wide_multiply.h

// Copyright 2017 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#ifndef ABSL_RANDOM_INTERNAL_WIDE_MULTIPLY_H_
#define ABSL_RANDOM_INTERNAL_WIDE_MULTIPLY_H_

#include <cstdint>
#include <limits>
#include <type_traits>

#if (defined(_WIN32) || defined(_WIN64)) && defined(_M_IA64)
#include <intrin.h>  // NOLINT(build/include_order)
#pragma intrinsic(_umul128)
#define ABSL_INTERNAL_USE_UMUL128 1
#endif

#include "absl/base/config.h"
#include "absl/base/internal/bits.h"
#include "absl/numeric/int128.h"
#include "absl/random/internal/traits.h"

namespace absl {
ABSL_NAMESPACE_BEGIN
namespace random_internal {

// Helper object to multiply two 64-bit values to a 128-bit value.
// MultiplyU64ToU128 multiplies two 64-bit values to a 128-bit value.
// If an intrinsic is available, it is used, otherwise use native 32-bit
// multiplies to construct the result.
inline uint128 MultiplyU64ToU128(uint64_t a, uint64_t b) {
#if defined(ABSL_HAVE_INTRINSIC_INT128)
  return uint128(static_cast<__uint128_t>(a) * b);
#elif defined(ABSL_INTERNAL_USE_UMUL128)
  // uint64_t * uint64_t => uint128 multiply using imul intrinsic on MSVC.
  uint64_t high = 0;
  const uint64_t low = _umul128(a, b, &high);
  return absl::MakeUint128(high, low);
#else
  // uint128(a) * uint128(b) in emulated mode computes a full 128-bit x 128-bit
  // multiply.  However there are many cases where that is not necessary, and it
  // is only necessary to support a 64-bit x 64-bit = 128-bit multiply.  This is
  // for those cases.
  const uint64_t a00 = static_cast<uint32_t>(a);
  const uint64_t a32 = a >> 32;
  const uint64_t b00 = static_cast<uint32_t>(b);
  const uint64_t b32 = b >> 32;

  const uint64_t c00 = a00 * b00;
  const uint64_t c32a = a00 * b32;
  const uint64_t c32b = a32 * b00;
  const uint64_t c64 = a32 * b32;

  const uint32_t carry =
      static_cast<uint32_t>(((c00 >> 32) + static_cast<uint32_t>(c32a) +
                             static_cast<uint32_t>(c32b)) >>
                            32);

  return absl::MakeUint128(c64 + (c32a >> 32) + (c32b >> 32) + carry,
                           c00 + (c32a << 32) + (c32b << 32));
#endif
}

// wide_multiply<T> multiplies two N-bit values to a 2N-bit result.
template <typename UIntType>
struct wide_multiply {
  static constexpr size_t kN = std::numeric_limits<UIntType>::digits;
  using input_type = UIntType;
  using result_type = typename random_internal::unsigned_bits<kN * 2>::type;

  static result_type multiply(input_type a, input_type b) {
    return static_cast<result_type>(a) * b;
  }

  static input_type hi(result_type r) { return r >> kN; }
  static input_type lo(result_type r) { return r; }

  static_assert(std::is_unsigned<UIntType>::value,
                "Class-template wide_multiply<> argument must be unsigned.");
};

#ifndef ABSL_HAVE_INTRINSIC_INT128
template <>
struct wide_multiply<uint64_t> {
  using input_type = uint64_t;
  using result_type = uint128;

  static result_type multiply(uint64_t a, uint64_t b) {
    return MultiplyU64ToU128(a, b);
  }

  static uint64_t hi(result_type r) { return Uint128High64(r); }
  static uint64_t lo(result_type r) { return Uint128Low64(r); }
};
#endif

}  // namespace random_internal
ABSL_NAMESPACE_END
}  // namespace absl

#endif  // ABSL_RANDOM_INTERNAL_WIDE_MULTIPLY_H_