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
25namespace 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.
31template <typename T, typename U>
32using 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.
36template <typename T, typename U, typename = enableif_int<T, U>>
37using common_uint =
38 std::common_type_t<std::make_unsigned_t<T>, std::make_unsigned_t<U>>;
39template <typename T, typename U, typename = enableif_int<T, U>>
40using common_sint =
41 std::common_type_t<std::make_signed_t<T>, std::make_signed_t<U>>;
42
43/// Mathematical constants.
44namespace numbers {
45// TODO: Track C++20 std::numbers.
46// clang-format off
47constexpr double e = 0x1.5bf0a8b145769P+1, // (2.7182818284590452354) https://oeis.org/A001113
48 egamma = 0x1.2788cfc6fb619P-1, // (.57721566490153286061) https://oeis.org/A001620
49 ln2 = 0x1.62e42fefa39efP-1, // (.69314718055994530942) https://oeis.org/A002162
50 ln10 = 0x1.26bb1bbb55516P+1, // (2.3025850929940456840) https://oeis.org/A002392
51 log2e = 0x1.71547652b82feP+0, // (1.4426950408889634074)
52 log10e = 0x1.bcb7b1526e50eP-2, // (.43429448190325182765)
53 pi = 0x1.921fb54442d18P+1, // (3.1415926535897932385) https://oeis.org/A000796
54 inv_pi = 0x1.45f306dc9c883P-2, // (.31830988618379067154) https://oeis.org/A049541
55 sqrtpi = 0x1.c5bf891b4ef6bP+0, // (1.7724538509055160273) https://oeis.org/A002161
56 inv_sqrtpi = 0x1.20dd750429b6dP-1, // (.56418958354775628695) https://oeis.org/A087197
57 sqrt2 = 0x1.6a09e667f3bcdP+0, // (1.4142135623730950488) https://oeis.org/A00219
58 inv_sqrt2 = 0x1.6a09e667f3bcdP-1, // (.70710678118654752440)
59 sqrt3 = 0x1.bb67ae8584caaP+0, // (1.7320508075688772935) https://oeis.org/A002194
60 inv_sqrt3 = 0x1.279a74590331cP-1, // (.57735026918962576451)
61 phi = 0x1.9e3779b97f4a8P+0; // (1.6180339887498948482) https://oeis.org/A001622
62constexpr float ef = 0x1.5bf0a8P+1F, // (2.71828183) https://oeis.org/A001113
63 egammaf = 0x1.2788d0P-1F, // (.577215665) https://oeis.org/A001620
64 ln2f = 0x1.62e430P-1F, // (.693147181) https://oeis.org/A002162
65 ln10f = 0x1.26bb1cP+1F, // (2.30258509) https://oeis.org/A002392
66 log2ef = 0x1.715476P+0F, // (1.44269504)
67 log10ef = 0x1.bcb7b2P-2F, // (.434294482)
68 pif = 0x1.921fb6P+1F, // (3.14159265) https://oeis.org/A000796
69 inv_pif = 0x1.45f306P-2F, // (.318309886) https://oeis.org/A049541
70 sqrtpif = 0x1.c5bf8aP+0F, // (1.77245385) https://oeis.org/A002161
71 inv_sqrtpif = 0x1.20dd76P-1F, // (.564189584) https://oeis.org/A087197
72 sqrt2f = 0x1.6a09e6P+0F, // (1.41421356) https://oeis.org/A002193
73 inv_sqrt2f = 0x1.6a09e6P-1F, // (.707106781)
74 sqrt3f = 0x1.bb67aeP+0F, // (1.73205081) https://oeis.org/A002194
75 inv_sqrt3f = 0x1.279a74P-1F, // (.577350269)
76 phif = 0x1.9e377aP+0F; // (1.61803399) https://oeis.org/A001622
77// clang-format on
78} // namespace numbers
79
80/// Create a bitmask with the N right-most bits set to 1, and all other
81/// bits set to 0. Only unsigned types are allowed.
82template <typename T> T maskTrailingOnes(unsigned N) {
83 static_assert(std::is_unsigned_v<T>, "Invalid type!");
84 const unsigned Bits = CHAR_BIT * sizeof(T);
85 assert(N <= Bits && "Invalid bit index");
86 if (N == 0)
87 return 0;
88 return T(-1) >> (Bits - N);
89}
90
91/// Create a bitmask with the N left-most bits set to 1, and all other
92/// bits set to 0. Only unsigned types are allowed.
93template <typename T> T maskLeadingOnes(unsigned N) {
94 return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
95}
96
97/// Create a bitmask with the N right-most bits set to 0, and all other
98/// bits set to 1. Only unsigned types are allowed.
99template <typename T> T maskTrailingZeros(unsigned N) {
100 return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
101}
102
103/// Create a bitmask with the N left-most bits set to 0, and all other
104/// bits set to 1. Only unsigned types are allowed.
105template <typename T> T maskLeadingZeros(unsigned N) {
106 return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
107}
108
109/// Macro compressed bit reversal table for 256 bits.
110///
111/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
112static const unsigned char BitReverseTable256[256] = {
113#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
114#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
115#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
116 R6(0), R6(2), R6(1), R6(3)
117#undef R2
118#undef R4
119#undef R6
120};
121
122/// Reverse the bits in \p Val.
123template <typename T> T reverseBits(T Val) {
124#if __has_builtin(__builtin_bitreverse8)
125 if constexpr (std::is_same_v<T, uint8_t>)
126 return __builtin_bitreverse8(Val);
127#endif
128#if __has_builtin(__builtin_bitreverse16)
129 if constexpr (std::is_same_v<T, uint16_t>)
130 return __builtin_bitreverse16(Val);
131#endif
132#if __has_builtin(__builtin_bitreverse32)
133 if constexpr (std::is_same_v<T, uint32_t>)
134 return __builtin_bitreverse32(Val);
135#endif
136#if __has_builtin(__builtin_bitreverse64)
137 if constexpr (std::is_same_v<T, uint64_t>)
138 return __builtin_bitreverse64(Val);
139#endif
140
141 unsigned char in[sizeof(Val)];
142 unsigned char out[sizeof(Val)];
143 std::memcpy(dest: in, src: &Val, n: sizeof(Val));
144 for (unsigned i = 0; i < sizeof(Val); ++i)
145 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
146 std::memcpy(dest: &Val, src: out, n: sizeof(Val));
147 return Val;
148}
149
150// NOTE: The following support functions use the _32/_64 extensions instead of
151// type overloading so that signed and unsigned integers can be used without
152// ambiguity.
153
154/// Return the high 32 bits of a 64 bit value.
155constexpr uint32_t Hi_32(uint64_t Value) {
156 return static_cast<uint32_t>(Value >> 32);
157}
158
159/// Return the low 32 bits of a 64 bit value.
160constexpr uint32_t Lo_32(uint64_t Value) {
161 return static_cast<uint32_t>(Value);
162}
163
164/// Make a 64-bit integer from a high / low pair of 32-bit integers.
165constexpr uint64_t Make_64(uint32_t High, uint32_t Low) {
166 return ((uint64_t)High << 32) | (uint64_t)Low;
167}
168
169/// Checks if an integer fits into the given bit width.
170template <unsigned N> constexpr bool isInt(int64_t x) {
171 if constexpr (N == 0)
172 return 0 == x;
173 if constexpr (N == 8)
174 return static_cast<int8_t>(x) == x;
175 if constexpr (N == 16)
176 return static_cast<int16_t>(x) == x;
177 if constexpr (N == 32)
178 return static_cast<int32_t>(x) == x;
179 if constexpr (N < 64)
180 return -(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1));
181 (void)x; // MSVC v19.25 warns that x is unused.
182 return true;
183}
184
185/// Checks if a signed integer is an N bit number shifted left by S.
186template <unsigned N, unsigned S>
187constexpr bool isShiftedInt(int64_t x) {
188 static_assert(S < 64, "isShiftedInt<N, S> with S >= 64 is too much.");
189 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
190 return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
191}
192
193/// Checks if an unsigned integer fits into the given bit width.
194template <unsigned N> constexpr bool isUInt(uint64_t x) {
195 if constexpr (N == 0)
196 return 0 == x;
197 if constexpr (N == 8)
198 return static_cast<uint8_t>(x) == x;
199 if constexpr (N == 16)
200 return static_cast<uint16_t>(x) == x;
201 if constexpr (N == 32)
202 return static_cast<uint32_t>(x) == x;
203 if constexpr (N < 64)
204 return x < (UINT64_C(1) << (N));
205 (void)x; // MSVC v19.25 warns that x is unused.
206 return true;
207}
208
209/// Checks if a unsigned integer is an N bit number shifted left by S.
210template <unsigned N, unsigned S>
211constexpr bool isShiftedUInt(uint64_t x) {
212 static_assert(S < 64, "isShiftedUInt<N, S> with S >= 64 is too much.");
213 static_assert(N + S <= 64,
214 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
215 // S must be strictly less than 64. So 1 << S is not undefined behavior.
216 return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
217}
218
219/// Gets the maximum value for a N-bit unsigned integer.
220inline uint64_t maxUIntN(uint64_t N) {
221 assert(N <= 64 && "integer width out of range");
222
223 // uint64_t(1) << 64 is undefined behavior, so we can't do
224 // (uint64_t(1) << N) - 1
225 // without checking first that N != 64. But this works and doesn't have a
226 // branch for N != 0.
227 // Unfortunately, shifting a uint64_t right by 64 bit is undefined
228 // behavior, so the condition on N == 0 is necessary. Fortunately, most
229 // optimizers do not emit branches for this check.
230 if (N == 0)
231 return 0;
232 return UINT64_MAX >> (64 - N);
233}
234
235/// Gets the minimum value for a N-bit signed integer.
236inline int64_t minIntN(int64_t N) {
237 assert(N <= 64 && "integer width out of range");
238
239 if (N == 0)
240 return 0;
241 return UINT64_C(1) + ~(UINT64_C(1) << (N - 1));
242}
243
244/// Gets the maximum value for a N-bit signed integer.
245inline int64_t maxIntN(int64_t N) {
246 assert(N <= 64 && "integer width out of range");
247
248 // This relies on two's complement wraparound when N == 64, so we convert to
249 // int64_t only at the very end to avoid UB.
250 if (N == 0)
251 return 0;
252 return (UINT64_C(1) << (N - 1)) - 1;
253}
254
255/// Checks if an unsigned integer fits into the given (dynamic) bit width.
256inline bool isUIntN(unsigned N, uint64_t x) {
257 return N >= 64 || x <= maxUIntN(N);
258}
259
260/// Checks if an signed integer fits into the given (dynamic) bit width.
261inline bool isIntN(unsigned N, int64_t x) {
262 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
263}
264
265/// Return true if the argument is a non-empty sequence of ones starting at the
266/// least significant bit with the remainder zero (32 bit version).
267/// Ex. isMask_32(0x0000FFFFU) == true.
268constexpr bool isMask_32(uint32_t Value) {
269 return Value && ((Value + 1) & Value) == 0;
270}
271
272/// Return true if the argument is a non-empty sequence of ones starting at the
273/// least significant bit with the remainder zero (64 bit version).
274constexpr bool isMask_64(uint64_t Value) {
275 return Value && ((Value + 1) & Value) == 0;
276}
277
278/// Return true if the argument contains a non-empty sequence of ones with the
279/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
280constexpr bool isShiftedMask_32(uint32_t Value) {
281 return Value && isMask_32(Value: (Value - 1) | Value);
282}
283
284/// Return true if the argument contains a non-empty sequence of ones with the
285/// remainder zero (64 bit version.)
286constexpr bool isShiftedMask_64(uint64_t Value) {
287 return Value && isMask_64(Value: (Value - 1) | Value);
288}
289
290/// Return true if the argument is a power of two > 0.
291/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
292constexpr bool isPowerOf2_32(uint32_t Value) {
293 return llvm::has_single_bit(Value);
294}
295
296/// Return true if the argument is a power of two > 0 (64 bit edition.)
297constexpr bool isPowerOf2_64(uint64_t Value) {
298 return llvm::has_single_bit(Value);
299}
300
301/// Return true if the argument contains a non-empty sequence of ones with the
302/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
303/// If true, \p MaskIdx will specify the index of the lowest set bit and \p
304/// MaskLen is updated to specify the length of the mask, else neither are
305/// updated.
306inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx,
307 unsigned &MaskLen) {
308 if (!isShiftedMask_32(Value))
309 return false;
310 MaskIdx = llvm::countr_zero(Val: Value);
311 MaskLen = llvm::popcount(Value);
312 return true;
313}
314
315/// Return true if the argument contains a non-empty sequence of ones with the
316/// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index
317/// of the lowest set bit and \p MaskLen is updated to specify the length of the
318/// mask, else neither are updated.
319inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx,
320 unsigned &MaskLen) {
321 if (!isShiftedMask_64(Value))
322 return false;
323 MaskIdx = llvm::countr_zero(Val: Value);
324 MaskLen = llvm::popcount(Value);
325 return true;
326}
327
328/// Compile time Log2.
329/// Valid only for positive powers of two.
330template <size_t kValue> constexpr size_t CTLog2() {
331 static_assert(llvm::isPowerOf2_64(Value: kValue), "Value is not a valid power of 2");
332 return 1 + CTLog2<kValue / 2>();
333}
334
335template <> 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
340inline unsigned Log2_32(uint32_t Value) {
341 return 31 - llvm::countl_zero(Val: Value);
342}
343
344/// Return the floor log base 2 of the specified value, -1 if the value is zero.
345/// (64 bit edition.)
346inline unsigned Log2_64(uint64_t Value) {
347 return 63 - llvm::countl_zero(Val: 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
353inline unsigned Log2_32_Ceil(uint32_t Value) {
354 return 32 - llvm::countl_zero(Val: 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.)
359inline unsigned Log2_64_Ceil(uint64_t Value) {
360 return 64 - llvm::countl_zero(Val: 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.
365template <typename U, typename V, typename T = common_uint<U, V>>
366constexpr 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.
376constexpr 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.
382constexpr uint64_t NextPowerOf2(uint64_t A) {
383 A |= (A >> 1);
384 A |= (A >> 2);
385 A |= (A >> 4);
386 A |= (A >> 8);
387 A |= (A >> 16);
388 A |= (A >> 32);
389 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.
394inline uint64_t PowerOf2Ceil(uint64_t A) {
395 if (!A || A > UINT64_MAX / 2)
396 return 0;
397 return UINT64_C(1) << Log2_64_Ceil(Value: A);
398}
399
400/// Returns the integer ceil(Numerator / Denominator). Unsigned version.
401/// Guaranteed to never overflow.
402template <typename U, typename V, typename T = common_uint<U, V>>
403constexpr 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.
410constexpr 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.
418template <typename U, typename V>
419constexpr 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.
425template <typename U, typename V, typename T = common_sint<U, V>>
426constexpr 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.
441template <typename U, typename V, typename T = common_sint<U, V>>
442constexpr 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.
457template <typename U, typename V, typename T = common_sint<U, V>>
458constexpr 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.
466template <typename U, typename V, typename T = common_uint<U, V>>
467constexpr 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.
486template <typename U, typename V, typename T = common_uint<U, V>>
487constexpr 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.
494constexpr uint64_t alignTo(uint64_t Value, uint64_t Align) {
495 assert(Align != 0u && "Align can't be 0.");
496 uint64_t CeilDiv = divideCeil(Numerator: Value, Denominator: Align);
497 return CeilDiv * Align;
498}
499
500/// Will overflow only if result is not representable in T.
501template <typename U, typename V, typename T = common_uint<U, V>>
502constexpr T alignToPowerOf2(U Value, V Align) {
503 assert(Align != 0 && (Align & (Align - 1)) == 0 &&
504 "Align must be a power of 2");
505 T NegAlign = static_cast<T>(0) - Align;
506 return (Value + (Align - 1)) & NegAlign;
507}
508
509/// Fallback when arguments aren't integral.
510constexpr uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) {
511 assert(Align != 0 && (Align & (Align - 1)) == 0 &&
512 "Align must be a power of 2");
513 uint64_t NegAlign = 0 - Align;
514 return (Value + (Align - 1)) & NegAlign;
515}
516
517/// If non-zero \p Skew is specified, the return value will be a minimal integer
518/// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
519/// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
520/// Skew mod \p A'. \p Align must be non-zero.
521///
522/// Examples:
523/// \code
524/// alignTo(5, 8, 7) = 7
525/// alignTo(17, 8, 1) = 17
526/// alignTo(~0LL, 8, 3) = 3
527/// alignTo(321, 255, 42) = 552
528/// \endcode
529///
530/// May overflow.
531template <typename U, typename V, typename W,
532 typename T = common_uint<common_uint<U, V>, W>>
533constexpr T alignTo(U Value, V Align, W Skew) {
534 assert(Align != 0u && "Align can't be 0.");
535 Skew %= Align;
536 return alignTo(Value - Skew, Align) + Skew;
537}
538
539/// Returns the next integer (mod 2**nbits) that is greater than or equal to
540/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
541///
542/// Will overflow only if result is not representable in T.
543template <auto Align, typename V, typename T = common_uint<decltype(Align), V>>
544constexpr T alignTo(V Value) {
545 static_assert(Align != 0u, "Align must be non-zero");
546 T CeilDiv = divideCeil(Value, Align);
547 return CeilDiv * Align;
548}
549
550/// Returns the largest unsigned integer less than or equal to \p Value and is
551/// \p Skew mod \p Align. \p Align must be non-zero. Guaranteed to never
552/// overflow.
553template <typename U, typename V, typename W = uint8_t,
554 typename T = common_uint<common_uint<U, V>, W>>
555constexpr T alignDown(U Value, V Align, W Skew = 0) {
556 assert(Align != 0u && "Align can't be 0.");
557 Skew %= Align;
558 return (Value - Skew) / Align * Align + Skew;
559}
560
561/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
562/// Requires B <= 32.
563template <unsigned B> constexpr int32_t SignExtend32(uint32_t X) {
564 static_assert(B <= 32, "Bit width out of range.");
565 if constexpr (B == 0)
566 return 0;
567 return int32_t(X << (32 - B)) >> (32 - B);
568}
569
570/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
571/// Requires B <= 32.
572inline int32_t SignExtend32(uint32_t X, unsigned B) {
573 assert(B <= 32 && "Bit width out of range.");
574 if (B == 0)
575 return 0;
576 return int32_t(X << (32 - B)) >> (32 - B);
577}
578
579/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
580/// Requires B <= 64.
581template <unsigned B> constexpr int64_t SignExtend64(uint64_t x) {
582 static_assert(B <= 64, "Bit width out of range.");
583 if constexpr (B == 0)
584 return 0;
585 return int64_t(x << (64 - B)) >> (64 - B);
586}
587
588/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
589/// Requires B <= 64.
590inline int64_t SignExtend64(uint64_t X, unsigned B) {
591 assert(B <= 64 && "Bit width out of range.");
592 if (B == 0)
593 return 0;
594 return int64_t(X << (64 - B)) >> (64 - B);
595}
596
597/// Return the absolute value of a signed integer, converted to the
598/// corresponding unsigned integer type. Avoids undefined behavior in std::abs
599/// when you pass it INT_MIN or similar.
600template <typename T, typename U = std::make_unsigned_t<T>>
601constexpr U AbsoluteValue(T X) {
602 // If X is negative, cast it to the unsigned type _before_ negating it.
603 return X < 0 ? -static_cast<U>(X) : X;
604}
605
606/// Subtract two unsigned integers, X and Y, of type T and return the absolute
607/// value of the result.
608template <typename U, typename V, typename T = common_uint<U, V>>
609constexpr T AbsoluteDifference(U X, V Y) {
610 return X > Y ? (X - Y) : (Y - X);
611}
612
613/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
614/// maximum representable value of T on overflow. ResultOverflowed indicates if
615/// the result is larger than the maximum representable value of type T.
616template <typename T>
617std::enable_if_t<std::is_unsigned_v<T>, T>
618SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
619 bool Dummy;
620 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
621 // Hacker's Delight, p. 29
622 T Z = X + Y;
623 Overflowed = (Z < X || Z < Y);
624 if (Overflowed)
625 return std::numeric_limits<T>::max();
626 else
627 return Z;
628}
629
630/// Add multiple unsigned integers of type T. Clamp the result to the
631/// maximum representable value of T on overflow.
632template <class T, class... Ts>
633std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z,
634 Ts... Args) {
635 bool Overflowed = false;
636 T XY = SaturatingAdd(X, Y, &Overflowed);
637 if (Overflowed)
638 return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...);
639 return SaturatingAdd(XY, Z, Args...);
640}
641
642/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
643/// maximum representable value of T on overflow. ResultOverflowed indicates if
644/// the result is larger than the maximum representable value of type T.
645template <typename T>
646std::enable_if_t<std::is_unsigned_v<T>, T>
647SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
648 bool Dummy;
649 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
650
651 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
652 // because it fails for uint16_t (where multiplication can have undefined
653 // behavior due to promotion to int), and requires a division in addition
654 // to the multiplication.
655
656 Overflowed = false;
657
658 // Log2(Z) would be either Log2Z or Log2Z + 1.
659 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
660 // will necessarily be less than Log2Max as desired.
661 int Log2Z = Log2_64(X) + Log2_64(Y);
662 const T Max = std::numeric_limits<T>::max();
663 int Log2Max = Log2_64(Max);
664 if (Log2Z < Log2Max) {
665 return X * Y;
666 }
667 if (Log2Z > Log2Max) {
668 Overflowed = true;
669 return Max;
670 }
671
672 // We're going to use the top bit, and maybe overflow one
673 // bit past it. Multiply all but the bottom bit then add
674 // that on at the end.
675 T Z = (X >> 1) * Y;
676 if (Z & ~(Max >> 1)) {
677 Overflowed = true;
678 return Max;
679 }
680 Z <<= 1;
681 if (X & 1)
682 return SaturatingAdd(Z, Y, ResultOverflowed);
683
684 return Z;
685}
686
687/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
688/// the product. Clamp the result to the maximum representable value of T on
689/// overflow. ResultOverflowed indicates if the result is larger than the
690/// maximum representable value of type T.
691template <typename T>
692std::enable_if_t<std::is_unsigned_v<T>, T>
693SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
694 bool Dummy;
695 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
696
697 T Product = SaturatingMultiply(X, Y, &Overflowed);
698 if (Overflowed)
699 return Product;
700
701 return SaturatingAdd(A, Product, &Overflowed);
702}
703
704/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
705LLVM_ABI extern const float huge_valf;
706
707/// Add two signed integers, computing the two's complement truncated result,
708/// returning true if overflow occurred.
709template <typename T>
710std::enable_if_t<std::is_signed_v<T>, T> AddOverflow(T X, T Y, T &Result) {
711#if __has_builtin(__builtin_add_overflow)
712 return __builtin_add_overflow(X, Y, &Result);
713#else
714 // Perform the unsigned addition.
715 using U = std::make_unsigned_t<T>;
716 const U UX = static_cast<U>(X);
717 const U UY = static_cast<U>(Y);
718 const U UResult = UX + UY;
719
720 // Convert to signed.
721 Result = static_cast<T>(UResult);
722
723 // Adding two positive numbers should result in a positive number.
724 if (X > 0 && Y > 0)
725 return Result <= 0;
726 // Adding two negatives should result in a negative number.
727 if (X < 0 && Y < 0)
728 return Result >= 0;
729 return false;
730#endif
731}
732
733/// Subtract two signed integers, computing the two's complement truncated
734/// result, returning true if an overflow occurred.
735template <typename T>
736std::enable_if_t<std::is_signed_v<T>, T> SubOverflow(T X, T Y, T &Result) {
737#if __has_builtin(__builtin_sub_overflow)
738 return __builtin_sub_overflow(X, Y, &Result);
739#else
740 // Perform the unsigned addition.
741 using U = std::make_unsigned_t<T>;
742 const U UX = static_cast<U>(X);
743 const U UY = static_cast<U>(Y);
744 const U UResult = UX - UY;
745
746 // Convert to signed.
747 Result = static_cast<T>(UResult);
748
749 // Subtracting a positive number from a negative results in a negative number.
750 if (X <= 0 && Y > 0)
751 return Result >= 0;
752 // Subtracting a negative number from a positive results in a positive number.
753 if (X >= 0 && Y < 0)
754 return Result <= 0;
755 return false;
756#endif
757}
758
759/// Multiply two signed integers, computing the two's complement truncated
760/// result, returning true if an overflow occurred.
761template <typename T>
762std::enable_if_t<std::is_signed_v<T>, T> MulOverflow(T X, T Y, T &Result) {
763#if __has_builtin(__builtin_mul_overflow)
764 return __builtin_mul_overflow(X, Y, &Result);
765#else
766 // Perform the unsigned multiplication on absolute values.
767 using U = std::make_unsigned_t<T>;
768 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
769 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
770 const U UResult = UX * UY;
771
772 // Convert to signed.
773 const bool IsNegative = (X < 0) ^ (Y < 0);
774 Result = IsNegative ? (0 - UResult) : UResult;
775
776 // If any of the args was 0, result is 0 and no overflow occurs.
777 if (UX == 0 || UY == 0)
778 return false;
779
780 // UX and UY are in [1, 2^n], where n is the number of digits.
781 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
782 // positive) divided by an argument compares to the other.
783 if (IsNegative)
784 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
785 else
786 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
787#endif
788}
789
790/// Type to force float point values onto the stack, so that x86 doesn't add
791/// hidden precision, avoiding rounding differences on various platforms.
792#if defined(__i386__) || defined(_M_IX86)
793using stack_float_t = volatile float;
794#else
795using stack_float_t = float;
796#endif
797
798} // namespace llvm
799
800#endif
801

source code of llvm/include/llvm/Support/MathExtras.h