64_C(1) << (N));
335 : }
336 : template <unsigned N>
337 : constexpr inline typename std::enable_if<N >= 64, bool>::type
338 : isUInt(uint64_t X) {
339 : return true;
340 : }
341 :
342 : // Template specializations to get better code for common cases.
343 : template <> constexpr inline bool isUInt<8>(uint64_t x) {
344 10881 : return static_cast<uint8_t>(x) == x;
345 : }
346 : template <> constexpr inline bool isUInt<16>(uint64_t x) {
347 723 : return static_cast<uint16_t>(x) == x;
348 : }
349 : template <> constexpr inline bool isUInt<32>(uint64_t x) {
350 34830 : return static_cast<uint32_t>(x) == x;
351 : }
352 :
353 : /// Checks if a unsigned integer is an N bit number shifted left by S.
354 : template <unsigned N, unsigned S>
355 : constexpr inline bool isShiftedUInt(uint64_t x) {
356 : static_assert(
357 : N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
358 : static_assert(N + S <= 64,
359 : "isShiftedUInt<N, S> with N + S > 64 is too wide.");
360 : // Per the two static_asserts above, S must be strictly less than 64. So
361 : // 1 << S is not undefined behavior.
362 13161 : return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
363 : }
364 :
365 : /// Gets the maximum value for a N-bit unsigned integer.
366 : inline uint64_t maxUIntN(uint64_t N) {
367 : assert(N > 0 && N <= 64 && "integer width out of range");
368 :
369 : // uint64_t(1) << 64 is undefined behavior, so we can't do
370 : // (uint64_t(1) << N) - 1
371 : // without checking first that N != 64. But this works and doesn't have a
372 : // branch.
373 9867 : return UINT64_MAX >> (64 - N);
374 : }
375 :
376 : /// Gets the minimum value for a N-bit signed integer.
377 : inline int64_t minIntN(int64_t N) {
378 : assert(N > 0 && N <= 64 && "integer width out of range");
379 :
380 31481 : return -(UINT64_C(1)<<(N-1));
381 : }
382 :
383 : /// Gets the maximum value for a N-bit signed integer.
384 : inline int64_t maxIntN(int64_t N) {
385 : assert(N > 0 && N <= 64 && "integer width out of range");
386 :
387 : // This relies on two's complement wraparound when N == 64, so we convert to
388 : // int64_t only at the very end to avoid UB.
389 31337 : return (UINT64_C(1) << (N - 1)) - 1;
390 : }
391 :
392 : /// Checks if an unsigned integer fits into the given (dynamic) bit width.
393 : inline bool isUIntN(unsigned N, uint64_t x) {
394 2252601 : return N >= 64 || x <= maxUIntN(N);
395 : }
396 :
397 : /// Checks if an signed integer fits into the given (dynamic) bit width.
398 : inline bool isIntN(unsigned N, int64_t x) {
399 56877 : return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
400 : }
401 :
402 : /// Return true if the argument is a non-empty sequence of ones starting at the
403 : /// least significant bit with the remainder zero (32 bit version).
404 : /// Ex. isMask_32(0x0000FFFFU) == true.
405 : constexpr inline bool isMask_32(uint32_t Value) {
406 6268 : return Value && ((Value + 1) & Value) == 0;
407 : }
408 :
409 : /// Return true if the argument is a non-empty sequence of ones starting at the
410 : /// least significant bit with the remainder zero (64 bit version).
411 : constexpr inline bool isMask_64(uint64_t Value) {
412 455078 : return Value && ((Value + 1) & Value) == 0;
413 : }
414 :
415 : /// Return true if the argument contains a non-empty sequence of ones with the
416 : /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
417 : constexpr inline bool isShiftedMask_32(uint32_t Value) {
418 1423 : return Value && isMask_32((Value - 1) | Value);
419 : }
420 :
421 : /// Return true if the argument contains a non-empty sequence of ones with the
422 : /// remainder zero (64 bit version.)
423 : constexpr inline bool isShiftedMask_64(uint64_t Value) {
424 19959 : return Value && isMask_64((Value - 1) | Value);
425 : }
426 :
427 : /// Return true if the argument is a power of two > 0.
428 : /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
429 : constexpr inline bool isPowerOf2_32(uint32_t Value) {
430 4541554 : return Value && !(Value & (Value - 1));
431 : }
432 :
433 : /// Return true if the argument is a power of two > 0 (64 bit edition.)
434 : constexpr inline bool isPowerOf2_64(uint64_t Value) {
435 5622961 : return Value && !(Value & (Value - 1));
436 : }
437 :
438 : /// Return a byte-swapped representation of the 16-bit argument.
439 : inline uint16_t ByteSwap_16(uint16_t Value) {
440 : return sys::SwapByteOrder_16(Value);
441 : }
442 :
443 : /// Return a byte-swapped representation of the 32-bit argument.
444 : inline uint32_t ByteSwap_32(uint32_t Value) {
445 : return sys::SwapByteOrder_32(Value);
446 : }
447 :
448 : /// Return a byte-swapped representation of the 64-bit argument.
449 : inline uint64_t ByteSwap_64(uint64_t Value) {
450 : return sys::SwapByteOrder_64(Value);
451 : }
452 :
453 : /// Count the number of ones from the most significant bit to the first
454 : /// zero bit.
455 : ///
456 : /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
457 : /// Only unsigned integral types are allowed.
458 : ///
459 : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
460 : /// ZB_Undefined are valid arguments.
461 : template <typename T>
462 : std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
463 : static_assert(std::numeric_limits<T>::is_integer &&
464 : !std::numeric_limits<T>::is_signed,
465 : "Only unsigned integral types are allowed.");
466 10966557 : return countLeadingZeros<T>(~Value, ZB);
467 : }
468 :
469 : /// Count the number of ones from the least significant bit to the first
470 : /// zero bit.
471 : ///
472 : /// Ex. countTrailingOnes(0x00FF00FF) == 8.
473 : /// Only unsigned integral types are allowed.
474 : ///
475 : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
476 : /// ZB_Undefined are valid arguments.
477 : template <typename T>
478 : std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
479 : static_assert(std::numeric_limits<T>::is_integer &&
480 : !std::numeric_limits<T>::is_signed,
481 : "Only unsigned integral types are allowed.");
482 61259230 : return countTrailingZeros<T>(~Value, ZB);
483 : }
484 :
485 : namespace detail {
486 : template <typename T, std::size_t SizeOfT> struct PopulationCounter {
487 : static unsigned count(T Value) {
488 : // Generic version, forward to 32 bits.
489 : static_assert(SizeOfT <= 4, "Not implemented!");
490 : #if __GNUC__ >= 4
491 1536365 : return __builtin_popcount(Value);
492 : #else
493 : uint32_t v = Value;
494 : v = v - ((v >> 1) & 0x55555555);
495 : v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
496 : return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
497 : #endif
498 : }
499 : };
500 :
501 : template <typename T> struct PopulationCounter<T, 8> {
502 : static unsigned count(T Value) {
503 : #if __GNUC__ >= 4
504 39160574 : return __builtin_popcountll(Value);
505 : #else
506 : uint64_t v = Value;
507 : v = v - ((v >> 1) & 0x5555555555555555ULL);
508 : v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
509 : v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
510 : return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
511 : #endif
512 : }
513 : };
514 : } // namespace detail
515 :
516 : /// Count the number of set bits in a value.
517 : /// Ex. countPopulation(0xF000F000) = 8
518 : /// Returns 0 if the word is zero.
519 : template <typename T>
520 458752 : inline unsigned countPopulation(T Value) {
521 : static_assert(std::numeric_limits<T>::is_integer &&
522 : !std::numeric_limits<T>::is_signed,
523 : "Only unsigned integral types are allowed.");
524 458752 : return detail::PopulationCounter<T, sizeof(T)>::count(Value);
525 : }
526 :
527 : /// Return the log base 2 of the specified value.
528 0 : inline double Log2(double Value) {
529 : #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
530 : return __builtin_log(Value) / __builtin_log(2.0);
531 : #else
532 0 : return log2(Value);
533 : #endif
534 : }
535 :
536 : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
537 : /// (32 bit edition.)
538 : /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
539 : inline unsigned Log2_32(uint32_t Value) {
540 55957523 : return 31 - countLeadingZeros(Value);
541 : }
542 :
543 : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
544 : /// (64 bit edition.)
545 : inline unsigned Log2_64(uint64_t Value) {
546 405152 : return 63 - countLeadingZeros(Value);
547 : }
548 :
549 : /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
550 : /// (32 bit edition).
551 : /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
552 : inline unsigned Log2_32_Ceil(uint32_t Value) {
553 23982209 : return 32 - countLeadingZeros(Value - 1);
554 : }
555 :
556 : /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
557 : /// (64 bit edition.)
558 : inline unsigned Log2_64_Ceil(uint64_t Value) {
559 177974329 : return 64 - countLeadingZeros(Value - 1);
560 : }
561 :
562 : /// Return the greatest common divisor of the values using Euclid's algorithm.
563 : inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
564 303682 : while (B) {
565 : uint64_t T = B;
566 190279 : B = A % B;
567 : A = T;
568 : }
569 : return A;
570 : }
571 :
572 : /// This function takes a 64-bit integer and returns the bit equivalent double.
573 : inline double BitsToDouble(uint64_t Bits) {
574 : double D;
575 : static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
576 : memcpy(&D, &Bits, sizeof(Bits));
577 : return D;
578 : }
579 :
580 : /// This function takes a 32-bit integer and returns the bit equivalent float.
581 : inline float BitsToFloat(uint32_t Bits) {
582 : float F;
583 : static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
584 : memcpy(&F, &Bits, sizeof(Bits));
585 : return F;
586 : }
587 :
588 : /// This function takes a double and returns the bit equivalent 64-bit integer.
589 : /// Note that copying doubles around changes the bits of NaNs on some hosts,
590 : /// notably x86, so this routine cannot be used if these bits are needed.
591 : inline uint64_t DoubleToBits(double Double) {
592 : uint64_t Bits;
593 : static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
594 4818861 : memcpy(&Bits, &Double, sizeof(Double));
595 : return Bits;
596 : }
597 :
598 : /// This function takes a float and returns the bit equivalent 32-bit integer.
599 : /// Note that copying floats around changes the bits of NaNs on some hosts,
600 : /// notably x86, so this routine cannot be used if these bits are needed.
601 : inline uint32_t FloatToBits(float Float) {
602 : uint32_t Bits;
603 : static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
604 26010 : memcpy(&Bits, &Float, sizeof(Float));
605 : return Bits;
606 : }
607 :
608 : /// A and B are either alignments or offsets. Return the minimum alignment that
609 : /// may be assumed after adding the two together.
610 : constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
611 : // The largest power of 2 that divides both A and B.
612 : //
613 : // Replace "-Value" by "1+~Value" in the following commented code to avoid
614 : // MSVC warning C4146
615 : // return (A | B) & -(A | B);
616 49432318 : return (A | B) & (1 + ~(A | B));
617 : }
618 :
619 : /// Aligns \c Addr to \c Alignment bytes, rounding up.
620 : ///
621 : /// Alignment should be a power of two. This method rounds up, so
622 : /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
623 : inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
624 : assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
625 : "Alignment is not a power of two!");
626 :
627 : assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
628 :
629 31171624 : return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
630 : }
631 :
632 : /// Returns the necessary adjustment for aligning \c Ptr to \c Alignment
633 : /// bytes, rounding up.
634 : inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
635 2447718844 : return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
636 : }
637 :
638 : /// Returns the next power of two (in 64-bits) that is strictly greater than A.
639 : /// Returns zero on overflow.
640 : inline uint64_t NextPowerOf2(uint64_t A) {
641 113999871 : A |= (A >> 1);
642 113999871 : A |= (A >> 2);
643 113999871 : A |= (A >> 4);
644 113999867 : A |= (A >> 8);
645 113999867 : A |= (A >> 16);
646 6175075 : A |= (A >> 32);
647 113434502 : return A + 1;
648 : }
649 :
650 : /// Returns the power of two which is less than or equal to the given value.
651 : /// Essentially, it is a floor operation across the domain of powers of two.
652 : inline uint64_t PowerOf2Floor(uint64_t A) {
653 94777 : if (!A) return 0;
654 112485 : return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
655 : }
656 :
657 : /// Returns the power of two which is greater than or equal to the given value.
658 : /// Essentially, it is a ceil operation across the domain of powers of two.
659 : inline uint64_t PowerOf2Ceil(uint64_t A) {
660 565562 : if (!A)
661 : return 0;
662 565370 : return NextPowerOf2(A - 1);
663 : }
664 :
665 : /// Returns the next integer (mod 2**64) that is greater than or equal to
666 : /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
667 : ///
668 : /// If non-zero \p Skew is specified, the return value will be a minimal
669 : /// integer that is greater than or equal to \p Value and equal to
670 : /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
671 : /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
672 : ///
673 : /// Examples:
674 : /// \code
675 : /// alignTo(5, 8) = 8
676 : /// alignTo(17, 8) = 24
677 : /// alignTo(~0LL, 8) = 0
678 : /// alignTo(321, 255) = 510
679 : ///
680 : /// alignTo(5, 8, 7) = 7
681 : /// alignTo(17, 8, 1) = 17
682 : /// alignTo(~0LL, 8, 3) = 3
683 : /// alignTo(321, 255, 42) = 552
684 : /// \endcode
685 : inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
686 : assert(Align != 0u && "Align can't be 0.");
687 8126978 : Skew %= Align;
688 662471559 : return (Value + Align - 1 - Skew) / Align * Align + Skew;
689 : }
690 :
691 : /// Returns the next integer (mod 2**64) that is greater than or equal to
692 : /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
693 : template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
694 : static_assert(Align != 0u, "Align must be non-zero");
695 45559022 : return (Value + Align - 1) / Align * Align;
696 : }
697 :
698 : /// Returns the integer ceil(Numerator / Denominator).
699 : inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
700 290454 : return alignTo(Numerator, Denominator) / Denominator;
701 : }
702 :
703 : /// \c alignTo for contexts where a constant expression is required.
704 : /// \sa alignTo
705 : ///
706 : /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
707 : template <uint64_t Align>
708 : struct AlignTo {
709 : static_assert(Align != 0u, "Align must be non-zero");
710 : template <uint64_t Value>
711 : struct from_value {
712 : static const uint64_t value = (Value + Align - 1) / Align * Align;
713 : };
714 : };
715 :
716 : /// Returns the largest uint64_t less than or equal to \p Value and is
717 : /// \p Skew mod \p Align. \p Align must be non-zero
718 : inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
719 : assert(Align != 0u && "Align can't be 0.");
720 : Skew %= Align;
721 605816 : return (Value - Skew) / Align * Align + Skew;
722 : }
723 :
724 : /// Returns the offset to the next integer (mod 2**64) that is greater than
725 : /// or equal to \p Value and is a multiple of \p Align. \p Align must be
726 : /// non-zero.
727 : inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
728 1361450 : return alignTo(Value, Align) - Value;
729 : }
730 :
731 : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
732 : /// Requires 0 < B <= 32.
733 : template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
734 : static_assert(B > 0, "Bit width can't be 0.");
735 : static_assert(B <= 32, "Bit width out of range.");
736 5254 : return int32_t(X << (32 - B)) >> (32 - B);
737 : }
738 :
739 : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
740 : /// Requires 0 < B < 32.
741 : inline int32_t SignExtend32(uint32_t X, unsigned B) {
742 : assert(B > 0 && "Bit width can't be 0.");
743 : assert(B <= 32 && "Bit width out of range.");
744 6095 : return int32_t(X << (32 - B)) >> (32 - B);
745 : }
746 :
747 : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
748 : /// Requires 0 < B < 64.
749 : template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
750 : static_assert(B > 0, "Bit width can't be 0.");
751 : static_assert(B <= 64, "Bit width out of range.");
752 8409 : return int64_t(x << (64 - B)) >> (64 - B);
753 : }
754 :
755 : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
756 : /// Requires 0 < B < 64.
757 : inline int64_t SignExtend64(uint64_t X, unsigned B) {
758 : assert(B > 0 && "Bit width can't be 0.");
759 : assert(B <= 64 && "Bit width out of range.");
760 224108198 : return int64_t(X << (64 - B)) >> (64 - B);
761 : }
762 :
763 : /// Subtract two unsigned integers, X and Y, of type T and return the absolute
764 : /// value of the result.
765 : template <typename T>
766 : typename std::enable_if<std::is_unsigned<T>::value, T>::type
767 : AbsoluteDifference(T X, T Y) {
768 309 : return std::max(X, Y) - std::min(X, Y);
769 : }
770 :
771 : /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
772 : /// maximum representable value of T on overflow. ResultOverflowed indicates if
773 : /// the result is larger than the maximum representable value of type T.
774 : template <typename T>
775 : typename std::enable_if<std::is_unsigned<T>::value, T>::type
776 : SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
777 : bool Dummy;
778 413 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
779 : // Hacker's Delight, p. 29
780 2602748 : T Z = X + Y;
781 2602748 : Overflowed = (Z < X || Z < Y);
782 2602748 : if (Overflowed)
783 : return std::numeric_limits<T>::max();
784 : else
785 : return Z;
786 : }
787 :
788 : /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
789 : /// maximum representable value of T on overflow. ResultOverflowed indicates if
790 : /// the result is larger than the maximum representable value of type T.
791 : template <typename T>
792 : typename std::enable_if<std::is_unsigned<T>::value, T>::type
793 3451 : SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
794 : bool Dummy;
795 3451 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
796 :
797 : // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
798 : // because it fails for uint16_t (where multiplication can have undefined
799 : // behavior due to promotion to int), and requires a division in addition
800 : // to the multiplication.
801 :
802 3479 : Overflowed = false;
803 :
804 : // Log2(Z) would be either Log2Z or Log2Z + 1.
805 : // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
806 : // will necessarily be less than Log2Max as desired.
807 3799 : int Log2Z = Log2_64(X) + Log2_64(Y);
808 : const T Max = std::numeric_limits<T>::max();
809 : int Log2Max = Log2_64(Max);
810 3451 : if (Log2Z < Log2Max) {
811 2910 : return X * Y;
812 : }
813 541 : if (Log2Z > Log2Max) {
814 27 : Overflowed = true;
815 15 : return Max;
816 : }
817 :
818 : // We're going to use the top bit, and maybe overflow one
819 : // bit past it. Multiply all but the bottom bit then add
820 : // that on at the end.
821 526 : T Z = (X >> 1) * Y;
822 526 : if (Z & ~(Max >> 1)) {
823 112 : Overflowed = true;
824 112 : return Max;
825 : }
826 414 : Z <<= 1;
827 414 : if (X & 1)
828 413 : return SaturatingAdd(Z, Y, ResultOverflowed);
829 :
830 : return Z;
831 : }
832 390 :
833 : /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
834 390 : /// the product. Clamp the result to the maximum representable value of T on
835 : /// overflow. ResultOverflowed indicates if the result is larger than the
836 : /// maximum representable value of type T.
837 : template <typename T>
838 : typename std::enable_if<std::is_unsigned<T>::value, T>::type
839 2596 : SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
840 : bool Dummy;
841 2986 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
842 :
843 2596 : T Product = SaturatingMultiply(X, Y, &Overflowed);
844 2596 : if (Overflowed)
845 : return Product;
846 390 :
847 2593 : return SaturatingAdd(A, Product, &Overflowed);
848 : }
849 390 :
850 134 : /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
851 : extern const float huge_valf;
852 256 : } // End llvm namespace
853 3 :
854 3 : #endif
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