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Andrew Scull5e1ddfa2018-08-14 10:06:54 +01001//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
2//
Andrew Walbran16937d02019-10-22 13:54:20 +01003// 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
Andrew Scull5e1ddfa2018-08-14 10:06:54 +01006//
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/Support/Compiler.h"
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010017#include <algorithm>
18#include <cassert>
19#include <climits>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +020020#include <cmath>
21#include <cstdint>
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010022#include <cstring>
23#include <limits>
24#include <type_traits>
25
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010026#ifdef __ANDROID_NDK__
27#include <android/api-level.h>
28#endif
29
Andrew Scullcdfcccc2018-10-05 20:58:37 +010030#ifdef _MSC_VER
31// Declare these intrinsics manually rather including intrin.h. It's very
32// expensive, and MathExtras.h is popular.
33// #include <intrin.h>
34extern "C" {
35unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
36unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
37unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
38unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
39}
40#endif
41
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010042namespace llvm {
Olivier Deprezf4ef2d02021-04-20 13:36:24 +020043
Andrew Scullcdfcccc2018-10-05 20:58:37 +010044/// The behavior an operation has on an input of 0.
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010045enum ZeroBehavior {
Andrew Scullcdfcccc2018-10-05 20:58:37 +010046 /// The returned value is undefined.
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010047 ZB_Undefined,
Andrew Scullcdfcccc2018-10-05 20:58:37 +010048 /// The returned value is numeric_limits<T>::max()
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010049 ZB_Max,
Andrew Scullcdfcccc2018-10-05 20:58:37 +010050 /// The returned value is numeric_limits<T>::digits
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010051 ZB_Width
52};
53
Olivier Deprezf4ef2d02021-04-20 13:36:24 +020054/// Mathematical constants.
55namespace numbers {
56// TODO: Track C++20 std::numbers.
57// TODO: Favor using the hexadecimal FP constants (requires C++17).
58constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
59 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
60 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
61 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
62 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0)
63 log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
64 pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
65 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
66 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
67 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
68 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
69 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
70 sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
71 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1)
72 phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
73constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
74 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
75 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
76 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
77 log2ef = 1.44269504F, // (0x1.715476P+0)
78 log10ef = .434294482F, // (0x1.bcb7b2P-2)
79 pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
80 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
81 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
82 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
83 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
84 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1)
85 sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
86 inv_sqrt3f = .577350269F, // (0x1.279a74P-1)
87 phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
88} // namespace numbers
89
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010090namespace detail {
91template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
Andrew Walbran3d2c1972020-04-07 12:24:26 +010092 static unsigned count(T Val, ZeroBehavior) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +010093 if (!Val)
94 return std::numeric_limits<T>::digits;
95 if (Val & 0x1)
96 return 0;
97
98 // Bisection method.
Andrew Walbran3d2c1972020-04-07 12:24:26 +010099 unsigned ZeroBits = 0;
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100100 T Shift = std::numeric_limits<T>::digits >> 1;
101 T Mask = std::numeric_limits<T>::max() >> Shift;
102 while (Shift) {
103 if ((Val & Mask) == 0) {
104 Val >>= Shift;
105 ZeroBits |= Shift;
106 }
107 Shift >>= 1;
108 Mask >>= Shift;
109 }
110 return ZeroBits;
111 }
112};
113
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200114#if defined(__GNUC__) || defined(_MSC_VER)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100115template <typename T> struct TrailingZerosCounter<T, 4> {
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100116 static unsigned count(T Val, ZeroBehavior ZB) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100117 if (ZB != ZB_Undefined && Val == 0)
118 return 32;
119
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200120#if __has_builtin(__builtin_ctz) || defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100121 return __builtin_ctz(Val);
122#elif defined(_MSC_VER)
123 unsigned long Index;
124 _BitScanForward(&Index, Val);
125 return Index;
126#endif
127 }
128};
129
130#if !defined(_MSC_VER) || defined(_M_X64)
131template <typename T> struct TrailingZerosCounter<T, 8> {
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100132 static unsigned count(T Val, ZeroBehavior ZB) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100133 if (ZB != ZB_Undefined && Val == 0)
134 return 64;
135
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200136#if __has_builtin(__builtin_ctzll) || defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100137 return __builtin_ctzll(Val);
138#elif defined(_MSC_VER)
139 unsigned long Index;
140 _BitScanForward64(&Index, Val);
141 return Index;
142#endif
143 }
144};
145#endif
146#endif
147} // namespace detail
148
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100149/// Count number of 0's from the least significant bit to the most
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100150/// stopping at the first 1.
151///
152/// Only unsigned integral types are allowed.
153///
154/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
155/// valid arguments.
156template <typename T>
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100157unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100158 static_assert(std::numeric_limits<T>::is_integer &&
159 !std::numeric_limits<T>::is_signed,
160 "Only unsigned integral types are allowed.");
161 return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
162}
163
164namespace detail {
165template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100166 static unsigned count(T Val, ZeroBehavior) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100167 if (!Val)
168 return std::numeric_limits<T>::digits;
169
170 // Bisection method.
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100171 unsigned ZeroBits = 0;
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100172 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
173 T Tmp = Val >> Shift;
174 if (Tmp)
175 Val = Tmp;
176 else
177 ZeroBits |= Shift;
178 }
179 return ZeroBits;
180 }
181};
182
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200183#if defined(__GNUC__) || defined(_MSC_VER)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100184template <typename T> struct LeadingZerosCounter<T, 4> {
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100185 static unsigned count(T Val, ZeroBehavior ZB) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100186 if (ZB != ZB_Undefined && Val == 0)
187 return 32;
188
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200189#if __has_builtin(__builtin_clz) || defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100190 return __builtin_clz(Val);
191#elif defined(_MSC_VER)
192 unsigned long Index;
193 _BitScanReverse(&Index, Val);
194 return Index ^ 31;
195#endif
196 }
197};
198
199#if !defined(_MSC_VER) || defined(_M_X64)
200template <typename T> struct LeadingZerosCounter<T, 8> {
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100201 static unsigned count(T Val, ZeroBehavior ZB) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100202 if (ZB != ZB_Undefined && Val == 0)
203 return 64;
204
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200205#if __has_builtin(__builtin_clzll) || defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100206 return __builtin_clzll(Val);
207#elif defined(_MSC_VER)
208 unsigned long Index;
209 _BitScanReverse64(&Index, Val);
210 return Index ^ 63;
211#endif
212 }
213};
214#endif
215#endif
216} // namespace detail
217
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100218/// Count number of 0's from the most significant bit to the least
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100219/// stopping at the first 1.
220///
221/// Only unsigned integral types are allowed.
222///
223/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
224/// valid arguments.
225template <typename T>
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100226unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100227 static_assert(std::numeric_limits<T>::is_integer &&
228 !std::numeric_limits<T>::is_signed,
229 "Only unsigned integral types are allowed.");
230 return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
231}
232
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100233/// Get the index of the first set bit starting from the least
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100234/// significant bit.
235///
236/// Only unsigned integral types are allowed.
237///
238/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
239/// valid arguments.
240template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
241 if (ZB == ZB_Max && Val == 0)
242 return std::numeric_limits<T>::max();
243
244 return countTrailingZeros(Val, ZB_Undefined);
245}
246
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100247/// Create a bitmask with the N right-most bits set to 1, and all other
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100248/// bits set to 0. Only unsigned types are allowed.
249template <typename T> T maskTrailingOnes(unsigned N) {
250 static_assert(std::is_unsigned<T>::value, "Invalid type!");
251 const unsigned Bits = CHAR_BIT * sizeof(T);
252 assert(N <= Bits && "Invalid bit index");
253 return N == 0 ? 0 : (T(-1) >> (Bits - N));
254}
255
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100256/// Create a bitmask with the N left-most bits set to 1, and all other
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100257/// bits set to 0. Only unsigned types are allowed.
258template <typename T> T maskLeadingOnes(unsigned N) {
259 return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
260}
261
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100262/// Create a bitmask with the N right-most bits set to 0, and all other
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100263/// bits set to 1. Only unsigned types are allowed.
264template <typename T> T maskTrailingZeros(unsigned N) {
265 return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
266}
267
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100268/// Create a bitmask with the N left-most bits set to 0, and all other
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100269/// bits set to 1. Only unsigned types are allowed.
270template <typename T> T maskLeadingZeros(unsigned N) {
271 return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
272}
273
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100274/// Get the index of the last set bit starting from the least
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100275/// significant bit.
276///
277/// Only unsigned integral types are allowed.
278///
279/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
280/// valid arguments.
281template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
282 if (ZB == ZB_Max && Val == 0)
283 return std::numeric_limits<T>::max();
284
285 // Use ^ instead of - because both gcc and llvm can remove the associated ^
286 // in the __builtin_clz intrinsic on x86.
287 return countLeadingZeros(Val, ZB_Undefined) ^
288 (std::numeric_limits<T>::digits - 1);
289}
290
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100291/// Macro compressed bit reversal table for 256 bits.
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100292///
293/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
294static const unsigned char BitReverseTable256[256] = {
295#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
296#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
297#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
298 R6(0), R6(2), R6(1), R6(3)
299#undef R2
300#undef R4
301#undef R6
302};
303
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100304/// Reverse the bits in \p Val.
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100305template <typename T>
306T reverseBits(T Val) {
307 unsigned char in[sizeof(Val)];
308 unsigned char out[sizeof(Val)];
309 std::memcpy(in, &Val, sizeof(Val));
310 for (unsigned i = 0; i < sizeof(Val); ++i)
311 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
312 std::memcpy(&Val, out, sizeof(Val));
313 return Val;
314}
315
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200316#if __has_builtin(__builtin_bitreverse8)
317template<>
318inline uint8_t reverseBits<uint8_t>(uint8_t Val) {
319 return __builtin_bitreverse8(Val);
320}
321#endif
322
323#if __has_builtin(__builtin_bitreverse16)
324template<>
325inline uint16_t reverseBits<uint16_t>(uint16_t Val) {
326 return __builtin_bitreverse16(Val);
327}
328#endif
329
330#if __has_builtin(__builtin_bitreverse32)
331template<>
332inline uint32_t reverseBits<uint32_t>(uint32_t Val) {
333 return __builtin_bitreverse32(Val);
334}
335#endif
336
337#if __has_builtin(__builtin_bitreverse64)
338template<>
339inline uint64_t reverseBits<uint64_t>(uint64_t Val) {
340 return __builtin_bitreverse64(Val);
341}
342#endif
343
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100344// NOTE: The following support functions use the _32/_64 extensions instead of
345// type overloading so that signed and unsigned integers can be used without
346// ambiguity.
347
348/// Return the high 32 bits of a 64 bit value.
349constexpr inline uint32_t Hi_32(uint64_t Value) {
350 return static_cast<uint32_t>(Value >> 32);
351}
352
353/// Return the low 32 bits of a 64 bit value.
354constexpr inline uint32_t Lo_32(uint64_t Value) {
355 return static_cast<uint32_t>(Value);
356}
357
358/// Make a 64-bit integer from a high / low pair of 32-bit integers.
359constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
360 return ((uint64_t)High << 32) | (uint64_t)Low;
361}
362
363/// Checks if an integer fits into the given bit width.
364template <unsigned N> constexpr inline bool isInt(int64_t x) {
365 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
366}
367// Template specializations to get better code for common cases.
368template <> constexpr inline bool isInt<8>(int64_t x) {
369 return static_cast<int8_t>(x) == x;
370}
371template <> constexpr inline bool isInt<16>(int64_t x) {
372 return static_cast<int16_t>(x) == x;
373}
374template <> constexpr inline bool isInt<32>(int64_t x) {
375 return static_cast<int32_t>(x) == x;
376}
377
378/// Checks if a signed integer is an N bit number shifted left by S.
379template <unsigned N, unsigned S>
380constexpr inline bool isShiftedInt(int64_t x) {
381 static_assert(
382 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
383 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
384 return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
385}
386
387/// Checks if an unsigned integer fits into the given bit width.
388///
389/// This is written as two functions rather than as simply
390///
391/// return N >= 64 || X < (UINT64_C(1) << N);
392///
393/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
394/// left too many places.
395template <unsigned N>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200396constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100397 static_assert(N > 0, "isUInt<0> doesn't make sense");
398 return X < (UINT64_C(1) << (N));
399}
400template <unsigned N>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200401constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t X) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100402 return true;
403}
404
405// Template specializations to get better code for common cases.
406template <> constexpr inline bool isUInt<8>(uint64_t x) {
407 return static_cast<uint8_t>(x) == x;
408}
409template <> constexpr inline bool isUInt<16>(uint64_t x) {
410 return static_cast<uint16_t>(x) == x;
411}
412template <> constexpr inline bool isUInt<32>(uint64_t x) {
413 return static_cast<uint32_t>(x) == x;
414}
415
416/// Checks if a unsigned integer is an N bit number shifted left by S.
417template <unsigned N, unsigned S>
418constexpr inline bool isShiftedUInt(uint64_t x) {
419 static_assert(
420 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
421 static_assert(N + S <= 64,
422 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
423 // Per the two static_asserts above, S must be strictly less than 64. So
424 // 1 << S is not undefined behavior.
425 return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
426}
427
428/// Gets the maximum value for a N-bit unsigned integer.
429inline uint64_t maxUIntN(uint64_t N) {
430 assert(N > 0 && N <= 64 && "integer width out of range");
431
432 // uint64_t(1) << 64 is undefined behavior, so we can't do
433 // (uint64_t(1) << N) - 1
434 // without checking first that N != 64. But this works and doesn't have a
435 // branch.
436 return UINT64_MAX >> (64 - N);
437}
438
439/// Gets the minimum value for a N-bit signed integer.
440inline int64_t minIntN(int64_t N) {
441 assert(N > 0 && N <= 64 && "integer width out of range");
442
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200443 return UINT64_C(1) + ~(UINT64_C(1) << (N - 1));
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100444}
445
446/// Gets the maximum value for a N-bit signed integer.
447inline int64_t maxIntN(int64_t N) {
448 assert(N > 0 && N <= 64 && "integer width out of range");
449
450 // This relies on two's complement wraparound when N == 64, so we convert to
451 // int64_t only at the very end to avoid UB.
452 return (UINT64_C(1) << (N - 1)) - 1;
453}
454
455/// Checks if an unsigned integer fits into the given (dynamic) bit width.
456inline bool isUIntN(unsigned N, uint64_t x) {
457 return N >= 64 || x <= maxUIntN(N);
458}
459
460/// Checks if an signed integer fits into the given (dynamic) bit width.
461inline bool isIntN(unsigned N, int64_t x) {
462 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
463}
464
465/// Return true if the argument is a non-empty sequence of ones starting at the
466/// least significant bit with the remainder zero (32 bit version).
467/// Ex. isMask_32(0x0000FFFFU) == true.
468constexpr inline bool isMask_32(uint32_t Value) {
469 return Value && ((Value + 1) & Value) == 0;
470}
471
472/// Return true if the argument is a non-empty sequence of ones starting at the
473/// least significant bit with the remainder zero (64 bit version).
474constexpr inline bool isMask_64(uint64_t Value) {
475 return Value && ((Value + 1) & Value) == 0;
476}
477
478/// Return true if the argument contains a non-empty sequence of ones with the
479/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
480constexpr inline bool isShiftedMask_32(uint32_t Value) {
481 return Value && isMask_32((Value - 1) | Value);
482}
483
484/// Return true if the argument contains a non-empty sequence of ones with the
485/// remainder zero (64 bit version.)
486constexpr inline bool isShiftedMask_64(uint64_t Value) {
487 return Value && isMask_64((Value - 1) | Value);
488}
489
490/// Return true if the argument is a power of two > 0.
491/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
492constexpr inline bool isPowerOf2_32(uint32_t Value) {
493 return Value && !(Value & (Value - 1));
494}
495
496/// Return true if the argument is a power of two > 0 (64 bit edition.)
497constexpr inline bool isPowerOf2_64(uint64_t Value) {
498 return Value && !(Value & (Value - 1));
499}
500
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100501/// Count the number of ones from the most significant bit to the first
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100502/// zero bit.
503///
504/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
505/// Only unsigned integral types are allowed.
506///
507/// \param ZB the behavior on an input of all ones. Only ZB_Width and
508/// ZB_Undefined are valid arguments.
509template <typename T>
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100510unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100511 static_assert(std::numeric_limits<T>::is_integer &&
512 !std::numeric_limits<T>::is_signed,
513 "Only unsigned integral types are allowed.");
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100514 return countLeadingZeros<T>(~Value, ZB);
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100515}
516
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100517/// Count the number of ones from the least significant bit to the first
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100518/// zero bit.
519///
520/// Ex. countTrailingOnes(0x00FF00FF) == 8.
521/// Only unsigned integral types are allowed.
522///
523/// \param ZB the behavior on an input of all ones. Only ZB_Width and
524/// ZB_Undefined are valid arguments.
525template <typename T>
Andrew Walbran3d2c1972020-04-07 12:24:26 +0100526unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100527 static_assert(std::numeric_limits<T>::is_integer &&
528 !std::numeric_limits<T>::is_signed,
529 "Only unsigned integral types are allowed.");
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100530 return countTrailingZeros<T>(~Value, ZB);
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100531}
532
533namespace detail {
534template <typename T, std::size_t SizeOfT> struct PopulationCounter {
535 static unsigned count(T Value) {
536 // Generic version, forward to 32 bits.
537 static_assert(SizeOfT <= 4, "Not implemented!");
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200538#if defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100539 return __builtin_popcount(Value);
540#else
541 uint32_t v = Value;
542 v = v - ((v >> 1) & 0x55555555);
543 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
544 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
545#endif
546 }
547};
548
549template <typename T> struct PopulationCounter<T, 8> {
550 static unsigned count(T Value) {
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200551#if defined(__GNUC__)
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100552 return __builtin_popcountll(Value);
553#else
554 uint64_t v = Value;
555 v = v - ((v >> 1) & 0x5555555555555555ULL);
556 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
557 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
558 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
559#endif
560 }
561};
562} // namespace detail
563
Andrew Scullcdfcccc2018-10-05 20:58:37 +0100564/// Count the number of set bits in a value.
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100565/// Ex. countPopulation(0xF000F000) = 8
566/// Returns 0 if the word is zero.
567template <typename T>
568inline unsigned countPopulation(T Value) {
569 static_assert(std::numeric_limits<T>::is_integer &&
570 !std::numeric_limits<T>::is_signed,
571 "Only unsigned integral types are allowed.");
572 return detail::PopulationCounter<T, sizeof(T)>::count(Value);
573}
574
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200575/// Compile time Log2.
576/// Valid only for positive powers of two.
577template <size_t kValue> constexpr inline size_t CTLog2() {
578 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
579 "Value is not a valid power of 2");
580 return 1 + CTLog2<kValue / 2>();
581}
582
583template <> constexpr inline size_t CTLog2<1>() { return 0; }
584
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100585/// Return the log base 2 of the specified value.
586inline double Log2(double Value) {
587#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
588 return __builtin_log(Value) / __builtin_log(2.0);
589#else
590 return log2(Value);
591#endif
592}
593
594/// Return the floor log base 2 of the specified value, -1 if the value is zero.
595/// (32 bit edition.)
596/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
597inline unsigned Log2_32(uint32_t Value) {
598 return 31 - countLeadingZeros(Value);
599}
600
601/// Return the floor log base 2 of the specified value, -1 if the value is zero.
602/// (64 bit edition.)
603inline unsigned Log2_64(uint64_t Value) {
604 return 63 - countLeadingZeros(Value);
605}
606
607/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
608/// (32 bit edition).
609/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
610inline unsigned Log2_32_Ceil(uint32_t Value) {
611 return 32 - countLeadingZeros(Value - 1);
612}
613
614/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
615/// (64 bit edition.)
616inline unsigned Log2_64_Ceil(uint64_t Value) {
617 return 64 - countLeadingZeros(Value - 1);
618}
619
620/// Return the greatest common divisor of the values using Euclid's algorithm.
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200621template <typename T>
622inline T greatestCommonDivisor(T A, T B) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100623 while (B) {
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200624 T Tmp = B;
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100625 B = A % B;
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200626 A = Tmp;
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100627 }
628 return A;
629}
630
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200631inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
632 return greatestCommonDivisor<uint64_t>(A, B);
633}
634
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100635/// This function takes a 64-bit integer and returns the bit equivalent double.
636inline double BitsToDouble(uint64_t Bits) {
637 double D;
638 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
639 memcpy(&D, &Bits, sizeof(Bits));
640 return D;
641}
642
643/// This function takes a 32-bit integer and returns the bit equivalent float.
644inline float BitsToFloat(uint32_t Bits) {
645 float F;
646 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
647 memcpy(&F, &Bits, sizeof(Bits));
648 return F;
649}
650
651/// This function takes a double and returns the bit equivalent 64-bit integer.
652/// Note that copying doubles around changes the bits of NaNs on some hosts,
653/// notably x86, so this routine cannot be used if these bits are needed.
654inline uint64_t DoubleToBits(double Double) {
655 uint64_t Bits;
656 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
657 memcpy(&Bits, &Double, sizeof(Double));
658 return Bits;
659}
660
661/// This function takes a float and returns the bit equivalent 32-bit integer.
662/// Note that copying floats around changes the bits of NaNs on some hosts,
663/// notably x86, so this routine cannot be used if these bits are needed.
664inline uint32_t FloatToBits(float Float) {
665 uint32_t Bits;
666 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
667 memcpy(&Bits, &Float, sizeof(Float));
668 return Bits;
669}
670
671/// A and B are either alignments or offsets. Return the minimum alignment that
672/// may be assumed after adding the two together.
673constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
674 // The largest power of 2 that divides both A and B.
675 //
676 // Replace "-Value" by "1+~Value" in the following commented code to avoid
677 // MSVC warning C4146
678 // return (A | B) & -(A | B);
679 return (A | B) & (1 + ~(A | B));
680}
681
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100682/// Returns the next power of two (in 64-bits) that is strictly greater than A.
683/// Returns zero on overflow.
684inline uint64_t NextPowerOf2(uint64_t A) {
685 A |= (A >> 1);
686 A |= (A >> 2);
687 A |= (A >> 4);
688 A |= (A >> 8);
689 A |= (A >> 16);
690 A |= (A >> 32);
691 return A + 1;
692}
693
694/// Returns the power of two which is less than or equal to the given value.
695/// Essentially, it is a floor operation across the domain of powers of two.
696inline uint64_t PowerOf2Floor(uint64_t A) {
697 if (!A) return 0;
698 return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
699}
700
701/// Returns the power of two which is greater than or equal to the given value.
702/// Essentially, it is a ceil operation across the domain of powers of two.
703inline uint64_t PowerOf2Ceil(uint64_t A) {
704 if (!A)
705 return 0;
706 return NextPowerOf2(A - 1);
707}
708
709/// Returns the next integer (mod 2**64) that is greater than or equal to
710/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
711///
712/// If non-zero \p Skew is specified, the return value will be a minimal
713/// integer that is greater than or equal to \p Value and equal to
714/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
715/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
716///
717/// Examples:
718/// \code
719/// alignTo(5, 8) = 8
720/// alignTo(17, 8) = 24
721/// alignTo(~0LL, 8) = 0
722/// alignTo(321, 255) = 510
723///
724/// alignTo(5, 8, 7) = 7
725/// alignTo(17, 8, 1) = 17
726/// alignTo(~0LL, 8, 3) = 3
727/// alignTo(321, 255, 42) = 552
728/// \endcode
729inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
730 assert(Align != 0u && "Align can't be 0.");
731 Skew %= Align;
732 return (Value + Align - 1 - Skew) / Align * Align + Skew;
733}
734
735/// Returns the next integer (mod 2**64) that is greater than or equal to
736/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
737template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
738 static_assert(Align != 0u, "Align must be non-zero");
739 return (Value + Align - 1) / Align * Align;
740}
741
742/// Returns the integer ceil(Numerator / Denominator).
743inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
744 return alignTo(Numerator, Denominator) / Denominator;
745}
746
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200747/// Returns the integer nearest(Numerator / Denominator).
748inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
749 return (Numerator + (Denominator / 2)) / Denominator;
750}
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100751
752/// Returns the largest uint64_t less than or equal to \p Value and is
753/// \p Skew mod \p Align. \p Align must be non-zero
754inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
755 assert(Align != 0u && "Align can't be 0.");
756 Skew %= Align;
757 return (Value - Skew) / Align * Align + Skew;
758}
759
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100760/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
761/// Requires 0 < B <= 32.
762template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
763 static_assert(B > 0, "Bit width can't be 0.");
764 static_assert(B <= 32, "Bit width out of range.");
765 return int32_t(X << (32 - B)) >> (32 - B);
766}
767
768/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
769/// Requires 0 < B < 32.
770inline int32_t SignExtend32(uint32_t X, unsigned B) {
771 assert(B > 0 && "Bit width can't be 0.");
772 assert(B <= 32 && "Bit width out of range.");
773 return int32_t(X << (32 - B)) >> (32 - B);
774}
775
776/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
777/// Requires 0 < B < 64.
778template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
779 static_assert(B > 0, "Bit width can't be 0.");
780 static_assert(B <= 64, "Bit width out of range.");
781 return int64_t(x << (64 - B)) >> (64 - B);
782}
783
784/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
785/// Requires 0 < B < 64.
786inline int64_t SignExtend64(uint64_t X, unsigned B) {
787 assert(B > 0 && "Bit width can't be 0.");
788 assert(B <= 64 && "Bit width out of range.");
789 return int64_t(X << (64 - B)) >> (64 - B);
790}
791
792/// Subtract two unsigned integers, X and Y, of type T and return the absolute
793/// value of the result.
794template <typename T>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200795std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100796 return std::max(X, Y) - std::min(X, Y);
797}
798
799/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
800/// maximum representable value of T on overflow. ResultOverflowed indicates if
801/// the result is larger than the maximum representable value of type T.
802template <typename T>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200803std::enable_if_t<std::is_unsigned<T>::value, T>
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100804SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
805 bool Dummy;
806 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
807 // Hacker's Delight, p. 29
808 T Z = X + Y;
809 Overflowed = (Z < X || Z < Y);
810 if (Overflowed)
811 return std::numeric_limits<T>::max();
812 else
813 return Z;
814}
815
816/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
817/// maximum representable value of T on overflow. ResultOverflowed indicates if
818/// the result is larger than the maximum representable value of type T.
819template <typename T>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200820std::enable_if_t<std::is_unsigned<T>::value, T>
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100821SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
822 bool Dummy;
823 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
824
825 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
826 // because it fails for uint16_t (where multiplication can have undefined
827 // behavior due to promotion to int), and requires a division in addition
828 // to the multiplication.
829
830 Overflowed = false;
831
832 // Log2(Z) would be either Log2Z or Log2Z + 1.
833 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
834 // will necessarily be less than Log2Max as desired.
835 int Log2Z = Log2_64(X) + Log2_64(Y);
836 const T Max = std::numeric_limits<T>::max();
837 int Log2Max = Log2_64(Max);
838 if (Log2Z < Log2Max) {
839 return X * Y;
840 }
841 if (Log2Z > Log2Max) {
842 Overflowed = true;
843 return Max;
844 }
845
846 // We're going to use the top bit, and maybe overflow one
847 // bit past it. Multiply all but the bottom bit then add
848 // that on at the end.
849 T Z = (X >> 1) * Y;
850 if (Z & ~(Max >> 1)) {
851 Overflowed = true;
852 return Max;
853 }
854 Z <<= 1;
855 if (X & 1)
856 return SaturatingAdd(Z, Y, ResultOverflowed);
857
858 return Z;
859}
860
861/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
862/// the product. Clamp the result to the maximum representable value of T on
863/// overflow. ResultOverflowed indicates if the result is larger than the
864/// maximum representable value of type T.
865template <typename T>
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200866std::enable_if_t<std::is_unsigned<T>::value, T>
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100867SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
868 bool Dummy;
869 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
870
871 T Product = SaturatingMultiply(X, Y, &Overflowed);
872 if (Overflowed)
873 return Product;
874
875 return SaturatingAdd(A, Product, &Overflowed);
876}
877
878/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
879extern const float huge_valf;
Olivier Deprezf4ef2d02021-04-20 13:36:24 +0200880
881
882/// Add two signed integers, computing the two's complement truncated result,
883/// returning true if overflow occured.
884template <typename T>
885std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
886#if __has_builtin(__builtin_add_overflow)
887 return __builtin_add_overflow(X, Y, &Result);
888#else
889 // Perform the unsigned addition.
890 using U = std::make_unsigned_t<T>;
891 const U UX = static_cast<U>(X);
892 const U UY = static_cast<U>(Y);
893 const U UResult = UX + UY;
894
895 // Convert to signed.
896 Result = static_cast<T>(UResult);
897
898 // Adding two positive numbers should result in a positive number.
899 if (X > 0 && Y > 0)
900 return Result <= 0;
901 // Adding two negatives should result in a negative number.
902 if (X < 0 && Y < 0)
903 return Result >= 0;
904 return false;
905#endif
906}
907
908/// Subtract two signed integers, computing the two's complement truncated
909/// result, returning true if an overflow ocurred.
910template <typename T>
911std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
912#if __has_builtin(__builtin_sub_overflow)
913 return __builtin_sub_overflow(X, Y, &Result);
914#else
915 // Perform the unsigned addition.
916 using U = std::make_unsigned_t<T>;
917 const U UX = static_cast<U>(X);
918 const U UY = static_cast<U>(Y);
919 const U UResult = UX - UY;
920
921 // Convert to signed.
922 Result = static_cast<T>(UResult);
923
924 // Subtracting a positive number from a negative results in a negative number.
925 if (X <= 0 && Y > 0)
926 return Result >= 0;
927 // Subtracting a negative number from a positive results in a positive number.
928 if (X >= 0 && Y < 0)
929 return Result <= 0;
930 return false;
931#endif
932}
933
934/// Multiply two signed integers, computing the two's complement truncated
935/// result, returning true if an overflow ocurred.
936template <typename T>
937std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
938 // Perform the unsigned multiplication on absolute values.
939 using U = std::make_unsigned_t<T>;
940 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
941 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
942 const U UResult = UX * UY;
943
944 // Convert to signed.
945 const bool IsNegative = (X < 0) ^ (Y < 0);
946 Result = IsNegative ? (0 - UResult) : UResult;
947
948 // If any of the args was 0, result is 0 and no overflow occurs.
949 if (UX == 0 || UY == 0)
950 return false;
951
952 // UX and UY are in [1, 2^n], where n is the number of digits.
953 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
954 // positive) divided by an argument compares to the other.
955 if (IsNegative)
956 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
957 else
958 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
959}
960
Andrew Scull5e1ddfa2018-08-14 10:06:54 +0100961} // End llvm namespace
962
963#endif