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
27 /// Mathematical constants.
28 namespace numbers {
29 // TODO: Track C++20 std::numbers.
30 // TODO: Favor using the hexadecimal FP constants (requires C++17).
31 constexpr 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
46 constexpr 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.
maskTrailingOnes(unsigned N)65 template <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.
maskLeadingOnes(unsigned N)74 template <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.
maskTrailingZeros(unsigned N)80 template <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.
maskLeadingZeros(unsigned N)86 template <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
93 static 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.
reverseBits(T Val)104 template <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(in, &Val, sizeof(Val));
125 for (unsigned i = 0; i < sizeof(Val); ++i)
126 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
127 std::memcpy(&Val, out, 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.
Hi_32(uint64_t Value)136 constexpr 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.
Lo_32(uint64_t Value)141 constexpr 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.
Make_64(uint32_t High,uint32_t Low)146 constexpr 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.
isInt(int64_t x)151 template <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.
165 template <unsigned N, unsigned S>
isShiftedInt(int64_t x)166 constexpr 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.
isUInt(uint64_t x)174 template <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.
189 template <unsigned N, unsigned S>
isShiftedUInt(uint64_t x)190 constexpr 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.
maxUIntN(uint64_t N)201 inline 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.
minIntN(int64_t N)212 inline 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.
maxIntN(int64_t N)219 inline 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.
isUIntN(unsigned N,uint64_t x)228 inline 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.
isIntN(unsigned N,int64_t x)233 inline 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.
isMask_32(uint32_t Value)240 constexpr 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).
isMask_64(uint64_t Value)246 constexpr 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.
isShiftedMask_32(uint32_t Value)252 constexpr inline bool isShiftedMask_32(uint32_t Value) {
253 return Value && isMask_32((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.)
isShiftedMask_64(uint64_t Value)258 constexpr inline bool isShiftedMask_64(uint64_t Value) {
259 return Value && isMask_64((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.)
isPowerOf2_32(uint32_t Value)264 constexpr 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.)
isPowerOf2_64(uint64_t Value)269 constexpr 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.
isShiftedMask_32(uint32_t Value,unsigned & MaskIdx,unsigned & MaskLen)278 inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx,
279 unsigned &MaskLen) {
280 if (!isShiftedMask_32(Value))
281 return false;
282 MaskIdx = llvm::countr_zero(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.
isShiftedMask_64(uint64_t Value,unsigned & MaskIdx,unsigned & MaskLen)291 inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx,
292 unsigned &MaskLen) {
293 if (!isShiftedMask_64(Value))
294 return false;
295 MaskIdx = llvm::countr_zero(Value);
296 MaskLen = llvm::popcount(Value);
297 return true;
298 }
299
300 /// Compile time Log2.
301 /// Valid only for positive powers of two.
CTLog2()302 template <size_t kValue> constexpr inline size_t CTLog2() {
303 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
304 "Value is not a valid power of 2");
305 return 1 + CTLog2<kValue / 2>();
306 }
307
308 template <> 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
Log2_32(uint32_t Value)313 inline unsigned Log2_32(uint32_t Value) {
314 return 31 - llvm::countl_zero(Value);
315 }
316
317 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
318 /// (64 bit edition.)
Log2_64(uint64_t Value)319 inline unsigned Log2_64(uint64_t Value) {
320 return 63 - llvm::countl_zero(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
Log2_32_Ceil(uint32_t Value)326 inline unsigned Log2_32_Ceil(uint32_t Value) {
327 return 32 - llvm::countl_zero(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.)
Log2_64_Ceil(uint64_t Value)332 inline unsigned Log2_64_Ceil(uint64_t Value) {
333 return 64 - llvm::countl_zero(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.
MinAlign(uint64_t A,uint64_t B)338 constexpr 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.
NextPowerOf2(uint64_t A)349 constexpr 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.
PowerOf2Ceil(uint64_t A)361 inline uint64_t PowerOf2Ceil(uint64_t A) {
362 if (!A || A > UINT64_MAX / 2)
363 return 0;
364 return UINT64_C(1) << Log2_64_Ceil(A);
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
alignTo(uint64_t Value,uint64_t Align)377 inline 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
alignToPowerOf2(uint64_t Value,uint64_t Align)382 inline 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 // Replace unary minus to avoid compilation error on Windows:
386 // "unary minus operator applied to unsigned type, result still unsigned"
387 uint64_t negAlign = (~Align) + 1;
388 return (Value + Align - 1) & negAlign;
389 }
390
391 /// If non-zero \p Skew is specified, the return value will be a minimal integer
392 /// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
393 /// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
394 /// Skew mod \p A'. \p Align must be non-zero.
395 ///
396 /// Examples:
397 /// \code
398 /// alignTo(5, 8, 7) = 7
399 /// alignTo(17, 8, 1) = 17
400 /// alignTo(~0LL, 8, 3) = 3
401 /// alignTo(321, 255, 42) = 552
402 /// \endcode
alignTo(uint64_t Value,uint64_t Align,uint64_t Skew)403 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew) {
404 assert(Align != 0u && "Align can't be 0.");
405 Skew %= Align;
406 return alignTo(Value - Skew, Align) + Skew;
407 }
408
409 /// Returns the next integer (mod 2**64) that is greater than or equal to
410 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
alignTo(uint64_t Value)411 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
412 static_assert(Align != 0u, "Align must be non-zero");
413 return (Value + Align - 1) / Align * Align;
414 }
415
416 /// Returns the integer ceil(Numerator / Denominator).
divideCeil(uint64_t Numerator,uint64_t Denominator)417 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
418 return alignTo(Numerator, Denominator) / Denominator;
419 }
420
421 /// Returns the integer nearest(Numerator / Denominator).
divideNearest(uint64_t Numerator,uint64_t Denominator)422 inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
423 return (Numerator + (Denominator / 2)) / Denominator;
424 }
425
426 /// Returns the largest uint64_t less than or equal to \p Value and is
427 /// \p Skew mod \p Align. \p Align must be non-zero
428 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
429 assert(Align != 0u && "Align can't be 0.");
430 Skew %= Align;
431 return (Value - Skew) / Align * Align + Skew;
432 }
433
434 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
435 /// Requires 0 < B <= 32.
SignExtend32(uint32_t X)436 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
437 static_assert(B > 0, "Bit width can't be 0.");
438 static_assert(B <= 32, "Bit width out of range.");
439 return int32_t(X << (32 - B)) >> (32 - B);
440 }
441
442 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
443 /// Requires 0 < B <= 32.
SignExtend32(uint32_t X,unsigned B)444 inline int32_t SignExtend32(uint32_t X, unsigned B) {
445 assert(B > 0 && "Bit width can't be 0.");
446 assert(B <= 32 && "Bit width out of range.");
447 return int32_t(X << (32 - B)) >> (32 - B);
448 }
449
450 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
451 /// Requires 0 < B <= 64.
SignExtend64(uint64_t x)452 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
453 static_assert(B > 0, "Bit width can't be 0.");
454 static_assert(B <= 64, "Bit width out of range.");
455 return int64_t(x << (64 - B)) >> (64 - B);
456 }
457
458 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
459 /// Requires 0 < B <= 64.
SignExtend64(uint64_t X,unsigned B)460 inline int64_t SignExtend64(uint64_t X, unsigned B) {
461 assert(B > 0 && "Bit width can't be 0.");
462 assert(B <= 64 && "Bit width out of range.");
463 return int64_t(X << (64 - B)) >> (64 - B);
464 }
465
466 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
467 /// value of the result.
468 template <typename T>
AbsoluteDifference(T X,T Y)469 std::enable_if_t<std::is_unsigned_v<T>, T> AbsoluteDifference(T X, T Y) {
470 return X > Y ? (X - Y) : (Y - X);
471 }
472
473 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the
474 /// maximum representable value of T on overflow. ResultOverflowed indicates if
475 /// the result is larger than the maximum representable value of type T.
476 template <typename T>
477 std::enable_if_t<std::is_unsigned_v<T>, T>
478 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
479 bool Dummy;
480 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
481 // Hacker's Delight, p. 29
482 T Z = X + Y;
483 Overflowed = (Z < X || Z < Y);
484 if (Overflowed)
485 return std::numeric_limits<T>::max();
486 else
487 return Z;
488 }
489
490 /// Add multiple unsigned integers of type T. Clamp the result to the
491 /// maximum representable value of T on overflow.
492 template <class T, class... Ts>
SaturatingAdd(T X,T Y,T Z,Ts...Args)493 std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z,
494 Ts... Args) {
495 bool Overflowed = false;
496 T XY = SaturatingAdd(X, Y, &Overflowed);
497 if (Overflowed)
498 return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...);
499 return SaturatingAdd(XY, Z, Args...);
500 }
501
502 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
503 /// maximum representable value of T on overflow. ResultOverflowed indicates if
504 /// the result is larger than the maximum representable value of type T.
505 template <typename T>
506 std::enable_if_t<std::is_unsigned_v<T>, T>
507 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
508 bool Dummy;
509 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
510
511 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
512 // because it fails for uint16_t (where multiplication can have undefined
513 // behavior due to promotion to int), and requires a division in addition
514 // to the multiplication.
515
516 Overflowed = false;
517
518 // Log2(Z) would be either Log2Z or Log2Z + 1.
519 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
520 // will necessarily be less than Log2Max as desired.
521 int Log2Z = Log2_64(X) + Log2_64(Y);
522 const T Max = std::numeric_limits<T>::max();
523 int Log2Max = Log2_64(Max);
524 if (Log2Z < Log2Max) {
525 return X * Y;
526 }
527 if (Log2Z > Log2Max) {
528 Overflowed = true;
529 return Max;
530 }
531
532 // We're going to use the top bit, and maybe overflow one
533 // bit past it. Multiply all but the bottom bit then add
534 // that on at the end.
535 T Z = (X >> 1) * Y;
536 if (Z & ~(Max >> 1)) {
537 Overflowed = true;
538 return Max;
539 }
540 Z <<= 1;
541 if (X & 1)
542 return SaturatingAdd(Z, Y, ResultOverflowed);
543
544 return Z;
545 }
546
547 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
548 /// the product. Clamp the result to the maximum representable value of T on
549 /// overflow. ResultOverflowed indicates if the result is larger than the
550 /// maximum representable value of type T.
551 template <typename T>
552 std::enable_if_t<std::is_unsigned_v<T>, T>
553 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
554 bool Dummy;
555 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
556
557 T Product = SaturatingMultiply(X, Y, &Overflowed);
558 if (Overflowed)
559 return Product;
560
561 return SaturatingAdd(A, Product, &Overflowed);
562 }
563
564 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
565 extern const float huge_valf;
566
567
568 /// Add two signed integers, computing the two's complement truncated result,
569 /// returning true if overflow occurred.
570 template <typename T>
AddOverflow(T X,T Y,T & Result)571 std::enable_if_t<std::is_signed_v<T>, T> AddOverflow(T X, T Y, T &Result) {
572 #if __has_builtin(__builtin_add_overflow)
573 return __builtin_add_overflow(X, Y, &Result);
574 #else
575 // Perform the unsigned addition.
576 using U = std::make_unsigned_t<T>;
577 const U UX = static_cast<U>(X);
578 const U UY = static_cast<U>(Y);
579 const U UResult = UX + UY;
580
581 // Convert to signed.
582 Result = static_cast<T>(UResult);
583
584 // Adding two positive numbers should result in a positive number.
585 if (X > 0 && Y > 0)
586 return Result <= 0;
587 // Adding two negatives should result in a negative number.
588 if (X < 0 && Y < 0)
589 return Result >= 0;
590 return false;
591 #endif
592 }
593
594 /// Subtract two signed integers, computing the two's complement truncated
595 /// result, returning true if an overflow ocurred.
596 template <typename T>
SubOverflow(T X,T Y,T & Result)597 std::enable_if_t<std::is_signed_v<T>, T> SubOverflow(T X, T Y, T &Result) {
598 #if __has_builtin(__builtin_sub_overflow)
599 return __builtin_sub_overflow(X, Y, &Result);
600 #else
601 // Perform the unsigned addition.
602 using U = std::make_unsigned_t<T>;
603 const U UX = static_cast<U>(X);
604 const U UY = static_cast<U>(Y);
605 const U UResult = UX - UY;
606
607 // Convert to signed.
608 Result = static_cast<T>(UResult);
609
610 // Subtracting a positive number from a negative results in a negative number.
611 if (X <= 0 && Y > 0)
612 return Result >= 0;
613 // Subtracting a negative number from a positive results in a positive number.
614 if (X >= 0 && Y < 0)
615 return Result <= 0;
616 return false;
617 #endif
618 }
619
620 /// Multiply two signed integers, computing the two's complement truncated
621 /// result, returning true if an overflow ocurred.
622 template <typename T>
MulOverflow(T X,T Y,T & Result)623 std::enable_if_t<std::is_signed_v<T>, T> MulOverflow(T X, T Y, T &Result) {
624 // Perform the unsigned multiplication on absolute values.
625 using U = std::make_unsigned_t<T>;
626 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
627 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
628 const U UResult = UX * UY;
629
630 // Convert to signed.
631 const bool IsNegative = (X < 0) ^ (Y < 0);
632 Result = IsNegative ? (0 - UResult) : UResult;
633
634 // If any of the args was 0, result is 0 and no overflow occurs.
635 if (UX == 0 || UY == 0)
636 return false;
637
638 // UX and UY are in [1, 2^n], where n is the number of digits.
639 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
640 // positive) divided by an argument compares to the other.
641 if (IsNegative)
642 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
643 else
644 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
645 }
646
647 } // End llvm namespace
648
649 #endif
650