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 |
15 | |
16 | #include "llvm/Support/Compiler.h" |
17 | #include <cassert> |
18 | #include <climits> |
19 | #include <cmath> |
20 | #include <cstdint> |
21 | #include <cstring> |
22 | #include <limits> |
23 | #include <type_traits> |
24 | |
25 | #ifdef __ANDROID_NDK__ |
26 | #include <android/api-level.h> |
27 | #endif |
28 | |
29 | #ifdef _MSC_VER |
30 | // Declare these intrinsics manually rather including intrin.h. It's very |
31 | // expensive, and MathExtras.h is popular. |
32 | // #include <intrin.h> |
33 | extern "C" { |
34 | unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); |
35 | unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); |
36 | unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); |
37 | unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); |
38 | } |
39 | #endif |
40 | |
41 | namespace llvm { |
42 | |
43 | /// The behavior an operation has on an input of 0. |
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 | /// Mathematical constants. |
54 | namespace numbers { |
55 | // TODO: Track C++20 std::numbers. |
56 | // TODO: Favor using the hexadecimal FP constants (requires C++17). |
57 | constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 |
58 | egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 |
59 | ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 |
60 | ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 |
61 | log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) |
62 | log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) |
63 | pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 |
64 | inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 |
65 | sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 |
66 | inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 |
67 | sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 |
68 | inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) |
69 | sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 |
70 | inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) |
71 | phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 |
72 | constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 |
73 | egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 |
74 | ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 |
75 | ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 |
76 | log2ef = 1.44269504F, // (0x1.715476P+0) |
77 | log10ef = .434294482F, // (0x1.bcb7b2P-2) |
78 | pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 |
79 | inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 |
80 | sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 |
81 | inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 |
82 | sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 |
83 | inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) |
84 | sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 |
85 | inv_sqrt3f = .577350269F, // (0x1.279a74P-1) |
86 | phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 |
87 | } // namespace numbers |
88 | |
89 | namespace detail { |
90 | template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter { |
91 | static unsigned count(T Val, ZeroBehavior) { |
92 | if (!Val) |
93 | return std::numeric_limits<T>::digits; |
94 | if (Val & 0x1) |
95 | return 0; |
96 | |
97 | // Bisection method. |
98 | unsigned ZeroBits = 0; |
99 | T Shift = std::numeric_limits<T>::digits >> 1; |
100 | T Mask = std::numeric_limits<T>::max() >> Shift; |
101 | while (Shift) { |
102 | if ((Val & Mask) == 0) { |
103 | Val >>= Shift; |
104 | ZeroBits |= Shift; |
105 | } |
106 | Shift >>= 1; |
107 | Mask >>= Shift; |
108 | } |
109 | return ZeroBits; |
110 | } |
111 | }; |
112 | |
113 | #if defined(__GNUC__) || defined(_MSC_VER) |
114 | template <typename T> struct TrailingZerosCounter<T, 4> { |
115 | static unsigned count(T Val, ZeroBehavior ZB) { |
116 | if (ZB != ZB_Undefined && Val == 0) |
117 | return 32; |
118 | |
119 | #if __has_builtin(__builtin_ctz) || defined(__GNUC__) |
120 | return __builtin_ctz(Val); |
121 | #elif defined(_MSC_VER) |
122 | unsigned long Index; |
123 | _BitScanForward(&Index, Val); |
124 | return Index; |
125 | #endif |
126 | } |
127 | }; |
128 | |
129 | #if !defined(_MSC_VER) || defined(_M_X64) |
130 | template <typename T> struct TrailingZerosCounter<T, 8> { |
131 | static unsigned count(T Val, ZeroBehavior ZB) { |
132 | if (ZB != ZB_Undefined && Val == 0) |
133 | return 64; |
134 | |
135 | #if __has_builtin(__builtin_ctzll) || defined(__GNUC__) |
136 | return __builtin_ctzll(Val); |
137 | #elif defined(_MSC_VER) |
138 | unsigned long Index; |
139 | _BitScanForward64(&Index, Val); |
140 | return Index; |
141 | #endif |
142 | } |
143 | }; |
144 | #endif |
145 | #endif |
146 | } // namespace detail |
147 | |
148 | /// Count number of 0's from the least significant bit to the most |
149 | /// stopping at the first 1. |
150 | /// |
151 | /// Only unsigned integral types are allowed. |
152 | /// |
153 | /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are |
154 | /// valid arguments. |
155 | template <typename T> |
156 | unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { |
157 | static_assert(std::numeric_limits<T>::is_integer && |
158 | !std::numeric_limits<T>::is_signed, |
159 | "Only unsigned integral types are allowed." ); |
160 | return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB); |
161 | } |
162 | |
163 | namespace detail { |
164 | template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter { |
165 | static unsigned count(T Val, ZeroBehavior) { |
166 | if (!Val) |
167 | return std::numeric_limits<T>::digits; |
168 | |
169 | // Bisection method. |
170 | unsigned ZeroBits = 0; |
171 | for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) { |
172 | T Tmp = Val >> Shift; |
173 | if (Tmp) |
174 | Val = Tmp; |
175 | else |
176 | ZeroBits |= Shift; |
177 | } |
178 | return ZeroBits; |
179 | } |
180 | }; |
181 | |
182 | #if defined(__GNUC__) || defined(_MSC_VER) |
183 | template <typename T> struct LeadingZerosCounter<T, 4> { |
184 | static unsigned count(T Val, ZeroBehavior ZB) { |
185 | if (ZB != ZB_Undefined && Val == 0) |
186 | return 32; |
187 | |
188 | #if __has_builtin(__builtin_clz) || defined(__GNUC__) |
189 | return __builtin_clz(Val); |
190 | #elif defined(_MSC_VER) |
191 | unsigned long Index; |
192 | _BitScanReverse(&Index, Val); |
193 | return Index ^ 31; |
194 | #endif |
195 | } |
196 | }; |
197 | |
198 | #if !defined(_MSC_VER) || defined(_M_X64) |
199 | template <typename T> struct LeadingZerosCounter<T, 8> { |
200 | static unsigned count(T Val, ZeroBehavior ZB) { |
201 | if (ZB != ZB_Undefined && Val == 0) |
202 | return 64; |
203 | |
204 | #if __has_builtin(__builtin_clzll) || defined(__GNUC__) |
205 | return __builtin_clzll(Val); |
206 | #elif defined(_MSC_VER) |
207 | unsigned long Index; |
208 | _BitScanReverse64(&Index, Val); |
209 | return Index ^ 63; |
210 | #endif |
211 | } |
212 | }; |
213 | #endif |
214 | #endif |
215 | } // namespace detail |
216 | |
217 | /// Count number of 0's from the most significant bit to the least |
218 | /// stopping at the first 1. |
219 | /// |
220 | /// Only unsigned integral types are allowed. |
221 | /// |
222 | /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are |
223 | /// valid arguments. |
224 | template <typename T> |
225 | unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { |
226 | static_assert(std::numeric_limits<T>::is_integer && |
227 | !std::numeric_limits<T>::is_signed, |
228 | "Only unsigned integral types are allowed." ); |
229 | return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB); |
230 | } |
231 | |
232 | /// Get the index of the first set bit starting from the least |
233 | /// significant bit. |
234 | /// |
235 | /// Only unsigned integral types are allowed. |
236 | /// |
237 | /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are |
238 | /// valid arguments. |
239 | template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { |
240 | if (ZB == ZB_Max && Val == 0) |
241 | return std::numeric_limits<T>::max(); |
242 | |
243 | return countTrailingZeros(Val, ZB_Undefined); |
244 | } |
245 | |
246 | /// Create a bitmask with the N right-most bits set to 1, and all other |
247 | /// bits set to 0. Only unsigned types are allowed. |
248 | template <typename T> T maskTrailingOnes(unsigned N) { |
249 | static_assert(std::is_unsigned<T>::value, "Invalid type!" ); |
250 | const unsigned Bits = CHAR_BIT * sizeof(T); |
251 | assert(N <= Bits && "Invalid bit index" ); |
252 | return N == 0 ? 0 : (T(-1) >> (Bits - N)); |
253 | } |
254 | |
255 | /// Create a bitmask with the N left-most bits set to 1, and all other |
256 | /// bits set to 0. Only unsigned types are allowed. |
257 | template <typename T> T maskLeadingOnes(unsigned N) { |
258 | return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
259 | } |
260 | |
261 | /// Create a bitmask with the N right-most bits set to 0, and all other |
262 | /// bits set to 1. Only unsigned types are allowed. |
263 | template <typename T> T maskTrailingZeros(unsigned N) { |
264 | return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); |
265 | } |
266 | |
267 | /// Create a bitmask with the N left-most bits set to 0, and all other |
268 | /// bits set to 1. Only unsigned types are allowed. |
269 | template <typename T> T maskLeadingZeros(unsigned N) { |
270 | return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
271 | } |
272 | |
273 | /// Get the index of the last set bit starting from the least |
274 | /// significant bit. |
275 | /// |
276 | /// Only unsigned integral types are allowed. |
277 | /// |
278 | /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are |
279 | /// valid arguments. |
280 | template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { |
281 | if (ZB == ZB_Max && Val == 0) |
282 | return std::numeric_limits<T>::max(); |
283 | |
284 | // Use ^ instead of - because both gcc and llvm can remove the associated ^ |
285 | // in the __builtin_clz intrinsic on x86. |
286 | return countLeadingZeros(Val, ZB_Undefined) ^ |
287 | (std::numeric_limits<T>::digits - 1); |
288 | } |
289 | |
290 | /// Macro compressed bit reversal table for 256 bits. |
291 | /// |
292 | /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable |
293 | static const unsigned char BitReverseTable256[256] = { |
294 | #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 |
295 | #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) |
296 | #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) |
297 | R6(0), R6(2), R6(1), R6(3) |
298 | #undef R2 |
299 | #undef R4 |
300 | #undef R6 |
301 | }; |
302 | |
303 | /// Reverse the bits in \p Val. |
304 | template <typename T> |
305 | T reverseBits(T Val) { |
306 | unsigned char in[sizeof(Val)]; |
307 | unsigned char out[sizeof(Val)]; |
308 | std::memcpy(in, &Val, sizeof(Val)); |
309 | for (unsigned i = 0; i < sizeof(Val); ++i) |
310 | out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; |
311 | std::memcpy(&Val, out, sizeof(Val)); |
312 | return Val; |
313 | } |
314 | |
315 | #if __has_builtin(__builtin_bitreverse8) |
316 | template<> |
317 | inline uint8_t reverseBits<uint8_t>(uint8_t Val) { |
318 | return __builtin_bitreverse8(Val); |
319 | } |
320 | #endif |
321 | |
322 | #if __has_builtin(__builtin_bitreverse16) |
323 | template<> |
324 | inline uint16_t reverseBits<uint16_t>(uint16_t Val) { |
325 | return __builtin_bitreverse16(Val); |
326 | } |
327 | #endif |
328 | |
329 | #if __has_builtin(__builtin_bitreverse32) |
330 | template<> |
331 | inline uint32_t reverseBits<uint32_t>(uint32_t Val) { |
332 | return __builtin_bitreverse32(Val); |
333 | } |
334 | #endif |
335 | |
336 | #if __has_builtin(__builtin_bitreverse64) |
337 | template<> |
338 | inline uint64_t reverseBits<uint64_t>(uint64_t Val) { |
339 | return __builtin_bitreverse64(Val); |
340 | } |
341 | #endif |
342 | |
343 | // NOTE: The following support functions use the _32/_64 extensions instead of |
344 | // type overloading so that signed and unsigned integers can be used without |
345 | // ambiguity. |
346 | |
347 | /// Return the high 32 bits of a 64 bit value. |
348 | constexpr inline uint32_t Hi_32(uint64_t Value) { |
349 | return static_cast<uint32_t>(Value >> 32); |
350 | } |
351 | |
352 | /// Return the low 32 bits of a 64 bit value. |
353 | constexpr inline uint32_t Lo_32(uint64_t Value) { |
354 | return static_cast<uint32_t>(Value); |
355 | } |
356 | |
357 | /// Make a 64-bit integer from a high / low pair of 32-bit integers. |
358 | constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { |
359 | return ((uint64_t)High << 32) | (uint64_t)Low; |
360 | } |
361 | |
362 | /// Checks if an integer fits into the given bit width. |
363 | template <unsigned N> constexpr inline bool isInt(int64_t x) { |
364 | return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); |
365 | } |
366 | // Template specializations to get better code for common cases. |
367 | template <> constexpr inline bool isInt<8>(int64_t x) { |
368 | return static_cast<int8_t>(x) == x; |
369 | } |
370 | template <> constexpr inline bool isInt<16>(int64_t x) { |
371 | return static_cast<int16_t>(x) == x; |
372 | } |
373 | template <> constexpr inline bool isInt<32>(int64_t x) { |
374 | return static_cast<int32_t>(x) == x; |
375 | } |
376 | |
377 | /// Checks if a signed integer is an N bit number shifted left by S. |
378 | template <unsigned N, unsigned S> |
379 | constexpr inline bool isShiftedInt(int64_t x) { |
380 | static_assert( |
381 | N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number." ); |
382 | static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide." ); |
383 | return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
384 | } |
385 | |
386 | /// Checks if an unsigned integer fits into the given bit width. |
387 | /// |
388 | /// This is written as two functions rather than as simply |
389 | /// |
390 | /// return N >= 64 || X < (UINT64_C(1) << N); |
391 | /// |
392 | /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting |
393 | /// left too many places. |
394 | template <unsigned N> |
395 | constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) { |
396 | static_assert(N > 0, "isUInt<0> doesn't make sense" ); |
397 | return X < (UINT64_C(1) << (N)); |
398 | } |
399 | template <unsigned N> |
400 | constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) { |
401 | return true; |
402 | } |
403 | |
404 | // Template specializations to get better code for common cases. |
405 | template <> constexpr inline bool isUInt<8>(uint64_t x) { |
406 | return static_cast<uint8_t>(x) == x; |
407 | } |
408 | template <> constexpr inline bool isUInt<16>(uint64_t x) { |
409 | return static_cast<uint16_t>(x) == x; |
410 | } |
411 | template <> constexpr inline bool isUInt<32>(uint64_t x) { |
412 | return static_cast<uint32_t>(x) == x; |
413 | } |
414 | |
415 | /// Checks if a unsigned integer is an N bit number shifted left by S. |
416 | template <unsigned N, unsigned S> |
417 | constexpr inline bool isShiftedUInt(uint64_t x) { |
418 | static_assert( |
419 | N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)" ); |
420 | static_assert(N + S <= 64, |
421 | "isShiftedUInt<N, S> with N + S > 64 is too wide." ); |
422 | // Per the two static_asserts above, S must be strictly less than 64. So |
423 | // 1 << S is not undefined behavior. |
424 | return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
425 | } |
426 | |
427 | /// Gets the maximum value for a N-bit unsigned integer. |
428 | inline uint64_t maxUIntN(uint64_t N) { |
429 | assert(N > 0 && N <= 64 && "integer width out of range" ); |
430 | |
431 | // uint64_t(1) << 64 is undefined behavior, so we can't do |
432 | // (uint64_t(1) << N) - 1 |
433 | // without checking first that N != 64. But this works and doesn't have a |
434 | // branch. |
435 | return UINT64_MAX >> (64 - N); |
436 | } |
437 | |
438 | /// Gets the minimum value for a N-bit signed integer. |
439 | inline int64_t minIntN(int64_t N) { |
440 | assert(N > 0 && N <= 64 && "integer width out of range" ); |
441 | |
442 | return UINT64_C(1) + ~(UINT64_C(1) << (N - 1)); |
443 | } |
444 | |
445 | /// Gets the maximum value for a N-bit signed integer. |
446 | inline int64_t maxIntN(int64_t N) { |
447 | assert(N > 0 && N <= 64 && "integer width out of range" ); |
448 | |
449 | // This relies on two's complement wraparound when N == 64, so we convert to |
450 | // int64_t only at the very end to avoid UB. |
451 | return (UINT64_C(1) << (N - 1)) - 1; |
452 | } |
453 | |
454 | /// Checks if an unsigned integer fits into the given (dynamic) bit width. |
455 | inline bool isUIntN(unsigned N, uint64_t x) { |
456 | return N >= 64 || x <= maxUIntN(N); |
457 | } |
458 | |
459 | /// Checks if an signed integer fits into the given (dynamic) bit width. |
460 | inline bool isIntN(unsigned N, int64_t x) { |
461 | return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); |
462 | } |
463 | |
464 | /// Return true if the argument is a non-empty sequence of ones starting at the |
465 | /// least significant bit with the remainder zero (32 bit version). |
466 | /// Ex. isMask_32(0x0000FFFFU) == true. |
467 | constexpr inline bool isMask_32(uint32_t Value) { |
468 | return Value && ((Value + 1) & Value) == 0; |
469 | } |
470 | |
471 | /// Return true if the argument is a non-empty sequence of ones starting at the |
472 | /// least significant bit with the remainder zero (64 bit version). |
473 | constexpr inline bool isMask_64(uint64_t Value) { |
474 | return Value && ((Value + 1) & Value) == 0; |
475 | } |
476 | |
477 | /// Return true if the argument contains a non-empty sequence of ones with the |
478 | /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. |
479 | constexpr inline bool isShiftedMask_32(uint32_t Value) { |
480 | return Value && isMask_32((Value - 1) | Value); |
481 | } |
482 | |
483 | /// Return true if the argument contains a non-empty sequence of ones with the |
484 | /// remainder zero (64 bit version.) |
485 | constexpr inline bool isShiftedMask_64(uint64_t Value) { |
486 | return Value && isMask_64((Value - 1) | Value); |
487 | } |
488 | |
489 | /// Return true if the argument is a power of two > 0. |
490 | /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) |
491 | constexpr inline bool isPowerOf2_32(uint32_t Value) { |
492 | return Value && !(Value & (Value - 1)); |
493 | } |
494 | |
495 | /// Return true if the argument is a power of two > 0 (64 bit edition.) |
496 | constexpr inline bool isPowerOf2_64(uint64_t Value) { |
497 | return Value && !(Value & (Value - 1)); |
498 | } |
499 | |
500 | /// Count the number of ones from the most significant bit to the first |
501 | /// zero bit. |
502 | /// |
503 | /// Ex. countLeadingOnes(0xFF0FFF00) == 8. |
504 | /// Only unsigned integral types are allowed. |
505 | /// |
506 | /// \param ZB the behavior on an input of all ones. Only ZB_Width and |
507 | /// ZB_Undefined are valid arguments. |
508 | template <typename T> |
509 | unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { |
510 | static_assert(std::numeric_limits<T>::is_integer && |
511 | !std::numeric_limits<T>::is_signed, |
512 | "Only unsigned integral types are allowed." ); |
513 | return countLeadingZeros<T>(~Value, ZB); |
514 | } |
515 | |
516 | /// Count the number of ones from the least significant bit to the first |
517 | /// zero bit. |
518 | /// |
519 | /// Ex. countTrailingOnes(0x00FF00FF) == 8. |
520 | /// Only unsigned integral types are allowed. |
521 | /// |
522 | /// \param ZB the behavior on an input of all ones. Only ZB_Width and |
523 | /// ZB_Undefined are valid arguments. |
524 | template <typename T> |
525 | unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { |
526 | static_assert(std::numeric_limits<T>::is_integer && |
527 | !std::numeric_limits<T>::is_signed, |
528 | "Only unsigned integral types are allowed." ); |
529 | return countTrailingZeros<T>(~Value, ZB); |
530 | } |
531 | |
532 | namespace detail { |
533 | template <typename T, std::size_t SizeOfT> struct PopulationCounter { |
534 | static unsigned count(T Value) { |
535 | // Generic version, forward to 32 bits. |
536 | static_assert(SizeOfT <= 4, "Not implemented!" ); |
537 | #if defined(__GNUC__) |
538 | return __builtin_popcount(Value); |
539 | #else |
540 | uint32_t v = Value; |
541 | v = v - ((v >> 1) & 0x55555555); |
542 | v = (v & 0x33333333) + ((v >> 2) & 0x33333333); |
543 | return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; |
544 | #endif |
545 | } |
546 | }; |
547 | |
548 | template <typename T> struct PopulationCounter<T, 8> { |
549 | static unsigned count(T Value) { |
550 | #if defined(__GNUC__) |
551 | return __builtin_popcountll(Value); |
552 | #else |
553 | uint64_t v = Value; |
554 | v = v - ((v >> 1) & 0x5555555555555555ULL); |
555 | v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL); |
556 | v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL; |
557 | return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56); |
558 | #endif |
559 | } |
560 | }; |
561 | } // namespace detail |
562 | |
563 | /// Count the number of set bits in a value. |
564 | /// Ex. countPopulation(0xF000F000) = 8 |
565 | /// Returns 0 if the word is zero. |
566 | template <typename T> |
567 | inline unsigned countPopulation(T Value) { |
568 | static_assert(std::numeric_limits<T>::is_integer && |
569 | !std::numeric_limits<T>::is_signed, |
570 | "Only unsigned integral types are allowed." ); |
571 | return detail::PopulationCounter<T, sizeof(T)>::count(Value); |
572 | } |
573 | |
574 | /// Compile time Log2. |
575 | /// Valid only for positive powers of two. |
576 | template <size_t kValue> constexpr inline size_t CTLog2() { |
577 | static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), |
578 | "Value is not a valid power of 2" ); |
579 | return 1 + CTLog2<kValue / 2>(); |
580 | } |
581 | |
582 | template <> constexpr inline size_t CTLog2<1>() { return 0; } |
583 | |
584 | /// Return the log base 2 of the specified value. |
585 | inline double Log2(double Value) { |
586 | #if defined(__ANDROID_API__) && __ANDROID_API__ < 18 |
587 | return __builtin_log(Value) / __builtin_log(2.0); |
588 | #else |
589 | return log2(Value); |
590 | #endif |
591 | } |
592 | |
593 | /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
594 | /// (32 bit edition.) |
595 | /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 |
596 | inline unsigned Log2_32(uint32_t Value) { |
597 | return 31 - countLeadingZeros(Value); |
598 | } |
599 | |
600 | /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
601 | /// (64 bit edition.) |
602 | inline unsigned Log2_64(uint64_t Value) { |
603 | return 63 - countLeadingZeros(Value); |
604 | } |
605 | |
606 | /// Return the ceil log base 2 of the specified value, 32 if the value is zero. |
607 | /// (32 bit edition). |
608 | /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 |
609 | inline unsigned Log2_32_Ceil(uint32_t Value) { |
610 | return 32 - countLeadingZeros(Value - 1); |
611 | } |
612 | |
613 | /// Return the ceil log base 2 of the specified value, 64 if the value is zero. |
614 | /// (64 bit edition.) |
615 | inline unsigned Log2_64_Ceil(uint64_t Value) { |
616 | return 64 - countLeadingZeros(Value - 1); |
617 | } |
618 | |
619 | /// Return the greatest common divisor of the values using Euclid's algorithm. |
620 | template <typename T> |
621 | inline T greatestCommonDivisor(T A, T B) { |
622 | while (B) { |
623 | T Tmp = B; |
624 | B = A % B; |
625 | A = Tmp; |
626 | } |
627 | return A; |
628 | } |
629 | |
630 | inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { |
631 | return greatestCommonDivisor<uint64_t>(A, B); |
632 | } |
633 | |
634 | /// This function takes a 64-bit integer and returns the bit equivalent double. |
635 | inline double BitsToDouble(uint64_t Bits) { |
636 | double D; |
637 | static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes" ); |
638 | memcpy(&D, &Bits, sizeof(Bits)); |
639 | return D; |
640 | } |
641 | |
642 | /// This function takes a 32-bit integer and returns the bit equivalent float. |
643 | inline float BitsToFloat(uint32_t Bits) { |
644 | float F; |
645 | static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes" ); |
646 | memcpy(&F, &Bits, sizeof(Bits)); |
647 | return F; |
648 | } |
649 | |
650 | /// This function takes a double and returns the bit equivalent 64-bit integer. |
651 | /// Note that copying doubles around changes the bits of NaNs on some hosts, |
652 | /// notably x86, so this routine cannot be used if these bits are needed. |
653 | inline uint64_t DoubleToBits(double Double) { |
654 | uint64_t Bits; |
655 | static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes" ); |
656 | memcpy(&Bits, &Double, sizeof(Double)); |
657 | return Bits; |
658 | } |
659 | |
660 | /// This function takes a float and returns the bit equivalent 32-bit integer. |
661 | /// Note that copying floats around changes the bits of NaNs on some hosts, |
662 | /// notably x86, so this routine cannot be used if these bits are needed. |
663 | inline uint32_t FloatToBits(float Float) { |
664 | uint32_t Bits; |
665 | static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes" ); |
666 | memcpy(&Bits, &Float, sizeof(Float)); |
667 | return Bits; |
668 | } |
669 | |
670 | /// A and B are either alignments or offsets. Return the minimum alignment that |
671 | /// may be assumed after adding the two together. |
672 | constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { |
673 | // The largest power of 2 that divides both A and B. |
674 | // |
675 | // Replace "-Value" by "1+~Value" in the following commented code to avoid |
676 | // MSVC warning C4146 |
677 | // return (A | B) & -(A | B); |
678 | return (A | B) & (1 + ~(A | B)); |
679 | } |
680 | |
681 | /// Returns the next power of two (in 64-bits) that is strictly greater than A. |
682 | /// Returns zero on overflow. |
683 | inline uint64_t NextPowerOf2(uint64_t A) { |
684 | A |= (A >> 1); |
685 | A |= (A >> 2); |
686 | A |= (A >> 4); |
687 | A |= (A >> 8); |
688 | A |= (A >> 16); |
689 | A |= (A >> 32); |
690 | return A + 1; |
691 | } |
692 | |
693 | /// Returns the power of two which is less than or equal to the given value. |
694 | /// Essentially, it is a floor operation across the domain of powers of two. |
695 | inline uint64_t PowerOf2Floor(uint64_t A) { |
696 | if (!A) return 0; |
697 | return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); |
698 | } |
699 | |
700 | /// Returns the power of two which is greater than or equal to the given value. |
701 | /// Essentially, it is a ceil operation across the domain of powers of two. |
702 | inline uint64_t PowerOf2Ceil(uint64_t A) { |
703 | if (!A) |
704 | return 0; |
705 | return NextPowerOf2(A - 1); |
706 | } |
707 | |
708 | /// Returns the next integer (mod 2**64) that is greater than or equal to |
709 | /// \p Value and is a multiple of \p Align. \p Align must be non-zero. |
710 | /// |
711 | /// If non-zero \p Skew is specified, the return value will be a minimal |
712 | /// integer that is greater than or equal to \p Value and equal to |
713 | /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than |
714 | /// \p Align, its value is adjusted to '\p Skew mod \p Align'. |
715 | /// |
716 | /// Examples: |
717 | /// \code |
718 | /// alignTo(5, 8) = 8 |
719 | /// alignTo(17, 8) = 24 |
720 | /// alignTo(~0LL, 8) = 0 |
721 | /// alignTo(321, 255) = 510 |
722 | /// |
723 | /// alignTo(5, 8, 7) = 7 |
724 | /// alignTo(17, 8, 1) = 17 |
725 | /// alignTo(~0LL, 8, 3) = 3 |
726 | /// alignTo(321, 255, 42) = 552 |
727 | /// \endcode |
728 | inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
729 | assert(Align != 0u && "Align can't be 0." ); |
730 | Skew %= Align; |
731 | return (Value + Align - 1 - Skew) / Align * Align + Skew; |
732 | } |
733 | |
734 | /// Returns the next integer (mod 2**64) that is greater than or equal to |
735 | /// \p Value and is a multiple of \c Align. \c Align must be non-zero. |
736 | template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { |
737 | static_assert(Align != 0u, "Align must be non-zero" ); |
738 | return (Value + Align - 1) / Align * Align; |
739 | } |
740 | |
741 | /// Returns the integer ceil(Numerator / Denominator). |
742 | inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { |
743 | return alignTo(Numerator, Denominator) / Denominator; |
744 | } |
745 | |
746 | /// Returns the integer nearest(Numerator / Denominator). |
747 | inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { |
748 | return (Numerator + (Denominator / 2)) / Denominator; |
749 | } |
750 | |
751 | /// Returns the largest uint64_t less than or equal to \p Value and is |
752 | /// \p Skew mod \p Align. \p Align must be non-zero |
753 | inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
754 | assert(Align != 0u && "Align can't be 0." ); |
755 | Skew %= Align; |
756 | return (Value - Skew) / Align * Align + Skew; |
757 | } |
758 | |
759 | /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
760 | /// Requires 0 < B <= 32. |
761 | template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { |
762 | static_assert(B > 0, "Bit width can't be 0." ); |
763 | static_assert(B <= 32, "Bit width out of range." ); |
764 | return int32_t(X << (32 - B)) >> (32 - B); |
765 | } |
766 | |
767 | /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
768 | /// Requires 0 < B <= 32. |
769 | inline int32_t SignExtend32(uint32_t X, unsigned B) { |
770 | assert(B > 0 && "Bit width can't be 0." ); |
771 | assert(B <= 32 && "Bit width out of range." ); |
772 | return int32_t(X << (32 - B)) >> (32 - B); |
773 | } |
774 | |
775 | /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
776 | /// Requires 0 < B <= 64. |
777 | template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { |
778 | static_assert(B > 0, "Bit width can't be 0." ); |
779 | static_assert(B <= 64, "Bit width out of range." ); |
780 | return int64_t(x << (64 - B)) >> (64 - B); |
781 | } |
782 | |
783 | /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
784 | /// Requires 0 < B <= 64. |
785 | inline int64_t SignExtend64(uint64_t X, unsigned B) { |
786 | assert(B > 0 && "Bit width can't be 0." ); |
787 | assert(B <= 64 && "Bit width out of range." ); |
788 | return int64_t(X << (64 - B)) >> (64 - B); |
789 | } |
790 | |
791 | /// Subtract two unsigned integers, X and Y, of type T and return the absolute |
792 | /// value of the result. |
793 | template <typename T> |
794 | std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) { |
795 | return X > Y ? (X - Y) : (Y - X); |
796 | } |
797 | |
798 | /// Add two unsigned integers, X and Y, of type T. Clamp the result to the |
799 | /// maximum representable value of T on overflow. ResultOverflowed indicates if |
800 | /// the result is larger than the maximum representable value of type T. |
801 | template <typename T> |
802 | std::enable_if_t<std::is_unsigned<T>::value, T> |
803 | SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { |
804 | bool Dummy; |
805 | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
806 | // Hacker's Delight, p. 29 |
807 | T Z = X + Y; |
808 | Overflowed = (Z < X || Z < Y); |
809 | if (Overflowed) |
810 | return std::numeric_limits<T>::max(); |
811 | else |
812 | return Z; |
813 | } |
814 | |
815 | /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the |
816 | /// maximum representable value of T on overflow. ResultOverflowed indicates if |
817 | /// the result is larger than the maximum representable value of type T. |
818 | template <typename T> |
819 | std::enable_if_t<std::is_unsigned<T>::value, T> |
820 | SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { |
821 | bool Dummy; |
822 | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
823 | |
824 | // Hacker's Delight, p. 30 has a different algorithm, but we don't use that |
825 | // because it fails for uint16_t (where multiplication can have undefined |
826 | // behavior due to promotion to int), and requires a division in addition |
827 | // to the multiplication. |
828 | |
829 | Overflowed = false; |
830 | |
831 | // Log2(Z) would be either Log2Z or Log2Z + 1. |
832 | // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z |
833 | // will necessarily be less than Log2Max as desired. |
834 | int Log2Z = Log2_64(X) + Log2_64(Y); |
835 | const T Max = std::numeric_limits<T>::max(); |
836 | int Log2Max = Log2_64(Max); |
837 | if (Log2Z < Log2Max) { |
838 | return X * Y; |
839 | } |
840 | if (Log2Z > Log2Max) { |
841 | Overflowed = true; |
842 | return Max; |
843 | } |
844 | |
845 | // We're going to use the top bit, and maybe overflow one |
846 | // bit past it. Multiply all but the bottom bit then add |
847 | // that on at the end. |
848 | T Z = (X >> 1) * Y; |
849 | if (Z & ~(Max >> 1)) { |
850 | Overflowed = true; |
851 | return Max; |
852 | } |
853 | Z <<= 1; |
854 | if (X & 1) |
855 | return SaturatingAdd(Z, Y, ResultOverflowed); |
856 | |
857 | return Z; |
858 | } |
859 | |
860 | /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to |
861 | /// the product. Clamp the result to the maximum representable value of T on |
862 | /// overflow. ResultOverflowed indicates if the result is larger than the |
863 | /// maximum representable value of type T. |
864 | template <typename T> |
865 | std::enable_if_t<std::is_unsigned<T>::value, T> |
866 | SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { |
867 | bool Dummy; |
868 | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
869 | |
870 | T Product = SaturatingMultiply(X, Y, &Overflowed); |
871 | if (Overflowed) |
872 | return Product; |
873 | |
874 | return SaturatingAdd(A, Product, &Overflowed); |
875 | } |
876 | |
877 | /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. |
878 | extern const float huge_valf; |
879 | |
880 | |
881 | /// Add two signed integers, computing the two's complement truncated result, |
882 | /// returning true if overflow occured. |
883 | template <typename T> |
884 | std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) { |
885 | #if __has_builtin(__builtin_add_overflow) |
886 | return __builtin_add_overflow(X, Y, &Result); |
887 | #else |
888 | // Perform the unsigned addition. |
889 | using U = std::make_unsigned_t<T>; |
890 | const U UX = static_cast<U>(X); |
891 | const U UY = static_cast<U>(Y); |
892 | const U UResult = UX + UY; |
893 | |
894 | // Convert to signed. |
895 | Result = static_cast<T>(UResult); |
896 | |
897 | // Adding two positive numbers should result in a positive number. |
898 | if (X > 0 && Y > 0) |
899 | return Result <= 0; |
900 | // Adding two negatives should result in a negative number. |
901 | if (X < 0 && Y < 0) |
902 | return Result >= 0; |
903 | return false; |
904 | #endif |
905 | } |
906 | |
907 | /// Subtract two signed integers, computing the two's complement truncated |
908 | /// result, returning true if an overflow ocurred. |
909 | template <typename T> |
910 | std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) { |
911 | #if __has_builtin(__builtin_sub_overflow) |
912 | return __builtin_sub_overflow(X, Y, &Result); |
913 | #else |
914 | // Perform the unsigned addition. |
915 | using U = std::make_unsigned_t<T>; |
916 | const U UX = static_cast<U>(X); |
917 | const U UY = static_cast<U>(Y); |
918 | const U UResult = UX - UY; |
919 | |
920 | // Convert to signed. |
921 | Result = static_cast<T>(UResult); |
922 | |
923 | // Subtracting a positive number from a negative results in a negative number. |
924 | if (X <= 0 && Y > 0) |
925 | return Result >= 0; |
926 | // Subtracting a negative number from a positive results in a positive number. |
927 | if (X >= 0 && Y < 0) |
928 | return Result <= 0; |
929 | return false; |
930 | #endif |
931 | } |
932 | |
933 | /// Multiply two signed integers, computing the two's complement truncated |
934 | /// result, returning true if an overflow ocurred. |
935 | template <typename T> |
936 | std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) { |
937 | // Perform the unsigned multiplication on absolute values. |
938 | using U = std::make_unsigned_t<T>; |
939 | const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); |
940 | const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); |
941 | const U UResult = UX * UY; |
942 | |
943 | // Convert to signed. |
944 | const bool IsNegative = (X < 0) ^ (Y < 0); |
945 | Result = IsNegative ? (0 - UResult) : UResult; |
946 | |
947 | // If any of the args was 0, result is 0 and no overflow occurs. |
948 | if (UX == 0 || UY == 0) |
949 | return false; |
950 | |
951 | // UX and UY are in [1, 2^n], where n is the number of digits. |
952 | // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for |
953 | // positive) divided by an argument compares to the other. |
954 | if (IsNegative) |
955 | return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; |
956 | else |
957 | return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; |
958 | } |
959 | |
960 | } // End llvm namespace |
961 | |
962 | #endif |
963 | |