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format-inl.h
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// Formatting library for C++ - implementation
//
// Copyright (c) 2012 - 2016, Victor Zverovich
// All rights reserved.
//
// For the license information refer to format.h.
#ifndef FMT_FORMAT_INL_H_
#define FMT_FORMAT_INL_H_
#ifndef FMT_MODULE
# include <algorithm>
# include <cerrno> // errno
# include <climits>
# include <cmath>
# include <exception>
#endif
#if defined(_WIN32) && !defined(FMT_USE_WRITE_CONSOLE)
# include <io.h> // _isatty
#endif
#include "format.h"
#if FMT_USE_LOCALE
# include <locale>
#endif
#ifndef FMT_FUNC
# define FMT_FUNC
#endif
FMT_BEGIN_NAMESPACE
namespace detail {
FMT_FUNC void assert_fail(const char* file, int line, const char* message) {
// Use unchecked std::fprintf to avoid triggering another assertion when
// writing to stderr fails.
fprintf(stderr, "%s:%d: assertion failed: %s", file, line, message);
abort();
}
FMT_FUNC void format_error_code(detail::buffer<char>& out, int error_code,
string_view message) noexcept {
// Report error code making sure that the output fits into
// inline_buffer_size to avoid dynamic memory allocation and potential
// bad_alloc.
out.try_resize(0);
static const char SEP[] = ": ";
static const char ERROR_STR[] = "error ";
// Subtract 2 to account for terminating null characters in SEP and ERROR_STR.
size_t error_code_size = sizeof(SEP) + sizeof(ERROR_STR) - 2;
auto abs_value = static_cast<uint32_or_64_or_128_t<int>>(error_code);
if (detail::is_negative(error_code)) {
abs_value = 0 - abs_value;
++error_code_size;
}
error_code_size += detail::to_unsigned(detail::count_digits(abs_value));
auto it = appender(out);
if (message.size() <= inline_buffer_size - error_code_size)
fmt::format_to(it, FMT_STRING("{}{}"), message, SEP);
fmt::format_to(it, FMT_STRING("{}{}"), ERROR_STR, error_code);
FMT_ASSERT(out.size() <= inline_buffer_size, "");
}
FMT_FUNC void do_report_error(format_func func, int error_code,
const char* message) noexcept {
memory_buffer full_message;
func(full_message, error_code, message);
// Don't use fwrite_all because the latter may throw.
if (std::fwrite(full_message.data(), full_message.size(), 1, stderr) > 0)
std::fputc('\n', stderr);
}
// A wrapper around fwrite that throws on error.
inline void fwrite_all(const void* ptr, size_t count, FILE* stream) {
size_t written = std::fwrite(ptr, 1, count, stream);
if (written < count)
FMT_THROW(system_error(errno, FMT_STRING("cannot write to file")));
}
#if FMT_USE_LOCALE
using std::locale;
using std::numpunct;
using std::use_facet;
template <typename Locale>
locale_ref::locale_ref(const Locale& loc) : locale_(&loc) {
static_assert(std::is_same<Locale, locale>::value, "");
}
#else
struct locale {};
template <typename Char> struct numpunct {
auto grouping() const -> std::string { return "\03"; }
auto thousands_sep() const -> Char { return ','; }
auto decimal_point() const -> Char { return '.'; }
};
template <typename Facet> Facet use_facet(locale) { return {}; }
#endif // FMT_USE_LOCALE
template <typename Locale> auto locale_ref::get() const -> Locale {
static_assert(std::is_same<Locale, locale>::value, "");
#if FMT_USE_LOCALE
if (locale_) return *static_cast<const locale*>(locale_);
#endif
return locale();
}
template <typename Char>
FMT_FUNC auto thousands_sep_impl(locale_ref loc) -> thousands_sep_result<Char> {
auto&& facet = use_facet<numpunct<Char>>(loc.get<locale>());
auto grouping = facet.grouping();
auto thousands_sep = grouping.empty() ? Char() : facet.thousands_sep();
return {std::move(grouping), thousands_sep};
}
template <typename Char>
FMT_FUNC auto decimal_point_impl(locale_ref loc) -> Char {
return use_facet<numpunct<Char>>(loc.get<locale>()).decimal_point();
}
#if FMT_USE_LOCALE
FMT_FUNC auto write_loc(appender out, loc_value value,
const format_specs& specs, locale_ref loc) -> bool {
auto locale = loc.get<std::locale>();
// We cannot use the num_put<char> facet because it may produce output in
// a wrong encoding.
using facet = format_facet<std::locale>;
if (std::has_facet<facet>(locale))
return use_facet<facet>(locale).put(out, value, specs);
return facet(locale).put(out, value, specs);
}
#endif
} // namespace detail
FMT_FUNC void report_error(const char* message) {
#if FMT_USE_EXCEPTIONS
// Use FMT_THROW instead of throw to avoid bogus unreachable code warnings
// from MSVC.
FMT_THROW(format_error(message));
#else
fputs(message, stderr);
abort();
#endif
}
template <typename Locale> typename Locale::id format_facet<Locale>::id;
template <typename Locale> format_facet<Locale>::format_facet(Locale& loc) {
auto& np = detail::use_facet<detail::numpunct<char>>(loc);
grouping_ = np.grouping();
if (!grouping_.empty()) separator_ = std::string(1, np.thousands_sep());
}
#if FMT_USE_LOCALE
template <>
FMT_API FMT_FUNC auto format_facet<std::locale>::do_put(
appender out, loc_value val, const format_specs& specs) const -> bool {
return val.visit(
detail::loc_writer<>{out, specs, separator_, grouping_, decimal_point_});
}
#endif
FMT_FUNC auto vsystem_error(int error_code, string_view fmt, format_args args)
-> std::system_error {
auto ec = std::error_code(error_code, std::generic_category());
return std::system_error(ec, vformat(fmt, args));
}
namespace detail {
template <typename F>
inline auto operator==(basic_fp<F> x, basic_fp<F> y) -> bool {
return x.f == y.f && x.e == y.e;
}
// Compilers should be able to optimize this into the ror instruction.
FMT_CONSTEXPR inline auto rotr(uint32_t n, uint32_t r) noexcept -> uint32_t {
r &= 31;
return (n >> r) | (n << (32 - r));
}
FMT_CONSTEXPR inline auto rotr(uint64_t n, uint32_t r) noexcept -> uint64_t {
r &= 63;
return (n >> r) | (n << (64 - r));
}
// Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox.
namespace dragonbox {
// Computes upper 64 bits of multiplication of a 32-bit unsigned integer and a
// 64-bit unsigned integer.
inline auto umul96_upper64(uint32_t x, uint64_t y) noexcept -> uint64_t {
return umul128_upper64(static_cast<uint64_t>(x) << 32, y);
}
// Computes lower 128 bits of multiplication of a 64-bit unsigned integer and a
// 128-bit unsigned integer.
inline auto umul192_lower128(uint64_t x, uint128_fallback y) noexcept
-> uint128_fallback {
uint64_t high = x * y.high();
uint128_fallback high_low = umul128(x, y.low());
return {high + high_low.high(), high_low.low()};
}
// Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a
// 64-bit unsigned integer.
inline auto umul96_lower64(uint32_t x, uint64_t y) noexcept -> uint64_t {
return x * y;
}
// Various fast log computations.
inline auto floor_log10_pow2_minus_log10_4_over_3(int e) noexcept -> int {
FMT_ASSERT(e <= 2936 && e >= -2985, "too large exponent");
return (e * 631305 - 261663) >> 21;
}
FMT_INLINE_VARIABLE constexpr struct {
uint32_t divisor;
int shift_amount;
} div_small_pow10_infos[] = {{10, 16}, {100, 16}};
// Replaces n by floor(n / pow(10, N)) returning true if and only if n is
// divisible by pow(10, N).
// Precondition: n <= pow(10, N + 1).
template <int N>
auto check_divisibility_and_divide_by_pow10(uint32_t& n) noexcept -> bool {
// The numbers below are chosen such that:
// 1. floor(n/d) = floor(nm / 2^k) where d=10 or d=100,
// 2. nm mod 2^k < m if and only if n is divisible by d,
// where m is magic_number, k is shift_amount
// and d is divisor.
//
// Item 1 is a common technique of replacing division by a constant with
// multiplication, see e.g. "Division by Invariant Integers Using
// Multiplication" by Granlund and Montgomery (1994). magic_number (m) is set
// to ceil(2^k/d) for large enough k.
// The idea for item 2 originates from Schubfach.
constexpr auto info = div_small_pow10_infos[N - 1];
FMT_ASSERT(n <= info.divisor * 10, "n is too large");
constexpr uint32_t magic_number =
(1u << info.shift_amount) / info.divisor + 1;
n *= magic_number;
const uint32_t comparison_mask = (1u << info.shift_amount) - 1;
bool result = (n & comparison_mask) < magic_number;
n >>= info.shift_amount;
return result;
}
// Computes floor(n / pow(10, N)) for small n and N.
// Precondition: n <= pow(10, N + 1).
template <int N> auto small_division_by_pow10(uint32_t n) noexcept -> uint32_t {
constexpr auto info = div_small_pow10_infos[N - 1];
FMT_ASSERT(n <= info.divisor * 10, "n is too large");
constexpr uint32_t magic_number =
(1u << info.shift_amount) / info.divisor + 1;
return (n * magic_number) >> info.shift_amount;
}
// Computes floor(n / 10^(kappa + 1)) (float)
inline auto divide_by_10_to_kappa_plus_1(uint32_t n) noexcept -> uint32_t {
// 1374389535 = ceil(2^37/100)
return static_cast<uint32_t>((static_cast<uint64_t>(n) * 1374389535) >> 37);
}
// Computes floor(n / 10^(kappa + 1)) (double)
inline auto divide_by_10_to_kappa_plus_1(uint64_t n) noexcept -> uint64_t {
// 2361183241434822607 = ceil(2^(64+7)/1000)
return umul128_upper64(n, 2361183241434822607ull) >> 7;
}
// Various subroutines using pow10 cache
template <typename T> struct cache_accessor;
template <> struct cache_accessor<float> {
using carrier_uint = float_info<float>::carrier_uint;
using cache_entry_type = uint64_t;
static auto get_cached_power(int k) noexcept -> uint64_t {
FMT_ASSERT(k >= float_info<float>::min_k && k <= float_info<float>::max_k,
"k is out of range");
static constexpr const uint64_t pow10_significands[] = {
0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f,
0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, 0xc612062576589ddb,
0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28,
0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb,
0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a,
0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810,
0xe12e13424bb40e14, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff,
0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd,
0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424,
0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b,
0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000,
0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000,
0xc350000000000000, 0xf424000000000000, 0x9896800000000000,
0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000,
0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000,
0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000,
0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000,
0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000,
0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0,
0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940985,
0xa18f07d736b90be6, 0xc9f2c9cd04674edf, 0xfc6f7c4045812297,
0x9dc5ada82b70b59e, 0xc5371912364ce306, 0xf684df56c3e01bc7,
0x9a130b963a6c115d, 0xc097ce7bc90715b4, 0xf0bdc21abb48db21,
0x96769950b50d88f5, 0xbc143fa4e250eb32, 0xeb194f8e1ae525fe,
0x92efd1b8d0cf37bf, 0xb7abc627050305ae, 0xe596b7b0c643c71a,
0x8f7e32ce7bea5c70, 0xb35dbf821ae4f38c, 0xe0352f62a19e306f};
return pow10_significands[k - float_info<float>::min_k];
}
struct compute_mul_result {
carrier_uint result;
bool is_integer;
};
struct compute_mul_parity_result {
bool parity;
bool is_integer;
};
static auto compute_mul(carrier_uint u,
const cache_entry_type& cache) noexcept
-> compute_mul_result {
auto r = umul96_upper64(u, cache);
return {static_cast<carrier_uint>(r >> 32),
static_cast<carrier_uint>(r) == 0};
}
static auto compute_delta(const cache_entry_type& cache, int beta) noexcept
-> uint32_t {
return static_cast<uint32_t>(cache >> (64 - 1 - beta));
}
static auto compute_mul_parity(carrier_uint two_f,
const cache_entry_type& cache,
int beta) noexcept
-> compute_mul_parity_result {
FMT_ASSERT(beta >= 1, "");
FMT_ASSERT(beta < 64, "");
auto r = umul96_lower64(two_f, cache);
return {((r >> (64 - beta)) & 1) != 0,
static_cast<uint32_t>(r >> (32 - beta)) == 0};
}
static auto compute_left_endpoint_for_shorter_interval_case(
const cache_entry_type& cache, int beta) noexcept -> carrier_uint {
return static_cast<carrier_uint>(
(cache - (cache >> (num_significand_bits<float>() + 2))) >>
(64 - num_significand_bits<float>() - 1 - beta));
}
static auto compute_right_endpoint_for_shorter_interval_case(
const cache_entry_type& cache, int beta) noexcept -> carrier_uint {
return static_cast<carrier_uint>(
(cache + (cache >> (num_significand_bits<float>() + 1))) >>
(64 - num_significand_bits<float>() - 1 - beta));
}
static auto compute_round_up_for_shorter_interval_case(
const cache_entry_type& cache, int beta) noexcept -> carrier_uint {
return (static_cast<carrier_uint>(
cache >> (64 - num_significand_bits<float>() - 2 - beta)) +
1) /
2;
}
};
template <> struct cache_accessor<double> {
using carrier_uint = float_info<double>::carrier_uint;
using cache_entry_type = uint128_fallback;
static auto get_cached_power(int k) noexcept -> uint128_fallback {
FMT_ASSERT(k >= float_info<double>::min_k && k <= float_info<double>::max_k,
"k is out of range");
static constexpr const uint128_fallback pow10_significands[] = {
#if FMT_USE_FULL_CACHE_DRAGONBOX
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b},
{0x9faacf3df73609b1, 0x77b191618c54e9ad},
{0xc795830d75038c1d, 0xd59df5b9ef6a2418},
{0xf97ae3d0d2446f25, 0x4b0573286b44ad1e},
{0x9becce62836ac577, 0x4ee367f9430aec33},
{0xc2e801fb244576d5, 0x229c41f793cda740},
{0xf3a20279ed56d48a, 0x6b43527578c11110},
{0x9845418c345644d6, 0x830a13896b78aaaa},
{0xbe5691ef416bd60c, 0x23cc986bc656d554},
{0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9},
{0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa},
{0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54},
{0xe858ad248f5c22c9, 0xd1b3400f8f9cff69},
{0x91376c36d99995be, 0x23100809b9c21fa2},
{0xb58547448ffffb2d, 0xabd40a0c2832a78b},
{0xe2e69915b3fff9f9, 0x16c90c8f323f516d},
{0x8dd01fad907ffc3b, 0xae3da7d97f6792e4},
{0xb1442798f49ffb4a, 0x99cd11cfdf41779d},
{0xdd95317f31c7fa1d, 0x40405643d711d584},
{0x8a7d3eef7f1cfc52, 0x482835ea666b2573},
{0xad1c8eab5ee43b66, 0xda3243650005eed0},
{0xd863b256369d4a40, 0x90bed43e40076a83},
{0x873e4f75e2224e68, 0x5a7744a6e804a292},
{0xa90de3535aaae202, 0x711515d0a205cb37},
{0xd3515c2831559a83, 0x0d5a5b44ca873e04},
{0x8412d9991ed58091, 0xe858790afe9486c3},
{0xa5178fff668ae0b6, 0x626e974dbe39a873},
{0xce5d73ff402d98e3, 0xfb0a3d212dc81290},
{0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a},
{0xa139029f6a239f72, 0x1c1fffc1ebc44e81},
{0xc987434744ac874e, 0xa327ffb266b56221},
{0xfbe9141915d7a922, 0x4bf1ff9f0062baa9},
{0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa},
{0xc4ce17b399107c22, 0xcb550fb4384d21d4},
{0xf6019da07f549b2b, 0x7e2a53a146606a49},
{0x99c102844f94e0fb, 0x2eda7444cbfc426e},
{0xc0314325637a1939, 0xfa911155fefb5309},
{0xf03d93eebc589f88, 0x793555ab7eba27cb},
{0x96267c7535b763b5, 0x4bc1558b2f3458df},
{0xbbb01b9283253ca2, 0x9eb1aaedfb016f17},
{0xea9c227723ee8bcb, 0x465e15a979c1cadd},
{0x92a1958a7675175f, 0x0bfacd89ec191eca},
{0xb749faed14125d36, 0xcef980ec671f667c},
{0xe51c79a85916f484, 0x82b7e12780e7401b},
{0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811},
{0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16},
{0xdfbdcece67006ac9, 0x67a791e093e1d49b},
{0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1},
{0xaecc49914078536d, 0x58fae9f773886e19},
{0xda7f5bf590966848, 0xaf39a475506a899f},
{0x888f99797a5e012d, 0x6d8406c952429604},
{0xaab37fd7d8f58178, 0xc8e5087ba6d33b84},
{0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65},
{0x855c3be0a17fcd26, 0x5cf2eea09a550680},
{0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f},
{0xd0601d8efc57b08b, 0xf13b94daf124da27},
{0x823c12795db6ce57, 0x76c53d08d6b70859},
{0xa2cb1717b52481ed, 0x54768c4b0c64ca6f},
{0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a},
{0xfe5d54150b090b02, 0xd3f93b35435d7c4d},
{0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0},
{0xc6b8e9b0709f109a, 0x359ab6419ca1091c},
{0xf867241c8cc6d4c0, 0xc30163d203c94b63},
{0x9b407691d7fc44f8, 0x79e0de63425dcf1e},
{0xc21094364dfb5636, 0x985915fc12f542e5},
{0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e},
{0x979cf3ca6cec5b5a, 0xa705992ceecf9c43},
{0xbd8430bd08277231, 0x50c6ff782a838354},
{0xece53cec4a314ebd, 0xa4f8bf5635246429},
{0x940f4613ae5ed136, 0x871b7795e136be9a},
{0xb913179899f68584, 0x28e2557b59846e40},
{0xe757dd7ec07426e5, 0x331aeada2fe589d0},
{0x9096ea6f3848984f, 0x3ff0d2c85def7622},
{0xb4bca50b065abe63, 0x0fed077a756b53aa},
{0xe1ebce4dc7f16dfb, 0xd3e8495912c62895},
{0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d},
{0xb080392cc4349dec, 0xbd8d794d96aacfb4},
{0xdca04777f541c567, 0xecf0d7a0fc5583a1},
{0x89e42caaf9491b60, 0xf41686c49db57245},
{0xac5d37d5b79b6239, 0x311c2875c522ced6},
{0xd77485cb25823ac7, 0x7d633293366b828c},
{0x86a8d39ef77164bc, 0xae5dff9c02033198},
{0xa8530886b54dbdeb, 0xd9f57f830283fdfd},
{0xd267caa862a12d66, 0xd072df63c324fd7c},
{0x8380dea93da4bc60, 0x4247cb9e59f71e6e},
{0xa46116538d0deb78, 0x52d9be85f074e609},
{0xcd795be870516656, 0x67902e276c921f8c},
{0x806bd9714632dff6, 0x00ba1cd8a3db53b7},
{0xa086cfcd97bf97f3, 0x80e8a40eccd228a5},
{0xc8a883c0fdaf7df0, 0x6122cd128006b2ce},
{0xfad2a4b13d1b5d6c, 0x796b805720085f82},
{0x9cc3a6eec6311a63, 0xcbe3303674053bb1},
{0xc3f490aa77bd60fc, 0xbedbfc4411068a9d},
{0xf4f1b4d515acb93b, 0xee92fb5515482d45},
{0x991711052d8bf3c5, 0x751bdd152d4d1c4b},
{0xbf5cd54678eef0b6, 0xd262d45a78a0635e},
{0xef340a98172aace4, 0x86fb897116c87c35},
{0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1},
{0xbae0a846d2195712, 0x8974836059cca10a},
{0xe998d258869facd7, 0x2bd1a438703fc94c},
{0x91ff83775423cc06, 0x7b6306a34627ddd0},
{0xb67f6455292cbf08, 0x1a3bc84c17b1d543},
{0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94},
{0x8e938662882af53e, 0x547eb47b7282ee9d},
{0xb23867fb2a35b28d, 0xe99e619a4f23aa44},
{0xdec681f9f4c31f31, 0x6405fa00e2ec94d5},
{0x8b3c113c38f9f37e, 0xde83bc408dd3dd05},
{0xae0b158b4738705e, 0x9624ab50b148d446},
{0xd98ddaee19068c76, 0x3badd624dd9b0958},
{0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7},
{0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d},
{0xd47487cc8470652b, 0x7647c32000696720},
{0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074},
{0xa5fb0a17c777cf09, 0xf468107100525891},
{0xcf79cc9db955c2cc, 0x7182148d4066eeb5},
{0x81ac1fe293d599bf, 0xc6f14cd848405531},
{0xa21727db38cb002f, 0xb8ada00e5a506a7d},
{0xca9cf1d206fdc03b, 0xa6d90811f0e4851d},
{0xfd442e4688bd304a, 0x908f4a166d1da664},
{0x9e4a9cec15763e2e, 0x9a598e4e043287ff},
{0xc5dd44271ad3cdba, 0x40eff1e1853f29fe},
{0xf7549530e188c128, 0xd12bee59e68ef47d},
{0x9a94dd3e8cf578b9, 0x82bb74f8301958cf},
{0xc13a148e3032d6e7, 0xe36a52363c1faf02},
{0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2},
{0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba},
{0xbcb2b812db11a5de, 0x7415d448f6b6f0e8},
{0xebdf661791d60f56, 0x111b495b3464ad22},
{0x936b9fcebb25c995, 0xcab10dd900beec35},
{0xb84687c269ef3bfb, 0x3d5d514f40eea743},
{0xe65829b3046b0afa, 0x0cb4a5a3112a5113},
{0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac},
{0xb3f4e093db73a093, 0x59ed216765690f57},
{0xe0f218b8d25088b8, 0x306869c13ec3532d},
{0x8c974f7383725573, 0x1e414218c73a13fc},
{0xafbd2350644eeacf, 0xe5d1929ef90898fb},
{0xdbac6c247d62a583, 0xdf45f746b74abf3a},
{0x894bc396ce5da772, 0x6b8bba8c328eb784},
{0xab9eb47c81f5114f, 0x066ea92f3f326565},
{0xd686619ba27255a2, 0xc80a537b0efefebe},
{0x8613fd0145877585, 0xbd06742ce95f5f37},
{0xa798fc4196e952e7, 0x2c48113823b73705},
{0xd17f3b51fca3a7a0, 0xf75a15862ca504c6},
{0x82ef85133de648c4, 0x9a984d73dbe722fc},
{0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb},
{0xcc963fee10b7d1b3, 0x318df905079926a9},
{0xffbbcfe994e5c61f, 0xfdf17746497f7053},
{0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634},
{0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1},
{0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1},
{0x9c1661a651213e2d, 0x06bea10ca65c084f},
{0xc31bfa0fe5698db8, 0x486e494fcff30a63},
{0xf3e2f893dec3f126, 0x5a89dba3c3efccfb},
{0x986ddb5c6b3a76b7, 0xf89629465a75e01d},
{0xbe89523386091465, 0xf6bbb397f1135824},
{0xee2ba6c0678b597f, 0x746aa07ded582e2d},
{0x94db483840b717ef, 0xa8c2a44eb4571cdd},
{0xba121a4650e4ddeb, 0x92f34d62616ce414},
{0xe896a0d7e51e1566, 0x77b020baf9c81d18},
{0x915e2486ef32cd60, 0x0ace1474dc1d122f},
{0xb5b5ada8aaff80b8, 0x0d819992132456bb},
{0xe3231912d5bf60e6, 0x10e1fff697ed6c6a},
{0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2},
{0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb3},
{0xddd0467c64bce4a0, 0xac7cb3f6d05ddbdf},
{0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96c},
{0xad4ab7112eb3929d, 0x86c16c98d2c953c7},
{0xd89d64d57a607744, 0xe871c7bf077ba8b8},
{0x87625f056c7c4a8b, 0x11471cd764ad4973},
{0xa93af6c6c79b5d2d, 0xd598e40d3dd89bd0},
{0xd389b47879823479, 0x4aff1d108d4ec2c4},
{0x843610cb4bf160cb, 0xcedf722a585139bb},
{0xa54394fe1eedb8fe, 0xc2974eb4ee658829},
{0xce947a3da6a9273e, 0x733d226229feea33},
{0x811ccc668829b887, 0x0806357d5a3f5260},
{0xa163ff802a3426a8, 0xca07c2dcb0cf26f8},
{0xc9bcff6034c13052, 0xfc89b393dd02f0b6},
{0xfc2c3f3841f17c67, 0xbbac2078d443ace3},
{0x9d9ba7832936edc0, 0xd54b944b84aa4c0e},
{0xc5029163f384a931, 0x0a9e795e65d4df12},
{0xf64335bcf065d37d, 0x4d4617b5ff4a16d6},
{0x99ea0196163fa42e, 0x504bced1bf8e4e46},
{0xc06481fb9bcf8d39, 0xe45ec2862f71e1d7},
{0xf07da27a82c37088, 0x5d767327bb4e5a4d},
{0x964e858c91ba2655, 0x3a6a07f8d510f870},
{0xbbe226efb628afea, 0x890489f70a55368c},
{0xeadab0aba3b2dbe5, 0x2b45ac74ccea842f},
{0x92c8ae6b464fc96f, 0x3b0b8bc90012929e},
{0xb77ada0617e3bbcb, 0x09ce6ebb40173745},
{0xe55990879ddcaabd, 0xcc420a6a101d0516},
{0x8f57fa54c2a9eab6, 0x9fa946824a12232e},
{0xb32df8e9f3546564, 0x47939822dc96abfa},
{0xdff9772470297ebd, 0x59787e2b93bc56f8},
{0x8bfbea76c619ef36, 0x57eb4edb3c55b65b},
{0xaefae51477a06b03, 0xede622920b6b23f2},
{0xdab99e59958885c4, 0xe95fab368e45ecee},
{0x88b402f7fd75539b, 0x11dbcb0218ebb415},
{0xaae103b5fcd2a881, 0xd652bdc29f26a11a},
{0xd59944a37c0752a2, 0x4be76d3346f04960},
{0x857fcae62d8493a5, 0x6f70a4400c562ddc},
{0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb953},
{0xd097ad07a71f26b2, 0x7e2000a41346a7a8},
{0x825ecc24c873782f, 0x8ed400668c0c28c9},
{0xa2f67f2dfa90563b, 0x728900802f0f32fb},
{0xcbb41ef979346bca, 0x4f2b40a03ad2ffba},
{0xfea126b7d78186bc, 0xe2f610c84987bfa9},
{0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7ca},
{0xc6ede63fa05d3143, 0x91503d1c79720dbc},
{0xf8a95fcf88747d94, 0x75a44c6397ce912b},
{0x9b69dbe1b548ce7c, 0xc986afbe3ee11abb},
{0xc24452da229b021b, 0xfbe85badce996169},
{0xf2d56790ab41c2a2, 0xfae27299423fb9c4},
{0x97c560ba6b0919a5, 0xdccd879fc967d41b},
{0xbdb6b8e905cb600f, 0x5400e987bbc1c921},
{0xed246723473e3813, 0x290123e9aab23b69},
{0x9436c0760c86e30b, 0xf9a0b6720aaf6522},
{0xb94470938fa89bce, 0xf808e40e8d5b3e6a},
{0xe7958cb87392c2c2, 0xb60b1d1230b20e05},
{0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c3},
{0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af4},
{0xe2280b6c20dd5232, 0x25c6da63c38de1b1},
{0x8d590723948a535f, 0x579c487e5a38ad0f},
{0xb0af48ec79ace837, 0x2d835a9df0c6d852},
{0xdcdb1b2798182244, 0xf8e431456cf88e66},
{0x8a08f0f8bf0f156b, 0x1b8e9ecb641b5900},
{0xac8b2d36eed2dac5, 0xe272467e3d222f40},
{0xd7adf884aa879177, 0x5b0ed81dcc6abb10},
{0x86ccbb52ea94baea, 0x98e947129fc2b4ea},
{0xa87fea27a539e9a5, 0x3f2398d747b36225},
{0xd29fe4b18e88640e, 0x8eec7f0d19a03aae},
{0x83a3eeeef9153e89, 0x1953cf68300424ad},
{0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd8},
{0xcdb02555653131b6, 0x3792f412cb06794e},
{0x808e17555f3ebf11, 0xe2bbd88bbee40bd1},
{0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec5},
{0xc8de047564d20a8b, 0xf245825a5a445276},
{0xfb158592be068d2e, 0xeed6e2f0f0d56713},
{0x9ced737bb6c4183d, 0x55464dd69685606c},
{0xc428d05aa4751e4c, 0xaa97e14c3c26b887},
{0xf53304714d9265df, 0xd53dd99f4b3066a9},
{0x993fe2c6d07b7fab, 0xe546a8038efe402a},
{0xbf8fdb78849a5f96, 0xde98520472bdd034},
{0xef73d256a5c0f77c, 0x963e66858f6d4441},
{0x95a8637627989aad, 0xdde7001379a44aa9},
{0xbb127c53b17ec159, 0x5560c018580d5d53},
{0xe9d71b689dde71af, 0xaab8f01e6e10b4a7},
{0x9226712162ab070d, 0xcab3961304ca70e9},
{0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d23},
{0xe45c10c42a2b3b05, 0x8cb89a7db77c506b},
{0x8eb98a7a9a5b04e3, 0x77f3608e92adb243},
{0xb267ed1940f1c61c, 0x55f038b237591ed4},
{0xdf01e85f912e37a3, 0x6b6c46dec52f6689},
{0x8b61313bbabce2c6, 0x2323ac4b3b3da016},
{0xae397d8aa96c1b77, 0xabec975e0a0d081b},
{0xd9c7dced53c72255, 0x96e7bd358c904a22},
{0x881cea14545c7575, 0x7e50d64177da2e55},
{0xaa242499697392d2, 0xdde50bd1d5d0b9ea},
{0xd4ad2dbfc3d07787, 0x955e4ec64b44e865},
{0x84ec3c97da624ab4, 0xbd5af13bef0b113f},
{0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58f},
{0xcfb11ead453994ba, 0x67de18eda5814af3},
{0x81ceb32c4b43fcf4, 0x80eacf948770ced8},
{0xa2425ff75e14fc31, 0xa1258379a94d028e},
{0xcad2f7f5359a3b3e, 0x096ee45813a04331},
{0xfd87b5f28300ca0d, 0x8bca9d6e188853fd},
{0x9e74d1b791e07e48, 0x775ea264cf55347e},
{0xc612062576589dda, 0x95364afe032a819e},
{0xf79687aed3eec551, 0x3a83ddbd83f52205},
{0x9abe14cd44753b52, 0xc4926a9672793543},
{0xc16d9a0095928a27, 0x75b7053c0f178294},
{0xf1c90080baf72cb1, 0x5324c68b12dd6339},
{0x971da05074da7bee, 0xd3f6fc16ebca5e04},
{0xbce5086492111aea, 0x88f4bb1ca6bcf585},
{0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6},
{0x9392ee8e921d5d07, 0x3aff322e62439fd0},
{0xb877aa3236a4b449, 0x09befeb9fad487c3},
{0xe69594bec44de15b, 0x4c2ebe687989a9b4},
{0x901d7cf73ab0acd9, 0x0f9d37014bf60a11},
{0xb424dc35095cd80f, 0x538484c19ef38c95},
{0xe12e13424bb40e13, 0x2865a5f206b06fba},
{0x8cbccc096f5088cb, 0xf93f87b7442e45d4},
{0xafebff0bcb24aafe, 0xf78f69a51539d749},
{0xdbe6fecebdedd5be, 0xb573440e5a884d1c},
{0x89705f4136b4a597, 0x31680a88f8953031},
{0xabcc77118461cefc, 0xfdc20d2b36ba7c3e},
{0xd6bf94d5e57a42bc, 0x3d32907604691b4d},
{0x8637bd05af6c69b5, 0xa63f9a49c2c1b110},
{0xa7c5ac471b478423, 0x0fcf80dc33721d54},
{0xd1b71758e219652b, 0xd3c36113404ea4a9},
{0x83126e978d4fdf3b, 0x645a1cac083126ea},
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{0xbc789925624c5fe0, 0xb67d16413d132073},
{0xeb96bf6ebadf77d8, 0xe41c5bd18c57e890},
{0x933e37a534cbaae7, 0x8e91b962f7b6f15a},