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

source code of include/llvm-17/llvm/Support/MathExtras.h