/home/arjun/llvm-project/llvm/include/llvm/Support/MathExtras.h
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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> |
34 | | extern "C" { |
35 | | unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); |
36 | | unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); |
37 | | unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); |
38 | | unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); |
39 | | } |
40 | | #endif |
41 | | |
42 | | namespace llvm { |
43 | | |
44 | | /// The behavior an operation has on an input of 0. |
45 | | enum 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. |
55 | | namespace numbers { |
56 | | // TODO: Track C++20 std::numbers. |
57 | | // TODO: Favor using the hexadecimal FP constants (requires C++17). |
58 | | constexpr 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 |
73 | | constexpr 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 | | |
90 | | namespace detail { |
91 | | template <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__) || defined(_MSC_VER) |
115 | | template <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) || defined(__GNUC__) |
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) |
131 | | template <typename T> struct TrailingZerosCounter<T, 8> { |
132 | 0 | static unsigned count(T Val, ZeroBehavior ZB) { |
133 | 0 | if (ZB != ZB_Undefined && Val == 0) |
134 | 0 | return 64; |
135 | 0 | |
136 | 0 | #if __has_builtin(__builtin_ctzll) || defined(__GNUC__) |
137 | 0 | 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. |
156 | | template <typename T> |
157 | 0 | unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { |
158 | 0 | static_assert(std::numeric_limits<T>::is_integer && |
159 | 0 | !std::numeric_limits<T>::is_signed, |
160 | 0 | "Only unsigned integral types are allowed."); |
161 | 0 | return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB); |
162 | 0 | } |
163 | | |
164 | | namespace detail { |
165 | | template <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__) || defined(_MSC_VER) |
184 | | template <typename T> struct LeadingZerosCounter<T, 4> { |
185 | 0 | static unsigned count(T Val, ZeroBehavior ZB) { |
186 | 0 | if (ZB != ZB_Undefined && Val == 0) |
187 | 0 | return 32; |
188 | 0 | |
189 | 0 | #if __has_builtin(__builtin_clz) || defined(__GNUC__) |
190 | 0 | 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) |
200 | | template <typename T> struct LeadingZerosCounter<T, 8> { |
201 | 0 | static unsigned count(T Val, ZeroBehavior ZB) { |
202 | 0 | if (ZB != ZB_Undefined && Val == 0) |
203 | 0 | return 64; |
204 | 0 | |
205 | 0 | #if __has_builtin(__builtin_clzll) || defined(__GNUC__) |
206 | 0 | 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. |
225 | | template <typename T> |
226 | 0 | unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { |
227 | 0 | static_assert(std::numeric_limits<T>::is_integer && |
228 | 0 | !std::numeric_limits<T>::is_signed, |
229 | 0 | "Only unsigned integral types are allowed."); |
230 | 0 | return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB); |
231 | 0 | } Unexecuted instantiation: _ZN4llvm17countLeadingZerosIjEEjT_NS_12ZeroBehaviorE Unexecuted instantiation: _ZN4llvm17countLeadingZerosImEEjT_NS_12ZeroBehaviorE |
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. |
240 | 0 | template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { |
241 | 0 | if (ZB == ZB_Max && Val == 0) |
242 | 0 | return std::numeric_limits<T>::max(); |
243 | 0 | |
244 | 0 | return countTrailingZeros(Val, ZB_Undefined); |
245 | 0 | } |
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. |
249 | 0 | template <typename T> T maskTrailingOnes(unsigned N) { |
250 | 0 | static_assert(std::is_unsigned<T>::value, "Invalid type!"); |
251 | 0 | const unsigned Bits = CHAR_BIT * sizeof(T); |
252 | 0 | assert(N <= Bits && "Invalid bit index"); |
253 | 0 | return N == 0 ? 0 : (T(-1) >> (Bits - N)); |
254 | 0 | } Unexecuted instantiation: _ZN4llvm16maskTrailingOnesImEET_j Unexecuted instantiation: _ZN4llvm16maskTrailingOnesIhEET_j |
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. |
258 | 0 | template <typename T> T maskLeadingOnes(unsigned N) { |
259 | 0 | return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
260 | 0 | } |
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. |
264 | 0 | template <typename T> T maskTrailingZeros(unsigned N) { |
265 | 0 | return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); |
266 | 0 | } |
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. |
270 | | template <typename T> T maskLeadingZeros(unsigned N) { |
271 | | return maskTrailingOnes<T>(CHAR_BIT * 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. |
281 | 0 | template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { |
282 | 0 | if (ZB == ZB_Max && Val == 0) |
283 | 0 | return std::numeric_limits<T>::max(); |
284 | 0 | |
285 | 0 | // Use ^ instead of - because both gcc and llvm can remove the associated ^ |
286 | 0 | // in the __builtin_clz intrinsic on x86. |
287 | 0 | return countLeadingZeros(Val, ZB_Undefined) ^ |
288 | 0 | (std::numeric_limits<T>::digits - 1); |
289 | 0 | } |
290 | | |
291 | | /// Macro compressed bit reversal table for 256 bits. |
292 | | /// |
293 | | /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable |
294 | | static 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. |
305 | | template <typename T> |
306 | | T 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 | | #if __has_builtin(__builtin_bitreverse8) |
317 | | template<> |
318 | 0 | inline uint8_t reverseBits<uint8_t>(uint8_t Val) { |
319 | 0 | return __builtin_bitreverse8(Val); |
320 | 0 | } |
321 | | #endif |
322 | | |
323 | | #if __has_builtin(__builtin_bitreverse16) |
324 | | template<> |
325 | 0 | inline uint16_t reverseBits<uint16_t>(uint16_t Val) { |
326 | 0 | return __builtin_bitreverse16(Val); |
327 | 0 | } |
328 | | #endif |
329 | | |
330 | | #if __has_builtin(__builtin_bitreverse32) |
331 | | template<> |
332 | 0 | inline uint32_t reverseBits<uint32_t>(uint32_t Val) { |
333 | 0 | return __builtin_bitreverse32(Val); |
334 | 0 | } |
335 | | #endif |
336 | | |
337 | | #if __has_builtin(__builtin_bitreverse64) |
338 | | template<> |
339 | 0 | inline uint64_t reverseBits<uint64_t>(uint64_t Val) { |
340 | 0 | return __builtin_bitreverse64(Val); |
341 | 0 | } |
342 | | #endif |
343 | | |
344 | | // NOTE: The following support functions use the _32/_64 extensions instead of |
345 | | // type overloading so that signed and unsigned integers can be used without |
346 | | // ambiguity. |
347 | | |
348 | | /// Return the high 32 bits of a 64 bit value. |
349 | 0 | constexpr inline uint32_t Hi_32(uint64_t Value) { |
350 | 0 | return static_cast<uint32_t>(Value >> 32); |
351 | 0 | } |
352 | | |
353 | | /// Return the low 32 bits of a 64 bit value. |
354 | 0 | constexpr inline uint32_t Lo_32(uint64_t Value) { |
355 | 0 | return static_cast<uint32_t>(Value); |
356 | 0 | } |
357 | | |
358 | | /// Make a 64-bit integer from a high / low pair of 32-bit integers. |
359 | 0 | constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { |
360 | 0 | return ((uint64_t)High << 32) | (uint64_t)Low; |
361 | 0 | } |
362 | | |
363 | | /// Checks if an integer fits into the given bit width. |
364 | | template <unsigned N> constexpr inline bool isInt(int64_t x) { |
365 | | return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); |
366 | | } |
367 | | // Template specializations to get better code for common cases. |
368 | 0 | template <> constexpr inline bool isInt<8>(int64_t x) { |
369 | 0 | return static_cast<int8_t>(x) == x; |
370 | 0 | } |
371 | 0 | template <> constexpr inline bool isInt<16>(int64_t x) { |
372 | 0 | return static_cast<int16_t>(x) == x; |
373 | 0 | } |
374 | 0 | template <> constexpr inline bool isInt<32>(int64_t x) { |
375 | 0 | return static_cast<int32_t>(x) == x; |
376 | 0 | } |
377 | | |
378 | | /// Checks if a signed integer is an N bit number shifted left by S. |
379 | | template <unsigned N, unsigned S> |
380 | | constexpr inline bool isShiftedInt(int64_t x) { |
381 | | static_assert( |
382 | | N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); |
383 | | static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide."); |
384 | | return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
385 | | } |
386 | | |
387 | | /// Checks if an unsigned integer fits into the given bit width. |
388 | | /// |
389 | | /// This is written as two functions rather than as simply |
390 | | /// |
391 | | /// return N >= 64 || X < (UINT64_C(1) << N); |
392 | | /// |
393 | | /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting |
394 | | /// left too many places. |
395 | | template <unsigned N> |
396 | | constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) { |
397 | | static_assert(N > 0, "isUInt<0> doesn't make sense"); |
398 | | return X < (UINT64_C(1) << (N)); |
399 | | } |
400 | | template <unsigned N> |
401 | | constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t X) { |
402 | | return true; |
403 | | } |
404 | | |
405 | | // Template specializations to get better code for common cases. |
406 | 0 | template <> constexpr inline bool isUInt<8>(uint64_t x) { |
407 | 0 | return static_cast<uint8_t>(x) == x; |
408 | 0 | } |
409 | 0 | template <> constexpr inline bool isUInt<16>(uint64_t x) { |
410 | 0 | return static_cast<uint16_t>(x) == x; |
411 | 0 | } |
412 | 0 | template <> constexpr inline bool isUInt<32>(uint64_t x) { |
413 | 0 | return static_cast<uint32_t>(x) == x; |
414 | 0 | } |
415 | | |
416 | | /// Checks if a unsigned integer is an N bit number shifted left by S. |
417 | | template <unsigned N, unsigned S> |
418 | | constexpr inline bool isShiftedUInt(uint64_t x) { |
419 | | static_assert( |
420 | | N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); |
421 | | static_assert(N + S <= 64, |
422 | | "isShiftedUInt<N, S> with N + S > 64 is too wide."); |
423 | | // Per the two static_asserts above, S must be strictly less than 64. So |
424 | | // 1 << S is not undefined behavior. |
425 | | return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
426 | | } |
427 | | |
428 | | /// Gets the maximum value for a N-bit unsigned integer. |
429 | 0 | inline uint64_t maxUIntN(uint64_t N) { |
430 | 0 | assert(N > 0 && N <= 64 && "integer width out of range"); |
431 | 0 |
|
432 | 0 | // uint64_t(1) << 64 is undefined behavior, so we can't do |
433 | 0 | // (uint64_t(1) << N) - 1 |
434 | 0 | // without checking first that N != 64. But this works and doesn't have a |
435 | 0 | // branch. |
436 | 0 | return UINT64_MAX >> (64 - N); |
437 | 0 | } |
438 | | |
439 | | /// Gets the minimum value for a N-bit signed integer. |
440 | 0 | inline int64_t minIntN(int64_t N) { |
441 | 0 | assert(N > 0 && N <= 64 && "integer width out of range"); |
442 | 0 |
|
443 | 0 | return -(UINT64_C(1)<<(N-1)); |
444 | 0 | } |
445 | | |
446 | | /// Gets the maximum value for a N-bit signed integer. |
447 | 0 | inline int64_t maxIntN(int64_t N) { |
448 | 0 | assert(N > 0 && N <= 64 && "integer width out of range"); |
449 | 0 |
|
450 | 0 | // This relies on two's complement wraparound when N == 64, so we convert to |
451 | 0 | // int64_t only at the very end to avoid UB. |
452 | 0 | return (UINT64_C(1) << (N - 1)) - 1; |
453 | 0 | } |
454 | | |
455 | | /// Checks if an unsigned integer fits into the given (dynamic) bit width. |
456 | 0 | inline bool isUIntN(unsigned N, uint64_t x) { |
457 | 0 | return N >= 64 || x <= maxUIntN(N); |
458 | 0 | } |
459 | | |
460 | | /// Checks if an signed integer fits into the given (dynamic) bit width. |
461 | 0 | inline bool isIntN(unsigned N, int64_t x) { |
462 | 0 | return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); |
463 | 0 | } |
464 | | |
465 | | /// Return true if the argument is a non-empty sequence of ones starting at the |
466 | | /// least significant bit with the remainder zero (32 bit version). |
467 | | /// Ex. isMask_32(0x0000FFFFU) == true. |
468 | 0 | constexpr inline bool isMask_32(uint32_t Value) { |
469 | 0 | return Value && ((Value + 1) & Value) == 0; |
470 | 0 | } |
471 | | |
472 | | /// Return true if the argument is a non-empty sequence of ones starting at the |
473 | | /// least significant bit with the remainder zero (64 bit version). |
474 | 0 | constexpr inline bool isMask_64(uint64_t Value) { |
475 | 0 | return Value && ((Value + 1) & Value) == 0; |
476 | 0 | } |
477 | | |
478 | | /// Return true if the argument contains a non-empty sequence of ones with the |
479 | | /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. |
480 | 0 | constexpr inline bool isShiftedMask_32(uint32_t Value) { |
481 | 0 | return Value && isMask_32((Value - 1) | Value); |
482 | 0 | } |
483 | | |
484 | | /// Return true if the argument contains a non-empty sequence of ones with the |
485 | | /// remainder zero (64 bit version.) |
486 | 0 | constexpr inline bool isShiftedMask_64(uint64_t Value) { |
487 | 0 | return Value && isMask_64((Value - 1) | Value); |
488 | 0 | } |
489 | | |
490 | | /// Return true if the argument is a power of two > 0. |
491 | | /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) |
492 | 0 | constexpr inline bool isPowerOf2_32(uint32_t Value) { |
493 | 0 | return Value && !(Value & (Value - 1)); |
494 | 0 | } |
495 | | |
496 | | /// Return true if the argument is a power of two > 0 (64 bit edition.) |
497 | 0 | constexpr inline bool isPowerOf2_64(uint64_t Value) { |
498 | 0 | return Value && !(Value & (Value - 1)); |
499 | 0 | } |
500 | | |
501 | | /// Count the number of ones from the most significant bit to the first |
502 | | /// zero bit. |
503 | | /// |
504 | | /// Ex. countLeadingOnes(0xFF0FFF00) == 8. |
505 | | /// Only unsigned integral types are allowed. |
506 | | /// |
507 | | /// \param ZB the behavior on an input of all ones. Only ZB_Width and |
508 | | /// ZB_Undefined are valid arguments. |
509 | | template <typename T> |
510 | 0 | unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { |
511 | 0 | static_assert(std::numeric_limits<T>::is_integer && |
512 | 0 | !std::numeric_limits<T>::is_signed, |
513 | 0 | "Only unsigned integral types are allowed."); |
514 | 0 | return countLeadingZeros<T>(~Value, ZB); |
515 | 0 | } |
516 | | |
517 | | /// Count the number of ones from the least significant bit to the first |
518 | | /// zero bit. |
519 | | /// |
520 | | /// Ex. countTrailingOnes(0x00FF00FF) == 8. |
521 | | /// Only unsigned integral types are allowed. |
522 | | /// |
523 | | /// \param ZB the behavior on an input of all ones. Only ZB_Width and |
524 | | /// ZB_Undefined are valid arguments. |
525 | | template <typename T> |
526 | 0 | unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { |
527 | 0 | static_assert(std::numeric_limits<T>::is_integer && |
528 | 0 | !std::numeric_limits<T>::is_signed, |
529 | 0 | "Only unsigned integral types are allowed."); |
530 | 0 | return countTrailingZeros<T>(~Value, ZB); |
531 | 0 | } |
532 | | |
533 | | namespace detail { |
534 | | template <typename T, std::size_t SizeOfT> struct PopulationCounter { |
535 | | static unsigned count(T Value) { |
536 | | // Generic version, forward to 32 bits. |
537 | | static_assert(SizeOfT <= 4, "Not implemented!"); |
538 | | #if defined(__GNUC__) |
539 | | return __builtin_popcount(Value); |
540 | | #else |
541 | | uint32_t v = Value; |
542 | | v = v - ((v >> 1) & 0x55555555); |
543 | | v = (v & 0x33333333) + ((v >> 2) & 0x33333333); |
544 | | return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; |
545 | | #endif |
546 | | } |
547 | | }; |
548 | | |
549 | | template <typename T> struct PopulationCounter<T, 8> { |
550 | 0 | static unsigned count(T Value) { |
551 | 0 | #if defined(__GNUC__) |
552 | 0 | return __builtin_popcountll(Value); |
553 | | #else |
554 | | uint64_t v = Value; |
555 | | v = v - ((v >> 1) & 0x5555555555555555ULL); |
556 | | v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL); |
557 | | v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL; |
558 | | return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56); |
559 | | #endif |
560 | | } |
561 | | }; |
562 | | } // namespace detail |
563 | | |
564 | | /// Count the number of set bits in a value. |
565 | | /// Ex. countPopulation(0xF000F000) = 8 |
566 | | /// Returns 0 if the word is zero. |
567 | | template <typename T> |
568 | 0 | inline unsigned countPopulation(T Value) { |
569 | 0 | static_assert(std::numeric_limits<T>::is_integer && |
570 | 0 | !std::numeric_limits<T>::is_signed, |
571 | 0 | "Only unsigned integral types are allowed."); |
572 | 0 | return detail::PopulationCounter<T, sizeof(T)>::count(Value); |
573 | 0 | } |
574 | | |
575 | | /// Compile time Log2. |
576 | | /// Valid only for positive powers of two. |
577 | 0 | template <size_t kValue> constexpr inline size_t CTLog2() { |
578 | 0 | static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), |
579 | 0 | "Value is not a valid power of 2"); |
580 | 0 | return 1 + CTLog2<kValue / 2>(); |
581 | 0 | } Unexecuted instantiation: _ZN4llvm6CTLog2ILm2EEEmv Unexecuted instantiation: _ZN4llvm6CTLog2ILm4EEEmv Unexecuted instantiation: _ZN4llvm6CTLog2ILm8EEEmv |
582 | | |
583 | 0 | template <> constexpr inline size_t CTLog2<1>() { return 0; } |
584 | | |
585 | | /// Return the log base 2 of the specified value. |
586 | 0 | inline double Log2(double Value) { |
587 | 0 | #if defined(__ANDROID_API__) && __ANDROID_API__ < 18 |
588 | 0 | return __builtin_log(Value) / __builtin_log(2.0); |
589 | 0 | #else |
590 | 0 | return log2(Value); |
591 | 0 | #endif |
592 | 0 | } |
593 | | |
594 | | /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
595 | | /// (32 bit edition.) |
596 | | /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 |
597 | 0 | inline unsigned Log2_32(uint32_t Value) { |
598 | 0 | return 31 - countLeadingZeros(Value); |
599 | 0 | } |
600 | | |
601 | | /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
602 | | /// (64 bit edition.) |
603 | 0 | inline unsigned Log2_64(uint64_t Value) { |
604 | 0 | return 63 - countLeadingZeros(Value); |
605 | 0 | } |
606 | | |
607 | | /// Return the ceil log base 2 of the specified value, 32 if the value is zero. |
608 | | /// (32 bit edition). |
609 | | /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 |
610 | 0 | inline unsigned Log2_32_Ceil(uint32_t Value) { |
611 | 0 | return 32 - countLeadingZeros(Value - 1); |
612 | 0 | } |
613 | | |
614 | | /// Return the ceil log base 2 of the specified value, 64 if the value is zero. |
615 | | /// (64 bit edition.) |
616 | 0 | inline unsigned Log2_64_Ceil(uint64_t Value) { |
617 | 0 | return 64 - countLeadingZeros(Value - 1); |
618 | 0 | } |
619 | | |
620 | | /// Return the greatest common divisor of the values using Euclid's algorithm. |
621 | | template <typename T> |
622 | 16.6k | inline T greatestCommonDivisor(T A, T B) { |
623 | 35.7k | while (B) { |
624 | 19.0k | T Tmp = B; |
625 | 19.0k | B = A % B; |
626 | 19.0k | A = Tmp; |
627 | 19.0k | } |
628 | 16.6k | return A; |
629 | 16.6k | } _ZN4llvm21greatestCommonDivisorImEET_S1_S1_ Line | Count | Source | 622 | 1.08k | inline T greatestCommonDivisor(T A, T B) { | 623 | 2.76k | while (B) { | 624 | 1.67k | T Tmp = B; | 625 | 1.67k | B = A % B; | 626 | 1.67k | A = Tmp; | 627 | 1.67k | } | 628 | 1.08k | return A; | 629 | 1.08k | } |
_ZN4llvm21greatestCommonDivisorIlEET_S1_S1_ Line | Count | Source | 622 | 15.5k | inline T greatestCommonDivisor(T A, T B) { | 623 | 32.9k | while (B) { | 624 | 17.3k | T Tmp = B; | 625 | 17.3k | B = A % B; | 626 | 17.3k | A = Tmp; | 627 | 17.3k | } | 628 | 15.5k | return A; | 629 | 15.5k | } |
|
630 | | |
631 | 1.08k | inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { |
632 | 1.08k | return greatestCommonDivisor<uint64_t>(A, B); |
633 | 1.08k | } |
634 | | |
635 | | /// This function takes a 64-bit integer and returns the bit equivalent double. |
636 | 0 | inline double BitsToDouble(uint64_t Bits) { |
637 | 0 | double D; |
638 | 0 | static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); |
639 | 0 | memcpy(&D, &Bits, sizeof(Bits)); |
640 | 0 | return D; |
641 | 0 | } |
642 | | |
643 | | /// This function takes a 32-bit integer and returns the bit equivalent float. |
644 | 0 | inline float BitsToFloat(uint32_t Bits) { |
645 | 0 | float F; |
646 | 0 | static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); |
647 | 0 | memcpy(&F, &Bits, sizeof(Bits)); |
648 | 0 | return F; |
649 | 0 | } |
650 | | |
651 | | /// This function takes a double and returns the bit equivalent 64-bit integer. |
652 | | /// Note that copying doubles around changes the bits of NaNs on some hosts, |
653 | | /// notably x86, so this routine cannot be used if these bits are needed. |
654 | 0 | inline uint64_t DoubleToBits(double Double) { |
655 | 0 | uint64_t Bits; |
656 | 0 | static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); |
657 | 0 | memcpy(&Bits, &Double, sizeof(Double)); |
658 | 0 | return Bits; |
659 | 0 | } |
660 | | |
661 | | /// This function takes a float and returns the bit equivalent 32-bit integer. |
662 | | /// Note that copying floats around changes the bits of NaNs on some hosts, |
663 | | /// notably x86, so this routine cannot be used if these bits are needed. |
664 | 0 | inline uint32_t FloatToBits(float Float) { |
665 | 0 | uint32_t Bits; |
666 | 0 | static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); |
667 | 0 | memcpy(&Bits, &Float, sizeof(Float)); |
668 | 0 | return Bits; |
669 | 0 | } |
670 | | |
671 | | /// A and B are either alignments or offsets. Return the minimum alignment that |
672 | | /// may be assumed after adding the two together. |
673 | 0 | constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { |
674 | 0 | // The largest power of 2 that divides both A and B. |
675 | 0 | // |
676 | 0 | // Replace "-Value" by "1+~Value" in the following commented code to avoid |
677 | 0 | // MSVC warning C4146 |
678 | 0 | // return (A | B) & -(A | B); |
679 | 0 | return (A | B) & (1 + ~(A | B)); |
680 | 0 | } |
681 | | |
682 | | /// Returns the next power of two (in 64-bits) that is strictly greater than A. |
683 | | /// Returns zero on overflow. |
684 | 1 | inline uint64_t NextPowerOf2(uint64_t A) { |
685 | 1 | A |= (A >> 1); |
686 | 1 | A |= (A >> 2); |
687 | 1 | A |= (A >> 4); |
688 | 1 | A |= (A >> 8); |
689 | 1 | A |= (A >> 16); |
690 | 1 | A |= (A >> 32); |
691 | 1 | return A + 1; |
692 | 1 | } |
693 | | |
694 | | /// Returns the power of two which is less than or equal to the given value. |
695 | | /// Essentially, it is a floor operation across the domain of powers of two. |
696 | 0 | inline uint64_t PowerOf2Floor(uint64_t A) { |
697 | 0 | if (!A) return 0; |
698 | 0 | return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); |
699 | 0 | } |
700 | | |
701 | | /// Returns the power of two which is greater than or equal to the given value. |
702 | | /// Essentially, it is a ceil operation across the domain of powers of two. |
703 | 0 | inline uint64_t PowerOf2Ceil(uint64_t A) { |
704 | 0 | if (!A) |
705 | 0 | return 0; |
706 | 0 | return NextPowerOf2(A - 1); |
707 | 0 | } |
708 | | |
709 | | /// Returns the next integer (mod 2**64) that is greater than or equal to |
710 | | /// \p Value and is a multiple of \p Align. \p Align must be non-zero. |
711 | | /// |
712 | | /// If non-zero \p Skew is specified, the return value will be a minimal |
713 | | /// integer that is greater than or equal to \p Value and equal to |
714 | | /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than |
715 | | /// \p Align, its value is adjusted to '\p Skew mod \p Align'. |
716 | | /// |
717 | | /// Examples: |
718 | | /// \code |
719 | | /// alignTo(5, 8) = 8 |
720 | | /// alignTo(17, 8) = 24 |
721 | | /// alignTo(~0LL, 8) = 0 |
722 | | /// alignTo(321, 255) = 510 |
723 | | /// |
724 | | /// alignTo(5, 8, 7) = 7 |
725 | | /// alignTo(17, 8, 1) = 17 |
726 | | /// alignTo(~0LL, 8, 3) = 3 |
727 | | /// alignTo(321, 255, 42) = 552 |
728 | | /// \endcode |
729 | 0 | inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
730 | 0 | assert(Align != 0u && "Align can't be 0."); |
731 | 0 | Skew %= Align; |
732 | 0 | return (Value + Align - 1 - Skew) / Align * Align + Skew; |
733 | 0 | } |
734 | | |
735 | | /// Returns the next integer (mod 2**64) that is greater than or equal to |
736 | | /// \p Value and is a multiple of \c Align. \c Align must be non-zero. |
737 | 0 | template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { |
738 | 0 | static_assert(Align != 0u, "Align must be non-zero"); |
739 | 0 | return (Value + Align - 1) / Align * Align; |
740 | 0 | } |
741 | | |
742 | | /// Returns the integer ceil(Numerator / Denominator). |
743 | 0 | inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { |
744 | 0 | return alignTo(Numerator, Denominator) / Denominator; |
745 | 0 | } |
746 | | |
747 | | /// Returns the integer nearest(Numerator / Denominator). |
748 | 0 | inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { |
749 | 0 | return (Numerator + (Denominator / 2)) / Denominator; |
750 | 0 | } |
751 | | |
752 | | /// Returns the largest uint64_t less than or equal to \p Value and is |
753 | | /// \p Skew mod \p Align. \p Align must be non-zero |
754 | 0 | inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
755 | 0 | assert(Align != 0u && "Align can't be 0."); |
756 | 0 | Skew %= Align; |
757 | 0 | return (Value - Skew) / Align * Align + Skew; |
758 | 0 | } |
759 | | |
760 | | /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
761 | | /// Requires 0 < B <= 32. |
762 | | template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { |
763 | | static_assert(B > 0, "Bit width can't be 0."); |
764 | | static_assert(B <= 32, "Bit width out of range."); |
765 | | return int32_t(X << (32 - B)) >> (32 - B); |
766 | | } |
767 | | |
768 | | /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
769 | | /// Requires 0 < B < 32. |
770 | 0 | inline int32_t SignExtend32(uint32_t X, unsigned B) { |
771 | 0 | assert(B > 0 && "Bit width can't be 0."); |
772 | 0 | assert(B <= 32 && "Bit width out of range."); |
773 | 0 | return int32_t(X << (32 - B)) >> (32 - B); |
774 | 0 | } |
775 | | |
776 | | /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
777 | | /// Requires 0 < B < 64. |
778 | | template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { |
779 | | static_assert(B > 0, "Bit width can't be 0."); |
780 | | static_assert(B <= 64, "Bit width out of range."); |
781 | | return int64_t(x << (64 - B)) >> (64 - B); |
782 | | } |
783 | | |
784 | | /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
785 | | /// Requires 0 < B < 64. |
786 | 0 | inline int64_t SignExtend64(uint64_t X, unsigned B) { |
787 | 0 | assert(B > 0 && "Bit width can't be 0."); |
788 | 0 | assert(B <= 64 && "Bit width out of range."); |
789 | 0 | return int64_t(X << (64 - B)) >> (64 - B); |
790 | 0 | } |
791 | | |
792 | | /// Subtract two unsigned integers, X and Y, of type T and return the absolute |
793 | | /// value of the result. |
794 | | template <typename T> |
795 | | std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) { |
796 | | return std::max(X, Y) - std::min(X, Y); |
797 | | } |
798 | | |
799 | | /// Add two unsigned integers, X and Y, of type T. Clamp the result to the |
800 | | /// maximum representable value of T on overflow. ResultOverflowed indicates if |
801 | | /// the result is larger than the maximum representable value of type T. |
802 | | template <typename T> |
803 | | std::enable_if_t<std::is_unsigned<T>::value, T> |
804 | | SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { |
805 | | bool Dummy; |
806 | | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
807 | | // Hacker's Delight, p. 29 |
808 | | T Z = X + Y; |
809 | | Overflowed = (Z < X || Z < Y); |
810 | | if (Overflowed) |
811 | | return std::numeric_limits<T>::max(); |
812 | | else |
813 | | return Z; |
814 | | } |
815 | | |
816 | | /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the |
817 | | /// maximum representable value of T on overflow. ResultOverflowed indicates if |
818 | | /// the result is larger than the maximum representable value of type T. |
819 | | template <typename T> |
820 | | std::enable_if_t<std::is_unsigned<T>::value, T> |
821 | | SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { |
822 | | bool Dummy; |
823 | | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
824 | | |
825 | | // Hacker's Delight, p. 30 has a different algorithm, but we don't use that |
826 | | // because it fails for uint16_t (where multiplication can have undefined |
827 | | // behavior due to promotion to int), and requires a division in addition |
828 | | // to the multiplication. |
829 | | |
830 | | Overflowed = false; |
831 | | |
832 | | // Log2(Z) would be either Log2Z or Log2Z + 1. |
833 | | // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z |
834 | | // will necessarily be less than Log2Max as desired. |
835 | | int Log2Z = Log2_64(X) + Log2_64(Y); |
836 | | const T Max = std::numeric_limits<T>::max(); |
837 | | int Log2Max = Log2_64(Max); |
838 | | if (Log2Z < Log2Max) { |
839 | | return X * Y; |
840 | | } |
841 | | if (Log2Z > Log2Max) { |
842 | | Overflowed = true; |
843 | | return Max; |
844 | | } |
845 | | |
846 | | // We're going to use the top bit, and maybe overflow one |
847 | | // bit past it. Multiply all but the bottom bit then add |
848 | | // that on at the end. |
849 | | T Z = (X >> 1) * Y; |
850 | | if (Z & ~(Max >> 1)) { |
851 | | Overflowed = true; |
852 | | return Max; |
853 | | } |
854 | | Z <<= 1; |
855 | | if (X & 1) |
856 | | return SaturatingAdd(Z, Y, ResultOverflowed); |
857 | | |
858 | | return Z; |
859 | | } |
860 | | |
861 | | /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to |
862 | | /// the product. Clamp the result to the maximum representable value of T on |
863 | | /// overflow. ResultOverflowed indicates if the result is larger than the |
864 | | /// maximum representable value of type T. |
865 | | template <typename T> |
866 | | std::enable_if_t<std::is_unsigned<T>::value, T> |
867 | | SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { |
868 | | bool Dummy; |
869 | | bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
870 | | |
871 | | T Product = SaturatingMultiply(X, Y, &Overflowed); |
872 | | if (Overflowed) |
873 | | return Product; |
874 | | |
875 | | return SaturatingAdd(A, Product, &Overflowed); |
876 | | } |
877 | | |
878 | | /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. |
879 | | extern const float huge_valf; |
880 | | |
881 | | |
882 | | /// Add two signed integers, computing the two's complement truncated result, |
883 | | /// returning true if overflow occured. |
884 | | template <typename T> |
885 | | std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) { |
886 | | #if __has_builtin(__builtin_add_overflow) |
887 | | return __builtin_add_overflow(X, Y, &Result); |
888 | | #else |
889 | | // Perform the unsigned addition. |
890 | | using U = std::make_unsigned_t<T>; |
891 | | const U UX = static_cast<U>(X); |
892 | | const U UY = static_cast<U>(Y); |
893 | | const U UResult = UX + UY; |
894 | | |
895 | | // Convert to signed. |
896 | | Result = static_cast<T>(UResult); |
897 | | |
898 | | // Adding two positive numbers should result in a positive number. |
899 | | if (X > 0 && Y > 0) |
900 | | return Result <= 0; |
901 | | // Adding two negatives should result in a negative number. |
902 | | if (X < 0 && Y < 0) |
903 | | return Result >= 0; |
904 | | return false; |
905 | | #endif |
906 | | } |
907 | | |
908 | | /// Subtract two signed integers, computing the two's complement truncated |
909 | | /// result, returning true if an overflow ocurred. |
910 | | template <typename T> |
911 | | std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) { |
912 | | #if __has_builtin(__builtin_sub_overflow) |
913 | | return __builtin_sub_overflow(X, Y, &Result); |
914 | | #else |
915 | | // Perform the unsigned addition. |
916 | | using U = std::make_unsigned_t<T>; |
917 | | const U UX = static_cast<U>(X); |
918 | | const U UY = static_cast<U>(Y); |
919 | | const U UResult = UX - UY; |
920 | | |
921 | | // Convert to signed. |
922 | | Result = static_cast<T>(UResult); |
923 | | |
924 | | // Subtracting a positive number from a negative results in a negative number. |
925 | | if (X <= 0 && Y > 0) |
926 | | return Result >= 0; |
927 | | // Subtracting a negative number from a positive results in a positive number. |
928 | | if (X >= 0 && Y < 0) |
929 | | return Result <= 0; |
930 | | return false; |
931 | | #endif |
932 | | } |
933 | | |
934 | | /// Multiply two signed integers, computing the two's complement truncated |
935 | | /// result, returning true if an overflow ocurred. |
936 | | template <typename T> |
937 | | std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) { |
938 | | // Perform the unsigned multiplication on absolute values. |
939 | | using U = std::make_unsigned_t<T>; |
940 | | const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); |
941 | | const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); |
942 | | const U UResult = UX * UY; |
943 | | |
944 | | // Convert to signed. |
945 | | const bool IsNegative = (X < 0) ^ (Y < 0); |
946 | | Result = IsNegative ? (0 - UResult) : UResult; |
947 | | |
948 | | // If any of the args was 0, result is 0 and no overflow occurs. |
949 | | if (UX == 0 || UY == 0) |
950 | | return false; |
951 | | |
952 | | // UX and UY are in [1, 2^n], where n is the number of digits. |
953 | | // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for |
954 | | // positive) divided by an argument compares to the other. |
955 | | if (IsNegative) |
956 | | return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; |
957 | | else |
958 | | return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; |
959 | | } |
960 | | |
961 | | } // End llvm namespace |
962 | | |
963 | | #endif |