src/base/intmath.hh - public/gem5 - Git at Google

 /*
  * 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_v<T>, 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__
	/*
	* 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_v<T>, 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__