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example014_pi_spigot_wide.cpp
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example014_pi_spigot_wide.cpp
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///////////////////////////////////////////////////////////////////
// Copyright Christopher Kormanyos 2023 - 2024. //
// Distributed under the Boost Software License, //
// Version 1.0. (See accompanying file LICENSE_1_0.txt //
// or copy at http://www.boost.org/LICENSE_1_0.txt) //
///////////////////////////////////////////////////////////////////
#include <algorithm>
#include <array>
#include <cstddef>
#include <cstdint>
#include <string>
#include <vector>
#include <examples/example_uintwide_t.h>
#include <math/wide_integer/uintwide_t.h>
namespace example014_pi_spigot
{
template<const std::uint32_t ResultDigit,
const std::uint32_t LoopDigit,
typename UnsignedSmallType,
typename UnsignedLargeType>
class pi_spigot
{
private:
using unsigned_small_type = UnsignedSmallType;
using unsigned_large_type = UnsignedLargeType;
static constexpr auto result_digit() noexcept -> std::uint32_t { return ResultDigit; }
static constexpr auto loop_digit () noexcept -> std::uint32_t { return LoopDigit; }
static_assert(result_digit() <= static_cast<std::uint32_t>(UINT16_C(10011)),
"Error: result_digit exceeds its limit of 10,011");
static_assert(std::numeric_limits<unsigned_small_type>::digits * 2 == std::numeric_limits<unsigned_large_type>::digits,
"Error: unsigned_large_type must be exactly twice as wide as unsigned_small_type");
static_assert((!std::numeric_limits<unsigned_small_type>::is_signed),
"Error: unsigned_small_type must be unsigned");
static_assert((!std::numeric_limits<unsigned_large_type>::is_signed),
"Error: unsigned_large_type must be unsigned");
static constexpr auto input_scale(std::uint32_t x) noexcept -> std::uint32_t
{
return
static_cast<std::uint32_t>
(
static_cast<std::uint32_t>
(
x
* static_cast<std::uint32_t>
(
static_cast<std::uint32_t>(static_cast<std::uint32_t>(UINT8_C(10) * loop_digit()) / static_cast<std::uint32_t>(UINT8_C(3)))
+ static_cast<std::uint32_t>(UINT8_C(1))
)
)
/ loop_digit()
);
}
public:
static constexpr auto get_output_static_size() noexcept -> std::uint32_t { return result_digit(); }
static constexpr auto get_input_static_size() noexcept -> std::uint32_t { return input_scale(get_output_static_size()); }
using input_container_type = std::vector<std::uint32_t>;
using output_value_type = std::uint8_t;
pi_spigot()
{
if(my_pi_in.empty())
{
constexpr auto input_size =
static_cast<typename input_container_type::size_type>(get_input_static_size());
my_pi_in.resize(input_size);
}
}
pi_spigot(const pi_spigot&) = delete;
pi_spigot(pi_spigot&&) = delete;
~pi_spigot() = default; // LCOV_EXCL_LINE
auto operator=(const pi_spigot&) -> pi_spigot& = delete;
auto operator=(pi_spigot&&) noexcept -> pi_spigot& = delete;
WIDE_INTEGER_NODISCARD auto get_operation_count() const noexcept -> std::uintmax_t { return my_operation_count; }
template<typename OutputIteratorType>
auto calculate(OutputIteratorType output_first) -> void
{
// Use pi_spigot::calculate() to calculate result_digit
// decimal digits of pi.
// The caller is responsible for providing the output memory
// for the result of pi.
// The input memory used for internal calculation details
// is managed by the pi_spigot class itself.
std::fill(my_pi_in.begin(),
my_pi_in.end(),
static_cast<typename input_container_type::value_type>(UINT8_C(0)));
auto val_c = static_cast<unsigned_small_type>(static_cast<unsigned>(UINT8_C(0)));
my_output_count = static_cast<std::uint32_t>(UINT8_C(0));
my_operation_count = static_cast<std::uintmax_t>(UINT8_C(0));
const auto local_pow10 = static_cast<unsigned_large_type>(pow10(loop_digit()));
// Operation count Mathematica(R), example for loop_digit=9.
// Sum[Floor[((d - j) (Floor[((10 9)/3)] + 1))/9], {j, 0, Floor[d/9] 9, 9}]
for(auto j = static_cast<std::uint32_t>(UINT8_C(0));
j < result_digit(); // NOLINT(altera-id-dependent-backward-branch)
j = static_cast<std::uint32_t>(j + loop_digit()))
{
auto val_d = static_cast<unsigned_large_type>(UINT8_C(0));
const auto ilim = input_scale(result_digit() - j);
for(auto i = static_cast<std::uint32_t>(INT8_C(0));
i < ilim; // NOLINT(altera-id-dependent-backward-branch)
++i)
{
const auto my_index =
static_cast<std::uint32_t>
(
static_cast<std::uint32_t>(ilim - static_cast<std::uint32_t>(UINT8_C(1)))
- i
);
unsigned_large_type di { my_pi_in[my_index] };
if(j == static_cast<std::uint32_t>(UINT8_C(0)))
{
di = std::move(static_cast<unsigned_large_type>(d_init()));
}
val_d += (di * local_pow10);
const auto val_b =
static_cast<std::uint32_t>
(
static_cast<std::uint32_t>
(
my_index * static_cast<std::uint32_t>(UINT8_C(2))
)
+ static_cast<std::uint32_t>(UINT8_C(1))
);
my_pi_in[my_index] = static_cast<std::uint32_t>(val_d % val_b);
val_d /= val_b;
if(my_index > static_cast<std::uint32_t>(UINT8_C(1)))
{
val_d *= my_index;
}
++my_operation_count;
}
// Parse the next digits of pi, where the group has loop_digit digits.
// If loop_digit is 4, for instance, then successive groups
// of digits have a form such as: 3141, 5926, ..., etc.
const auto next_digits =
static_cast<unsigned_small_type>
(
val_c + static_cast<unsigned_small_type>(val_d / local_pow10)
);
val_c = static_cast<unsigned_small_type>(val_d % local_pow10);
const auto n =
(std::min)
(
loop_digit(),
static_cast<std::uint32_t>(result_digit() - j)
);
auto scale10 = pow10(loop_digit() - UINT32_C(1));
for(auto i = static_cast<std::size_t>(UINT8_C(0)); i < static_cast<std::size_t>(n); ++i) // NOLINT(altera-id-dependent-backward-branch)
{
using local_diff_type = typename std::iterator_traits<OutputIteratorType>::difference_type;
const auto out_index =
static_cast<local_diff_type>
(
static_cast<std::size_t>(static_cast<std::size_t>(j) + i)
);
output_first[out_index] =
static_cast<output_value_type>
(
static_cast<unsigned_small_type>(static_cast<unsigned_small_type>(next_digits / scale10) % UINT32_C(10))
);
scale10 = static_cast<unsigned_small_type>(scale10 / UINT32_C(10));
}
my_output_count += n;
}
}
private:
static input_container_type my_pi_in; // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
std::uintmax_t my_operation_count { }; // NOLINT(readability-identifier-naming)
std::uint32_t my_output_count { }; // NOLINT(readability-identifier-naming)
static auto pow10(std::uint32_t n) -> unsigned_small_type // NOLINT(misc-no-recursion)
{
return
(
(n == static_cast<std::uint32_t>(UINT8_C(0)))
? static_cast<unsigned_small_type>(UINT32_C(1))
: static_cast<unsigned_small_type>(pow10(n - static_cast<std::uint32_t>(UINT8_C(1))) * UINT32_C(10))
);
}
static auto d_init() -> unsigned_small_type
{
return
static_cast<unsigned_small_type>
(
pow10(loop_digit()) / static_cast<unsigned>(UINT8_C(5))
);
}
};
template<const std::uint32_t ResultDigit,
const std::uint32_t LoopDigit,
typename UnsignedSmallType,
typename UnsignedLargeType>
typename pi_spigot<ResultDigit, LoopDigit, UnsignedSmallType, UnsignedLargeType>::input_container_type pi_spigot<ResultDigit, LoopDigit, UnsignedSmallType, UnsignedLargeType>::my_pi_in { }; // NOLINT(cppcoreguidelines-avoid-non-const-global-variables,hicpp-uppercase-literal-suffix,readability-uppercase-literal-suffix)
const std::array<const char*, static_cast<std::size_t>(UINT8_C(12))> pi_control_data =
{
"3",
"1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989",
"3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009",
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};
inline auto pi_control_string() -> std::string
{
auto str = std::string { };
for(auto pstr : pi_control_data) // NOLINT(llvm-qualified-auto,readability-qualified-auto)
{
str.insert(str.length(), pstr); // LCOV_EXCL_LINE
}
return str;
}
} // namespace example014_pi_spigot
#if defined(WIDE_INTEGER_NAMESPACE)
auto WIDE_INTEGER_NAMESPACE::math::wide_integer::example014_pi_spigot_wide() -> bool
#else
auto ::math::wide_integer::example014_pi_spigot_wide() -> bool
#endif
{
#if defined(WIDE_INTEGER_NAMESPACE)
using unsigned_small_type = WIDE_INTEGER_NAMESPACE::math::wide_integer::uint256_t;
using unsigned_large_type = WIDE_INTEGER_NAMESPACE::math::wide_integer::uint512_t;
#else
using unsigned_small_type = ::math::wide_integer::uint256_t;
using unsigned_large_type = ::math::wide_integer::uint512_t;
#endif
using pi_spigot_type = example014_pi_spigot::pi_spigot<static_cast<std::uint32_t>(UINT16_C(10001)),
static_cast<std::uint32_t>(std::numeric_limits<unsigned_small_type>::digits10),
unsigned_small_type,
unsigned_large_type>;
using output_container_type = std::vector<std::uint8_t>;
output_container_type pi_out(pi_spigot_type::get_output_static_size());
pi_spigot_type().calculate(pi_out.begin());
const auto result_is_ok =
std::equal(pi_out.cbegin(),
pi_out.cend(),
example014_pi_spigot::pi_control_string().cbegin(),
[](const std::uint8_t& by, const char& c)
{
const auto by_val_to_check =
static_cast<std::uint8_t>
(
static_cast<std::uint8_t>(c)
- static_cast<std::uint8_t>(UINT8_C(0x30))
);
return (by == by_val_to_check);
});
return result_is_ok;
}
// Enable this if you would like to activate this main() as a standalone example.
#if defined(WIDE_INTEGER_STANDALONE_EXAMPLE014_PI_SPIGOT_WIDE)
#include <iomanip>
#include <iostream>
auto main() -> int
{
#if defined(WIDE_INTEGER_NAMESPACE)
const auto result_is_ok = WIDE_INTEGER_NAMESPACE::math::wide_integer::example011_pi_spigot_wide();
#else
const auto result_is_ok = ::math::wide_integer::example011_pi_spigot_wide();
#endif
std::cout << "result_is_ok: " << std::boolalpha << result_is_ok << std::endl;
return (result_is_ok ? 0 : -1);
}
#endif