include/ck/utility/magic_division.hpp Source File

include/ck/utility/magic_division.hpp Source File#

Composable Kernel: include/ck/utility/magic_division.hpp Source File
 // SPDX-License-Identifier: MIT
 // Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
  
 #pragma once
  
 #include "ck/ck.hpp"
 #include "integral_constant.hpp"
 #include "number.hpp"
 #include "type.hpp"
 #include "tuple.hpp"
  
 #ifdef CK_CODE_GEN_RTC
 #define INT32_MAX 2147483647
 #endif
  
 namespace ck {
  
 // magic number division
 // Caution:
 //   1. For uint32_t as dividend: magic number division implementation being used would produce
 //   correct result if the dividend is uint32_t and its value is within 31-bit value range.
 //   2. For int32_t as dividendd: magic number division for int32_t dividened has not been
 //   implemented, the int32_t dividend would be bit-wise interpreted as uint32_t and magic number
 //   division implementation for uint32_t is then used. Therefore, dividend value need to be
 //   non-negative.
 // TODO:
 //   1. Implement magic number divison for int32_t
 //   2. Implement magic number divison for unit32_t with 32-bit value range
 struct MagicDivision
 {
     // uint32_t
     __host__ __device__ static constexpr auto CalculateMagicNumbers(uint32_t divisor)
     {
         // WARNING: magic division is only applicable for division inside this range.
         // You should use the return value of CalculateMagicNumbers, if division is not inside this
         // range. The "else" logic below is to quiet down run-time error.
         if(divisor >= 1 && divisor <= INT32_MAX)
         {
             uint32_t shift = 0;
             for(shift = 0; shift < 32; ++shift)
             {
                 if((1U << shift) >= divisor)
                 {
                     break;
                 }
             }
  
             uint64_t one        = 1;
             uint64_t multiplier = ((one << 32) * ((one << shift) - divisor)) / divisor + 1;
             // assert(multiplier <= 0xffffffffUL);
  
             return make_tuple(uint32_t(multiplier), shift);
         }
         else
         {
             return make_tuple(uint32_t(0), uint32_t(0));
         }
     }
  
     __host__ __device__ static constexpr uint32_t CalculateMagicMultiplier(uint32_t divisor)
     {
         auto tmp = CalculateMagicNumbers(divisor);
  
         return tmp[Number<0>{}];
     }
  
     __host__ __device__ static constexpr uint32_t CalculateMagicShift(uint32_t divisor)
     {
         auto tmp = CalculateMagicNumbers(divisor);
  
         return tmp[Number<1>{}];
     }
  
     // integral_constant<uint32_t, .>
     template <uint32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicNumbers(integral_constant<uint32_t, Divisor>)
     {
         constexpr auto tmp = CalculateMagicNumbers(uint32_t{Divisor});
  
         constexpr uint32_t multiplier = tmp[Number<0>{}];
         constexpr uint32_t shift      = tmp[Number<1>{}];
  
         return make_tuple(integral_constant<uint32_t, multiplier>{},
                           integral_constant<uint32_t, shift>{});
     }
  
     template <uint32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicMultiplier(integral_constant<uint32_t, Divisor>)
     {
         constexpr uint32_t multiplier = CalculateMagicMultiplier(uint32_t{Divisor});
  
         return integral_constant<uint32_t, multiplier>{};
     }
  
     template <uint32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicShift(integral_constant<uint32_t, Divisor>)
     {
         constexpr uint32_t shift = CalculateMagicShift(uint32_t{Divisor});
  
         return integral_constant<uint32_t, shift>{};
     }
  
     // integral_constant<int32_t, .>
     template <int32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicNumbers(integral_constant<int32_t, Divisor>)
     {
         return CalculateMagicNumbers(integral_constant<uint32_t, Divisor>{});
     }
  
     template <int32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicMultiplier(integral_constant<int32_t, Divisor>)
     {
         return CalculateMagicMultiplier(integral_constant<uint32_t, Divisor>{});
     }
  
     template <int32_t Divisor>
     __host__ __device__ static constexpr auto
         CalculateMagicShift(integral_constant<int32_t, Divisor>)
     {
         return CalculateMagicShift(integral_constant<uint32_t, Divisor>{});
     }
  
     // magic division for uint32_t
     __device__ static constexpr uint32_t
     DoMagicDivision(uint32_t dividend, uint32_t multiplier, uint32_t shift)
     {
         uint32_t tmp = __umulhi(dividend, multiplier);
         return (tmp + dividend) >> shift;
     }
  
     __host__ static constexpr uint32_t
     DoMagicDivision(uint32_t dividend, uint32_t multiplier, uint32_t shift)
     {
         uint32_t tmp = static_cast<uint64_t>(dividend) * multiplier >> 32;
         return (tmp + dividend) >> shift;
     }
  
     // magic division for int32_t
     // HACK: use dividend_i32 as if it's uint32_t, dividend_i32 need to be
     // non-negative for result to be correct
     // TODO: figure out how to do magic number divison for int32_t as dividended
     __device__ static constexpr int32_t
     DoMagicDivision(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
     {
         uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
         uint32_t tmp          = __umulhi(dividend_u32, multiplier);
         return (tmp + dividend_u32) >> shift;
     }
  
     __host__ static constexpr int32_t
     DoMagicDivision(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
     {
         uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
         uint32_t tmp          = static_cast<uint64_t>(dividend_u32) * multiplier >> 32;
         return (tmp + dividend_u32) >> shift;
     }
 };
  
 struct MDiv
 {
     // 1 dword -> 3 dword storage
     uint32_t divisor;
     uint32_t multiplier;
     uint32_t shift; // TODO: 8 bit is enough
  
     // prefer construct on host
     __host__ __device__ MDiv(uint32_t divisor_) : divisor(divisor_)
     {
         auto tmp = MagicDivision::CalculateMagicNumbers(divisor_);
  
         multiplier = tmp[Number<0>{}];
         shift      = tmp[Number<1>{}];
     }
  
     __host__ __device__ MDiv() : divisor(0), multiplier(0), shift(0) {}
  
     __host__ __device__ void update(uint32_t divisor_)
     {
         divisor  = divisor_;
         auto tmp = MagicDivision::CalculateMagicNumbers(divisor_);
  
         multiplier = tmp[Number<0>{}];
         shift      = tmp[Number<1>{}];
     }
  
     __host__ __device__ uint32_t div(uint32_t dividend_) const
     {
         return MagicDivision::DoMagicDivision(dividend_, multiplier, shift);
     }
  
     __host__ __device__ void
     divmod(uint32_t dividend_, uint32_t& quotient_, uint32_t& remainder_) const
     {
         quotient_  = div(dividend_);
         remainder_ = dividend_ - (quotient_ * divisor);
     }
  
     __host__ __device__ uint32_t get() const { return divisor; }
 };
  
 struct MDiv2
 {
     // 1 dword -> 2 dword storage, divisor need compute from runtime
     uint32_t multiplier;
     uint32_t shift; // TODO: 8 bit is enough
  
     // prefer construct on host
     __host__ __device__ MDiv2(uint32_t divisor_)
     {
         auto tmp = MagicDivision::CalculateMagicNumbers(divisor_);
  
         multiplier = tmp[Number<0>{}];
         shift      = tmp[Number<1>{}];
     }
  
     __host__ __device__ MDiv2() : multiplier(0), shift(0) {}
  
     __host__ __device__ uint32_t div(uint32_t dividend_) const
     {
         return MagicDivision::DoMagicDivision(dividend_, multiplier, shift);
     }
  
     __host__ __device__ void
     divmod(uint32_t dividend_, uint32_t divisor_, uint32_t& quotient_, uint32_t& remainder_) const
     {
         quotient_  = div(dividend_);
         remainder_ = dividend_ - (quotient_ * divisor_);
     }
 };
  
 } // namespace ck