Bug Summary

File:llvm/lib/Target/RISCV/MCTargetDesc/RISCVMatInt.cpp
Warning:line 105, column 28
The result of the right shift is undefined because the right operand is negative

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name RISCVMatInt.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 -mframe-pointer=none -fmath-errno -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -ffunction-sections -fdata-sections -fcoverage-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/lib/Target/RISCV/MCTargetDesc -resource-dir /usr/lib/llvm-14/lib/clang/14.0.0 -D _GNU_SOURCE -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D __STDC_LIMIT_MACROS -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/lib/Target/RISCV/MCTargetDesc -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/lib/Target/RISCV/MCTargetDesc -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/lib/Target/RISCV -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/lib/Target/RISCV -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/include -I /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/include -D NDEBUG -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/x86_64-linux-gnu/c++/10 -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../include/c++/10/backward -internal-isystem /usr/lib/llvm-14/lib/clang/14.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/10/../../../../x86_64-linux-gnu/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-class-memaccess -Wno-redundant-move -Wno-pessimizing-move -Wno-noexcept-type -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/build-llvm/lib/Target/RISCV/MCTargetDesc -fdebug-prefix-map=/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e=. -ferror-limit 19 -fvisibility hidden -fvisibility-inlines-hidden -stack-protector 2 -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2021-09-04-040900-46481-1 -x c++ /build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/lib/Target/RISCV/MCTargetDesc/RISCVMatInt.cpp

/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/llvm/lib/Target/RISCV/MCTargetDesc/RISCVMatInt.cpp

→
1//===- RISCVMatInt.cpp - Immediate materialisation -------------*- 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#include "RISCVMatInt.h"
10#include "MCTargetDesc/RISCVMCTargetDesc.h"
11#include "llvm/ADT/APInt.h"
12#include "llvm/Support/MathExtras.h"
13using namespace llvm;
14
15static int getInstSeqCost(RISCVMatInt::InstSeq &Res, bool HasRVC) {
16 if (!HasRVC)
17 return Res.size();
18
19 int Cost = 0;
20 for (auto Instr : Res) {
21 bool Compressed;
22 switch (Instr.Opc) {
23 default: llvm_unreachable("Unexpected opcode")__builtin_unreachable();
24 case RISCV::SLLI:
25 case RISCV::SRLI:
26 Compressed = true;
27 break;
28 case RISCV::ADDI:
29 case RISCV::ADDIW:
30 case RISCV::LUI:
31 Compressed = isInt<6>(Instr.Imm);
32 break;
33 case RISCV::ADDUW:
34 Compressed = false;
35 break;
36 }
37 // Two RVC instructions take the same space as one RVI instruction, but
38 // can take longer to execute than the single RVI instruction. Thus, we
39 // consider that two RVC instruction are slightly more costly than one
40 // RVI instruction. For longer sequences of RVC instructions the space
41 // savings can be worth it, though. The costs below try to model that.
42 if (!Compressed)
43 Cost += 100; // Baseline cost of one RVI instruction: 100%.
44 else
45 Cost += 70; // 70% cost of baseline.
46 }
47 return Cost;
48}
49
50// Recursively generate a sequence for materializing an integer.
51static void generateInstSeqImpl(int64_t Val,
52 const FeatureBitset &ActiveFeatures,
53 RISCVMatInt::InstSeq &Res) {
54 bool IsRV64 = ActiveFeatures[RISCV::Feature64Bit];
55
56 if (isInt<32>(Val)) {
15
←
Calling 'isInt<32U>'
→
18
←
Returning from 'isInt<32U>'
→
19
←
Taking false branch
→
57 // Depending on the active bits in the immediate Value v, the following
58 // instruction sequences are emitted:
59 //
60 // v == 0 : ADDI
61 // v[0,12) != 0 && v[12,32) == 0 : ADDI
62 // v[0,12) == 0 && v[12,32) != 0 : LUI
63 // v[0,32) != 0 : LUI+ADDI(W)
64 int64_t Hi20 = ((Val + 0x800) >> 12) & 0xFFFFF;
65 int64_t Lo12 = SignExtend64<12>(Val);
66
67 if (Hi20)
68 Res.push_back(RISCVMatInt::Inst(RISCV::LUI, Hi20));
69
70 if (Lo12 || Hi20 == 0) {
71 unsigned AddiOpc = (IsRV64 && Hi20) ? RISCV::ADDIW : RISCV::ADDI;
72 Res.push_back(RISCVMatInt::Inst(AddiOpc, Lo12));
73 }
74 return;
75 }
76
77 assert(IsRV64 && "Can't emit >32-bit imm for non-RV64 target")(static_cast<void> (0));
78
79 // In the worst case, for a full 64-bit constant, a sequence of 8 instructions
80 // (i.e., LUI+ADDIW+SLLI+ADDI+SLLI+ADDI+SLLI+ADDI) has to be emitted. Note
81 // that the first two instructions (LUI+ADDIW) can contribute up to 32 bits
82 // while the following ADDI instructions contribute up to 12 bits each.
83 //
84 // On the first glance, implementing this seems to be possible by simply
85 // emitting the most significant 32 bits (LUI+ADDIW) followed by as many left
86 // shift (SLLI) and immediate additions (ADDI) as needed. However, due to the
87 // fact that ADDI performs a sign extended addition, doing it like that would
88 // only be possible when at most 11 bits of the ADDI instructions are used.
89 // Using all 12 bits of the ADDI instructions, like done by GAS, actually
90 // requires that the constant is processed starting with the least significant
91 // bit.
92 //
93 // In the following, constants are processed from LSB to MSB but instruction
94 // emission is performed from MSB to LSB by recursively calling
95 // generateInstSeq. In each recursion, first the lowest 12 bits are removed
96 // from the constant and the optimal shift amount, which can be greater than
97 // 12 bits if the constant is sparse, is determined. Then, the shifted
98 // remaining constant is processed recursively and gets emitted as soon as it
99 // fits into 32 bits. The emission of the shifts and additions is subsequently
100 // performed when the recursion returns.
101
102 int64_t Lo12 = SignExtend64<12>(Val);
103 int64_t Hi52 = ((uint64_t)Val + 0x800ull) >> 12;
104 int ShiftAmount = 12 + findFirstSet((uint64_t)Hi52);
105 Hi52 = SignExtend64(Hi52 >> (ShiftAmount - 12), 64 - ShiftAmount);
20
←
The result of the right shift is undefined because the right operand is negative
106
107 // If the remaining bits don't fit in 12 bits, we might be able to reduce the
108 // shift amount in order to use LUI which will zero the lower 12 bits.
109 if (ShiftAmount > 12 && !isInt<12>(Hi52) && isInt<32>((uint64_t)Hi52 << 12)) {
110 // Reduce the shift amount and add zeros to the LSBs so it will match LUI.
111 ShiftAmount -= 12;
112 Hi52 = (uint64_t)Hi52 << 12;
113 }
114
115 generateInstSeqImpl(Hi52, ActiveFeatures, Res);
116
117 Res.push_back(RISCVMatInt::Inst(RISCV::SLLI, ShiftAmount));
118 if (Lo12)
119 Res.push_back(RISCVMatInt::Inst(RISCV::ADDI, Lo12));
120}
121
122namespace llvm {
123namespace RISCVMatInt {
124InstSeq generateInstSeq(int64_t Val, const FeatureBitset &ActiveFeatures) {
125 RISCVMatInt::InstSeq Res;
126 generateInstSeqImpl(Val, ActiveFeatures, Res);
127
128 // If the constant is positive we might be able to generate a shifted constant
129 // with no leading zeros and use a final SRLI to restore them.
130 if (Val > 0 && Res.size() > 2) {
6
←
Assuming 'Val' is > 0
→
7
←
Assuming the condition is true
→
8
←
Taking true branch
→
131 assert(ActiveFeatures[RISCV::Feature64Bit] &&(static_cast<void> (0))
132 "Expected RV32 to only need 2 instructions")(static_cast<void> (0));
133 unsigned LeadingZeros = countLeadingZeros((uint64_t)Val);
134 uint64_t ShiftedVal = (uint64_t)Val << LeadingZeros;
135 // Fill in the bits that will be shifted out with 1s. An example where this
136 // helps is trailing one masks with 32 or more ones. This will generate
137 // ADDI -1 and an SRLI.
138 ShiftedVal |= maskTrailingOnes<uint64_t>(LeadingZeros);
139
140 RISCVMatInt::InstSeq TmpSeq;
141 generateInstSeqImpl(ShiftedVal, ActiveFeatures, TmpSeq);
142 TmpSeq.push_back(RISCVMatInt::Inst(RISCV::SRLI, LeadingZeros));
143
144 // Keep the new sequence if it is an improvement.
145 if (TmpSeq.size() < Res.size()) {
9
←
Assuming the condition is false
→
10
←
Taking false branch
→
146 Res = TmpSeq;
147 // A 2 instruction sequence is the best we can do.
148 if (Res.size() <= 2)
149 return Res;
150 }
151
152 // Some cases can benefit from filling the lower bits with zeros instead.
153 ShiftedVal &= maskTrailingZeros<uint64_t>(LeadingZeros);
154 TmpSeq.clear();
155 generateInstSeqImpl(ShiftedVal, ActiveFeatures, TmpSeq);
156 TmpSeq.push_back(RISCVMatInt::Inst(RISCV::SRLI, LeadingZeros));
157
158 // Keep the new sequence if it is an improvement.
159 if (TmpSeq.size() < Res.size()) {
11
←
Assuming the condition is false
→
160 Res = TmpSeq;
161 // A 2 instruction sequence is the best we can do.
162 if (Res.size() <= 2)
163 return Res;
164 }
165
166 // If we have exactly 32 leading zeros and Zba, we can try using zext.w at
167 // the end of the sequence.
168 if (LeadingZeros == 32 && ActiveFeatures[RISCV::FeatureExtZba]) {
12
←
Assuming 'LeadingZeros' is equal to 32
→
13
←
Taking true branch
→
169 // Try replacing upper bits with 1.
170 uint64_t LeadingOnesVal = Val | maskLeadingOnes<uint64_t>(LeadingZeros);
171 TmpSeq.clear();
172 generateInstSeqImpl(LeadingOnesVal, ActiveFeatures, TmpSeq);
14
←
Calling 'generateInstSeqImpl'
→
173 TmpSeq.push_back(RISCVMatInt::Inst(RISCV::ADDUW, 0));
174
175 // Keep the new sequence if it is an improvement.
176 if (TmpSeq.size() < Res.size()) {
177 Res = TmpSeq;
178 // A 2 instruction sequence is the best we can do.
179 if (Res.size() <= 2)
180 return Res;
181 }
182 }
183 }
184
185 return Res;
186}
187
188int getIntMatCost(const APInt &Val, unsigned Size,
189 const FeatureBitset &ActiveFeatures,
190 bool CompressionCost) {
191 bool IsRV64 = ActiveFeatures[RISCV::Feature64Bit];
192 bool HasRVC = CompressionCost && ActiveFeatures[RISCV::FeatureStdExtC];
1
Assuming 'CompressionCost' is false
→
193 int PlatRegSize = IsRV64
1.1
'IsRV64' is false
1.1
'IsRV64' is false
 ? 64 : 32;
2
←
'?' condition is false
→
194
195 // Split the constant into platform register sized chunks, and calculate cost
196 // of each chunk.
197 int Cost = 0;
198 for (unsigned ShiftVal = 0; ShiftVal < Size; ShiftVal += PlatRegSize) {
3
←
Assuming 'ShiftVal' is < 'Size'
→
4
←
Loop condition is true. Entering loop body
→
199 APInt Chunk = Val.ashr(ShiftVal).sextOrTrunc(PlatRegSize);
200 InstSeq MatSeq = generateInstSeq(Chunk.getSExtValue(), ActiveFeatures);
5
←
Calling 'generateInstSeq'
→
201 Cost += getInstSeqCost(MatSeq, HasRVC);
202 }
203 return std::max(1, Cost);
204}
205} // namespace RISCVMatInt
206} // namespace llvm
←

/build/llvm-toolchain-snapshot-14~++20210903100615+fd66b44ec19e/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 <cassert>
18#include <climits>
19#include <cmath>
20#include <cstdint>
21#include <cstring>
22#include <limits>
23#include <type_traits>
24
25#ifdef __ANDROID_NDK__
26#include <android/api-level.h>
27#endif
28
29#ifdef _MSC_VER
30// Declare these intrinsics manually rather including intrin.h. It's very
31// expensive, and MathExtras.h is popular.
32// #include <intrin.h>
33extern "C" {
34unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
35unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
36unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
37unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
38}
39#endif
40
41namespace llvm {
42
43/// The behavior an operation has on an input of 0.
44enum ZeroBehavior {
45 /// The returned value is undefined.
46 ZB_Undefined,
47 /// The returned value is numeric_limits<T>::max()
48 ZB_Max,
49 /// The returned value is numeric_limits<T>::digits
50 ZB_Width
51};
52
53/// Mathematical constants.
54namespace numbers {
55// TODO: Track C++20 std::numbers.
56// TODO: Favor using the hexadecimal FP constants (requires C++17).
57constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113
58 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620
59 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162
60 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392
61 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0)
62 log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2)
63 pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796
64 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541
65 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161
66 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197
67 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219
68 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1)
69 sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194
70 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1)
71 phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622
72constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113
73 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620
74 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162
75 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392
76 log2ef = 1.44269504F, // (0x1.715476P+0)
77 log10ef = .434294482F, // (0x1.bcb7b2P-2)
78 pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796
79 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541
80 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161
81 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197
82 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193
83 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1)
84 sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194
85 inv_sqrt3f = .577350269F, // (0x1.279a74P-1)
86 phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622
87} // namespace numbers
88
89namespace detail {
90template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
91 static unsigned count(T Val, ZeroBehavior) {
92 if (!Val)
93 return std::numeric_limits<T>::digits;
94 if (Val & 0x1)
95 return 0;
96
97 // Bisection method.
98 unsigned ZeroBits = 0;
99 T Shift = std::numeric_limits<T>::digits >> 1;
100 T Mask = std::numeric_limits<T>::max() >> Shift;
101 while (Shift) {
102 if ((Val & Mask) == 0) {
103 Val >>= Shift;
104 ZeroBits |= Shift;
105 }
106 Shift >>= 1;
107 Mask >>= Shift;
108 }
109 return ZeroBits;
110 }
111};
112
113#if defined(__GNUC__4) || defined(_MSC_VER)
114template <typename T> struct TrailingZerosCounter<T, 4> {
115 static unsigned count(T Val, ZeroBehavior ZB) {
116 if (ZB != ZB_Undefined && Val == 0)
117 return 32;
118
119#if __has_builtin(__builtin_ctz)1 || defined(__GNUC__4)
120 return __builtin_ctz(Val);
121#elif defined(_MSC_VER)
122 unsigned long Index;
123 _BitScanForward(&Index, Val);
124 return Index;
125#endif
126 }
127};
128
129#if !defined(_MSC_VER) || defined(_M_X64)
130template <typename T> struct TrailingZerosCounter<T, 8> {
131 static unsigned count(T Val, ZeroBehavior ZB) {
132 if (ZB != ZB_Undefined && Val == 0)
133 return 64;
134
135#if __has_builtin(__builtin_ctzll)1 || defined(__GNUC__4)
136 return __builtin_ctzll(Val);
137#elif defined(_MSC_VER)
138 unsigned long Index;
139 _BitScanForward64(&Index, Val);
140 return Index;
141#endif
142 }
143};
144#endif
145#endif
146} // namespace detail
147
148/// Count number of 0's from the least significant bit to the most
149/// stopping at the first 1.
150///
151/// Only unsigned integral types are allowed.
152///
153/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
154/// valid arguments.
155template <typename T>
156unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
157 static_assert(std::numeric_limits<T>::is_integer &&
158 !std::numeric_limits<T>::is_signed,
159 "Only unsigned integral types are allowed.");
160 return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
161}
162
163namespace detail {
164template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
165 static unsigned count(T Val, ZeroBehavior) {
166 if (!Val)
167 return std::numeric_limits<T>::digits;
168
169 // Bisection method.
170 unsigned ZeroBits = 0;
171 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
172 T Tmp = Val >> Shift;
173 if (Tmp)
174 Val = Tmp;
175 else
176 ZeroBits |= Shift;
177 }
178 return ZeroBits;
179 }
180};
181
182#if defined(__GNUC__4) || defined(_MSC_VER)
183template <typename T> struct LeadingZerosCounter<T, 4> {
184 static unsigned count(T Val, ZeroBehavior ZB) {
185 if (ZB != ZB_Undefined && Val == 0)
186 return 32;
187
188#if __has_builtin(__builtin_clz)1 || defined(__GNUC__4)
189 return __builtin_clz(Val);
190#elif defined(_MSC_VER)
191 unsigned long Index;
192 _BitScanReverse(&Index, Val);
193 return Index ^ 31;
194#endif
195 }
196};
197
198#if !defined(_MSC_VER) || defined(_M_X64)
199template <typename T> struct LeadingZerosCounter<T, 8> {
200 static unsigned count(T Val, ZeroBehavior ZB) {
201 if (ZB != ZB_Undefined && Val == 0)
202 return 64;
203
204#if __has_builtin(__builtin_clzll)1 || defined(__GNUC__4)
205 return __builtin_clzll(Val);
206#elif defined(_MSC_VER)
207 unsigned long Index;
208 _BitScanReverse64(&Index, Val);
209 return Index ^ 63;
210#endif
211 }
212};
213#endif
214#endif
215} // namespace detail
216
217/// Count number of 0's from the most significant bit to the least
218/// stopping at the first 1.
219///
220/// Only unsigned integral types are allowed.
221///
222/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
223/// valid arguments.
224template <typename T>
225unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
226 static_assert(std::numeric_limits<T>::is_integer &&
227 !std::numeric_limits<T>::is_signed,
228 "Only unsigned integral types are allowed.");
229 return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
230}
231
232/// Get the index of the first set bit starting from the least
233/// significant bit.
234///
235/// Only unsigned integral types are allowed.
236///
237/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
238/// valid arguments.
239template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
240 if (ZB == ZB_Max && Val == 0)
241 return std::numeric_limits<T>::max();
242
243 return countTrailingZeros(Val, ZB_Undefined);
244}
245
246/// Create a bitmask with the N right-most bits set to 1, and all other
247/// bits set to 0. Only unsigned types are allowed.
248template <typename T> T maskTrailingOnes(unsigned N) {
249 static_assert(std::is_unsigned<T>::value, "Invalid type!");
250 const unsigned Bits = CHAR_BIT8 * sizeof(T);
251 assert(N <= Bits && "Invalid bit index")(static_cast<void> (0));
252 return N == 0 ? 0 : (T(-1) >> (Bits - N));
253}
254
255/// Create a bitmask with the N left-most bits set to 1, and all other
256/// bits set to 0. Only unsigned types are allowed.
257template <typename T> T maskLeadingOnes(unsigned N) {
258 return ~maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
259}
260
261/// Create a bitmask with the N right-most bits set to 0, and all other
262/// bits set to 1. Only unsigned types are allowed.
263template <typename T> T maskTrailingZeros(unsigned N) {
264 return maskLeadingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
265}
266
267/// Create a bitmask with the N left-most bits set to 0, and all other
268/// bits set to 1. Only unsigned types are allowed.
269template <typename T> T maskLeadingZeros(unsigned N) {
270 return maskTrailingOnes<T>(CHAR_BIT8 * sizeof(T) - N);
271}
272
273/// Get the index of the last set bit starting from the least
274/// significant bit.
275///
276/// Only unsigned integral types are allowed.
277///
278/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
279/// valid arguments.
280template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
281 if (ZB == ZB_Max && Val == 0)
282 return std::numeric_limits<T>::max();
283
284 // Use ^ instead of - because both gcc and llvm can remove the associated ^
285 // in the __builtin_clz intrinsic on x86.
286 return countLeadingZeros(Val, ZB_Undefined) ^
287 (std::numeric_limits<T>::digits - 1);
288}
289
290/// Macro compressed bit reversal table for 256 bits.
291///
292/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
293static const unsigned char BitReverseTable256[256] = {
294#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
295#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
296#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
297 R6(0), R6(2), R6(1), R6(3)
298#undef R2
299#undef R4
300#undef R6
301};
302
303/// Reverse the bits in \p Val.
304template <typename T>
305T reverseBits(T Val) {
306 unsigned char in[sizeof(Val)];
307 unsigned char out[sizeof(Val)];
308 std::memcpy(in, &Val, sizeof(Val));
309 for (unsigned i = 0; i < sizeof(Val); ++i)
310 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
311 std::memcpy(&Val, out, sizeof(Val));
312 return Val;
313}
314
315#if __has_builtin(__builtin_bitreverse8)1
316template<>
317inline uint8_t reverseBits<uint8_t>(uint8_t Val) {
318 return __builtin_bitreverse8(Val);
319}
320#endif
321
322#if __has_builtin(__builtin_bitreverse16)1
323template<>
324inline uint16_t reverseBits<uint16_t>(uint16_t Val) {
325 return __builtin_bitreverse16(Val);
326}
327#endif
328
329#if __has_builtin(__builtin_bitreverse32)1
330template<>
331inline uint32_t reverseBits<uint32_t>(uint32_t Val) {
332 return __builtin_bitreverse32(Val);
333}
334#endif
335
336#if __has_builtin(__builtin_bitreverse64)1
337template<>
338inline uint64_t reverseBits<uint64_t>(uint64_t Val) {
339 return __builtin_bitreverse64(Val);
340}
341#endif
342
343// NOTE: The following support functions use the _32/_64 extensions instead of
344// type overloading so that signed and unsigned integers can be used without
345// ambiguity.
346
347/// Return the high 32 bits of a 64 bit value.
348constexpr inline uint32_t Hi_32(uint64_t Value) {
349 return static_cast<uint32_t>(Value >> 32);
350}
351
352/// Return the low 32 bits of a 64 bit value.
353constexpr inline uint32_t Lo_32(uint64_t Value) {
354 return static_cast<uint32_t>(Value);
355}
356
357/// Make a 64-bit integer from a high / low pair of 32-bit integers.
358constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
359 return ((uint64_t)High << 32) | (uint64_t)Low;
360}
361
362/// Checks if an integer fits into the given bit width.
363template <unsigned N> constexpr inline bool isInt(int64_t x) {
364 return N >= 64 || (-(INT64_C(1)1L<<(N-1)) <= x && x < (INT64_C(1)1L<<(N-1)));
365}
366// Template specializations to get better code for common cases.
367template <> constexpr inline bool isInt<8>(int64_t x) {
368 return static_cast<int8_t>(x) == x;
369}
370template <> constexpr inline bool isInt<16>(int64_t x) {
371 return static_cast<int16_t>(x) == x;
372}
373template <> constexpr inline bool isInt<32>(int64_t x) {
374 return static_cast<int32_t>(x) == x;
16
←
Assuming 'x' is not equal to 'x'
→
17
←
Returning zero, which participates in a condition later
→
375}
376
377/// Checks if a signed integer is an N bit number shifted left by S.
378template <unsigned N, unsigned S>
379constexpr inline bool isShiftedInt(int64_t x) {
380 static_assert(
381 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
382 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
383 return isInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
384}
385
386/// Checks if an unsigned integer fits into the given bit width.
387///
388/// This is written as two functions rather than as simply
389///
390/// return N >= 64 || X < (UINT64_C(1) << N);
391///
392/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
393/// left too many places.
394template <unsigned N>
395constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) {
396 static_assert(N > 0, "isUInt<0> doesn't make sense");
397 return X < (UINT64_C(1)1UL << (N));
398}
399template <unsigned N>
400constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) {
401 return true;
402}
403
404// Template specializations to get better code for common cases.
405template <> constexpr inline bool isUInt<8>(uint64_t x) {
406 return static_cast<uint8_t>(x) == x;
407}
408template <> constexpr inline bool isUInt<16>(uint64_t x) {
409 return static_cast<uint16_t>(x) == x;
410}
411template <> constexpr inline bool isUInt<32>(uint64_t x) {
412 return static_cast<uint32_t>(x) == x;
413}
414
415/// Checks if a unsigned integer is an N bit number shifted left by S.
416template <unsigned N, unsigned S>
417constexpr inline bool isShiftedUInt(uint64_t x) {
418 static_assert(
419 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
420 static_assert(N + S <= 64,
421 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
422 // Per the two static_asserts above, S must be strictly less than 64. So
423 // 1 << S is not undefined behavior.
424 return isUInt<N + S>(x) && (x % (UINT64_C(1)1UL << S) == 0);
425}
426
427/// Gets the maximum value for a N-bit unsigned integer.
428inline uint64_t maxUIntN(uint64_t N) {
429 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast<void> (0));
430
431 // uint64_t(1) << 64 is undefined behavior, so we can't do
432 // (uint64_t(1) << N) - 1
433 // without checking first that N != 64. But this works and doesn't have a
434 // branch.
435 return UINT64_MAX(18446744073709551615UL) >> (64 - N);
436}
437
438/// Gets the minimum value for a N-bit signed integer.
439inline int64_t minIntN(int64_t N) {
440 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast<void> (0));
441
442 return UINT64_C(1)1UL + ~(UINT64_C(1)1UL << (N - 1));
443}
444
445/// Gets the maximum value for a N-bit signed integer.
446inline int64_t maxIntN(int64_t N) {
447 assert(N > 0 && N <= 64 && "integer width out of range")(static_cast<void> (0));
448
449 // This relies on two's complement wraparound when N == 64, so we convert to
450 // int64_t only at the very end to avoid UB.
451 return (UINT64_C(1)1UL << (N - 1)) - 1;
452}
453
454/// Checks if an unsigned integer fits into the given (dynamic) bit width.
455inline bool isUIntN(unsigned N, uint64_t x) {
456 return N >= 64 || x <= maxUIntN(N);
457}
458
459/// Checks if an signed integer fits into the given (dynamic) bit width.
460inline bool isIntN(unsigned N, int64_t x) {
461 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
462}
463
464/// Return true if the argument is a non-empty sequence of ones starting at the
465/// least significant bit with the remainder zero (32 bit version).
466/// Ex. isMask_32(0x0000FFFFU) == true.
467constexpr inline bool isMask_32(uint32_t Value) {
468 return Value && ((Value + 1) & Value) == 0;
469}
470
471/// Return true if the argument is a non-empty sequence of ones starting at the
472/// least significant bit with the remainder zero (64 bit version).
473constexpr inline bool isMask_64(uint64_t Value) {
474 return Value && ((Value + 1) & Value) == 0;
475}
476
477/// Return true if the argument contains a non-empty sequence of ones with the
478/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
479constexpr inline bool isShiftedMask_32(uint32_t Value) {
480 return Value && isMask_32((Value - 1) | Value);
481}
482
483/// Return true if the argument contains a non-empty sequence of ones with the
484/// remainder zero (64 bit version.)
485constexpr inline bool isShiftedMask_64(uint64_t Value) {
486 return Value && isMask_64((Value - 1) | Value);
487}
488
489/// Return true if the argument is a power of two > 0.
490/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
491constexpr inline bool isPowerOf2_32(uint32_t Value) {
492 return Value && !(Value & (Value - 1));
493}
494
495/// Return true if the argument is a power of two > 0 (64 bit edition.)
496constexpr inline bool isPowerOf2_64(uint64_t Value) {
497 return Value && !(Value & (Value - 1));
498}
499
500/// Count the number of ones from the most significant bit to the first
501/// zero bit.
502///
503/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
504/// Only unsigned integral types are allowed.
505///
506/// \param ZB the behavior on an input of all ones. Only ZB_Width and
507/// ZB_Undefined are valid arguments.
508template <typename T>
509unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
510 static_assert(std::numeric_limits<T>::is_integer &&
511 !std::numeric_limits<T>::is_signed,
512 "Only unsigned integral types are allowed.");
513 return countLeadingZeros<T>(~Value, ZB);
514}
515
516/// Count the number of ones from the least significant bit to the first
517/// zero bit.
518///
519/// Ex. countTrailingOnes(0x00FF00FF) == 8.
520/// Only unsigned integral types are allowed.
521///
522/// \param ZB the behavior on an input of all ones. Only ZB_Width and
523/// ZB_Undefined are valid arguments.
524template <typename T>
525unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
526 static_assert(std::numeric_limits<T>::is_integer &&
527 !std::numeric_limits<T>::is_signed,
528 "Only unsigned integral types are allowed.");
529 return countTrailingZeros<T>(~Value, ZB);
530}
531
532namespace detail {
533template <typename T, std::size_t SizeOfT> struct PopulationCounter {
534 static unsigned count(T Value) {
535 // Generic version, forward to 32 bits.
536 static_assert(SizeOfT <= 4, "Not implemented!");
537#if defined(__GNUC__4)
538 return __builtin_popcount(Value);
539#else
540 uint32_t v = Value;
541 v = v - ((v >> 1) & 0x55555555);
542 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
543 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
544#endif
545 }
546};
547
548template <typename T> struct PopulationCounter<T, 8> {
549 static unsigned count(T Value) {
550#if defined(__GNUC__4)
551 return __builtin_popcountll(Value);
552#else
553 uint64_t v = Value;
554 v = v - ((v >> 1) & 0x5555555555555555ULL);
555 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
556 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
557 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
558#endif
559 }
560};
561} // namespace detail
562
563/// Count the number of set bits in a value.
564/// Ex. countPopulation(0xF000F000) = 8
565/// Returns 0 if the word is zero.
566template <typename T>
567inline unsigned countPopulation(T Value) {
568 static_assert(std::numeric_limits<T>::is_integer &&
569 !std::numeric_limits<T>::is_signed,
570 "Only unsigned integral types are allowed.");
571 return detail::PopulationCounter<T, sizeof(T)>::count(Value);
572}
573
574/// Compile time Log2.
575/// Valid only for positive powers of two.
576template <size_t kValue> constexpr inline size_t CTLog2() {
577 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue),
578 "Value is not a valid power of 2");
579 return 1 + CTLog2<kValue / 2>();
580}
581
582template <> constexpr inline size_t CTLog2<1>() { return 0; }
583
584/// Return the log base 2 of the specified value.
585inline double Log2(double Value) {
586#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
587 return __builtin_log(Value) / __builtin_log(2.0);
588#else
589 return log2(Value);
590#endif
591}
592
593/// Return the floor log base 2 of the specified value, -1 if the value is zero.
594/// (32 bit edition.)
595/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
596inline unsigned Log2_32(uint32_t Value) {
597 return 31 - countLeadingZeros(Value);
598}
599
600/// Return the floor log base 2 of the specified value, -1 if the value is zero.
601/// (64 bit edition.)
602inline unsigned Log2_64(uint64_t Value) {
603 return 63 - countLeadingZeros(Value);
604}
605
606/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
607/// (32 bit edition).
608/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
609inline unsigned Log2_32_Ceil(uint32_t Value) {
610 return 32 - countLeadingZeros(Value - 1);
611}
612
613/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
614/// (64 bit edition.)
615inline unsigned Log2_64_Ceil(uint64_t Value) {
616 return 64 - countLeadingZeros(Value - 1);
617}
618
619/// Return the greatest common divisor of the values using Euclid's algorithm.
620template <typename T>
621inline T greatestCommonDivisor(T A, T B) {
622 while (B) {
623 T Tmp = B;
624 B = A % B;
625 A = Tmp;
626 }
627 return A;
628}
629
630inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
631 return greatestCommonDivisor<uint64_t>(A, B);
632}
633
634/// This function takes a 64-bit integer and returns the bit equivalent double.
635inline double BitsToDouble(uint64_t Bits) {
636 double D;
637 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
638 memcpy(&D, &Bits, sizeof(Bits));
639 return D;
640}
641
642/// This function takes a 32-bit integer and returns the bit equivalent float.
643inline float BitsToFloat(uint32_t Bits) {
644 float F;
645 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
646 memcpy(&F, &Bits, sizeof(Bits));
647 return F;
648}
649
650/// This function takes a double and returns the bit equivalent 64-bit integer.
651/// Note that copying doubles around changes the bits of NaNs on some hosts,
652/// notably x86, so this routine cannot be used if these bits are needed.
653inline uint64_t DoubleToBits(double Double) {
654 uint64_t Bits;
655 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
656 memcpy(&Bits, &Double, sizeof(Double));
657 return Bits;
658}
659
660/// This function takes a float and returns the bit equivalent 32-bit integer.
661/// Note that copying floats around changes the bits of NaNs on some hosts,
662/// notably x86, so this routine cannot be used if these bits are needed.
663inline uint32_t FloatToBits(float Float) {
664 uint32_t Bits;
665 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
666 memcpy(&Bits, &Float, sizeof(Float));
667 return Bits;
668}
669
670/// A and B are either alignments or offsets. Return the minimum alignment that
671/// may be assumed after adding the two together.
672constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
673 // The largest power of 2 that divides both A and B.
674 //
675 // Replace "-Value" by "1+~Value" in the following commented code to avoid
676 // MSVC warning C4146
677 // return (A | B) & -(A | B);
678 return (A | B) & (1 + ~(A | B));
679}
680
681/// Returns the next power of two (in 64-bits) that is strictly greater than A.
682/// Returns zero on overflow.
683inline uint64_t NextPowerOf2(uint64_t A) {
684 A |= (A >> 1);
685 A |= (A >> 2);
686 A |= (A >> 4);
687 A |= (A >> 8);
688 A |= (A >> 16);
689 A |= (A >> 32);
690 return A + 1;
691}
692
693/// Returns the power of two which is less than or equal to the given value.
694/// Essentially, it is a floor operation across the domain of powers of two.
695inline uint64_t PowerOf2Floor(uint64_t A) {
696 if (!A) return 0;
697 return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
698}
699
700/// Returns the power of two which is greater than or equal to the given value.
701/// Essentially, it is a ceil operation across the domain of powers of two.
702inline uint64_t PowerOf2Ceil(uint64_t A) {
703 if (!A)
704 return 0;
705 return NextPowerOf2(A - 1);
706}
707
708/// Returns the next integer (mod 2**64) that is greater than or equal to
709/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
710///
711/// If non-zero \p Skew is specified, the return value will be a minimal
712/// integer that is greater than or equal to \p Value and equal to
713/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
714/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
715///
716/// Examples:
717/// \code
718/// alignTo(5, 8) = 8
719/// alignTo(17, 8) = 24
720/// alignTo(~0LL, 8) = 0
721/// alignTo(321, 255) = 510
722///
723/// alignTo(5, 8, 7) = 7
724/// alignTo(17, 8, 1) = 17
725/// alignTo(~0LL, 8, 3) = 3
726/// alignTo(321, 255, 42) = 552
727/// \endcode
728inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
729 assert(Align != 0u && "Align can't be 0.")(static_cast<void> (0));
730 Skew %= Align;
731 return (Value + Align - 1 - Skew) / Align * Align + Skew;
732}
733
734/// Returns the next integer (mod 2**64) that is greater than or equal to
735/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
736template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
737 static_assert(Align != 0u, "Align must be non-zero");
738 return (Value + Align - 1) / Align * Align;
739}
740
741/// Returns the integer ceil(Numerator / Denominator).
742inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
743 return alignTo(Numerator, Denominator) / Denominator;
744}
745
746/// Returns the integer nearest(Numerator / Denominator).
747inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) {
748 return (Numerator + (Denominator / 2)) / Denominator;
749}
750
751/// Returns the largest uint64_t less than or equal to \p Value and is
752/// \p Skew mod \p Align. \p Align must be non-zero
753inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
754 assert(Align != 0u && "Align can't be 0.")(static_cast<void> (0));
755 Skew %= Align;
756 return (Value - Skew) / Align * Align + Skew;
757}
758
759/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
760/// Requires 0 < B <= 32.
761template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
762 static_assert(B > 0, "Bit width can't be 0.");
763 static_assert(B <= 32, "Bit width out of range.");
764 return int32_t(X << (32 - B)) >> (32 - B);
765}
766
767/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
768/// Requires 0 < B <= 32.
769inline int32_t SignExtend32(uint32_t X, unsigned B) {
770 assert(B > 0 && "Bit width can't be 0.")(static_cast<void> (0));
771 assert(B <= 32 && "Bit width out of range.")(static_cast<void> (0));
772 return int32_t(X << (32 - B)) >> (32 - B);
773}
774
775/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
776/// Requires 0 < B <= 64.
777template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
778 static_assert(B > 0, "Bit width can't be 0.");
779 static_assert(B <= 64, "Bit width out of range.");
780 return int64_t(x << (64 - B)) >> (64 - B);
781}
782
783/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
784/// Requires 0 < B <= 64.
785inline int64_t SignExtend64(uint64_t X, unsigned B) {
786 assert(B > 0 && "Bit width can't be 0.")(static_cast<void> (0));
787 assert(B <= 64 && "Bit width out of range.")(static_cast<void> (0));
788 return int64_t(X << (64 - B)) >> (64 - B);
789}
790
791/// Subtract two unsigned integers, X and Y, of type T and return the absolute
792/// value of the result.
793template <typename T>
794std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) {
795 return X > Y ? (X - Y) : (Y - X);
796}
797
798/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
799/// maximum representable value of T on overflow. ResultOverflowed indicates if
800/// the result is larger than the maximum representable value of type T.
801template <typename T>
802std::enable_if_t<std::is_unsigned<T>::value, T>
803SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
804 bool Dummy;
805 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
806 // Hacker's Delight, p. 29
807 T Z = X + Y;
808 Overflowed = (Z < X || Z < Y);
809 if (Overflowed)
810 return std::numeric_limits<T>::max();
811 else
812 return Z;
813}
814
815/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
816/// maximum representable value of T on overflow. ResultOverflowed indicates if
817/// the result is larger than the maximum representable value of type T.
818template <typename T>
819std::enable_if_t<std::is_unsigned<T>::value, T>
820SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
821 bool Dummy;
822 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
823
824 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
825 // because it fails for uint16_t (where multiplication can have undefined
826 // behavior due to promotion to int), and requires a division in addition
827 // to the multiplication.
828
829 Overflowed = false;
830
831 // Log2(Z) would be either Log2Z or Log2Z + 1.
832 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
833 // will necessarily be less than Log2Max as desired.
834 int Log2Z = Log2_64(X) + Log2_64(Y);
835 const T Max = std::numeric_limits<T>::max();
836 int Log2Max = Log2_64(Max);
837 if (Log2Z < Log2Max) {
838 return X * Y;
839 }
840 if (Log2Z > Log2Max) {
841 Overflowed = true;
842 return Max;
843 }
844
845 // We're going to use the top bit, and maybe overflow one
846 // bit past it. Multiply all but the bottom bit then add
847 // that on at the end.
848 T Z = (X >> 1) * Y;
849 if (Z & ~(Max >> 1)) {
850 Overflowed = true;
851 return Max;
852 }
853 Z <<= 1;
854 if (X & 1)
855 return SaturatingAdd(Z, Y, ResultOverflowed);
856
857 return Z;
858}
859
860/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
861/// the product. Clamp the result to the maximum representable value of T on
862/// overflow. ResultOverflowed indicates if the result is larger than the
863/// maximum representable value of type T.
864template <typename T>
865std::enable_if_t<std::is_unsigned<T>::value, T>
866SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
867 bool Dummy;
868 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
869
870 T Product = SaturatingMultiply(X, Y, &Overflowed);
871 if (Overflowed)
872 return Product;
873
874 return SaturatingAdd(A, Product, &Overflowed);
875}
876
877/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
878extern const float huge_valf;
879
880
881/// Add two signed integers, computing the two's complement truncated result,
882/// returning true if overflow occured.
883template <typename T>
884std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) {
885#if __has_builtin(__builtin_add_overflow)1
886 return __builtin_add_overflow(X, Y, &Result);
887#else
888 // Perform the unsigned addition.
889 using U = std::make_unsigned_t<T>;
890 const U UX = static_cast<U>(X);
891 const U UY = static_cast<U>(Y);
892 const U UResult = UX + UY;
893
894 // Convert to signed.
895 Result = static_cast<T>(UResult);
896
897 // Adding two positive numbers should result in a positive number.
898 if (X > 0 && Y > 0)
899 return Result <= 0;
900 // Adding two negatives should result in a negative number.
901 if (X < 0 && Y < 0)
902 return Result >= 0;
903 return false;
904#endif
905}
906
907/// Subtract two signed integers, computing the two's complement truncated
908/// result, returning true if an overflow ocurred.
909template <typename T>
910std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) {
911#if __has_builtin(__builtin_sub_overflow)1
912 return __builtin_sub_overflow(X, Y, &Result);
913#else
914 // Perform the unsigned addition.
915 using U = std::make_unsigned_t<T>;
916 const U UX = static_cast<U>(X);
917 const U UY = static_cast<U>(Y);
918 const U UResult = UX - UY;
919
920 // Convert to signed.
921 Result = static_cast<T>(UResult);
922
923 // Subtracting a positive number from a negative results in a negative number.
924 if (X <= 0 && Y > 0)
925 return Result >= 0;
926 // Subtracting a negative number from a positive results in a positive number.
927 if (X >= 0 && Y < 0)
928 return Result <= 0;
929 return false;
930#endif
931}
932
933/// Multiply two signed integers, computing the two's complement truncated
934/// result, returning true if an overflow ocurred.
935template <typename T>
936std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) {
937 // Perform the unsigned multiplication on absolute values.
938 using U = std::make_unsigned_t<T>;
939 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X);
940 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y);
941 const U UResult = UX * UY;
942
943 // Convert to signed.
944 const bool IsNegative = (X < 0) ^ (Y < 0);
945 Result = IsNegative ? (0 - UResult) : UResult;
946
947 // If any of the args was 0, result is 0 and no overflow occurs.
948 if (UX == 0 || UY == 0)
949 return false;
950
951 // UX and UY are in [1, 2^n], where n is the number of digits.
952 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for
953 // positive) divided by an argument compares to the other.
954 if (IsNegative)
955 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY;
956 else
957 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY;
958}
959
960} // End llvm namespace
961
962#endif