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// Copyright 2020-2022 Junekey Jeon
//
// The contents of this file may be used under the terms of
// the Apache License v2.0 with LLVM Exceptions.
//
// (See accompanying file LICENSE-Apache or copy at
// https://llvm.org/foundation/relicensing/LICENSE.txt)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#include "dragonbox/dragonbox.h"
#include "big_uint.h"
#include "continued_fractions.h"
#include <iostream>
template <class Float, class CachePolicy>
static bool verify_fast_multiplication_xz(CachePolicy&& cache_policy) {
using impl = jkj::dragonbox::detail::impl<Float>;
using format = typename impl::format;
using carrier_uint = typename impl::carrier_uint;
constexpr auto four_fl = (carrier_uint(1) << (impl::significand_bits + 2)) - 1;
constexpr auto two_fr = (carrier_uint(1) << (impl::significand_bits + 1)) + 1;
using jkj::dragonbox::detail::log::floor_log10_pow2_minus_log10_4_over_3;
using jkj::dragonbox::detail::log::floor_log2_pow10;
bool success = true;
for (int e = impl::min_exponent + 1 - impl::significand_bits;
e <= impl::max_exponent - impl::significand_bits; ++e) {
// Compute k and beta.
int const k = -floor_log10_pow2_minus_log10_4_over_3(e);
int const beta = e + floor_log2_pow10(k);
// Load cache.
auto const cache = cache_policy.template get_cache<format>(k);
// Compute the endpoints using the fast method.
auto x_fast = impl::compute_left_endpoint_for_shorter_interval_case(cache, beta);
auto z_fast = impl::compute_right_endpoint_for_shorter_interval_case(cache, beta);
// Precisely compute the endpoints.
jkj::unsigned_rational<jkj::big_uint> precise_multiplier{1, 1};
if (k >= 0) {
precise_multiplier.numerator = jkj::big_uint::pow(5, k);
}
else {
precise_multiplier.denominator = jkj::big_uint::pow(5, -k);
}
if (e + k >= 0) {
precise_multiplier.numerator *= jkj::big_uint::power_of_2(e + k);
}
else {
precise_multiplier.denominator *= jkj::big_uint::power_of_2(-e - k);
}
auto x_exact =
(four_fl * precise_multiplier.numerator) / (4 * precise_multiplier.denominator);
auto z_exact =
(two_fr * precise_multiplier.numerator) / (2 * precise_multiplier.denominator);
if (x_exact != x_fast) {
std::cout << "(e = " << e << ") left endpoint is not correct; computed = " << x_fast
<< "; true_value = " << x_exact[0] << "\n";
success = false;
}
if (z_exact != z_fast) {
std::cout << "(e = " << e << ") right endpoint is not correct; computed = " << z_fast
<< "; true_value = " << z_exact[0] << "\n";
success = false;
}
}
if (success) {
std::cout << "All cases are verified.\n";
}
else {
std::cout << "Error detected.\n";
}
return success;
}
template <class Float, class CachePolicy>
static bool verify_fast_multiplication_yru(CachePolicy&& cache_policy) {
using impl = jkj::dragonbox::detail::impl<Float>;
using format = typename impl::format;
bool success = true;
for (int k = impl::min_k; k <= impl::max_k; ++k) {
auto const cache = cache_policy.template get_cache<format>(k);
// Since Q - p - beta - 2 >= q, it suffices to check that the lower half of the cache is not 0.
auto const lower_half = [cache] {
if constexpr (std::is_same_v<typename impl::format, jkj::dragonbox::ieee754_binary32>) {
return std::uint32_t(cache);
}
else {
return cache.low();
}
}();
// If the lower half is zero, we need to check if the cache is precise.
if (lower_half == 0) {
if (k < 0 || k > jkj::dragonbox::detail::log::floor_log5_pow2(impl::cache_bits)) {
std::cout << "(k = " << k << ") computation might be incorrect\n";
success = false;
}
}
}
if (success) {
std::cout << "All cases are verified.\n";
}
else {
std::cout << "Error detected.\n";
}
return success;
}
int main() {
bool success = true;
std::cout << "[Verifying fast computation of xi and zi for the shorter interval case "
"with full cache (binary32)...]\n";
success &= verify_fast_multiplication_xz<float>(jkj::dragonbox::policy::cache::full);
std::cout << "Done.\n\n\n";
std::cout << "[Verifying fast computation of yru for the shorter interval case "
"with full cache (binary32)...]\n";
success &= verify_fast_multiplication_yru<float>(jkj::dragonbox::policy::cache::full);
std::cout << "Done.\n\n\n";
std::cout << "[Verifying fast computation of xi and zi for the shorter interval case "
"with full cache (binary64)...]\n";
success &= verify_fast_multiplication_xz<double>(jkj::dragonbox::policy::cache::full);
std::cout << "Done.\n\n\n";
std::cout << "[Verifying fast computation of xi and zi for the shorter interval case "
"with compressed cache (binary64)...]\n";
success &= verify_fast_multiplication_xz<double>(jkj::dragonbox::policy::cache::compact);
std::cout << "Done.\n\n\n";
std::cout << "[Verifying fast computation of yru for the shorter interval case "
"with full cache (binary64)...]\n";
success &= verify_fast_multiplication_yru<double>(jkj::dragonbox::policy::cache::full);
std::cout << "Done.\n\n\n";
std::cout << "[Verifying fast computation of yru for the shorter interval case "
"with compressed cache (binary64)...]\n";
success &= verify_fast_multiplication_yru<double>(jkj::dragonbox::policy::cache::compact);
std::cout << "Done.\n\n\n";
if (!success) {
return -1;
}
}
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