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1 : //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
2 : //
3 : // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 : // See https://llvm.org/LICENSE.txt for license information.
5 : // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 : //
7 : //===----------------------------------------------------------------------===//
8 : //
9 : // This file contains some functions that are useful for math stuff.
10 : //
11 : //===----------------------------------------------------------------------===//
12 :
13 : #ifndef LLVM_SUPPORT_MATHEXTRAS_H
14 : #define LLVM_SUPPORT_MATHEXTRAS_H
15 :
16 : #include "llvm/ADT/bit.h"
17 : #include "llvm/Support/Compiler.h"
18 : #include <cassert>
19 : #include <climits>
20 : #include <cstdint>
21 : #include <cstring>
22 : #include <limits>
23 : #include <type_traits>
24 :
25 : namespace llvm {
26 : /// Some template parameter helpers to optimize for bitwidth, for functions that
27 : /// take multiple arguments.
28 :
29 : // We can't verify signedness, since callers rely on implicit coercions to
30 : // signed/unsigned.
31 : template <typename T, typename U>
32 : using enableif_int =
33 : std::enable_if_t<std::is_integral_v<T> && std::is_integral_v<U>>;
34 :
35 : // Use std::common_type_t to widen only up to the widest argument.
36 : template <typename T, typename U, typename = enableif_int<T, U>>
37 : using common_uint =
38 : std::common_type_t<std::make_unsigned_t<T>, std::make_unsigned_t<U>>;
39 : template <typename T, typename U, typename = enableif_int<T, U>>
40 : using common_sint =
41 : std::common_type_t<std::make_signed_t<T>, std::make_signed_t<U>>;
42 :
43 : /// Mathematical constants.
44 : namespace numbers {
45 : // TODO: Track C++20 std::numbers.
46 : // TODO: Favor using the hexadecimal FP constants (requires C++17).
47 : constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
48 : egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
49 : ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
50 : ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
51 : log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0)
52 : log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
53 : pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
54 : inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
55 : sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
56 : inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
57 : sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
58 : inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
59 : sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
60 : inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1)
61 : phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
62 : constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
63 : egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
64 : ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
65 : ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
66 : log2ef = 1.44269504F, // (0x1.715476P+0)
67 : log10ef = .434294482F, // (0x1.bcb7b2P-2)
68 : pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
69 : inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
70 : sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
71 : inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
72 : sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
73 : inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1)
74 : sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
75 : inv_sqrt3f = .577350269F, // (0x1.279a74P-1)
76 : phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
77 : } // namespace numbers
78 :
79 : /// Create a bitmask with the N right-most bits set to 1, and all other
80 : /// bits set to 0. Only unsigned types are allowed.
81 : template <typename T> T maskTrailingOnes(unsigned N) {
82 : static_assert(std::is_unsigned_v<T>, "Invalid type!");
83 : const unsigned Bits = CHAR_BIT * sizeof(T);
84 : assert(N <= Bits && "Invalid bit index");
85 : if (N == 0)
86 : return 0;
87 : return T(-1) >> (Bits - N);
88 : }
89 :
90 : /// Create a bitmask with the N left-most bits set to 1, and all other
91 : /// bits set to 0. Only unsigned types are allowed.
92 : template <typename T> T maskLeadingOnes(unsigned N) {
93 : return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
94 : }
95 :
96 : /// Create a bitmask with the N right-most bits set to 0, and all other
97 : /// bits set to 1. Only unsigned types are allowed.
98 : template <typename T> T maskTrailingZeros(unsigned N) {
99 : return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
100 : }
101 :
102 : /// Create a bitmask with the N left-most bits set to 0, and all other
103 : /// bits set to 1. Only unsigned types are allowed.
104 : template <typename T> T maskLeadingZeros(unsigned N) {
105 : return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
106 : }
107 :
108 : /// Macro compressed bit reversal table for 256 bits.
109 : ///
110 : /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
111 : static const unsigned char BitReverseTable256[256] = {
112 : #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
113 : #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
114 : #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
115 : R6(0), R6(2), R6(1), R6(3)
116 : #undef R2
117 : #undef R4
118 : #undef R6
119 : };
120 :
121 : /// Reverse the bits in \p Val.
122 : template <typename T> T reverseBits(T Val) {
123 : #if __has_builtin(__builtin_bitreverse8)
124 : if constexpr (std::is_same_v<T, uint8_t>)
125 : return __builtin_bitreverse8(Val);
126 : #endif
127 : #if __has_builtin(__builtin_bitreverse16)
128 : if constexpr (std::is_same_v<T, uint16_t>)
129 : return __builtin_bitreverse16(Val);
130 : #endif
131 : #if __has_builtin(__builtin_bitreverse32)
132 : if constexpr (std::is_same_v<T, uint32_t>)
133 : return __builtin_bitreverse32(Val);
134 : #endif
135 : #if __has_builtin(__builtin_bitreverse64)
136 : if constexpr (std::is_same_v<T, uint64_t>)
137 : return __builtin_bitreverse64(Val);
138 : #endif
139 :
140 : unsigned char in[sizeof(Val)];
141 : unsigned char out[sizeof(Val)];
142 : std::memcpy(in, &Val, sizeof(Val));
143 : for (unsigned i = 0; i < sizeof(Val); ++i)
144 : out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
145 : std::memcpy(&Val, out, sizeof(Val));
146 : return Val;
147 : }
148 :
149 : // NOTE: The following support functions use the _32/_64 extensions instead of
150 : // type overloading so that signed and unsigned integers can be used without
151 : // ambiguity.
152 :
153 : /// Return the high 32 bits of a 64 bit value.
154 : constexpr uint32_t Hi_32(uint64_t Value) {
155 : return static_cast<uint32_t>(Value >> 32);
156 : }
157 :
158 : /// Return the low 32 bits of a 64 bit value.
159 : constexpr uint32_t Lo_32(uint64_t Value) {
160 : return static_cast<uint32_t>(Value);
161 : }
162 :
163 : /// Make a 64-bit integer from a high / low pair of 32-bit integers.
164 : constexpr uint64_t Make_64(uint32_t High, uint32_t Low) {
165 : return ((uint64_t)High << 32) | (uint64_t)Low;
166 : }
167 :
168 : /// Checks if an integer fits into the given bit width.
169 : template <unsigned N> constexpr bool isInt(int64_t x) {
170 : if constexpr (N == 0)
171 : return 0 == x;
172 : if constexpr (N == 8)
173 : return static_cast<int8_t>(x) == x;
174 : if constexpr (N == 16)
175 : return static_cast<int16_t>(x) == x;
176 : if constexpr (N == 32)
177 : return static_cast<int32_t>(x) == x;
178 : if constexpr (N < 64)
179 : return -(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1));
180 : (void)x; // MSVC v19.25 warns that x is unused.
181 : return true;
182 : }
183 :
184 : /// Checks if a signed integer is an N bit number shifted left by S.
185 : template <unsigned N, unsigned S>
186 : constexpr bool isShiftedInt(int64_t x) {
187 : static_assert(S < 64, "isShiftedInt<N, S> with S >= 64 is too much.");
188 : static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
189 : return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
190 : }
191 :
192 : /// Checks if an unsigned integer fits into the given bit width.
193 : template <unsigned N> constexpr bool isUInt(uint64_t x) {
194 : if constexpr (N == 0)
195 : return 0 == x;
196 : if constexpr (N == 8)
197 : return static_cast<uint8_t>(x) == x;
198 : if constexpr (N == 16)
199 : return static_cast<uint16_t>(x) == x;
200 : if constexpr (N == 32)
201 : return static_cast<uint32_t>(x) == x;
202 : if constexpr (N < 64)
203 : return x < (UINT64_C(1) << (N));
204 : (void)x; // MSVC v19.25 warns that x is unused.
205 : return true;
206 : }
207 :
208 : /// Checks if a unsigned integer is an N bit number shifted left by S.
209 : template <unsigned N, unsigned S>
210 : constexpr bool isShiftedUInt(uint64_t x) {
211 : static_assert(S < 64, "isShiftedUInt<N, S> with S >= 64 is too much.");
212 : static_assert(N + S <= 64,
213 : "isShiftedUInt<N, S> with N + S > 64 is too wide.");
214 : // S must be strictly less than 64. So 1 << S is not undefined behavior.
215 : return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
216 : }
217 :
218 : /// Gets the maximum value for a N-bit unsigned integer.
219 : inline uint64_t maxUIntN(uint64_t N) {
220 : assert(N <= 64 && "integer width out of range");
221 :
222 : // uint64_t(1) << 64 is undefined behavior, so we can't do
223 : // (uint64_t(1) << N) - 1
224 : // without checking first that N != 64. But this works and doesn't have a
225 : // branch for N != 0.
226 : // Unfortunately, shifting a uint64_t right by 64 bit is undefined
227 : // behavior, so the condition on N == 0 is necessary. Fortunately, most
228 : // optimizers do not emit branches for this check.
229 : if (N == 0)
230 : return 0;
231 : return UINT64_MAX >> (64 - N);
232 : }
233 :
234 : /// Gets the minimum value for a N-bit signed integer.
235 : inline int64_t minIntN(int64_t N) {
236 : assert(N <= 64 && "integer width out of range");
237 :
238 : if (N == 0)
239 : return 0;
240 : return UINT64_C(1) + ~(UINT64_C(1) << (N - 1));
241 : }
242 :
243 : /// Gets the maximum value for a N-bit signed integer.
244 : inline int64_t maxIntN(int64_t N) {
245 : assert(N <= 64 && "integer width out of range");
246 :
247 : // This relies on two's complement wraparound when N == 64, so we convert to
248 : // int64_t only at the very end to avoid UB.
249 : if (N == 0)
250 : return 0;
251 : return (UINT64_C(1) << (N - 1)) - 1;
252 : }
253 :
254 : /// Checks if an unsigned integer fits into the given (dynamic) bit width.
255 : inline bool isUIntN(unsigned N, uint64_t x) {
256 : return N >= 64 || x <= maxUIntN(N);
257 : }
258 :
259 : /// Checks if an signed integer fits into the given (dynamic) bit width.
260 : inline bool isIntN(unsigned N, int64_t x) {
261 : return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
262 : }
263 :
264 : /// Return true if the argument is a non-empty sequence of ones starting at the
265 : /// least significant bit with the remainder zero (32 bit version).
266 : /// Ex. isMask_32(0x0000FFFFU) == true.
267 : constexpr bool isMask_32(uint32_t Value) {
268 : return Value && ((Value + 1) & Value) == 0;
269 : }
270 :
271 : /// Return true if the argument is a non-empty sequence of ones starting at the
272 : /// least significant bit with the remainder zero (64 bit version).
273 : constexpr bool isMask_64(uint64_t Value) {
274 : return Value && ((Value + 1) & Value) == 0;
275 : }
276 :
277 : /// Return true if the argument contains a non-empty sequence of ones with the
278 : /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
279 : constexpr bool isShiftedMask_32(uint32_t Value) {
280 : return Value && isMask_32((Value - 1) | Value);
281 : }
282 :
283 : /// Return true if the argument contains a non-empty sequence of ones with the
284 : /// remainder zero (64 bit version.)
285 : constexpr bool isShiftedMask_64(uint64_t Value) {
286 : return Value && isMask_64((Value - 1) | Value);
287 : }
288 :
289 : /// Return true if the argument is a power of two > 0.
290 : /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
291 : constexpr bool isPowerOf2_32(uint32_t Value) {
292 : return llvm::has_single_bit(Value);
293 : }
294 :
295 : /// Return true if the argument is a power of two > 0 (64 bit edition.)
296 : constexpr bool isPowerOf2_64(uint64_t Value) {
297 : return llvm::has_single_bit(Value);
298 : }
299 :
300 : /// Return true if the argument contains a non-empty sequence of ones with the
301 : /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
302 : /// If true, \p MaskIdx will specify the index of the lowest set bit and \p
303 : /// MaskLen is updated to specify the length of the mask, else neither are
304 : /// updated.
305 : inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx,
306 : unsigned &MaskLen) {
307 : if (!isShiftedMask_32(Value))
308 : return false;
309 : MaskIdx = llvm::countr_zero(Value);
310 : MaskLen = llvm::popcount(Value);
311 : return true;
312 : }
313 :
314 : /// Return true if the argument contains a non-empty sequence of ones with the
315 : /// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index
316 : /// of the lowest set bit and \p MaskLen is updated to specify the length of the
317 : /// mask, else neither are updated.
318 : inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx,
319 : unsigned &MaskLen) {
320 : if (!isShiftedMask_64(Value))
321 : return false;
322 : MaskIdx = llvm::countr_zero(Value);
323 : MaskLen = llvm::popcount(Value);
324 : return true;
325 : }
326 :
327 : /// Compile time Log2.
328 : /// Valid only for positive powers of two.
329 : template <size_t kValue> constexpr size_t CTLog2() {
330 : static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
331 : "Value is not a valid power of 2");
332 : return 1 + CTLog2<kValue / 2>();
333 : }
334 :
335 : template <> constexpr size_t CTLog2<1>() { return 0; }
336 :
337 : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
338 : /// (32 bit edition.)
339 : /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
340 : inline unsigned Log2_32(uint32_t Value) {
341 : return 31 - llvm::countl_zero(Value);
342 : }
343 :
344 : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
345 : /// (64 bit edition.)
346 : inline unsigned Log2_64(uint64_t Value) {
347 : return 63 - llvm::countl_zero(Value);
348 : }
349 :
350 : /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
351 : /// (32 bit edition).
352 : /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
353 : inline unsigned Log2_32_Ceil(uint32_t Value) {
354 : return 32 - llvm::countl_zero(Value - 1);
355 : }
356 :
357 : /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
358 : /// (64 bit edition.)
359 : inline unsigned Log2_64_Ceil(uint64_t Value) {
360 : return 64 - llvm::countl_zero(Value - 1);
361 : }
362 :
363 : /// A and B are either alignments or offsets. Return the minimum alignment that
364 : /// may be assumed after adding the two together.
365 : template <typename U, typename V, typename T = common_uint<U, V>>
366 : constexpr T MinAlign(U A, V B) {
367 : // The largest power of 2 that divides both A and B.
368 : //
369 : // Replace "-Value" by "1+~Value" in the following commented code to avoid
370 : // MSVC warning C4146
371 : // return (A | B) & -(A | B);
372 : return (A | B) & (1 + ~(A | B));
373 : }
374 :
375 : /// Fallback when arguments aren't integral.
376 : constexpr uint64_t MinAlign(uint64_t A, uint64_t B) {
377 : return (A | B) & (1 + ~(A | B));
378 : }
379 :
380 : /// Returns the next power of two (in 64-bits) that is strictly greater than A.
381 : /// Returns zero on overflow.
382 1005 : constexpr uint64_t NextPowerOf2(uint64_t A) {
383 1005 : A |= (A >> 1);
384 1005 : A |= (A >> 2);
385 1005 : A |= (A >> 4);
386 1005 : A |= (A >> 8);
387 1005 : A |= (A >> 16);
388 1005 : A |= (A >> 32);
389 1005 : return A + 1;
390 : }
391 :
392 : /// Returns the power of two which is greater than or equal to the given value.
393 : /// Essentially, it is a ceil operation across the domain of powers of two.
394 : inline uint64_t PowerOf2Ceil(uint64_t A) {
395 : if (!A || A > UINT64_MAX / 2)
396 : return 0;
397 : return UINT64_C(1) << Log2_64_Ceil(A);
398 : }
399 :
400 : /// Returns the integer ceil(Numerator / Denominator). Unsigned version.
401 : /// Guaranteed to never overflow.
402 : template <typename U, typename V, typename T = common_uint<U, V>>
403 : constexpr T divideCeil(U Numerator, V Denominator) {
404 : assert(Denominator && "Division by zero");
405 : T Bias = (Numerator != 0);
406 : return (Numerator - Bias) / Denominator + Bias;
407 : }
408 :
409 : /// Fallback when arguments aren't integral.
410 : constexpr uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
411 : assert(Denominator && "Division by zero");
412 : uint64_t Bias = (Numerator != 0);
413 : return (Numerator - Bias) / Denominator + Bias;
414 : }
415 :
416 : // Check whether divideCeilSigned or divideFloorSigned would overflow. This
417 : // happens only when Numerator = INT_MIN and Denominator = -1.
418 : template <typename U, typename V>
419 : constexpr bool divideSignedWouldOverflow(U Numerator, V Denominator) {
420 : return Numerator == std::numeric_limits<U>::min() && Denominator == -1;
421 : }
422 :
423 : /// Returns the integer ceil(Numerator / Denominator). Signed version.
424 : /// Overflow is explicitly forbidden with an assert.
425 : template <typename U, typename V, typename T = common_sint<U, V>>
426 : constexpr T divideCeilSigned(U Numerator, V Denominator) {
427 : assert(Denominator && "Division by zero");
428 : assert(!divideSignedWouldOverflow(Numerator, Denominator) &&
429 : "Divide would overflow");
430 : if (!Numerator)
431 : return 0;
432 : // C's integer division rounds towards 0.
433 : T Bias = Denominator >= 0 ? 1 : -1;
434 : bool SameSign = (Numerator >= 0) == (Denominator >= 0);
435 : return SameSign ? (Numerator - Bias) / Denominator + 1
436 : : Numerator / Denominator;
437 : }
438 :
439 : /// Returns the integer floor(Numerator / Denominator). Signed version.
440 : /// Overflow is explicitly forbidden with an assert.
441 : template <typename U, typename V, typename T = common_sint<U, V>>
442 : constexpr T divideFloorSigned(U Numerator, V Denominator) {
443 : assert(Denominator && "Division by zero");
444 : assert(!divideSignedWouldOverflow(Numerator, Denominator) &&
445 : "Divide would overflow");
446 : if (!Numerator)
447 : return 0;
448 : // C's integer division rounds towards 0.
449 : T Bias = Denominator >= 0 ? -1 : 1;
450 : bool SameSign = (Numerator >= 0) == (Denominator >= 0);
451 : return SameSign ? Numerator / Denominator
452 : : (Numerator - Bias) / Denominator - 1;
453 : }
454 :
455 : /// Returns the remainder of the Euclidean division of LHS by RHS. Result is
456 : /// always non-negative.
457 : template <typename U, typename V, typename T = common_sint<U, V>>
458 : constexpr T mod(U Numerator, V Denominator) {
459 : assert(Denominator >= 1 && "Mod by non-positive number");
460 : T Mod = Numerator % Denominator;
461 : return Mod < 0 ? Mod + Denominator : Mod;
462 : }
463 :
464 : /// Returns (Numerator / Denominator) rounded by round-half-up. Guaranteed to
465 : /// never overflow.
466 : template <typename U, typename V, typename T = common_uint<U, V>>
467 : constexpr T divideNearest(U Numerator, V Denominator) {
468 : assert(Denominator && "Division by zero");
469 : T Mod = Numerator % Denominator;
470 : return (Numerator / Denominator) +
471 : (Mod > (static_cast<T>(Denominator) - 1) / 2);
472 : }
473 :
474 : /// Returns the next integer (mod 2**nbits) that is greater than or equal to
475 : /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
476 : ///
477 : /// Examples:
478 : /// \code
479 : /// alignTo(5, 8) = 8
480 : /// alignTo(17, 8) = 24
481 : /// alignTo(~0LL, 8) = 0
482 : /// alignTo(321, 255) = 510
483 : /// \endcode
484 : ///
485 : /// Will overflow only if result is not representable in T.
486 : template <typename U, typename V, typename T = common_uint<U, V>>
487 : constexpr T alignTo(U Value, V Align) {
488 : assert(Align != 0u && "Align can't be 0.");
489 : T CeilDiv = divideCeil(Value, Align);
490 : return CeilDiv * Align;
491 : }
492 :
493 : /// Fallback when arguments aren't integral.
494 : constexpr uint64_t alignTo(uint64_t Value, uint64_t Align) {
495 : assert(Align != 0u && "Align can't be 0.");
496 : uint64_t CeilDiv = divideCeil(Value, Align);
497 : return CeilDiv * Align;
498 : }
499 :
500 : constexpr uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) {
501 : assert(Align != 0 && (Align & (Align - 1)) == 0 &&
502 : "Align must be a power of 2");
503 : // Replace unary minus to avoid compilation error on Windows:
504 : // "unary minus operator applied to unsigned type, result still unsigned"
505 : uint64_t NegAlign = (~Align) + 1;
506 : return (Value + Align - 1) & NegAlign;
507 : }
508 :
509 : /// If non-zero \p Skew is specified, the return value will be a minimal integer
510 : /// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
511 : /// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
512 : /// Skew mod \p A'. \p Align must be non-zero.
513 : ///
514 : /// Examples:
515 : /// \code
516 : /// alignTo(5, 8, 7) = 7
517 : /// alignTo(17, 8, 1) = 17
518 : /// alignTo(~0LL, 8, 3) = 3
519 : /// alignTo(321, 255, 42) = 552
520 : /// \endcode
521 : ///
522 : /// May overflow.
523 : template <typename U, typename V, typename W,
524 : typename T = common_uint<common_uint<U, V>, W>>
525 : constexpr T alignTo(U Value, V Align, W Skew) {
526 : assert(Align != 0u && "Align can't be 0.");
527 : Skew %= Align;
528 : return alignTo(Value - Skew, Align) + Skew;
529 : }
530 :
531 : /// Returns the next integer (mod 2**nbits) that is greater than or equal to
532 : /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
533 : ///
534 : /// Will overflow only if result is not representable in T.
535 : template <auto Align, typename V, typename T = common_uint<decltype(Align), V>>
536 : constexpr T alignTo(V Value) {
537 : static_assert(Align != 0u, "Align must be non-zero");
538 : T CeilDiv = divideCeil(Value, Align);
539 : return CeilDiv * Align;
540 : }
541 :
542 : /// Returns the largest unsigned integer less than or equal to \p Value and is
543 : /// \p Skew mod \p Align. \p Align must be non-zero. Guaranteed to never
544 : /// overflow.
545 : template <typename U, typename V, typename W = uint8_t,
546 : typename T = common_uint<common_uint<U, V>, W>>
547 : constexpr T alignDown(U Value, V Align, W Skew = 0) {
548 : assert(Align != 0u && "Align can't be 0.");
549 : Skew %= Align;
550 : return (Value - Skew) / Align * Align + Skew;
551 : }
552 :
553 : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
554 : /// Requires B <= 32.
555 : template <unsigned B> constexpr int32_t SignExtend32(uint32_t X) {
556 : static_assert(B <= 32, "Bit width out of range.");
557 : if constexpr (B == 0)
558 : return 0;
559 : return int32_t(X << (32 - B)) >> (32 - B);
560 : }
561 :
562 : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
563 : /// Requires B <= 32.
564 : inline int32_t SignExtend32(uint32_t X, unsigned B) {
565 : assert(B <= 32 && "Bit width out of range.");
566 : if (B == 0)
567 : return 0;
568 : return int32_t(X << (32 - B)) >> (32 - B);
569 : }
570 :
571 : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
572 : /// Requires B <= 64.
573 : template <unsigned B> constexpr int64_t SignExtend64(uint64_t x) {
574 : static_assert(B <= 64, "Bit width out of range.");
575 : if constexpr (B == 0)
576 : return 0;
577 : return int64_t(x << (64 - B)) >> (64 - B);
578 : }
579 :
580 : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
581 : /// Requires B <= 64.
582 : inline int64_t SignExtend64(uint64_t X, unsigned B) {
583 : assert(B <= 64 && "Bit width out of range.");
584 : if (B == 0)
585 : return 0;
586 : return int64_t(X << (64 - B)) >> (64 - B);
587 : }
588 :
589 : /// Subtract two unsigned integers, X and Y, of type T and return the absolute
590 : /// value of the result.
591 : template <typename U, typename V, typename T = common_uint<U, V>>
592 : constexpr T AbsoluteDifference(U X, V Y) {
593 : return X > Y ? (X - Y) : (Y - X);
594 : }
595 :
596 : /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
597 : /// maximum representable value of T on overflow. ResultOverflowed indicates if
598 : /// the result is larger than the maximum representable value of type T.
599 : template <typename T>
600 : std::enable_if_t<std::is_unsigned_v<T>, T>
601 : SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
602 : bool Dummy;
603 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
604 : // Hacker's Delight, p. 29
605 : T Z = X + Y;
606 : Overflowed = (Z < X || Z < Y);
607 : if (Overflowed)
608 : return std::numeric_limits<T>::max();
609 : else
610 : return Z;
611 : }
612 :
613 : /// Add multiple unsigned integers of type T. Clamp the result to the
614 : /// maximum representable value of T on overflow.
615 : template <class T, class... Ts>
616 : std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z,
617 : Ts... Args) {
618 : bool Overflowed = false;
619 : T XY = SaturatingAdd(X, Y, &Overflowed);
620 : if (Overflowed)
621 : return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...);
622 : return SaturatingAdd(XY, Z, Args...);
623 : }
624 :
625 : /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
626 : /// maximum representable value of T on overflow. ResultOverflowed indicates if
627 : /// the result is larger than the maximum representable value of type T.
628 : template <typename T>
629 : std::enable_if_t<std::is_unsigned_v<T>, T>
630 : SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
631 : bool Dummy;
632 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
633 :
634 : // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
635 : // because it fails for uint16_t (where multiplication can have undefined
636 : // behavior due to promotion to int), and requires a division in addition
637 : // to the multiplication.
638 :
639 : Overflowed = false;
640 :
641 : // Log2(Z) would be either Log2Z or Log2Z + 1.
642 : // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
643 : // will necessarily be less than Log2Max as desired.
644 : int Log2Z = Log2_64(X) + Log2_64(Y);
645 : const T Max = std::numeric_limits<T>::max();
646 : int Log2Max = Log2_64(Max);
647 : if (Log2Z < Log2Max) {
648 : return X * Y;
649 : }
650 : if (Log2Z > Log2Max) {
651 : Overflowed = true;
652 : return Max;
653 : }
654 :
655 : // We're going to use the top bit, and maybe overflow one
656 : // bit past it. Multiply all but the bottom bit then add
657 : // that on at the end.
658 : T Z = (X >> 1) * Y;
659 : if (Z & ~(Max >> 1)) {
660 : Overflowed = true;
661 : return Max;
662 : }
663 : Z <<= 1;
664 : if (X & 1)
665 : return SaturatingAdd(Z, Y, ResultOverflowed);
666 :
667 : return Z;
668 : }
669 :
670 : /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
671 : /// the product. Clamp the result to the maximum representable value of T on
672 : /// overflow. ResultOverflowed indicates if the result is larger than the
673 : /// maximum representable value of type T.
674 : template <typename T>
675 : std::enable_if_t<std::is_unsigned_v<T>, T>
676 : SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
677 : bool Dummy;
678 : bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
679 :
680 : T Product = SaturatingMultiply(X, Y, &Overflowed);
681 : if (Overflowed)
682 : return Product;
683 :
684 : return SaturatingAdd(A, Product, &Overflowed);
685 : }
686 :
687 : /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
688 : extern const float huge_valf;
689 :
690 : /// Add two signed integers, computing the two's complement truncated result,
691 : /// returning true if overflow occurred.
692 : template <typename T>
693 : std::enable_if_t<std::is_signed_v<T>, T> AddOverflow(T X, T Y, T &Result) {
694 : #if __has_builtin(__builtin_add_overflow)
695 : return __builtin_add_overflow(X, Y, &Result);
696 : #else
697 : // Perform the unsigned addition.
698 : using U = std::make_unsigned_t<T>;
699 : const U UX = static_cast<U>(X);
700 : const U UY = static_cast<U>(Y);
701 : const U UResult = UX + UY;
702 :
703 : // Convert to signed.
704 : Result = static_cast<T>(UResult);
705 :
706 : // Adding two positive numbers should result in a positive number.
707 : if (X > 0 && Y > 0)
708 : return Result <= 0;
709 : // Adding two negatives should result in a negative number.
710 : if (X < 0 && Y < 0)
711 : return Result >= 0;
712 : return false;
713 : #endif
714 : }
715 :
716 : /// Subtract two signed integers, computing the two's complement truncated
717 : /// result, returning true if an overflow ocurred.
718 : template <typename T>
719 : std::enable_if_t<std::is_signed_v<T>, T> SubOverflow(T X, T Y, T &Result) {
720 : #if __has_builtin(__builtin_sub_overflow)
721 : return __builtin_sub_overflow(X, Y, &Result);
722 : #else
723 : // Perform the unsigned addition.
724 : using U = std::make_unsigned_t<T>;
725 : const U UX = static_cast<U>(X);
726 : const U UY = static_cast<U>(Y);
727 : const U UResult = UX - UY;
728 :
729 : // Convert to signed.
730 : Result = static_cast<T>(UResult);
731 :
732 : // Subtracting a positive number from a negative results in a negative number.
733 : if (X <= 0 && Y > 0)
734 : return Result >= 0;
735 : // Subtracting a negative number from a positive results in a positive number.
736 : if (X >= 0 && Y < 0)
737 : return Result <= 0;
738 : return false;
739 : #endif
740 : }
741 :
742 : /// Multiply two signed integers, computing the two's complement truncated
743 : /// result, returning true if an overflow ocurred.
744 : template <typename T>
745 : std::enable_if_t<std::is_signed_v<T>, T> MulOverflow(T X, T Y, T &Result) {
746 : #if __has_builtin(__builtin_mul_overflow)
747 : return __builtin_mul_overflow(X, Y, &Result);
748 : #else
749 : // Perform the unsigned multiplication on absolute values.
750 : using U = std::make_unsigned_t<T>;
751 : const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
752 : const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
753 : const U UResult = UX * UY;
754 :
755 : // Convert to signed.
756 : const bool IsNegative = (X < 0) ^ (Y < 0);
757 : Result = IsNegative ? (0 - UResult) : UResult;
758 :
759 : // If any of the args was 0, result is 0 and no overflow occurs.
760 : if (UX == 0 || UY == 0)
761 : return false;
762 :
763 : // UX and UY are in [1, 2^n], where n is the number of digits.
764 : // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
765 : // positive) divided by an argument compares to the other.
766 : if (IsNegative)
767 : return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
768 : else
769 : return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
770 : #endif
771 : }
772 :
773 : /// Type to force float point values onto the stack, so that x86 doesn't add
774 : /// hidden precision, avoiding rounding differences on various platforms.
775 : #if defined(__i386__) || defined(_M_IX86)
776 : using stack_float_t = volatile float;
777 : #else
778 : using stack_float_t = float;
779 : #endif
780 :
781 : } // namespace llvm
782 :
783 : #endif
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