| /* |
| * Copyright (c) 2021 ARM Limited |
| * All rights reserved |
| * |
| * The license below extends only to copyright in the software and shall |
| * not be construed as granting a license to any other intellectual |
| * property including but not limited to intellectual property relating |
| * to a hardware implementation of the functionality of the software |
| * licensed hereunder. You may use the software subject to the license |
| * terms below provided that you ensure that this notice is replicated |
| * unmodified and in its entirety in all distributions of the software, |
| * modified or unmodified, in source code or in binary form. |
| * |
| * Copyright (c) 2001, 2003-2005 The Regents of The University of Michigan |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions are |
| * met: redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer; |
| * redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution; |
| * neither the name of the copyright holders nor the names of its |
| * contributors may be used to endorse or promote products derived from |
| * this software without specific prior written permission. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| */ |
| |
| #ifndef __BASE_INTMATH_HH__ |
| #define __BASE_INTMATH_HH__ |
| |
| #include <cassert> |
| #include <cstdint> |
| #include <type_traits> |
| #include <utility> |
| |
| #include "base/bitfield.hh" |
| |
| namespace gem5 |
| { |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <class T> |
| static constexpr std::enable_if_t<std::is_integral<T>::value, int> |
| floorLog2(T x) |
| { |
| assert(x > 0); |
| |
| // A guaranteed unsigned version of x. |
| uint64_t ux = (typename std::make_unsigned<T>::type)x; |
| |
| int y = 0; |
| constexpr auto ts = sizeof(T); |
| |
| if (ts >= 8 && (ux & 0xffffffff00000000ULL)) { y += 32; ux >>= 32; } |
| if (ts >= 4 && (ux & 0x00000000ffff0000ULL)) { y += 16; ux >>= 16; } |
| if (ts >= 2 && (ux & 0x000000000000ff00ULL)) { y += 8; ux >>= 8; } |
| if (ux & 0x00000000000000f0ULL) { y += 4; ux >>= 4; } |
| if (ux & 0x000000000000000cULL) { y += 2; ux >>= 2; } |
| if (ux & 0x0000000000000002ULL) { y += 1; } |
| |
| return y; |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <class T> |
| static constexpr int |
| ceilLog2(const T& n) |
| { |
| assert(n > 0); |
| if (n == 1) |
| return 0; |
| |
| return floorLog2(n - (T)1) + 1; |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <class T> |
| static constexpr bool |
| isPowerOf2(const T& n) |
| { |
| // If n is non-zero, and subtracting one borrows all the way to the MSB |
| // and flips all bits, then this is a power of 2. |
| return n && !(n & (n - 1)); |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <class T, class U> |
| static constexpr T |
| divCeil(const T& a, const U& b) |
| { |
| return (a + b - 1) / b; |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) <= sizeof(uint32_t)> |
| mulUnsigned(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low, |
| std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b) |
| { |
| uint64_t product = (uint64_t)val_a * (uint64_t)val_b; |
| low = product; |
| high = (product >> (sizeof(low) * 8)); |
| }; |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) <= sizeof(uint32_t)> |
| mulSigned(std::make_signed_t<T> &high, std::make_signed_t<T> &low, |
| std::make_signed_t<T> val_a, std::make_signed_t<T> val_b) |
| { |
| uint64_t product = (int64_t)val_a * (int64_t)val_b; |
| low = product; |
| high = (product >> (sizeof(low) * 8)); |
| }; |
| |
| /** |
| * Multiply two values with place value p. |
| * |
| * (A * p + a) * (B * p + b) = |
| * (A * B) * p^2 + (a * B + A * b) * p + (a * b) |
| * |
| * low result = (a * B + A * b) * p + (a * b) |
| * high result = (A * B) + carry out from low result. |
| * |
| * As long as p is at most half the capacity of the underlying type, no |
| * individual multiplication will overflow. We just have to carefully manage |
| * carries to avoid losing any during the addition steps. |
| */ |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)> |
| mulUnsignedManual(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low, |
| std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b) |
| { |
| low = val_a * val_b; |
| |
| uint64_t A = (uint32_t)(val_a >> 32); |
| uint64_t a = (uint32_t)val_a; |
| uint64_t B = (uint32_t)(val_b >> 32); |
| uint64_t b = (uint32_t)val_b; |
| |
| uint64_t c1 = 0, c2 = 0; // Carry between place values. |
| uint64_t ab = a * b, Ab = A * b, aB = a * B, AB = A * B; |
| |
| c1 = (uint32_t)(ab >> 32); |
| |
| // Be careful to avoid overflow. |
| c2 = (c1 >> 1) + (Ab >> 1) + (aB >> 1); |
| c2 += ((c1 & 0x1) + (Ab & 0x1) + (aB & 0x1)) >> 1; |
| c2 >>= 31; |
| |
| high = AB + c2; |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)> |
| mulUnsigned(std::make_unsigned_t<T> &high, std::make_unsigned_t<T> &low, |
| std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b) |
| { |
| #ifdef __SIZEOF_INT128__ |
| __uint128_t val = (__uint128_t)val_a * (__uint128_t)val_b; |
| low = val; |
| high = (val >> 64); |
| #else |
| mulUnsignedManual<T>(high, low, val_a, val_b); |
| #endif |
| } |
| |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)> |
| mulSignedManual(std::make_signed_t<T> &high, std::make_signed_t<T> &low, |
| std::make_signed_t<T> val_a, std::make_signed_t<T> val_b) |
| { |
| uint64_t u_high = 0, u_low = 0; |
| mulUnsigned<T>(u_high, u_low, val_a, val_b); |
| |
| if (val_a < 0) |
| u_high -= val_b; |
| if (val_b < 0) |
| u_high -= val_a; |
| |
| high = u_high; |
| low = u_low; |
| } |
| |
| /** |
| * @ingroup api_base_utils |
| */ |
| template <typename T> |
| static constexpr std::enable_if_t<sizeof(T) == sizeof(uint64_t)> |
| mulSigned(std::make_signed_t<T> &high, std::make_signed_t<T> &low, |
| std::make_signed_t<T> val_a, std::make_signed_t<T> val_b) |
| { |
| #ifdef __SIZEOF_INT128__ |
| __int128_t val = (__int128_t)val_a * (__int128_t)val_b; |
| low = val; |
| high = (val >> 64); |
| #else |
| mulSignedManual<T>(high, low, val_a, val_b); |
| #endif |
| } |
| |
| template <typename T> |
| static constexpr std::pair<std::make_unsigned_t<T>, std::make_unsigned_t<T>> |
| mulUnsigned(std::make_unsigned_t<T> val_a, std::make_unsigned_t<T> val_b) |
| { |
| std::make_unsigned_t<T> hi{}, low{}; |
| mulUnsigned<T>(hi, low, val_a, val_b); |
| return {hi, low}; |
| }; |
| |
| template <typename T> |
| static constexpr std::pair<std::make_signed_t<T>, std::make_signed_t<T>> |
| mulSigned(std::make_signed_t<T> val_a, std::make_signed_t<T> val_b) |
| { |
| std::make_signed_t<T> hi{}, low{}; |
| mulSigned<T>(hi, low, val_a, val_b); |
| return {hi, low}; |
| }; |
| |
| /** |
| * This function is used to align addresses in memory. |
| * |
| * @param val is the address to be aligned. |
| * @param align is the alignment. Can only be a power of 2. |
| * @return The aligned address. The smallest number divisible |
| * by @param align which is greater than or equal to @param val. |
| * |
| * @ingroup api_base_utils |
| */ |
| template <class T, class U> |
| static constexpr T |
| roundUp(const T& val, const U& align) |
| { |
| assert(isPowerOf2(align)); |
| T mask = (T)align - 1; |
| return (val + mask) & ~mask; |
| } |
| |
| /** |
| * This function is used to align addresses in memory. |
| * |
| * @param val is the address to be aligned. |
| * @param align is the alignment. Can only be a power of 2. |
| * @return The aligned address. The biggest number divisible |
| * by @param align which is less than or equal to @param val. |
| * |
| * @ingroup api_base_utils |
| */ |
| template <class T, class U> |
| static constexpr T |
| roundDown(const T& val, const U& align) |
| { |
| assert(isPowerOf2(align)); |
| T mask = (T)align - 1; |
| return val & ~mask; |
| } |
| |
| /** |
| * Calculate the log2 of a power of 2 integer |
| * |
| * @param An input value |
| * @return The base 2 log of value |
| * |
| * @ingroup api_base_utils |
| */ |
| static constexpr int |
| log2i(int value) |
| { |
| assert(isPowerOf2(value) && value > 0); |
| return ctz32(value); |
| } |
| |
| } // namespace gem5 |
| |
| #endif // __BASE_INTMATH_HH__ |