Bug Summary

File:llvm/lib/Target/Mips/MipsAnalyzeImmediate.cpp
Warning:line 47, column 20
The result of the right shift is undefined due to shifting by '64', which is greater or equal to the width of type 'uint64_t'

Annotated Source Code

Press '?' to see keyboard shortcuts

clang -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name MipsAnalyzeImmediate.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -mthread-model posix -mframe-pointer=none -fmath-errno -fno-rounding-math -masm-verbose -mconstructor-aliases -munwind-tables -target-cpu x86-64 -dwarf-column-info -fno-split-dwarf-inlining -debugger-tuning=gdb -ffunction-sections -fdata-sections -resource-dir /usr/lib/llvm-11/lib/clang/11.0.0 -D _DEBUG -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/build-llvm/lib/Target/Mips -I /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/lib/Target/Mips -I /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/build-llvm/include -I /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include -U NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/x86_64-linux-gnu/c++/6.3.0 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/6.3.0/../../../../include/c++/6.3.0/backward -internal-isystem /usr/local/include -internal-isystem /usr/lib/llvm-11/lib/clang/11.0.0/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-maybe-uninitialized -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/build-llvm/lib/Target/Mips -fdebug-prefix-map=/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347=. -ferror-limit 19 -fmessage-length 0 -fvisibility hidden -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -fobjc-runtime=gcc -fdiagnostics-show-option -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -o /tmp/scan-build-2020-03-09-184146-41876-1 -x c++ /build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/lib/Target/Mips/MipsAnalyzeImmediate.cpp

/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/lib/Target/Mips/MipsAnalyzeImmediate.cpp

1//===- MipsAnalyzeImmediate.cpp - Analyze Immediates ----------------------===//
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#include "MipsAnalyzeImmediate.h"
10#include "Mips.h"
11#include "llvm/Support/MathExtras.h"
12#include <cassert>
13#include <cstdint>
14#include <iterator>
15
16using namespace llvm;
17
18MipsAnalyzeImmediate::Inst::Inst(unsigned O, unsigned I) : Opc(O), ImmOpnd(I) {}
19
20// Add I to the instruction sequences.
21void MipsAnalyzeImmediate::AddInstr(InstSeqLs &SeqLs, const Inst &I) {
22 // Add an instruction seqeunce consisting of just I.
23 if (SeqLs.empty()) {
24 SeqLs.push_back(InstSeq(1, I));
25 return;
26 }
27
28 for (InstSeqLs::iterator Iter = SeqLs.begin(); Iter != SeqLs.end(); ++Iter)
29 Iter->push_back(I);
30}
31
32void MipsAnalyzeImmediate::GetInstSeqLsADDiu(uint64_t Imm, unsigned RemSize,
33 InstSeqLs &SeqLs) {
34 GetInstSeqLs((Imm + 0x8000ULL) & 0xffffffffffff0000ULL, RemSize, SeqLs);
7
Calling 'MipsAnalyzeImmediate::GetInstSeqLs'
35 AddInstr(SeqLs, Inst(ADDiu, Imm & 0xffffULL));
36}
37
38void MipsAnalyzeImmediate::GetInstSeqLsORi(uint64_t Imm, unsigned RemSize,
39 InstSeqLs &SeqLs) {
40 GetInstSeqLs(Imm & 0xffffffffffff0000ULL, RemSize, SeqLs);
41 AddInstr(SeqLs, Inst(ORi, Imm & 0xffffULL));
42}
43
44void MipsAnalyzeImmediate::GetInstSeqLsSLL(uint64_t Imm, unsigned RemSize,
45 InstSeqLs &SeqLs) {
46 unsigned Shamt = countTrailingZeros(Imm);
14
Calling 'countTrailingZeros<unsigned long>'
21
Returning from 'countTrailingZeros<unsigned long>'
22
'Shamt' initialized to 64
47 GetInstSeqLs(Imm >> Shamt, RemSize - Shamt, SeqLs);
23
The result of the right shift is undefined due to shifting by '64', which is greater or equal to the width of type 'uint64_t'
48 AddInstr(SeqLs, Inst(SLL, Shamt));
49}
50
51void MipsAnalyzeImmediate::GetInstSeqLs(uint64_t Imm, unsigned RemSize,
52 InstSeqLs &SeqLs) {
53 uint64_t MaskedImm = Imm & (0xffffffffffffffffULL >> (64 - Size));
54
55 // Do nothing if Imm is 0.
56 if (!MaskedImm)
8
Assuming 'MaskedImm' is not equal to 0
9
Taking false branch
57 return;
58
59 // A single ADDiu will do if RemSize <= 16.
60 if (RemSize
9.1
'RemSize' is > 16
9.1
'RemSize' is > 16
<= 16) {
10
Taking false branch
61 AddInstr(SeqLs, Inst(ADDiu, MaskedImm));
62 return;
63 }
64
65 // Shift if the lower 16-bit is cleared.
66 if (!(Imm & 0xffff)) {
11
Assuming the condition is true
12
Taking true branch
67 GetInstSeqLsSLL(Imm, RemSize, SeqLs);
13
Calling 'MipsAnalyzeImmediate::GetInstSeqLsSLL'
68 return;
69 }
70
71 GetInstSeqLsADDiu(Imm, RemSize, SeqLs);
72
73 // If bit 15 is cleared, it doesn't make a difference whether the last
74 // instruction is an ADDiu or ORi. In that case, do not call GetInstSeqLsORi.
75 if (Imm & 0x8000) {
76 InstSeqLs SeqLsORi;
77 GetInstSeqLsORi(Imm, RemSize, SeqLsORi);
78 SeqLs.append(std::make_move_iterator(SeqLsORi.begin()),
79 std::make_move_iterator(SeqLsORi.end()));
80 }
81}
82
83// Replace a ADDiu & SLL pair with a LUi.
84// e.g. the following two instructions
85// ADDiu 0x0111
86// SLL 18
87// are replaced with
88// LUi 0x444
89void MipsAnalyzeImmediate::ReplaceADDiuSLLWithLUi(InstSeq &Seq) {
90 // Check if the first two instructions are ADDiu and SLL and the shift amount
91 // is at least 16.
92 if ((Seq.size() < 2) || (Seq[0].Opc != ADDiu) ||
93 (Seq[1].Opc != SLL) || (Seq[1].ImmOpnd < 16))
94 return;
95
96 // Sign-extend and shift operand of ADDiu and see if it still fits in 16-bit.
97 int64_t Imm = SignExtend64<16>(Seq[0].ImmOpnd);
98 int64_t ShiftedImm = (uint64_t)Imm << (Seq[1].ImmOpnd - 16);
99
100 if (!isInt<16>(ShiftedImm))
101 return;
102
103 // Replace the first instruction and erase the second.
104 Seq[0].Opc = LUi;
105 Seq[0].ImmOpnd = (unsigned)(ShiftedImm & 0xffff);
106 Seq.erase(Seq.begin() + 1);
107}
108
109void MipsAnalyzeImmediate::GetShortestSeq(InstSeqLs &SeqLs, InstSeq &Insts) {
110 InstSeqLs::iterator ShortestSeq = SeqLs.end();
111 // The length of an instruction sequence is at most 7.
112 unsigned ShortestLength = 8;
113
114 for (InstSeqLs::iterator S = SeqLs.begin(); S != SeqLs.end(); ++S) {
115 ReplaceADDiuSLLWithLUi(*S);
116 assert(S->size() <= 7)((S->size() <= 7) ? static_cast<void> (0) : __assert_fail
("S->size() <= 7", "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/lib/Target/Mips/MipsAnalyzeImmediate.cpp"
, 116, __PRETTY_FUNCTION__))
;
117
118 if (S->size() < ShortestLength) {
119 ShortestSeq = S;
120 ShortestLength = S->size();
121 }
122 }
123
124 Insts.clear();
125 Insts.append(ShortestSeq->begin(), ShortestSeq->end());
126}
127
128const MipsAnalyzeImmediate::InstSeq
129&MipsAnalyzeImmediate::Analyze(uint64_t Imm, unsigned Size,
130 bool LastInstrIsADDiu) {
131 this->Size = Size;
132
133 if (Size == 32) {
1
Assuming 'Size' is equal to 32
2
Taking true branch
134 ADDiu = Mips::ADDiu;
135 ORi = Mips::ORi;
136 SLL = Mips::SLL;
137 LUi = Mips::LUi;
138 } else {
139 ADDiu = Mips::DADDiu;
140 ORi = Mips::ORi64;
141 SLL = Mips::DSLL;
142 LUi = Mips::LUi64;
143 }
144
145 InstSeqLs SeqLs;
146
147 // Get the list of instruction sequences.
148 if (LastInstrIsADDiu | !Imm)
3
Assuming 'Imm' is not equal to 0
4
Assuming the condition is true
5
Taking true branch
149 GetInstSeqLsADDiu(Imm, Size, SeqLs);
6
Calling 'MipsAnalyzeImmediate::GetInstSeqLsADDiu'
150 else
151 GetInstSeqLs(Imm, Size, SeqLs);
152
153 // Set Insts to the shortest instruction sequence.
154 GetShortestSeq(SeqLs, Insts);
155
156 return Insts;
157}

/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h

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/Support/Compiler.h"
17#include <algorithm>
18#include <cassert>
19#include <climits>
20#include <cmath>
21#include <cstdint>
22#include <cstring>
23#include <limits>
24#include <type_traits>
25
26#ifdef __ANDROID_NDK__
27#include <android/api-level.h>
28#endif
29
30#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
42namespace llvm {
43
44/// The behavior an operation has on an input of 0.
45enum ZeroBehavior {
46 /// The returned value is undefined.
47 ZB_Undefined,
48 /// The returned value is numeric_limits<T>::max()
49 ZB_Max,
50 /// The returned value is numeric_limits<T>::digits
51 ZB_Width
52};
53
54/// 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
90namespace detail {
91template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
92 static unsigned count(T Val, ZeroBehavior) {
93 if (!Val)
94 return std::numeric_limits<T>::digits;
95 if (Val & 0x1)
96 return 0;
97
98 // Bisection method.
99 unsigned ZeroBits = 0;
100 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
114#if defined(__GNUC__4) || defined(_MSC_VER)
115template <typename T> struct TrailingZerosCounter<T, 4> {
116 static unsigned count(T Val, ZeroBehavior ZB) {
117 if (ZB != ZB_Undefined && Val == 0)
118 return 32;
119
120#if __has_builtin(__builtin_ctz)1 || defined(__GNUC__4)
121 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> {
132 static unsigned count(T Val, ZeroBehavior ZB) {
133 if (ZB
15.1
'ZB' is not equal to ZB_Undefined
15.1
'ZB' is not equal to ZB_Undefined
!= ZB_Undefined && Val == 0)
16
Assuming 'Val' is equal to 0
17
Taking true branch
134 return 64;
18
Returning the value 64
135
136#if __has_builtin(__builtin_ctzll)1 || defined(__GNUC__4)
137 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
149/// Count number of 0's from the least significant bit to the most
150/// 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>
157unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
158 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);
15
Calling 'TrailingZerosCounter::count'
19
Returning from 'TrailingZerosCounter::count'
20
Returning the value 64
162}
163
164namespace detail {
165template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
166 static unsigned count(T Val, ZeroBehavior) {
167 if (!Val)
168 return std::numeric_limits<T>::digits;
169
170 // Bisection method.
171 unsigned ZeroBits = 0;
172 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
183#if defined(__GNUC__4) || defined(_MSC_VER)
184template <typename T> struct LeadingZerosCounter<T, 4> {
185 static unsigned count(T Val, ZeroBehavior ZB) {
186 if (ZB != ZB_Undefined && Val == 0)
187 return 32;
188
189#if __has_builtin(__builtin_clz)1 || defined(__GNUC__4)
190 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> {
201 static unsigned count(T Val, ZeroBehavior ZB) {
202 if (ZB != ZB_Undefined && Val == 0)
203 return 64;
204
205#if __has_builtin(__builtin_clzll)1 || defined(__GNUC__4)
206 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
218/// Count number of 0's from the most significant bit to the least
219/// 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>
226unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
227 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
233/// Get the index of the first set bit starting from the least
234/// 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
247/// Create a bitmask with the N right-most bits set to 1, and all other
248/// 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_BIT8 * sizeof(T);
252 assert(N <= Bits && "Invalid bit index")((N <= Bits && "Invalid bit index") ? static_cast<
void> (0) : __assert_fail ("N <= Bits && \"Invalid bit index\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 252, __PRETTY_FUNCTION__))
;
253 return N == 0 ? 0 : (T(-1) >> (Bits - N));
254}
255
256/// Create a bitmask with the N left-most bits set to 1, and all other
257/// bits set to 0. Only unsigned types are allowed.
258template <typename T> T maskLeadingOnes(unsigned N) {
259 return ~maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
260}
261
262/// Create a bitmask with the N right-most bits set to 0, and all other
263/// bits set to 1. Only unsigned types are allowed.
264template <typename T> T maskTrailingZeros(unsigned N) {
265 return maskLeadingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
266}
267
268/// Create a bitmask with the N left-most bits set to 0, and all other
269/// bits set to 1. Only unsigned types are allowed.
270template <typename T> T maskLeadingZeros(unsigned N) {
271 return maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
272}
273
274/// Get the index of the last set bit starting from the least
275/// 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
291/// Macro compressed bit reversal table for 256 bits.
292///
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
304/// Reverse the bits in \p Val.
305template <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
316// NOTE: The following support functions use the _32/_64 extensions instead of
317// type overloading so that signed and unsigned integers can be used without
318// ambiguity.
319
320/// Return the high 32 bits of a 64 bit value.
321constexpr inline uint32_t Hi_32(uint64_t Value) {
322 return static_cast<uint32_t>(Value >> 32);
323}
324
325/// Return the low 32 bits of a 64 bit value.
326constexpr inline uint32_t Lo_32(uint64_t Value) {
327 return static_cast<uint32_t>(Value);
328}
329
330/// Make a 64-bit integer from a high / low pair of 32-bit integers.
331constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
332 return ((uint64_t)High << 32) | (uint64_t)Low;
333}
334
335/// Checks if an integer fits into the given bit width.
336template <unsigned N> constexpr inline bool isInt(int64_t x) {
337 return N >= 64 || (-(INT64_C(1)1L<<(N-1)) <= x && x < (INT64_C(1)1L<<(N-1)));
338}
339// Template specializations to get better code for common cases.
340template <> constexpr inline bool isInt<8>(int64_t x) {
341 return static_cast<int8_t>(x) == x;
342}
343template <> constexpr inline bool isInt<16>(int64_t x) {
344 return static_cast<int16_t>(x) == x;
345}
346template <> constexpr inline bool isInt<32>(int64_t x) {
347 return static_cast<int32_t>(x) == x;
348}
349
350/// Checks if a signed integer is an N bit number shifted left by S.
351template <unsigned N, unsigned S>
352constexpr inline bool isShiftedInt(int64_t x) {
353 static_assert(
354 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
355 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
356 return isInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
357}
358
359/// Checks if an unsigned integer fits into the given bit width.
360///
361/// This is written as two functions rather than as simply
362///
363/// return N >= 64 || X < (UINT64_C(1) << N);
364///
365/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
366/// left too many places.
367template <unsigned N>
368constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) {
369 static_assert(N > 0, "isUInt<0> doesn't make sense");
370 return X < (UINT64_C(1)1UL << (N));
371}
372template <unsigned N>
373constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t X) {
374 return true;
375}
376
377// Template specializations to get better code for common cases.
378template <> constexpr inline bool isUInt<8>(uint64_t x) {
379 return static_cast<uint8_t>(x) == x;
380}
381template <> constexpr inline bool isUInt<16>(uint64_t x) {
382 return static_cast<uint16_t>(x) == x;
383}
384template <> constexpr inline bool isUInt<32>(uint64_t x) {
385 return static_cast<uint32_t>(x) == x;
386}
387
388/// Checks if a unsigned integer is an N bit number shifted left by S.
389template <unsigned N, unsigned S>
390constexpr inline bool isShiftedUInt(uint64_t x) {
391 static_assert(
392 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
393 static_assert(N + S <= 64,
394 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
395 // Per the two static_asserts above, S must be strictly less than 64. So
396 // 1 << S is not undefined behavior.
397 return isUInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
398}
399
400/// Gets the maximum value for a N-bit unsigned integer.
401inline uint64_t maxUIntN(uint64_t N) {
402 assert(N > 0 && N <= 64 && "integer width out of range")((N > 0 && N <= 64 && "integer width out of range"
) ? static_cast<void> (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 402, __PRETTY_FUNCTION__))
;
403
404 // uint64_t(1) << 64 is undefined behavior, so we can't do
405 // (uint64_t(1) << N) - 1
406 // without checking first that N != 64. But this works and doesn't have a
407 // branch.
408 return UINT64_MAX(18446744073709551615UL) >> (64 - N);
409}
410
411/// Gets the minimum value for a N-bit signed integer.
412inline int64_t minIntN(int64_t N) {
413 assert(N > 0 && N <= 64 && "integer width out of range")((N > 0 && N <= 64 && "integer width out of range"
) ? static_cast<void> (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 413, __PRETTY_FUNCTION__))
;
414
415 return -(UINT64_C(1)1UL<<(N-1));
416}
417
418/// Gets the maximum value for a N-bit signed integer.
419inline int64_t maxIntN(int64_t N) {
420 assert(N > 0 && N <= 64 && "integer width out of range")((N > 0 && N <= 64 && "integer width out of range"
) ? static_cast<void> (0) : __assert_fail ("N > 0 && N <= 64 && \"integer width out of range\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 420, __PRETTY_FUNCTION__))
;
421
422 // This relies on two's complement wraparound when N == 64, so we convert to
423 // int64_t only at the very end to avoid UB.
424 return (UINT64_C(1)1UL << (N - 1)) - 1;
425}
426
427/// Checks if an unsigned integer fits into the given (dynamic) bit width.
428inline bool isUIntN(unsigned N, uint64_t x) {
429 return N >= 64 || x <= maxUIntN(N);
430}
431
432/// Checks if an signed integer fits into the given (dynamic) bit width.
433inline bool isIntN(unsigned N, int64_t x) {
434 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
435}
436
437/// Return true if the argument is a non-empty sequence of ones starting at the
438/// least significant bit with the remainder zero (32 bit version).
439/// Ex. isMask_32(0x0000FFFFU) == true.
440constexpr inline bool isMask_32(uint32_t Value) {
441 return Value && ((Value + 1) & Value) == 0;
442}
443
444/// Return true if the argument is a non-empty sequence of ones starting at the
445/// least significant bit with the remainder zero (64 bit version).
446constexpr inline bool isMask_64(uint64_t Value) {
447 return Value && ((Value + 1) & Value) == 0;
448}
449
450/// Return true if the argument contains a non-empty sequence of ones with the
451/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
452constexpr inline bool isShiftedMask_32(uint32_t Value) {
453 return Value && isMask_32((Value - 1) | Value);
454}
455
456/// Return true if the argument contains a non-empty sequence of ones with the
457/// remainder zero (64 bit version.)
458constexpr inline bool isShiftedMask_64(uint64_t Value) {
459 return Value && isMask_64((Value - 1) | Value);
460}
461
462/// Return true if the argument is a power of two > 0.
463/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
464constexpr inline bool isPowerOf2_32(uint32_t Value) {
465 return Value && !(Value & (Value - 1));
466}
467
468/// Return true if the argument is a power of two > 0 (64 bit edition.)
469constexpr inline bool isPowerOf2_64(uint64_t Value) {
470 return Value && !(Value & (Value - 1));
471}
472
473/// Count the number of ones from the most significant bit to the first
474/// zero bit.
475///
476/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
477/// Only unsigned integral types are allowed.
478///
479/// \param ZB the behavior on an input of all ones. Only ZB_Width and
480/// ZB_Undefined are valid arguments.
481template <typename T>
482unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
483 static_assert(std::numeric_limits<T>::is_integer &&
484 !std::numeric_limits<T>::is_signed,
485 "Only unsigned integral types are allowed.");
486 return countLeadingZeros<T>(~Value, ZB);
487}
488
489/// Count the number of ones from the least significant bit to the first
490/// zero bit.
491///
492/// Ex. countTrailingOnes(0x00FF00FF) == 8.
493/// Only unsigned integral types are allowed.
494///
495/// \param ZB the behavior on an input of all ones. Only ZB_Width and
496/// ZB_Undefined are valid arguments.
497template <typename T>
498unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
499 static_assert(std::numeric_limits<T>::is_integer &&
500 !std::numeric_limits<T>::is_signed,
501 "Only unsigned integral types are allowed.");
502 return countTrailingZeros<T>(~Value, ZB);
503}
504
505namespace detail {
506template <typename T, std::size_t SizeOfT> struct PopulationCounter {
507 static unsigned count(T Value) {
508 // Generic version, forward to 32 bits.
509 static_assert(SizeOfT <= 4, "Not implemented!");
510#if defined(__GNUC__4)
511 return __builtin_popcount(Value);
512#else
513 uint32_t v = Value;
514 v = v - ((v >> 1) & 0x55555555);
515 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
516 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
517#endif
518 }
519};
520
521template <typename T> struct PopulationCounter<T, 8> {
522 static unsigned count(T Value) {
523#if defined(__GNUC__4)
524 return __builtin_popcountll(Value);
525#else
526 uint64_t v = Value;
527 v = v - ((v >> 1) & 0x5555555555555555ULL);
528 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
529 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
530 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
531#endif
532 }
533};
534} // namespace detail
535
536/// Count the number of set bits in a value.
537/// Ex. countPopulation(0xF000F000) = 8
538/// Returns 0 if the word is zero.
539template <typename T>
540inline unsigned countPopulation(T Value) {
541 static_assert(std::numeric_limits<T>::is_integer &&
542 !std::numeric_limits<T>::is_signed,
543 "Only unsigned integral types are allowed.");
544 return detail::PopulationCounter<T, sizeof(T)>::count(Value);
545}
546
547/// Compile time Log2.
548/// Valid only for positive powers of two.
549template <size_t kValue> constexpr inline size_t CTLog2() {
550 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
551 "Value is not a valid power of 2");
552 return 1 + CTLog2<kValue / 2>();
553}
554
555template <> constexpr inline size_t CTLog2<1>() { return 0; }
556
557/// Return the log base 2 of the specified value.
558inline double Log2(double Value) {
559#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
560 return __builtin_log(Value) / __builtin_log(2.0);
561#else
562 return log2(Value);
563#endif
564}
565
566/// Return the floor log base 2 of the specified value, -1 if the value is zero.
567/// (32 bit edition.)
568/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
569inline unsigned Log2_32(uint32_t Value) {
570 return 31 - countLeadingZeros(Value);
571}
572
573/// Return the floor log base 2 of the specified value, -1 if the value is zero.
574/// (64 bit edition.)
575inline unsigned Log2_64(uint64_t Value) {
576 return 63 - countLeadingZeros(Value);
577}
578
579/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
580/// (32 bit edition).
581/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
582inline unsigned Log2_32_Ceil(uint32_t Value) {
583 return 32 - countLeadingZeros(Value - 1);
584}
585
586/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
587/// (64 bit edition.)
588inline unsigned Log2_64_Ceil(uint64_t Value) {
589 return 64 - countLeadingZeros(Value - 1);
590}
591
592/// Return the greatest common divisor of the values using Euclid's algorithm.
593template <typename T>
594inline T greatestCommonDivisor(T A, T B) {
595 while (B) {
596 T Tmp = B;
597 B = A % B;
598 A = Tmp;
599 }
600 return A;
601}
602
603inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
604 return greatestCommonDivisor<uint64_t>(A, B);
605}
606
607/// This function takes a 64-bit integer and returns the bit equivalent double.
608inline double BitsToDouble(uint64_t Bits) {
609 double D;
610 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
611 memcpy(&D, &Bits, sizeof(Bits));
612 return D;
613}
614
615/// This function takes a 32-bit integer and returns the bit equivalent float.
616inline float BitsToFloat(uint32_t Bits) {
617 float F;
618 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
619 memcpy(&F, &Bits, sizeof(Bits));
620 return F;
621}
622
623/// This function takes a double and returns the bit equivalent 64-bit integer.
624/// Note that copying doubles around changes the bits of NaNs on some hosts,
625/// notably x86, so this routine cannot be used if these bits are needed.
626inline uint64_t DoubleToBits(double Double) {
627 uint64_t Bits;
628 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
629 memcpy(&Bits, &Double, sizeof(Double));
630 return Bits;
631}
632
633/// This function takes a float and returns the bit equivalent 32-bit integer.
634/// Note that copying floats around changes the bits of NaNs on some hosts,
635/// notably x86, so this routine cannot be used if these bits are needed.
636inline uint32_t FloatToBits(float Float) {
637 uint32_t Bits;
638 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
639 memcpy(&Bits, &Float, sizeof(Float));
640 return Bits;
641}
642
643/// A and B are either alignments or offsets. Return the minimum alignment that
644/// may be assumed after adding the two together.
645constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
646 // The largest power of 2 that divides both A and B.
647 //
648 // Replace "-Value" by "1+~Value" in the following commented code to avoid
649 // MSVC warning C4146
650 // return (A | B) & -(A | B);
651 return (A | B) & (1 + ~(A | B));
652}
653
654/// Returns the next power of two (in 64-bits) that is strictly greater than A.
655/// Returns zero on overflow.
656inline uint64_t NextPowerOf2(uint64_t A) {
657 A |= (A >> 1);
658 A |= (A >> 2);
659 A |= (A >> 4);
660 A |= (A >> 8);
661 A |= (A >> 16);
662 A |= (A >> 32);
663 return A + 1;
664}
665
666/// Returns the power of two which is less than or equal to the given value.
667/// Essentially, it is a floor operation across the domain of powers of two.
668inline uint64_t PowerOf2Floor(uint64_t A) {
669 if (!A) return 0;
670 return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
671}
672
673/// Returns the power of two which is greater than or equal to the given value.
674/// Essentially, it is a ceil operation across the domain of powers of two.
675inline uint64_t PowerOf2Ceil(uint64_t A) {
676 if (!A)
677 return 0;
678 return NextPowerOf2(A - 1);
679}
680
681/// Returns the next integer (mod 2**64) that is greater than or equal to
682/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
683///
684/// If non-zero \p Skew is specified, the return value will be a minimal
685/// integer that is greater than or equal to \p Value and equal to
686/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
687/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
688///
689/// Examples:
690/// \code
691/// alignTo(5, 8) = 8
692/// alignTo(17, 8) = 24
693/// alignTo(~0LL, 8) = 0
694/// alignTo(321, 255) = 510
695///
696/// alignTo(5, 8, 7) = 7
697/// alignTo(17, 8, 1) = 17
698/// alignTo(~0LL, 8, 3) = 3
699/// alignTo(321, 255, 42) = 552
700/// \endcode
701inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
702 assert(Align != 0u && "Align can't be 0.")((Align != 0u && "Align can't be 0.") ? static_cast<
void> (0) : __assert_fail ("Align != 0u && \"Align can't be 0.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 702, __PRETTY_FUNCTION__))
;
703 Skew %= Align;
704 return (Value + Align - 1 - Skew) / Align * Align + Skew;
705}
706
707/// Returns the next integer (mod 2**64) that is greater than or equal to
708/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
709template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
710 static_assert(Align != 0u, "Align must be non-zero");
711 return (Value + Align - 1) / Align * Align;
712}
713
714/// Returns the integer ceil(Numerator / Denominator).
715inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
716 return alignTo(Numerator, Denominator) / Denominator;
717}
718
719/// Returns the integer nearest(Numerator / Denominator).
720inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
721 return (Numerator + (Denominator / 2)) / Denominator;
722}
723
724/// Returns the largest uint64_t less than or equal to \p Value and is
725/// \p Skew mod \p Align. \p Align must be non-zero
726inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
727 assert(Align != 0u && "Align can't be 0.")((Align != 0u && "Align can't be 0.") ? static_cast<
void> (0) : __assert_fail ("Align != 0u && \"Align can't be 0.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 727, __PRETTY_FUNCTION__))
;
728 Skew %= Align;
729 return (Value - Skew) / Align * Align + Skew;
730}
731
732/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
733/// Requires 0 < B <= 32.
734template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
735 static_assert(B > 0, "Bit width can't be 0.");
736 static_assert(B <= 32, "Bit width out of range.");
737 return int32_t(X << (32 - B)) >> (32 - B);
738}
739
740/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
741/// Requires 0 < B < 32.
742inline int32_t SignExtend32(uint32_t X, unsigned B) {
743 assert(B > 0 && "Bit width can't be 0.")((B > 0 && "Bit width can't be 0.") ? static_cast<
void> (0) : __assert_fail ("B > 0 && \"Bit width can't be 0.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 743, __PRETTY_FUNCTION__))
;
744 assert(B <= 32 && "Bit width out of range.")((B <= 32 && "Bit width out of range.") ? static_cast
<void> (0) : __assert_fail ("B <= 32 && \"Bit width out of range.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 744, __PRETTY_FUNCTION__))
;
745 return int32_t(X << (32 - B)) >> (32 - B);
746}
747
748/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
749/// Requires 0 < B < 64.
750template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
751 static_assert(B > 0, "Bit width can't be 0.");
752 static_assert(B <= 64, "Bit width out of range.");
753 return int64_t(x << (64 - B)) >> (64 - B);
754}
755
756/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
757/// Requires 0 < B < 64.
758inline int64_t SignExtend64(uint64_t X, unsigned B) {
759 assert(B > 0 && "Bit width can't be 0.")((B > 0 && "Bit width can't be 0.") ? static_cast<
void> (0) : __assert_fail ("B > 0 && \"Bit width can't be 0.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 759, __PRETTY_FUNCTION__))
;
760 assert(B <= 64 && "Bit width out of range.")((B <= 64 && "Bit width out of range.") ? static_cast
<void> (0) : __assert_fail ("B <= 64 && \"Bit width out of range.\""
, "/build/llvm-toolchain-snapshot-11~++20200309111110+2c36c23f347/llvm/include/llvm/Support/MathExtras.h"
, 760, __PRETTY_FUNCTION__))
;
761 return int64_t(X << (64 - B)) >> (64 - B);
762}
763
764/// Subtract two unsigned integers, X and Y, of type T and return the absolute
765/// value of the result.
766template <typename T>
767std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
768 return std::max(X, Y) - std::min(X, Y);
769}
770
771/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
772/// maximum representable value of T on overflow. ResultOverflowed indicates if
773/// the result is larger than the maximum representable value of type T.
774template <typename T>
775std::enable_if_t<std::is_unsigned<T>::value, T>
776SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
777 bool Dummy;
778 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
779 // Hacker's Delight, p. 29
780 T Z = X + Y;
781 Overflowed = (Z < X || Z < Y);
782 if (Overflowed)
783 return std::numeric_limits<T>::max();
784 else
785 return Z;
786}
787
788/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
789/// maximum representable value of T on overflow. ResultOverflowed indicates if
790/// the result is larger than the maximum representable value of type T.
791template <typename T>
792std::enable_if_t<std::is_unsigned<T>::value, T>
793SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
794 bool Dummy;
795 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
796
797 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
798 // because it fails for uint16_t (where multiplication can have undefined
799 // behavior due to promotion to int), and requires a division in addition
800 // to the multiplication.
801
802 Overflowed = false;
803
804 // Log2(Z) would be either Log2Z or Log2Z + 1.
805 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
806 // will necessarily be less than Log2Max as desired.
807 int Log2Z = Log2_64(X) + Log2_64(Y);
808 const T Max = std::numeric_limits<T>::max();
809 int Log2Max = Log2_64(Max);
810 if (Log2Z < Log2Max) {
811 return X * Y;
812 }
813 if (Log2Z > Log2Max) {
814 Overflowed = true;
815 return Max;
816 }
817
818 // We're going to use the top bit, and maybe overflow one
819 // bit past it. Multiply all but the bottom bit then add
820 // that on at the end.
821 T Z = (X >> 1) * Y;
822 if (Z & ~(Max >> 1)) {
823 Overflowed = true;
824 return Max;
825 }
826 Z <<= 1;
827 if (X & 1)
828 return SaturatingAdd(Z, Y, ResultOverflowed);
829
830 return Z;
831}
832
833/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
834/// the product. Clamp the result to the maximum representable value of T on
835/// overflow. ResultOverflowed indicates if the result is larger than the
836/// maximum representable value of type T.
837template <typename T>
838std::enable_if_t<std::is_unsigned<T>::value, T>
839SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
840 bool Dummy;
841 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
842
843 T Product = SaturatingMultiply(X, Y, &Overflowed);
844 if (Overflowed)
845 return Product;
846
847 return SaturatingAdd(A, Product, &Overflowed);
848}
849
850/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
851extern const float huge_valf;
852
853
854/// Add two signed integers, computing the two's complement truncated result,
855/// returning true if overflow occured.
856template <typename T>
857std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
858#if __has_builtin(__builtin_add_overflow)1
859 return __builtin_add_overflow(X, Y, &Result);
860#else
861 // Perform the unsigned addition.
862 using U = std::make_unsigned_t<T>;
863 const U UX = static_cast<U>(X);
864 const U UY = static_cast<U>(Y);
865 const U UResult = UX + UY;
866
867 // Convert to signed.
868 Result = static_cast<T>(UResult);
869
870 // Adding two positive numbers should result in a positive number.
871 if (X > 0 && Y > 0)
872 return Result <= 0;
873 // Adding two negatives should result in a negative number.
874 if (X < 0 && Y < 0)
875 return Result >= 0;
876 return false;
877#endif
878}
879
880/// Subtract two signed integers, computing the two's complement truncated
881/// result, returning true if an overflow ocurred.
882template <typename T>
883std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
884#if __has_builtin(__builtin_sub_overflow)1
885 return __builtin_sub_overflow(X, Y, &Result);
886#else
887 // Perform the unsigned addition.
888 using U = std::make_unsigned_t<T>;
889 const U UX = static_cast<U>(X);
890 const U UY = static_cast<U>(Y);
891 const U UResult = UX - UY;
892
893 // Convert to signed.
894 Result = static_cast<T>(UResult);
895
896 // Subtracting a positive number from a negative results in a negative number.
897 if (X <= 0 && Y > 0)
898 return Result >= 0;
899 // Subtracting a negative number from a positive results in a positive number.
900 if (X >= 0 && Y < 0)
901 return Result <= 0;
902 return false;
903#endif
904}
905
906/// Multiply two signed integers, computing the two's complement truncated
907/// result, returning true if an overflow ocurred.
908template <typename T>
909std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
910 // Perform the unsigned multiplication on absolute values.
911 using U = std::make_unsigned_t<T>;
912 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
913 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
914 const U UResult = UX * UY;
915
916 // Convert to signed.
917 const bool IsNegative = (X < 0) ^ (Y < 0);
918 Result = IsNegative ? (0 - UResult) : UResult;
919
920 // If any of the args was 0, result is 0 and no overflow occurs.
921 if (UX == 0 || UY == 0)
922 return false;
923
924 // UX and UY are in [1, 2^n], where n is the number of digits.
925 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
926 // positive) divided by an argument compares to the other.
927 if (IsNegative)
928 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
929 else
930 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
931}
932
933} // End llvm namespace
934
935#endif