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naimul.hpp
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naimul.hpp
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#ifndef INTT_ARITH_NAIMUL_HPP
# define INTT_ARITH_NAIMUL_HPP
# pragma once
#include "arith.hpp"
namespace ar
{ // provides naive implementations of mul
constexpr auto&& seqmul(uarray_c auto&& a, uarray_c auto const& b) noexcept
requires(
(size<decltype(a)>() == size<decltype(b)>()) &&
std::is_same_v<
std::remove_cvref_t<decltype(a[0])>,
std::remove_cvref_t<decltype(b[0])>
>
)
{
using T = std::remove_cvref_t<decltype(a[0])>;
enum : std::size_t { N = size<decltype(a)>(), M = 2 * N };
enum : std::size_t { wbits = bit_size_v<T> };
array_t<T, M> A;
rcopy<M - 1>(A, a);
array_t<T, M> r{};
[&]<auto ...I>(std::index_sequence<I...>) noexcept
{
(
[&]() noexcept
{
if (test_bit<I>(b)) add(r, A);
lshr<1>(r);
}(),
...
);
}(std::make_index_sequence<wbits * N>());
//
return copy(a, r);
}
constexpr auto&& naimul(uarray_c auto&& a, uarray_c auto const& b) noexcept
requires(
(size<decltype(a)>() == size<decltype(b)>()) &&
std::is_same_v<
std::remove_cvref_t<decltype(a[0])>,
std::remove_cvref_t<decltype(b[0])>
>
)
{
using T = std::remove_cvref_t<decltype(a[0])>;
enum : std::size_t { N = size<decltype(a)>(), wbits = bit_size_v<T> };
array_t<T, N> r{};
#if defined(__SIZEOF_INT128__)
if constexpr(std::is_same_v<T, std::uint64_t>)
{
using D = unsigned __int128;
for (std::size_t i{}; N != i; ++i)
{ // bit_size_v<T> * (i + j) < bit_size_v<T> * N
auto S(i);
do
{
D const pp(D(a[i]) * b[S - i]); // S = i + j < N
add(r, array_t<T, 2>{T(pp), T(pp >> wbits)}, S);
}
while (N != ++S);
}
}
else
#endif // __SIZEOF_INT128__
if constexpr(std::is_same_v<T, std::uintmax_t>)
{ // multiplying half-words, wbits per iteration
enum : std::size_t { M = 2 * N, hwbits = wbits / 2 };
for (std::size_t i{}; M != i; ++i)
{ // bit_size_v<H> * (i + j) < wbits * N
auto S(i);
do
{
auto const j(S - i); // S = i + j < M
T const pp(T(H<T>(a[i / 2] >> (i % 2 ? std::size_t(hwbits) : 0))) *
H<T>(b[j / 2] >> (j % 2 ? std::size_t(hwbits) : 0)));
S % 2 ?
add(r, array_t<T, 2>{pp << hwbits, pp >> hwbits}, S / 2) :
add(r, array_t<T, 1>{pp}, S / 2);
}
while (M != ++S);
}
}
else
{ // multiplying words, 2 * wbits per iteration
for (std::size_t i{}; N != i; ++i)
{ // bit_size_v<T> * (i + j) < bit_size_v<T> * N
auto S(i);
do
{
D<T> const pp(D<T>(a[i]) * b[S - i]); // S = i + j < N
add(r, array_t<T, 2>{T(pp), T(pp >> wbits)}, S);
}
while (N != ++S);
}
}
//
return copy(a, r);
}
}
#endif // INTT_ARITH_MUL_HPP