clang -cc1 -cc1 -triple amd64-unknown-openbsd7.0 -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name ScaledNumber.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 -mrelocation-model static -mframe-pointer=all -relaxed-aliasing -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVMSupport/obj -resource-dir /usr/local/lib/clang/13.0.0 -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/../../../llvm/llvm/include/llvm/ADT -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/../../../llvm/llvm/include/llvm/Support -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/../../../llvm/llvm/include -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/../include -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/obj -I /usr/src/gnu/usr.bin/clang/libLLVMSupport/obj/../include -D NDEBUG -D __STDC_LIMIT_MACROS -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D LLVM_PREFIX="/usr" -internal-isystem /usr/include/c++/v1 -internal-isystem /usr/local/lib/clang/13.0.0/include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVMSupport/obj -ferror-limit 19 -fvisibility-inlines-hidden -fwrapv -stack-protector 2 -fno-rtti -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -fno-builtin-malloc -fno-builtin-calloc -fno-builtin-realloc -fno-builtin-valloc -fno-builtin-free -fno-builtin-strdup -fno-builtin-strndup -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /home/ben/Projects/vmm/scan-build/2022-01-12-194120-40624-1 -x c++ /usr/src/gnu/usr.bin/clang/libLLVMSupport/../../../llvm/llvm/lib/Support/ScaledNumber.cpp
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 | |
11 | |
12 | |
13 | #include "llvm/Support/ScaledNumber.h" |
14 | #include "llvm/ADT/APFloat.h" |
15 | #include "llvm/ADT/ArrayRef.h" |
16 | #include "llvm/Support/Debug.h" |
17 | #include "llvm/Support/raw_ostream.h" |
18 | |
19 | using namespace llvm; |
20 | using namespace llvm::ScaledNumbers; |
21 | |
22 | std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS, |
23 | uint64_t RHS) { |
24 | |
25 | auto getU = [](uint64_t N) { return N >> 32; }; |
26 | auto getL = [](uint64_t N) { return N & UINT32_MAX; }; |
27 | uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS); |
28 | |
29 | |
30 | uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR; |
31 | |
32 | |
33 | uint64_t Upper = P1, Lower = P4; |
34 | auto addWithCarry = [&](uint64_t N) { |
35 | uint64_t NewLower = Lower + (getL(N) << 32); |
36 | Upper += getU(N) + (NewLower < Lower); |
37 | Lower = NewLower; |
38 | }; |
39 | addWithCarry(P2); |
40 | addWithCarry(P3); |
41 | |
42 | |
43 | if (!Upper) |
44 | return std::make_pair(Lower, 0); |
45 | |
46 | |
47 | unsigned LeadingZeros = countLeadingZeros(Upper); |
48 | int Shift = 64 - LeadingZeros; |
49 | if (LeadingZeros) |
50 | Upper = Upper << LeadingZeros | Lower >> Shift; |
51 | return getRounded(Upper, Shift, |
52 | Shift && (Lower & UINT64_C(1) << (Shift - 1))); |
53 | } |
54 | |
55 | static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); } |
56 | |
57 | std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend, |
58 | uint32_t Divisor) { |
59 | assert(Dividend && "expected non-zero dividend"); |
60 | assert(Divisor && "expected non-zero divisor"); |
61 | |
62 | |
63 | uint64_t Dividend64 = Dividend; |
64 | int Shift = 0; |
65 | if (int Zeros = countLeadingZeros(Dividend64)) { |
66 | Shift -= Zeros; |
67 | Dividend64 <<= Zeros; |
68 | } |
69 | uint64_t Quotient = Dividend64 / Divisor; |
70 | uint64_t Remainder = Dividend64 % Divisor; |
71 | |
72 | |
73 | if (Quotient > UINT32_MAX) |
74 | return getAdjusted<uint32_t>(Quotient, Shift); |
75 | |
76 | |
77 | return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor)); |
78 | } |
79 | |
80 | std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend, |
81 | uint64_t Divisor) { |
82 | assert(Dividend && "expected non-zero dividend"); |
83 | assert(Divisor && "expected non-zero divisor"); |
84 | |
85 | |
86 | int Shift = 0; |
87 | if (int Zeros = countTrailingZeros(Divisor)) { |
| |
| |
88 | Shift -= Zeros; |
89 | Divisor >>= Zeros; |
90 | } |
91 | |
92 | |
93 | if (Divisor == 1) |
| 3 | | Assuming 'Divisor' is not equal to 1 | |
|
| |
94 | return std::make_pair(Dividend, Shift); |
95 | |
96 | |
97 | if (int Zeros = countLeadingZeros(Dividend)) { |
| 5 | | Calling 'countLeadingZeros<unsigned long long>' | |
|
| 14 | | Returning from 'countLeadingZeros<unsigned long long>' | |
|
| 15 | | 'Zeros' initialized to 64 | |
|
| |
98 | Shift -= Zeros; |
99 | Dividend <<= Zeros; |
| 17 | | Assigned value is garbage or undefined |
|
100 | } |
101 | |
102 | |
103 | uint64_t Quotient = Dividend / Divisor; |
104 | Dividend %= Divisor; |
105 | |
106 | |
107 | while (!(Quotient >> 63) && Dividend) { |
108 | |
109 | bool IsOverflow = Dividend >> 63; |
110 | Dividend <<= 1; |
111 | --Shift; |
112 | |
113 | |
114 | Quotient <<= 1; |
115 | if (IsOverflow || Divisor <= Dividend) { |
116 | Quotient |= 1; |
117 | Dividend -= Divisor; |
118 | } |
119 | } |
120 | |
121 | return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor)); |
122 | } |
123 | |
124 | int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) { |
125 | assert(ScaleDiff >= 0 && "wrong argument order"); |
126 | assert(ScaleDiff < 64 && "numbers too far apart"); |
127 | |
128 | uint64_t L_adjusted = L >> ScaleDiff; |
129 | if (L_adjusted < R) |
130 | return -1; |
131 | if (L_adjusted > R) |
132 | return 1; |
133 | |
134 | return L > L_adjusted << ScaleDiff ? 1 : 0; |
135 | } |
136 | |
137 | static void appendDigit(std::string &Str, unsigned D) { |
138 | assert(D < 10); |
139 | Str += '0' + D % 10; |
140 | } |
141 | |
142 | static void appendNumber(std::string &Str, uint64_t N) { |
143 | while (N) { |
144 | appendDigit(Str, N % 10); |
145 | N /= 10; |
146 | } |
147 | } |
148 | |
149 | static bool doesRoundUp(char Digit) { |
150 | switch (Digit) { |
151 | case '5': |
152 | case '6': |
153 | case '7': |
154 | case '8': |
155 | case '9': |
156 | return true; |
157 | default: |
158 | return false; |
159 | } |
160 | } |
161 | |
162 | static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) { |
163 | assert(E >= ScaledNumbers::MinScale); |
164 | assert(E <= ScaledNumbers::MaxScale); |
165 | |
166 | |
167 | int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D); |
168 | int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros); |
169 | int Shift = 63 - (NewE - E); |
170 | assert(Shift <= LeadingZeros); |
171 | assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale); |
172 | assert(Shift >= 0 && Shift < 64 && "undefined behavior"); |
173 | D <<= Shift; |
174 | E = NewE; |
175 | |
176 | |
177 | unsigned AdjustedE = E + 16383; |
178 | if (!(D >> 63)) { |
179 | assert(E == ScaledNumbers::MaxScale); |
180 | AdjustedE = 0; |
181 | } |
182 | |
183 | |
184 | uint64_t RawBits[2] = {D, AdjustedE}; |
185 | APFloat Float(APFloat::x87DoubleExtended(), APInt(80, RawBits)); |
186 | SmallVector<char, 24> Chars; |
187 | Float.toString(Chars, Precision, 0); |
188 | return std::string(Chars.begin(), Chars.end()); |
189 | } |
190 | |
191 | static std::string stripTrailingZeros(const std::string &Float) { |
192 | size_t NonZero = Float.find_last_not_of('0'); |
193 | assert(NonZero != std::string::npos && "no . in floating point string"); |
194 | |
195 | if (Float[NonZero] == '.') |
196 | ++NonZero; |
197 | |
198 | return Float.substr(0, NonZero + 1); |
199 | } |
200 | |
201 | std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width, |
202 | unsigned Precision) { |
203 | if (!D) |
204 | return "0.0"; |
205 | |
206 | |
207 | uint64_t Above0 = 0; |
208 | uint64_t Below0 = 0; |
209 | uint64_t Extra = 0; |
210 | int ExtraShift = 0; |
211 | if (E == 0) { |
212 | Above0 = D; |
213 | } else if (E > 0) { |
214 | if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) { |
215 | D <<= Shift; |
216 | E -= Shift; |
217 | |
218 | if (!E) |
219 | Above0 = D; |
220 | } |
221 | } else if (E > -64) { |
222 | Above0 = D >> -E; |
223 | Below0 = D << (64 + E); |
224 | } else if (E == -64) { |
225 | |
226 | Below0 = D; |
227 | } else if (E > -120) { |
228 | Below0 = D >> (-E - 64); |
229 | Extra = D << (128 + E); |
230 | ExtraShift = -64 - E; |
231 | } |
232 | |
233 | |
234 | if (!Above0 && !Below0) |
235 | return toStringAPFloat(D, E, Precision); |
236 | |
237 | |
238 | std::string Str; |
239 | size_t DigitsOut = 0; |
240 | if (Above0) { |
241 | appendNumber(Str, Above0); |
242 | DigitsOut = Str.size(); |
243 | } else |
244 | appendDigit(Str, 0); |
245 | std::reverse(Str.begin(), Str.end()); |
246 | |
247 | |
248 | if (!Below0) |
249 | return Str + ".0"; |
250 | |
251 | |
252 | Str += '.'; |
253 | uint64_t Error = UINT64_C(1) << (64 - Width); |
254 | |
255 | |
256 | |
257 | Extra = (Below0 & 0xf) << 56 | (Extra >> 8); |
258 | Below0 >>= 4; |
259 | size_t SinceDot = 0; |
260 | size_t AfterDot = Str.size(); |
261 | do { |
262 | if (ExtraShift) { |
263 | --ExtraShift; |
264 | Error *= 5; |
265 | } else |
266 | Error *= 10; |
267 | |
268 | Below0 *= 10; |
269 | Extra *= 10; |
270 | Below0 += (Extra >> 60); |
271 | Extra = Extra & (UINT64_MAX >> 4); |
272 | appendDigit(Str, Below0 >> 60); |
273 | Below0 = Below0 & (UINT64_MAX >> 4); |
274 | if (DigitsOut || Str.back() != '0') |
275 | ++DigitsOut; |
276 | ++SinceDot; |
277 | } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 && |
278 | (!Precision || DigitsOut <= Precision || SinceDot < 2)); |
279 | |
280 | |
281 | if (!Precision || DigitsOut <= Precision) |
282 | return stripTrailingZeros(Str); |
283 | |
284 | |
285 | size_t Truncate = |
286 | std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1); |
287 | |
288 | |
289 | if (Truncate >= Str.size()) |
290 | return stripTrailingZeros(Str); |
291 | |
292 | bool Carry = doesRoundUp(Str[Truncate]); |
293 | if (!Carry) |
294 | return stripTrailingZeros(Str.substr(0, Truncate)); |
295 | |
296 | |
297 | for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend(); |
298 | I != E; ++I) { |
299 | if (*I == '.') |
300 | continue; |
301 | if (*I == '9') { |
302 | *I = '0'; |
303 | continue; |
304 | } |
305 | |
306 | ++*I; |
307 | Carry = false; |
308 | break; |
309 | } |
310 | |
311 | |
312 | return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate)); |
313 | } |
314 | |
315 | raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E, |
316 | int Width, unsigned Precision) { |
317 | return OS << toString(D, E, Width, Precision); |
318 | } |
319 | |
320 | void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) { |
321 | print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E |
322 | << "]"; |
323 | } |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
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 | |
31 | |
32 | |
33 | extern "C" { |
34 | unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); |
35 | unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); |
36 | unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); |
37 | unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); |
38 | } |
39 | #endif |
40 | |
41 | namespace llvm { |
42 | |
43 | |
44 | enum ZeroBehavior { |
45 | |
46 | ZB_Undefined, |
47 | |
48 | ZB_Max, |
49 | |
50 | ZB_Width |
51 | }; |
52 | |
53 | |
54 | namespace numbers { |
55 | |
56 | |
57 | constexpr double e = 2.7182818284590452354, |
58 | egamma = .57721566490153286061, |
59 | ln2 = .69314718055994530942, |
60 | ln10 = 2.3025850929940456840, |
61 | log2e = 1.4426950408889634074, |
62 | log10e = .43429448190325182765, |
63 | pi = 3.1415926535897932385, |
64 | inv_pi = .31830988618379067154, |
65 | sqrtpi = 1.7724538509055160273, |
66 | inv_sqrtpi = .56418958354775628695, |
67 | sqrt2 = 1.4142135623730950488, |
68 | inv_sqrt2 = .70710678118654752440, |
69 | sqrt3 = 1.7320508075688772935, |
70 | inv_sqrt3 = .57735026918962576451, |
71 | phi = 1.6180339887498948482; |
72 | constexpr float ef = 2.71828183F, |
73 | egammaf = .577215665F, |
74 | ln2f = .693147181F, |
75 | ln10f = 2.30258509F, |
76 | log2ef = 1.44269504F, |
77 | log10ef = .434294482F, |
78 | pif = 3.14159265F, |
79 | inv_pif = .318309886F, |
80 | sqrtpif = 1.77245385F, |
81 | inv_sqrtpif = .564189584F, |
82 | sqrt2f = 1.41421356F, |
83 | inv_sqrt2f = .707106781F, |
84 | sqrt3f = 1.73205081F, |
85 | inv_sqrt3f = .577350269F, |
86 | phif = 1.61803399F; |
87 | } |
88 | |
89 | namespace detail { |
90 | template <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 | |
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__) || defined(_MSC_VER) |
114 | template <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) || defined(__GNUC__) |
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) |
130 | template <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) || defined(__GNUC__) |
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 | } |
147 | |
148 | |
149 | |
150 | |
151 | |
152 | |
153 | |
154 | |
155 | template <typename T> |
156 | unsigned 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 | |
163 | namespace detail { |
164 | template <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 | |
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__) || defined(_MSC_VER) |
183 | template <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) || defined(__GNUC__) |
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) |
199 | template <typename T> struct LeadingZerosCounter<T, 8> { |
200 | static unsigned count(T Val, ZeroBehavior ZB) { |
201 | if (ZB != ZB_Undefined && Val == 0) |
| 7 | | Assuming 'Val' is equal to 0 | |
|
| |
202 | return 64; |
| 9 | | Returning the value 64, which participates in a condition later | |
|
| |
203 | |
204 | #if __has_builtin(__builtin_clzll) || defined(__GNUC__) |
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 | } |
216 | |
217 | |
218 | |
219 | |
220 | |
221 | |
222 | |
223 | |
224 | template <typename T> |
225 | unsigned 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); |
| 6 | | Calling 'LeadingZerosCounter::count' | |
|
| 11 | | Returning from 'LeadingZerosCounter::count' | |
|
| 12 | | Returning the value 64, which participates in a condition later | |
|
| |
230 | } |
231 | |
232 | |
233 | |
234 | |
235 | |
236 | |
237 | |
238 | |
239 | template <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 | |
247 | |
248 | template <typename T> T maskTrailingOnes(unsigned N) { |
249 | static_assert(std::is_unsigned<T>::value, "Invalid type!"); |
250 | const unsigned Bits = CHAR_BIT * sizeof(T); |
251 | assert(N <= Bits && "Invalid bit index"); |
252 | return N == 0 ? 0 : (T(-1) >> (Bits - N)); |
253 | } |
254 | |
255 | |
256 | |
257 | template <typename T> T maskLeadingOnes(unsigned N) { |
258 | return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
259 | } |
260 | |
261 | |
262 | |
263 | template <typename T> T maskTrailingZeros(unsigned N) { |
264 | return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); |
265 | } |
266 | |
267 | |
268 | |
269 | template <typename T> T maskLeadingZeros(unsigned N) { |
270 | return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
271 | } |
272 | |
273 | |
274 | |
275 | |
276 | |
277 | |
278 | |
279 | |
280 | template <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 | |
285 | |
286 | return countLeadingZeros(Val, ZB_Undefined) ^ |
287 | (std::numeric_limits<T>::digits - 1); |
288 | } |
289 | |
290 | |
291 | |
292 | |
293 | static 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 | |
304 | template <typename T> |
305 | T 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) |
316 | template<> |
317 | inline uint8_t reverseBits<uint8_t>(uint8_t Val) { |
318 | return __builtin_bitreverse8(Val); |
319 | } |
320 | #endif |
321 | |
322 | #if __has_builtin(__builtin_bitreverse16) |
323 | template<> |
324 | inline uint16_t reverseBits<uint16_t>(uint16_t Val) { |
325 | return __builtin_bitreverse16(Val); |
326 | } |
327 | #endif |
328 | |
329 | #if __has_builtin(__builtin_bitreverse32) |
330 | template<> |
331 | inline uint32_t reverseBits<uint32_t>(uint32_t Val) { |
332 | return __builtin_bitreverse32(Val); |
333 | } |
334 | #endif |
335 | |
336 | #if __has_builtin(__builtin_bitreverse64) |
337 | template<> |
338 | inline uint64_t reverseBits<uint64_t>(uint64_t Val) { |
339 | return __builtin_bitreverse64(Val); |
340 | } |
341 | #endif |
342 | |
343 | |
344 | |
345 | |
346 | |
347 | |
348 | constexpr inline uint32_t Hi_32(uint64_t Value) { |
349 | return static_cast<uint32_t>(Value >> 32); |
350 | } |
351 | |
352 | |
353 | constexpr inline uint32_t Lo_32(uint64_t Value) { |
354 | return static_cast<uint32_t>(Value); |
355 | } |
356 | |
357 | |
358 | constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { |
359 | return ((uint64_t)High << 32) | (uint64_t)Low; |
360 | } |
361 | |
362 | |
363 | template <unsigned N> constexpr inline bool isInt(int64_t x) { |
364 | return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); |
365 | } |
366 | |
367 | template <> constexpr inline bool isInt<8>(int64_t x) { |
368 | return static_cast<int8_t>(x) == x; |
369 | } |
370 | template <> constexpr inline bool isInt<16>(int64_t x) { |
371 | return static_cast<int16_t>(x) == x; |
372 | } |
373 | template <> constexpr inline bool isInt<32>(int64_t x) { |
374 | return static_cast<int32_t>(x) == x; |
375 | } |
376 | |
377 | |
378 | template <unsigned N, unsigned S> |
379 | constexpr 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) << S) == 0); |
384 | } |
385 | |
386 | |
387 | |
388 | |
389 | |
390 | |
391 | |
392 | |
393 | |
394 | template <unsigned N> |
395 | constexpr 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) << (N)); |
398 | } |
399 | template <unsigned N> |
400 | constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) { |
401 | return true; |
402 | } |
403 | |
404 | |
405 | template <> constexpr inline bool isUInt<8>(uint64_t x) { |
406 | return static_cast<uint8_t>(x) == x; |
407 | } |
408 | template <> constexpr inline bool isUInt<16>(uint64_t x) { |
409 | return static_cast<uint16_t>(x) == x; |
410 | } |
411 | template <> constexpr inline bool isUInt<32>(uint64_t x) { |
412 | return static_cast<uint32_t>(x) == x; |
413 | } |
414 | |
415 | |
416 | template <unsigned N, unsigned S> |
417 | constexpr 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 | |
423 | |
424 | return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
425 | } |
426 | |
427 | |
428 | inline uint64_t maxUIntN(uint64_t N) { |
429 | assert(N > 0 && N <= 64 && "integer width out of range"); |
430 | |
431 | |
432 | |
433 | |
434 | |
435 | return UINT64_MAX >> (64 - N); |
436 | } |
437 | |
438 | |
439 | inline int64_t minIntN(int64_t N) { |
440 | assert(N > 0 && N <= 64 && "integer width out of range"); |
441 | |
442 | return UINT64_C(1) + ~(UINT64_C(1) << (N - 1)); |
443 | } |
444 | |
445 | |
446 | inline int64_t maxIntN(int64_t N) { |
447 | assert(N > 0 && N <= 64 && "integer width out of range"); |
448 | |
449 | |
450 | |
451 | return (UINT64_C(1) << (N - 1)) - 1; |
452 | } |
453 | |
454 | |
455 | inline bool isUIntN(unsigned N, uint64_t x) { |
456 | return N >= 64 || x <= maxUIntN(N); |
457 | } |
458 | |
459 | |
460 | inline bool isIntN(unsigned N, int64_t x) { |
461 | return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); |
462 | } |
463 | |
464 | |
465 | |
466 | |
467 | constexpr inline bool isMask_32(uint32_t Value) { |
468 | return Value && ((Value + 1) & Value) == 0; |
469 | } |
470 | |
471 | |
472 | |
473 | constexpr inline bool isMask_64(uint64_t Value) { |
474 | return Value && ((Value + 1) & Value) == 0; |
475 | } |
476 | |
477 | |
478 | |
479 | constexpr inline bool isShiftedMask_32(uint32_t Value) { |
480 | return Value && isMask_32((Value - 1) | Value); |
481 | } |
482 | |
483 | |
484 | |
485 | constexpr inline bool isShiftedMask_64(uint64_t Value) { |
486 | return Value && isMask_64((Value - 1) | Value); |
487 | } |
488 | |
489 | |
490 | |
491 | constexpr inline bool isPowerOf2_32(uint32_t Value) { |
492 | return Value && !(Value & (Value - 1)); |
493 | } |
494 | |
495 | |
496 | constexpr inline bool isPowerOf2_64(uint64_t Value) { |
497 | return Value && !(Value & (Value - 1)); |
498 | } |
499 | |
500 | |
501 | |
502 | |
503 | |
504 | |
505 | |
506 | |
507 | |
508 | template <typename T> |
509 | unsigned 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 | |
517 | |
518 | |
519 | |
520 | |
521 | |
522 | |
523 | |
524 | template <typename T> |
525 | unsigned 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 | |
532 | namespace detail { |
533 | template <typename T, std::size_t SizeOfT> struct PopulationCounter { |
534 | static unsigned count(T Value) { |
535 | |
536 | static_assert(SizeOfT <= 4, "Not implemented!"); |
537 | #if defined(__GNUC__) |
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 | |
548 | template <typename T> struct PopulationCounter<T, 8> { |
549 | static unsigned count(T Value) { |
550 | #if defined(__GNUC__) |
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 | } |
562 | |
563 | |
564 | |
565 | |
566 | template <typename T> |
567 | inline 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 | |
575 | |
576 | template <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 | |
582 | template <> constexpr inline size_t CTLog2<1>() { return 0; } |
583 | |
584 | |
585 | inline 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 | |
594 | |
595 | |
596 | inline unsigned Log2_32(uint32_t Value) { |
597 | return 31 - countLeadingZeros(Value); |
598 | } |
599 | |
600 | |
601 | |
602 | inline unsigned Log2_64(uint64_t Value) { |
603 | return 63 - countLeadingZeros(Value); |
604 | } |
605 | |
606 | |
607 | |
608 | |
609 | inline unsigned Log2_32_Ceil(uint32_t Value) { |
610 | return 32 - countLeadingZeros(Value - 1); |
611 | } |
612 | |
613 | |
614 | |
615 | inline unsigned Log2_64_Ceil(uint64_t Value) { |
616 | return 64 - countLeadingZeros(Value - 1); |
617 | } |
618 | |
619 | |
620 | template <typename T> |
621 | inline 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 | |
630 | inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { |
631 | return greatestCommonDivisor<uint64_t>(A, B); |
632 | } |
633 | |
634 | |
635 | inline 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 | |
643 | inline 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 | |
651 | |
652 | |
653 | inline 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 | |
661 | |
662 | |
663 | inline 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 | |
671 | |
672 | constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { |
673 | |
674 | |
675 | |
676 | |
677 | |
678 | return (A | B) & (1 + ~(A | B)); |
679 | } |
680 | |
681 | |
682 | |
683 | inline 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 | |
694 | |
695 | inline uint64_t PowerOf2Floor(uint64_t A) { |
696 | if (!A) return 0; |
697 | return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); |
698 | } |
699 | |
700 | |
701 | |
702 | inline uint64_t PowerOf2Ceil(uint64_t A) { |
703 | if (!A) |
704 | return 0; |
705 | return NextPowerOf2(A - 1); |
706 | } |
707 | |
708 | |
709 | |
710 | |
711 | |
712 | |
713 | |
714 | |
715 | |
716 | |
717 | |
718 | |
719 | |
720 | |
721 | |
722 | |
723 | |
724 | |
725 | |
726 | |
727 | |
728 | inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
729 | assert(Align != 0u && "Align can't be 0."); |
730 | Skew %= Align; |
731 | return (Value + Align - 1 - Skew) / Align * Align + Skew; |
732 | } |
733 | |
734 | |
735 | |
736 | template <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 | |
742 | inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { |
743 | return alignTo(Numerator, Denominator) / Denominator; |
744 | } |
745 | |
746 | |
747 | inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { |
748 | return (Numerator + (Denominator / 2)) / Denominator; |
749 | } |
750 | |
751 | |
752 | |
753 | inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
754 | assert(Align != 0u && "Align can't be 0."); |
755 | Skew %= Align; |
756 | return (Value - Skew) / Align * Align + Skew; |
757 | } |
758 | |
759 | |
760 | |
761 | template <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 | |
768 | |
769 | inline int32_t SignExtend32(uint32_t X, unsigned B) { |
770 | assert(B > 0 && "Bit width can't be 0."); |
771 | assert(B <= 32 && "Bit width out of range."); |
772 | return int32_t(X << (32 - B)) >> (32 - B); |
773 | } |
774 | |
775 | |
776 | |
777 | template <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 | |
784 | |
785 | inline int64_t SignExtend64(uint64_t X, unsigned B) { |
786 | assert(B > 0 && "Bit width can't be 0."); |
787 | assert(B <= 64 && "Bit width out of range."); |
788 | return int64_t(X << (64 - B)) >> (64 - B); |
789 | } |
790 | |
791 | |
792 | |
793 | template <typename T> |
794 | std::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 | |
799 | |
800 | |
801 | template <typename T> |
802 | std::enable_if_t<std::is_unsigned<T>::value, T> |
803 | SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { |
804 | bool Dummy; |
805 | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
806 | |
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 | |
816 | |
817 | |
818 | template <typename T> |
819 | std::enable_if_t<std::is_unsigned<T>::value, T> |
820 | SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { |
821 | bool Dummy; |
822 | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
823 | |
824 | |
825 | |
826 | |
827 | |
828 | |
829 | Overflowed = false; |
830 | |
831 | |
832 | |
833 | |
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 | |
846 | |
847 | |
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 | |
861 | |
862 | |
863 | |
864 | template <typename T> |
865 | std::enable_if_t<std::is_unsigned<T>::value, T> |
866 | SaturatingMultiplyAdd(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 | |
878 | extern const float huge_valf; |
879 | |
880 | |
881 | |
882 | |
883 | template <typename T> |
884 | std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) { |
885 | #if __has_builtin(__builtin_add_overflow) |
886 | return __builtin_add_overflow(X, Y, &Result); |
887 | #else |
888 | |
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 | |
895 | Result = static_cast<T>(UResult); |
896 | |
897 | |
898 | if (X > 0 && Y > 0) |
899 | return Result <= 0; |
900 | |
901 | if (X < 0 && Y < 0) |
902 | return Result >= 0; |
903 | return false; |
904 | #endif |
905 | } |
906 | |
907 | |
908 | |
909 | template <typename T> |
910 | std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) { |
911 | #if __has_builtin(__builtin_sub_overflow) |
912 | return __builtin_sub_overflow(X, Y, &Result); |
913 | #else |
914 | |
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 | |
921 | Result = static_cast<T>(UResult); |
922 | |
923 | |
924 | if (X <= 0 && Y > 0) |
925 | return Result >= 0; |
926 | |
927 | if (X >= 0 && Y < 0) |
928 | return Result <= 0; |
929 | return false; |
930 | #endif |
931 | } |
932 | |
933 | |
934 | |
935 | template <typename T> |
936 | std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) { |
937 | |
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 | |
944 | const bool IsNegative = (X < 0) ^ (Y < 0); |
945 | Result = IsNegative ? (0 - UResult) : UResult; |
946 | |
947 | |
948 | if (UX == 0 || UY == 0) |
949 | return false; |
950 | |
951 | |
952 | |
953 | |
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 | } |
961 | |
962 | #endif |