| //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // This file contains some functions that are useful for math stuff. |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #ifndef LLVM_SUPPORT_MATHEXTRAS_H |
| #define LLVM_SUPPORT_MATHEXTRAS_H |
| |
| #include "llvm/ADT/bit.h" |
| #include "llvm/Support/Compiler.h" |
| #include <cassert> |
| #include <climits> |
| #include <cstdint> |
| #include <cstring> |
| #include <limits> |
| #include <type_traits> |
| |
| namespace llvm { |
| |
| /// Mathematical constants. |
| namespace numbers { |
| // TODO: Track C++20 std::numbers. |
| // TODO: Favor using the hexadecimal FP constants (requires C++17). |
| constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 |
| egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 |
| ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 |
| ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 |
| log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) |
| log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) |
| pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 |
| inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 |
| sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 |
| inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 |
| sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 |
| inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) |
| sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 |
| inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) |
| phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 |
| constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 |
| egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 |
| ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 |
| ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 |
| log2ef = 1.44269504F, // (0x1.715476P+0) |
| log10ef = .434294482F, // (0x1.bcb7b2P-2) |
| pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 |
| inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 |
| sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 |
| inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 |
| sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 |
| inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) |
| sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 |
| inv_sqrt3f = .577350269F, // (0x1.279a74P-1) |
| phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 |
| } // namespace numbers |
| |
| /// Create a bitmask with the N right-most bits set to 1, and all other |
| /// bits set to 0. Only unsigned types are allowed. |
| template <typename T> T maskTrailingOnes(unsigned N) { |
| static_assert(std::is_unsigned_v<T>, "Invalid type!"); |
| const unsigned Bits = CHAR_BIT * sizeof(T); |
| assert(N <= Bits && "Invalid bit index"); |
| return N == 0 ? 0 : (T(-1) >> (Bits - N)); |
| } |
| |
| /// Create a bitmask with the N left-most bits set to 1, and all other |
| /// bits set to 0. Only unsigned types are allowed. |
| template <typename T> T maskLeadingOnes(unsigned N) { |
| return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
| } |
| |
| /// Create a bitmask with the N right-most bits set to 0, and all other |
| /// bits set to 1. Only unsigned types are allowed. |
| template <typename T> T maskTrailingZeros(unsigned N) { |
| return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); |
| } |
| |
| /// Create a bitmask with the N left-most bits set to 0, and all other |
| /// bits set to 1. Only unsigned types are allowed. |
| template <typename T> T maskLeadingZeros(unsigned N) { |
| return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); |
| } |
| |
| /// Macro compressed bit reversal table for 256 bits. |
| /// |
| /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable |
| static const unsigned char BitReverseTable256[256] = { |
| #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 |
| #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) |
| #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) |
| R6(0), R6(2), R6(1), R6(3) |
| #undef R2 |
| #undef R4 |
| #undef R6 |
| }; |
| |
| /// Reverse the bits in \p Val. |
| template <typename T> T reverseBits(T Val) { |
| #if __has_builtin(__builtin_bitreverse8) |
| if constexpr (std::is_same_v<T, uint8_t>) |
| return __builtin_bitreverse8(Val); |
| #endif |
| #if __has_builtin(__builtin_bitreverse16) |
| if constexpr (std::is_same_v<T, uint16_t>) |
| return __builtin_bitreverse16(Val); |
| #endif |
| #if __has_builtin(__builtin_bitreverse32) |
| if constexpr (std::is_same_v<T, uint32_t>) |
| return __builtin_bitreverse32(Val); |
| #endif |
| #if __has_builtin(__builtin_bitreverse64) |
| if constexpr (std::is_same_v<T, uint64_t>) |
| return __builtin_bitreverse64(Val); |
| #endif |
| |
| unsigned char in[sizeof(Val)]; |
| unsigned char out[sizeof(Val)]; |
| std::memcpy(in, &Val, sizeof(Val)); |
| for (unsigned i = 0; i < sizeof(Val); ++i) |
| out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; |
| std::memcpy(&Val, out, sizeof(Val)); |
| return Val; |
| } |
| |
| // NOTE: The following support functions use the _32/_64 extensions instead of |
| // type overloading so that signed and unsigned integers can be used without |
| // ambiguity. |
| |
| /// Return the high 32 bits of a 64 bit value. |
| constexpr inline uint32_t Hi_32(uint64_t Value) { |
| return static_cast<uint32_t>(Value >> 32); |
| } |
| |
| /// Return the low 32 bits of a 64 bit value. |
| constexpr inline uint32_t Lo_32(uint64_t Value) { |
| return static_cast<uint32_t>(Value); |
| } |
| |
| /// Make a 64-bit integer from a high / low pair of 32-bit integers. |
| constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { |
| return ((uint64_t)High << 32) | (uint64_t)Low; |
| } |
| |
| /// Checks if an integer fits into the given bit width. |
| template <unsigned N> constexpr inline bool isInt(int64_t x) { |
| if constexpr (N == 8) |
| return static_cast<int8_t>(x) == x; |
| if constexpr (N == 16) |
| return static_cast<int16_t>(x) == x; |
| if constexpr (N == 32) |
| return static_cast<int32_t>(x) == x; |
| if constexpr (N < 64) |
| return -(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1)); |
| (void)x; // MSVC v19.25 warns that x is unused. |
| return true; |
| } |
| |
| /// Checks if a signed integer is an N bit number shifted left by S. |
| template <unsigned N, unsigned S> |
| constexpr inline bool isShiftedInt(int64_t x) { |
| static_assert( |
| N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); |
| static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide."); |
| return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
| } |
| |
| /// Checks if an unsigned integer fits into the given bit width. |
| template <unsigned N> constexpr inline bool isUInt(uint64_t x) { |
| static_assert(N > 0, "isUInt<0> doesn't make sense"); |
| if constexpr (N == 8) |
| return static_cast<uint8_t>(x) == x; |
| if constexpr (N == 16) |
| return static_cast<uint16_t>(x) == x; |
| if constexpr (N == 32) |
| return static_cast<uint32_t>(x) == x; |
| if constexpr (N < 64) |
| return x < (UINT64_C(1) << (N)); |
| (void)x; // MSVC v19.25 warns that x is unused. |
| return true; |
| } |
| |
| /// Checks if a unsigned integer is an N bit number shifted left by S. |
| template <unsigned N, unsigned S> |
| constexpr inline bool isShiftedUInt(uint64_t x) { |
| static_assert( |
| N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); |
| static_assert(N + S <= 64, |
| "isShiftedUInt<N, S> with N + S > 64 is too wide."); |
| // Per the two static_asserts above, S must be strictly less than 64. So |
| // 1 << S is not undefined behavior. |
| return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); |
| } |
| |
| /// Gets the maximum value for a N-bit unsigned integer. |
| inline uint64_t maxUIntN(uint64_t N) { |
| assert(N > 0 && N <= 64 && "integer width out of range"); |
| |
| // uint64_t(1) << 64 is undefined behavior, so we can't do |
| // (uint64_t(1) << N) - 1 |
| // without checking first that N != 64. But this works and doesn't have a |
| // branch. |
| return UINT64_MAX >> (64 - N); |
| } |
| |
| /// Gets the minimum value for a N-bit signed integer. |
| inline int64_t minIntN(int64_t N) { |
| assert(N > 0 && N <= 64 && "integer width out of range"); |
| |
| return UINT64_C(1) + ~(UINT64_C(1) << (N - 1)); |
| } |
| |
| /// Gets the maximum value for a N-bit signed integer. |
| inline int64_t maxIntN(int64_t N) { |
| assert(N > 0 && N <= 64 && "integer width out of range"); |
| |
| // This relies on two's complement wraparound when N == 64, so we convert to |
| // int64_t only at the very end to avoid UB. |
| return (UINT64_C(1) << (N - 1)) - 1; |
| } |
| |
| /// Checks if an unsigned integer fits into the given (dynamic) bit width. |
| inline bool isUIntN(unsigned N, uint64_t x) { |
| return N >= 64 || x <= maxUIntN(N); |
| } |
| |
| /// Checks if an signed integer fits into the given (dynamic) bit width. |
| inline bool isIntN(unsigned N, int64_t x) { |
| return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); |
| } |
| |
| /// Return true if the argument is a non-empty sequence of ones starting at the |
| /// least significant bit with the remainder zero (32 bit version). |
| /// Ex. isMask_32(0x0000FFFFU) == true. |
| constexpr inline bool isMask_32(uint32_t Value) { |
| return Value && ((Value + 1) & Value) == 0; |
| } |
| |
| /// Return true if the argument is a non-empty sequence of ones starting at the |
| /// least significant bit with the remainder zero (64 bit version). |
| constexpr inline bool isMask_64(uint64_t Value) { |
| return Value && ((Value + 1) & Value) == 0; |
| } |
| |
| /// Return true if the argument contains a non-empty sequence of ones with the |
| /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. |
| constexpr inline bool isShiftedMask_32(uint32_t Value) { |
| return Value && isMask_32((Value - 1) | Value); |
| } |
| |
| /// Return true if the argument contains a non-empty sequence of ones with the |
| /// remainder zero (64 bit version.) |
| constexpr inline bool isShiftedMask_64(uint64_t Value) { |
| return Value && isMask_64((Value - 1) | Value); |
| } |
| |
| /// Return true if the argument is a power of two > 0. |
| /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) |
| constexpr inline bool isPowerOf2_32(uint32_t Value) { |
| return llvm::has_single_bit(Value); |
| } |
| |
| /// Return true if the argument is a power of two > 0 (64 bit edition.) |
| constexpr inline bool isPowerOf2_64(uint64_t Value) { |
| return llvm::has_single_bit(Value); |
| } |
| |
| /// Return true if the argument contains a non-empty sequence of ones with the |
| /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. |
| /// If true, \p MaskIdx will specify the index of the lowest set bit and \p |
| /// MaskLen is updated to specify the length of the mask, else neither are |
| /// updated. |
| inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx, |
| unsigned &MaskLen) { |
| if (!isShiftedMask_32(Value)) |
| return false; |
| MaskIdx = llvm::countr_zero(Value); |
| MaskLen = llvm::popcount(Value); |
| return true; |
| } |
| |
| /// Return true if the argument contains a non-empty sequence of ones with the |
| /// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index |
| /// of the lowest set bit and \p MaskLen is updated to specify the length of the |
| /// mask, else neither are updated. |
| inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx, |
| unsigned &MaskLen) { |
| if (!isShiftedMask_64(Value)) |
| return false; |
| MaskIdx = llvm::countr_zero(Value); |
| MaskLen = llvm::popcount(Value); |
| return true; |
| } |
| |
| /// Compile time Log2. |
| /// Valid only for positive powers of two. |
| template <size_t kValue> constexpr inline size_t CTLog2() { |
| static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), |
| "Value is not a valid power of 2"); |
| return 1 + CTLog2<kValue / 2>(); |
| } |
| |
| template <> constexpr inline size_t CTLog2<1>() { return 0; } |
| |
| /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
| /// (32 bit edition.) |
| /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 |
| inline unsigned Log2_32(uint32_t Value) { |
| return 31 - llvm::countl_zero(Value); |
| } |
| |
| /// Return the floor log base 2 of the specified value, -1 if the value is zero. |
| /// (64 bit edition.) |
| inline unsigned Log2_64(uint64_t Value) { |
| return 63 - llvm::countl_zero(Value); |
| } |
| |
| /// Return the ceil log base 2 of the specified value, 32 if the value is zero. |
| /// (32 bit edition). |
| /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 |
| inline unsigned Log2_32_Ceil(uint32_t Value) { |
| return 32 - llvm::countl_zero(Value - 1); |
| } |
| |
| /// Return the ceil log base 2 of the specified value, 64 if the value is zero. |
| /// (64 bit edition.) |
| inline unsigned Log2_64_Ceil(uint64_t Value) { |
| return 64 - llvm::countl_zero(Value - 1); |
| } |
| |
| /// A and B are either alignments or offsets. Return the minimum alignment that |
| /// may be assumed after adding the two together. |
| constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { |
| // The largest power of 2 that divides both A and B. |
| // |
| // Replace "-Value" by "1+~Value" in the following commented code to avoid |
| // MSVC warning C4146 |
| // return (A | B) & -(A | B); |
| return (A | B) & (1 + ~(A | B)); |
| } |
| |
| /// Returns the next power of two (in 64-bits) that is strictly greater than A. |
| /// Returns zero on overflow. |
| constexpr inline uint64_t NextPowerOf2(uint64_t A) { |
| A |= (A >> 1); |
| A |= (A >> 2); |
| A |= (A >> 4); |
| A |= (A >> 8); |
| A |= (A >> 16); |
| A |= (A >> 32); |
| return A + 1; |
| } |
| |
| /// Returns the power of two which is greater than or equal to the given value. |
| /// Essentially, it is a ceil operation across the domain of powers of two. |
| inline uint64_t PowerOf2Ceil(uint64_t A) { |
| if (!A || A > UINT64_MAX / 2) |
| return 0; |
| return UINT64_C(1) << Log2_64_Ceil(A); |
| } |
| |
| /// Returns the next integer (mod 2**64) that is greater than or equal to |
| /// \p Value and is a multiple of \p Align. \p Align must be non-zero. |
| /// |
| /// Examples: |
| /// \code |
| /// alignTo(5, 8) = 8 |
| /// alignTo(17, 8) = 24 |
| /// alignTo(~0LL, 8) = 0 |
| /// alignTo(321, 255) = 510 |
| /// \endcode |
| inline uint64_t alignTo(uint64_t Value, uint64_t Align) { |
| assert(Align != 0u && "Align can't be 0."); |
| return (Value + Align - 1) / Align * Align; |
| } |
| |
| inline uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) { |
| assert(Align != 0 && (Align & (Align - 1)) == 0 && |
| "Align must be a power of 2"); |
| // Replace unary minus to avoid compilation error on Windows: |
| // "unary minus operator applied to unsigned type, result still unsigned" |
| uint64_t negAlign = (~Align) + 1; |
| return (Value + Align - 1) & negAlign; |
| } |
| |
| /// If non-zero \p Skew is specified, the return value will be a minimal integer |
| /// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for |
| /// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p |
| /// Skew mod \p A'. \p Align must be non-zero. |
| /// |
| /// Examples: |
| /// \code |
| /// alignTo(5, 8, 7) = 7 |
| /// alignTo(17, 8, 1) = 17 |
| /// alignTo(~0LL, 8, 3) = 3 |
| /// alignTo(321, 255, 42) = 552 |
| /// \endcode |
| inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew) { |
| assert(Align != 0u && "Align can't be 0."); |
| Skew %= Align; |
| return alignTo(Value - Skew, Align) + Skew; |
| } |
| |
| /// Returns the next integer (mod 2**64) that is greater than or equal to |
| /// \p Value and is a multiple of \c Align. \c Align must be non-zero. |
| template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { |
| static_assert(Align != 0u, "Align must be non-zero"); |
| return (Value + Align - 1) / Align * Align; |
| } |
| |
| /// Returns the integer ceil(Numerator / Denominator). |
| inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { |
| return alignTo(Numerator, Denominator) / Denominator; |
| } |
| |
| /// Returns the integer nearest(Numerator / Denominator). |
| inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { |
| return (Numerator + (Denominator / 2)) / Denominator; |
| } |
| |
| /// Returns the largest uint64_t less than or equal to \p Value and is |
| /// \p Skew mod \p Align. \p Align must be non-zero |
| inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { |
| assert(Align != 0u && "Align can't be 0."); |
| Skew %= Align; |
| return (Value - Skew) / Align * Align + Skew; |
| } |
| |
| /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
| /// Requires 0 < B <= 32. |
| template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { |
| static_assert(B > 0, "Bit width can't be 0."); |
| static_assert(B <= 32, "Bit width out of range."); |
| return int32_t(X << (32 - B)) >> (32 - B); |
| } |
| |
| /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. |
| /// Requires 0 < B <= 32. |
| inline int32_t SignExtend32(uint32_t X, unsigned B) { |
| assert(B > 0 && "Bit width can't be 0."); |
| assert(B <= 32 && "Bit width out of range."); |
| return int32_t(X << (32 - B)) >> (32 - B); |
| } |
| |
| /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
| /// Requires 0 < B <= 64. |
| template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { |
| static_assert(B > 0, "Bit width can't be 0."); |
| static_assert(B <= 64, "Bit width out of range."); |
| return int64_t(x << (64 - B)) >> (64 - B); |
| } |
| |
| /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. |
| /// Requires 0 < B <= 64. |
| inline int64_t SignExtend64(uint64_t X, unsigned B) { |
| assert(B > 0 && "Bit width can't be 0."); |
| assert(B <= 64 && "Bit width out of range."); |
| return int64_t(X << (64 - B)) >> (64 - B); |
| } |
| |
| /// Subtract two unsigned integers, X and Y, of type T and return the absolute |
| /// value of the result. |
| template <typename T> |
| std::enable_if_t<std::is_unsigned_v<T>, T> AbsoluteDifference(T X, T Y) { |
| return X > Y ? (X - Y) : (Y - X); |
| } |
| |
| /// Add two unsigned integers, X and Y, of type T. Clamp the result to the |
| /// maximum representable value of T on overflow. ResultOverflowed indicates if |
| /// the result is larger than the maximum representable value of type T. |
| template <typename T> |
| std::enable_if_t<std::is_unsigned_v<T>, T> |
| SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { |
| bool Dummy; |
| bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
| // Hacker's Delight, p. 29 |
| T Z = X + Y; |
| Overflowed = (Z < X || Z < Y); |
| if (Overflowed) |
| return std::numeric_limits<T>::max(); |
| else |
| return Z; |
| } |
| |
| /// Add multiple unsigned integers of type T. Clamp the result to the |
| /// maximum representable value of T on overflow. |
| template <class T, class... Ts> |
| std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z, |
| Ts... Args) { |
| bool Overflowed = false; |
| T XY = SaturatingAdd(X, Y, &Overflowed); |
| if (Overflowed) |
| return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...); |
| return SaturatingAdd(XY, Z, Args...); |
| } |
| |
| /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the |
| /// maximum representable value of T on overflow. ResultOverflowed indicates if |
| /// the result is larger than the maximum representable value of type T. |
| template <typename T> |
| std::enable_if_t<std::is_unsigned_v<T>, T> |
| SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { |
| bool Dummy; |
| bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
| |
| // Hacker's Delight, p. 30 has a different algorithm, but we don't use that |
| // because it fails for uint16_t (where multiplication can have undefined |
| // behavior due to promotion to int), and requires a division in addition |
| // to the multiplication. |
| |
| Overflowed = false; |
| |
| // Log2(Z) would be either Log2Z or Log2Z + 1. |
| // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z |
| // will necessarily be less than Log2Max as desired. |
| int Log2Z = Log2_64(X) + Log2_64(Y); |
| const T Max = std::numeric_limits<T>::max(); |
| int Log2Max = Log2_64(Max); |
| if (Log2Z < Log2Max) { |
| return X * Y; |
| } |
| if (Log2Z > Log2Max) { |
| Overflowed = true; |
| return Max; |
| } |
| |
| // We're going to use the top bit, and maybe overflow one |
| // bit past it. Multiply all but the bottom bit then add |
| // that on at the end. |
| T Z = (X >> 1) * Y; |
| if (Z & ~(Max >> 1)) { |
| Overflowed = true; |
| return Max; |
| } |
| Z <<= 1; |
| if (X & 1) |
| return SaturatingAdd(Z, Y, ResultOverflowed); |
| |
| return Z; |
| } |
| |
| /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to |
| /// the product. Clamp the result to the maximum representable value of T on |
| /// overflow. ResultOverflowed indicates if the result is larger than the |
| /// maximum representable value of type T. |
| template <typename T> |
| std::enable_if_t<std::is_unsigned_v<T>, T> |
| SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { |
| bool Dummy; |
| bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; |
| |
| T Product = SaturatingMultiply(X, Y, &Overflowed); |
| if (Overflowed) |
| return Product; |
| |
| return SaturatingAdd(A, Product, &Overflowed); |
| } |
| |
| /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. |
| extern const float huge_valf; |
| |
| |
| /// Add two signed integers, computing the two's complement truncated result, |
| /// returning true if overflow occurred. |
| template <typename T> |
| std::enable_if_t<std::is_signed_v<T>, T> AddOverflow(T X, T Y, T &Result) { |
| #if __has_builtin(__builtin_add_overflow) |
| return __builtin_add_overflow(X, Y, &Result); |
| #else |
| // Perform the unsigned addition. |
| using U = std::make_unsigned_t<T>; |
| const U UX = static_cast<U>(X); |
| const U UY = static_cast<U>(Y); |
| const U UResult = UX + UY; |
| |
| // Convert to signed. |
| Result = static_cast<T>(UResult); |
| |
| // Adding two positive numbers should result in a positive number. |
| if (X > 0 && Y > 0) |
| return Result <= 0; |
| // Adding two negatives should result in a negative number. |
| if (X < 0 && Y < 0) |
| return Result >= 0; |
| return false; |
| #endif |
| } |
| |
| /// Subtract two signed integers, computing the two's complement truncated |
| /// result, returning true if an overflow ocurred. |
| template <typename T> |
| std::enable_if_t<std::is_signed_v<T>, T> SubOverflow(T X, T Y, T &Result) { |
| #if __has_builtin(__builtin_sub_overflow) |
| return __builtin_sub_overflow(X, Y, &Result); |
| #else |
| // Perform the unsigned addition. |
| using U = std::make_unsigned_t<T>; |
| const U UX = static_cast<U>(X); |
| const U UY = static_cast<U>(Y); |
| const U UResult = UX - UY; |
| |
| // Convert to signed. |
| Result = static_cast<T>(UResult); |
| |
| // Subtracting a positive number from a negative results in a negative number. |
| if (X <= 0 && Y > 0) |
| return Result >= 0; |
| // Subtracting a negative number from a positive results in a positive number. |
| if (X >= 0 && Y < 0) |
| return Result <= 0; |
| return false; |
| #endif |
| } |
| |
| /// Multiply two signed integers, computing the two's complement truncated |
| /// result, returning true if an overflow ocurred. |
| template <typename T> |
| std::enable_if_t<std::is_signed_v<T>, T> MulOverflow(T X, T Y, T &Result) { |
| // Perform the unsigned multiplication on absolute values. |
| using U = std::make_unsigned_t<T>; |
| const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); |
| const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); |
| const U UResult = UX * UY; |
| |
| // Convert to signed. |
| const bool IsNegative = (X < 0) ^ (Y < 0); |
| Result = IsNegative ? (0 - UResult) : UResult; |
| |
| // If any of the args was 0, result is 0 and no overflow occurs. |
| if (UX == 0 || UY == 0) |
| return false; |
| |
| // UX and UY are in [1, 2^n], where n is the number of digits. |
| // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for |
| // positive) divided by an argument compares to the other. |
| if (IsNegative) |
| return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; |
| else |
| return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; |
| } |
| |
| } // End llvm namespace |
| |
| #endif |