diff --git a/Makefile b/Makefile
index 1d4a4d2..ede166b 100644
--- a/Makefile
+++ b/Makefile
@@ -8,15 +8,15 @@ ifeq ($(AQ_DEBUG), 1)
LINKFLAGS =
else
OPTFLAGS = -O3 -DNDEBUG -fno-stack-protector
- LINKFLAGS = -flto
+ LINKFLAGS = -flto -s
endif
SHAREDFLAGS = -shared
FPIC = -fPIC
COMPILER = $(shell $(CXX) --version | grep -q clang && echo clang|| echo gcc)
LIBTOOL = ar rcs
USELIB_FLAG = -Wl,--whole-archive,libaquery.a -Wl,-no-whole-archive
-LIBAQ_SRC = server/server.cpp server/monetdb_conn.cpp server/io.cpp
-LIBAQ_OBJ = server.o monetdb_conn.o io.o
+LIBAQ_SRC = server/monetdb_conn.cpp server/libaquery.cpp
+LIBAQ_OBJ = monetdb_conn.o libaquery.o
SEMANTIC_INTERPOSITION = -fno-semantic-interposition
RANLIB = ranlib
@@ -118,19 +118,21 @@ info:
pch:
$(CXX) -x c++-header server/pch.hpp $(FPIC) $(CXXFLAGS)
libaquery.a:
- $(CXX) -c $(FPIC) $(PCHFLAGS) $(LIBAQ_SRC) $(MonetDB_LIB) $(OS_SUPPORT) $(CXXFLAGS) &&\
+ $(CXX) -c $(FPIC) $(PCHFLAGS) $(LIBAQ_SRC) $(OS_SUPPORT) $(CXXFLAGS) &&\
$(LIBTOOL) libaquery.a $(LIBAQ_OBJ) &&\
$(RANLIB) libaquery.a
+warmup:
+ $(CXX) $(SHAREDFLAGS) msc-plugin/dummy.cpp libaquery.a -o dll.so
server.bin:
$(CXX) $(LIBAQ_SRC) $(BINARYFLAGS) $(OS_SUPPORT) -o server.bin
launcher:
$(CXX) -D__AQ_BUILD_LAUNCHER__ $(LIBAQ_SRC) $(OS_SUPPORT) $(BINARYFLAGS) -o aq
server.so:
# $(CXX) -z muldefs server/server.cpp server/monetdb_conn.cpp -fPIC -shared $(OS_SUPPORT) monetdb/msvc/monetdbe.dll --std=c++1z -O3 -march=native -o server.so -I./monetdb/msvc
- $(CXX) $(SHAREDFLAGS) $(PCHFLAGS) $(LIBAQ_SRC) $(OS_SUPPORT) -o server.so
+ $(CXX) $(SHAREDFLAGS) $(PCHFLAGS) $(LIBAQ_SRC) server/server.cpp server/dragonbox/dragonbox_to_chars.cpp $(OS_SUPPORT) -o server.so
server_uselib:
- $(CXX) $(SHAREDFLAGS) $(USELIB_FLAG),libaquery.a -o server.so
+ $(CXX) $(SHAREDFLAGS) server/server.cpp libaquery.a server/dragonbox/dragonbox_to_chars.cpp -o server.so
snippet:
$(CXX) $(SHAREDFLAGS) $(PCHFLAGS) out.cpp $(LIBAQ_SRC) -o dll.so
diff --git a/README.md b/README.md
index 1de828d..36d2182 100644
--- a/README.md
+++ b/README.md
@@ -231,7 +231,7 @@ DROP TABLE my_table IF EXISTS
- `next(col), prev(col)`: moving column back and forth by 1, e.g. `next(col)[i] = col[i+1]`.
- `first(col), last(col)`: first and last value of a column, i.e. `first(col)= col[0]`, `last(col) = col[n-1]`.
- `sqrt(x), trunc(x), and other builtin math functions`: value-wise math operations. `sqrt(x)[i] = sqrt(x[i])`
-- `pack(cols, ...)`: pack multiple columns into a single column.
+- `pack(cols, ...)`: pack multiple columns with exact same type into a single column.
# Architecture
![Architecture](./docs/arch-hybrid.svg)
@@ -287,3 +287,24 @@ DROP TABLE my_table IF EXISTS
- [ ] Bug: Order By after Group By
- [ ] Functionality: Having clause, With clause
- [ ] Decouple expr.py
+
+# Credit:
+- [mo-sql-parsing](https://github.com/klahnakoski/mo-sql-parsing)
+ Author: Kyle Lahnakoski
+ License (Mozilla Public License 2.0): https://github.com/klahnakoski/mo-sql-parsing/blob/dev/LICENSE
+
+- [Fast C++ CSV pParser](https://github.com/ben-strasser/fast-cpp-csv-parser)
+ Author: Ben Strasser
+ License (BSD 3-Clause License): https://github.com/ben-strasser/fast-cpp-csv-parser/blob/master/LICENSE
+
+- [Dragonbox](https://github.com/jk-jeon/dragonbox)
+ Author: Junekey Jeon
+ License (Boost, Apache2-LLVM):
https://github.com/jk-jeon/dragonbox/blob/master/LICENSE-Boost
+ https://github.com/jk-jeon/dragonbox/blob/master/LICENSE-Apache2-LLVM
+
+- [itoa](https://github.com/jeaiii/itoa)
+ Author: James Edward Anhalt III
+ License (MIT): https://github.com/jeaiii/itoa/blob/main/LICENSE
+
+- [MobetDB] (https://www.monetdb.org)
+ License (Mozilla Public License): https://github.com/MonetDB/MonetDB/blob/master/license.txt
diff --git a/aquery_config.py b/aquery_config.py
index 9e80e4b..0327d06 100644
--- a/aquery_config.py
+++ b/aquery_config.py
@@ -11,6 +11,7 @@ cygroot = 'c:/msys64/usr/bin'
msbuildroot = ''
os_platform = 'unknown'
build_driver = 'Auto'
+compilation_output = True
def init_config():
global __config_initialized__, os_platform, msbuildroot, build_driver
diff --git a/build.py b/build.py
index d817dc8..5d3bf0d 100644
--- a/build.py
+++ b/build.py
@@ -73,7 +73,7 @@ class checksums:
class build_manager:
sourcefiles = [
'build.py', 'Makefile',
- 'server/server.cpp', 'server/io.cpp',
+ 'server/server.cpp', 'server/libaquery.cpp',
'server/monetdb_conn.cpp', 'server/threading.cpp',
'server/winhelper.cpp'
]
@@ -94,6 +94,9 @@ class build_manager:
return False
def build(self, stdout = sys.stdout, stderr = sys.stderr):
ret = True
+ if not aquery_config.compilation_output:
+ stdout = nullstream
+ stderr = nullstream
for c in self.build_cmd:
if c:
try: # only last success matters
@@ -102,6 +105,8 @@ class build_manager:
ret = False
pass
return ret
+ def warmup(self):
+ return True
class MakefileDriver(DriverBase):
def __init__(self, mgr : 'build_manager') -> None:
@@ -113,7 +118,7 @@ class build_manager:
mgr.cxx = os.environ['CXX']
if 'AQ_DEBUG' not in os.environ:
os.environ['AQ_DEBUG'] = '0' if mgr.OptimizationLv else '1'
-
+
def libaquery_a(self):
self.build_cmd = [['rm', 'libaquery.a'],['make', 'libaquery.a']]
return self.build()
@@ -168,6 +173,10 @@ class build_manager:
self.build_cmd = [[aquery_config.msbuildroot, loc, self.opt, self.platform]]
return self.build()
+ def warmup(self):
+ self.build_cmd = [['make', 'warmup']]
+ return self.build()
+
#class PythonDriver(DriverBase):
# def __init__(self, mgr : 'build_manager') -> None:
# super().__init__(mgr)
@@ -223,6 +232,9 @@ class build_manager:
current.calc(self.cxx, libaquery_a)
with open('.cached', 'wb') as cache_sig:
cache_sig.write(pickle.dumps(current))
+ self.driver.warmup()
+
+
else:
if aquery_config.os_platform == 'mac':
os.system('./arch-check.sh')
diff --git a/msc-plugin/libaquery.vcxproj b/msc-plugin/libaquery.vcxproj
index cb493e4..a727a3c 100644
--- a/msc-plugin/libaquery.vcxproj
+++ b/msc-plugin/libaquery.vcxproj
@@ -238,7 +238,7 @@
-
+
diff --git a/reconstruct/storage.py b/reconstruct/storage.py
index e8dfe94..983f866 100644
--- a/reconstruct/storage.py
+++ b/reconstruct/storage.py
@@ -156,6 +156,7 @@ class Context:
self.queries = []
self.module_init_loc = 0
self.special_gb = False
+ self.has_dll = False
def __init__(self):
self.tables_byname = dict()
@@ -169,7 +170,6 @@ class Context:
self.udf_agg_map = dict()
self.use_columnstore = False
self.print = print
- self.has_dll = False
self.dialect = 'MonetDB'
self.is_msvc = False
self.have_hge = False
diff --git a/server/Makefile b/server/Makefile
index cb082c8..a2d4e44 100644
--- a/server/Makefile
+++ b/server/Makefile
@@ -1,6 +1,6 @@
debug:
- g++ -g3 -O0 server/server.cpp server/io.cpp -o a.out -Wall -Wextra -Wpedantic -lpthread
+ g++ -g3 -O0 server/server.cpp server/libaquery.cpp -o a.out -Wall -Wextra -Wpedantic -lpthread
test:
- g++ --std=c++1z -g3 -O0 server.cpp io.cpp -o a.out -Wall -Wextra -Wpedantic -lpthread
+ g++ --std=c++1z -g3 -O0 server.cpp libaquery.cpp -o a.out -Wall -Wextra -Wpedantic -lpthread
diff --git a/server/dragonbox/dragonbox.h b/server/dragonbox/dragonbox.h
new file mode 100644
index 0000000..e4b954d
--- /dev/null
+++ b/server/dragonbox/dragonbox.h
@@ -0,0 +1,2658 @@
+// 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.
+
+
+#ifndef JKJ_HEADER_DRAGONBOX
+#define JKJ_HEADER_DRAGONBOX
+
+#include
+#include
+#include
+#include
+#include
+
+// Suppress additional buffer overrun check.
+// I have no idea why MSVC thinks some functions here are vulnerable to the buffer overrun
+// attacks. No, they aren't.
+#if defined(__GNUC__) || defined(__clang__)
+ #define JKJ_SAFEBUFFERS
+ #define JKJ_FORCEINLINE inline __attribute__((always_inline))
+#elif defined(_MSC_VER)
+ #define JKJ_SAFEBUFFERS __declspec(safebuffers)
+ #define JKJ_FORCEINLINE __forceinline
+#else
+ #define JKJ_SAFEBUFFERS
+ #define JKJ_FORCEINLINE inline
+#endif
+
+#if defined(__has_builtin)
+ #define JKJ_DRAGONBOX_HAS_BUILTIN(x) __has_builtin(x)
+#else
+ #define JKJ_DRAGONBOX_HAS_BUILTIN(x) false
+#endif
+
+#if defined(_MSC_VER)
+ #include
+#endif
+
+namespace jkj::dragonbox {
+ namespace detail {
+ template
+ constexpr std::size_t
+ physical_bits = sizeof(T) * std::numeric_limits::digits;
+
+ template
+ constexpr std::size_t value_bits =
+ std::numeric_limits, T>>::digits;
+ }
+
+ // These classes expose encoding specs of IEEE-754-like floating-point formats.
+ // Currently available formats are IEEE754-binary32 & IEEE754-binary64.
+
+ struct ieee754_binary32 {
+ static constexpr int significand_bits = 23;
+ static constexpr int exponent_bits = 8;
+ static constexpr int min_exponent = -126;
+ static constexpr int max_exponent = 127;
+ static constexpr int exponent_bias = -127;
+ static constexpr int decimal_digits = 9;
+ };
+ struct ieee754_binary64 {
+ static constexpr int significand_bits = 52;
+ static constexpr int exponent_bits = 11;
+ static constexpr int min_exponent = -1022;
+ static constexpr int max_exponent = 1023;
+ static constexpr int exponent_bias = -1023;
+ static constexpr int decimal_digits = 17;
+ };
+
+ // A floating-point traits class defines ways to interpret a bit pattern of given size as an
+ // encoding of floating-point number. This is a default implementation of such a traits class,
+ // supporting ways to interpret 32-bits into a binary32-encoded floating-point number and to
+ // interpret 64-bits into a binary64-encoded floating-point number. Users might specialize this
+ // class to change the default behavior for certain types.
+ template
+ struct default_float_traits {
+ // I don't know if there is a truly reliable way of detecting
+ // IEEE-754 binary32/binary64 formats; I just did my best here.
+ static_assert(std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2 &&
+ (detail::physical_bits == 32 || detail::physical_bits == 64),
+ "default_ieee754_traits only works for 32-bits or 64-bits types "
+ "supporting binary32 or binary64 formats!");
+
+ // The type that is being viewed.
+ using type = T;
+
+ // Refers to the format specification class.
+ using format =
+ std::conditional_t == 32, ieee754_binary32, ieee754_binary64>;
+
+ // Defines an unsigned integer type that is large enough to carry a variable of type T.
+ // Most of the operations will be done on this integer type.
+ using carrier_uint =
+ std::conditional_t == 32, std::uint32_t, std::uint64_t>;
+ static_assert(sizeof(carrier_uint) == sizeof(T));
+
+ // Number of bits in the above unsigned integer type.
+ static constexpr int carrier_bits = int(detail::physical_bits);
+
+ // Convert from carrier_uint into the original type.
+ // Depending on the floating-point encoding format, this operation might not be possible for
+ // some specific bit patterns. However, the contract is that u always denotes a
+ // valid bit pattern, so this function must be assumed to be noexcept.
+ static T carrier_to_float(carrier_uint u) noexcept {
+ T x;
+ std::memcpy(&x, &u, sizeof(carrier_uint));
+ return x;
+ }
+
+ // Same as above.
+ static carrier_uint float_to_carrier(T x) noexcept {
+ carrier_uint u;
+ std::memcpy(&u, &x, sizeof(carrier_uint));
+ return u;
+ }
+
+ // Extract exponent bits from a bit pattern.
+ // The result must be aligned to the LSB so that there is no additional zero paddings
+ // on the right. This function does not do bias adjustment.
+ static constexpr unsigned int extract_exponent_bits(carrier_uint u) noexcept {
+ constexpr int significand_bits = format::significand_bits;
+ constexpr int exponent_bits = format::exponent_bits;
+ static_assert(detail::value_bits > exponent_bits);
+ constexpr auto exponent_bits_mask =
+ (unsigned int)(((unsigned int)(1) << exponent_bits) - 1);
+ return (unsigned int)(u >> significand_bits) & exponent_bits_mask;
+ }
+
+ // Extract significand bits from a bit pattern.
+ // The result must be aligned to the LSB so that there is no additional zero paddings
+ // on the right. The result does not contain the implicit bit.
+ static constexpr carrier_uint extract_significand_bits(carrier_uint u) noexcept {
+ constexpr auto mask = carrier_uint((carrier_uint(1) << format::significand_bits) - 1);
+ return carrier_uint(u & mask);
+ }
+
+ // Remove the exponent bits and extract significand bits together with the sign bit.
+ static constexpr carrier_uint remove_exponent_bits(carrier_uint u,
+ unsigned int exponent_bits) noexcept {
+ return u ^ (carrier_uint(exponent_bits) << format::significand_bits);
+ }
+
+ // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
+ static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept {
+ return carrier_uint(carrier_uint(u) << 1);
+ }
+
+ // The actual value of exponent is obtained by adding this value to the extracted exponent
+ // bits.
+ static constexpr int exponent_bias =
+ 1 - (1 << (carrier_bits - format::significand_bits - 2));
+
+ // Obtain the actual value of the binary exponent from the extracted exponent bits.
+ static constexpr int binary_exponent(unsigned int exponent_bits) noexcept {
+ if (exponent_bits == 0) {
+ return format::min_exponent;
+ }
+ else {
+ return int(exponent_bits) + format::exponent_bias;
+ }
+ }
+
+ // Obtain the actual value of the binary exponent from the extracted significand bits and
+ // exponent bits.
+ static constexpr carrier_uint binary_significand(carrier_uint significand_bits,
+ unsigned int exponent_bits) noexcept {
+ if (exponent_bits == 0) {
+ return significand_bits;
+ }
+ else {
+ return significand_bits | (carrier_uint(1) << format::significand_bits);
+ }
+ }
+
+
+ /* Various boolean observer functions */
+
+ static constexpr bool is_nonzero(carrier_uint u) noexcept { return (u << 1) != 0; }
+ static constexpr bool is_positive(carrier_uint u) noexcept {
+ constexpr auto sign_bit = carrier_uint(1)
+ << (format::significand_bits + format::exponent_bits);
+ return u < sign_bit;
+ }
+ static constexpr bool is_negative(carrier_uint u) noexcept { return !is_positive(u); }
+ static constexpr bool is_finite(unsigned int exponent_bits) noexcept {
+ constexpr unsigned int exponent_bits_all_set = (1u << format::exponent_bits) - 1;
+ return exponent_bits != exponent_bits_all_set;
+ }
+ static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept {
+ return (u << 1) == 0;
+ }
+ static constexpr bool has_even_significand_bits(carrier_uint u) noexcept {
+ return u % 2 == 0;
+ }
+ };
+
+ // Convenient wrappers for floating-point traits classes.
+ // In order to reduce the argument passing overhead, these classes should be as simple as
+ // possible (e.g., no inheritance, no private non-static data member, etc.; this is an
+ // unfortunate fact about common ABI convention).
+
+ template >
+ struct float_bits;
+
+ template >
+ struct signed_significand_bits;
+
+ template
+ struct float_bits {
+ using type = T;
+ using traits_type = Traits;
+ using carrier_uint = typename traits_type::carrier_uint;
+
+ carrier_uint u;
+
+ float_bits() = default;
+ constexpr explicit float_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {}
+ constexpr explicit float_bits(T float_value) noexcept
+ : u{traits_type::float_to_carrier(float_value)} {}
+
+ constexpr T to_float() const noexcept { return traits_type::carrier_to_float(u); }
+
+ // Extract exponent bits from a bit pattern.
+ // The result must be aligned to the LSB so that there is no additional zero paddings
+ // on the right. This function does not do bias adjustment.
+ constexpr unsigned int extract_exponent_bits() const noexcept {
+ return traits_type::extract_exponent_bits(u);
+ }
+
+ // Extract significand bits from a bit pattern.
+ // The result must be aligned to the LSB so that there is no additional zero paddings
+ // on the right. The result does not contain the implicit bit.
+ constexpr carrier_uint extract_significand_bits() const noexcept {
+ return traits_type::extract_significand_bits(u);
+ }
+
+ // Remove the exponent bits and extract significand bits together with the sign bit.
+ constexpr auto remove_exponent_bits(unsigned int exponent_bits) const noexcept {
+ return signed_significand_bits(
+ traits_type::remove_exponent_bits(u, exponent_bits));
+ }
+
+ // Obtain the actual value of the binary exponent from the extracted exponent bits.
+ static constexpr int binary_exponent(unsigned int exponent_bits) noexcept {
+ return traits_type::binary_exponent(exponent_bits);
+ }
+ constexpr int binary_exponent() const noexcept {
+ return binary_exponent(extract_exponent_bits());
+ }
+
+ // Obtain the actual value of the binary exponent from the extracted significand bits and
+ // exponent bits.
+ static constexpr carrier_uint binary_significand(carrier_uint significand_bits,
+ unsigned int exponent_bits) noexcept {
+ return traits_type::binary_significand(significand_bits, exponent_bits);
+ }
+ constexpr carrier_uint binary_significand() const noexcept {
+ return binary_significand(extract_significand_bits(), extract_exponent_bits());
+ }
+
+ constexpr bool is_nonzero() const noexcept { return traits_type::is_nonzero(u); }
+ constexpr bool is_positive() const noexcept { return traits_type::is_positive(u); }
+ constexpr bool is_negative() const noexcept { return traits_type::is_negative(u); }
+ constexpr bool is_finite(unsigned int exponent_bits) const noexcept {
+ return traits_type::is_finite(exponent_bits);
+ }
+ constexpr bool is_finite() const noexcept {
+ return traits_type::is_finite(extract_exponent_bits());
+ }
+ constexpr bool has_even_significand_bits() const noexcept {
+ return traits_type::has_even_significand_bits(u);
+ }
+ };
+
+ template
+ struct signed_significand_bits {
+ using type = T;
+ using traits_type = Traits;
+ using carrier_uint = typename traits_type::carrier_uint;
+
+ carrier_uint u;
+
+ signed_significand_bits() = default;
+ constexpr explicit signed_significand_bits(carrier_uint bit_pattern) noexcept
+ : u{bit_pattern} {}
+
+ // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
+ constexpr carrier_uint remove_sign_bit_and_shift() const noexcept {
+ return traits_type::remove_sign_bit_and_shift(u);
+ }
+
+ constexpr bool is_positive() const noexcept { return traits_type::is_positive(u); }
+ constexpr bool is_negative() const noexcept { return traits_type::is_negative(u); }
+ constexpr bool has_all_zero_significand_bits() const noexcept {
+ return traits_type::has_all_zero_significand_bits(u);
+ }
+ constexpr bool has_even_significand_bits() const noexcept {
+ return traits_type::has_even_significand_bits(u);
+ }
+ };
+
+ namespace detail {
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Bit operation intrinsics.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace bits {
+ // Most compilers should be able to optimize this into the ROR instruction.
+ inline std::uint32_t rotr(std::uint32_t n, std::uint32_t r) noexcept {
+ r &= 31;
+ return (n >> r) | (n << (32 - r));
+ }
+ inline std::uint64_t rotr(std::uint64_t n, std::uint32_t r) noexcept {
+ r &= 63;
+ return (n >> r) | (n << (64 - r));
+ }
+ }
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Utilities for wide unsigned integer arithmetic.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace wuint {
+ // Compilers might support built-in 128-bit integer types. However, it seems that
+ // emulating them with a pair of 64-bit integers actually produces a better code,
+ // so we avoid using those built-ins. That said, they are still useful for
+ // implementing 64-bit x 64-bit -> 128-bit multiplication.
+
+ // clang-format off
+#if defined(__SIZEOF_INT128__)
+ // To silence "error: ISO C++ does not support '__int128' for 'type name'
+ // [-Wpedantic]"
+#if defined(__GNUC__)
+ __extension__
+#endif
+ using builtin_uint128_t = unsigned __int128;
+#endif
+ // clang-format on
+
+ struct uint128 {
+ uint128() = default;
+
+ std::uint64_t high_;
+ std::uint64_t low_;
+
+ constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept
+ : high_{high}, low_{low} {}
+
+ constexpr std::uint64_t high() const noexcept { return high_; }
+ constexpr std::uint64_t low() const noexcept { return low_; }
+
+ uint128& operator+=(std::uint64_t n) & noexcept {
+#if JKJ_DRAGONBOX_HAS_BUILTIN(__builtin_addcll)
+ unsigned long long carry;
+ low_ = __builtin_addcll(low_, n, 0, &carry);
+ high_ = __builtin_addcll(high_, 0, carry, &carry);
+#elif JKJ_DRAGONBOX_HAS_BUILTIN(__builtin_ia32_addcarryx_u64)
+ unsigned long long result;
+ auto carry = __builtin_ia32_addcarryx_u64(0, low_, n, &result);
+ low_ = result;
+ __builtin_ia32_addcarryx_u64(carry, high_, 0, &result);
+ high_ = result;
+#elif defined(_MSC_VER) && defined(_M_X64)
+ auto carry = _addcarry_u64(0, low_, n, &low_);
+ _addcarry_u64(carry, high_, 0, &high_);
+#else
+ auto sum = low_ + n;
+ high_ += (sum < low_ ? 1 : 0);
+ low_ = sum;
+#endif
+ return *this;
+ }
+ };
+
+ static inline std::uint64_t umul64(std::uint32_t x, std::uint32_t y) noexcept {
+#if defined(_MSC_VER) && defined(_M_IX86)
+ return __emulu(x, y);
+#else
+ return x * std::uint64_t(y);
+#endif
+ }
+
+ // Get 128-bit result of multiplication of two 64-bit unsigned integers.
+ JKJ_SAFEBUFFERS inline uint128 umul128(std::uint64_t x, std::uint64_t y) noexcept {
+#if defined(__SIZEOF_INT128__)
+ auto result = builtin_uint128_t(x) * builtin_uint128_t(y);
+ return {std::uint64_t(result >> 64), std::uint64_t(result)};
+#elif defined(_MSC_VER) && defined(_M_X64)
+ uint128 result;
+ result.low_ = _umul128(x, y, &result.high_);
+ return result;
+#else
+ auto a = std::uint32_t(x >> 32);
+ auto b = std::uint32_t(x);
+ auto c = std::uint32_t(y >> 32);
+ auto d = std::uint32_t(y);
+
+ auto ac = umul64(a, c);
+ auto bc = umul64(b, c);
+ auto ad = umul64(a, d);
+ auto bd = umul64(b, d);
+
+ auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc);
+
+ return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32),
+ (intermediate << 32) + std::uint32_t(bd)};
+#endif
+ }
+
+ JKJ_SAFEBUFFERS inline std::uint64_t umul128_upper64(std::uint64_t x,
+ std::uint64_t y) noexcept {
+#if defined(__SIZEOF_INT128__)
+ auto result = builtin_uint128_t(x) * builtin_uint128_t(y);
+ return std::uint64_t(result >> 64);
+#elif defined(_MSC_VER) && defined(_M_X64)
+ return __umulh(x, y);
+#else
+ auto a = std::uint32_t(x >> 32);
+ auto b = std::uint32_t(x);
+ auto c = std::uint32_t(y >> 32);
+ auto d = std::uint32_t(y);
+
+ auto ac = umul64(a, c);
+ auto bc = umul64(b, c);
+ auto ad = umul64(a, d);
+ auto bd = umul64(b, d);
+
+ auto intermediate = (bd >> 32) + std::uint32_t(ad) + std::uint32_t(bc);
+
+ return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32);
+#endif
+ }
+
+ // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit
+ // unsigned integer.
+ JKJ_SAFEBUFFERS inline uint128 umul192_upper128(std::uint64_t x, uint128 y) noexcept {
+ auto r = umul128(x, y.high());
+ r += umul128_upper64(x, y.low());
+ return r;
+ }
+
+ // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit
+ // unsigned integer.
+ inline std::uint64_t umul96_upper64(std::uint32_t x, std::uint64_t y) noexcept {
+#if defined(__SIZEOF_INT128__) || (defined(_MSC_VER) && defined(_M_X64))
+ return umul128_upper64(std::uint64_t(x) << 32, y);
+#else
+ auto yh = std::uint32_t(y >> 32);
+ auto yl = std::uint32_t(y);
+
+ auto xyh = umul64(x, yh);
+ auto xyl = umul64(x, yl);
+
+ return xyh + (xyl >> 32);
+#endif
+ }
+
+ // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit
+ // unsigned integer.
+ JKJ_SAFEBUFFERS inline uint128 umul192_lower128(std::uint64_t x, uint128 y) noexcept {
+ auto high = x * y.high();
+ auto high_low = umul128(x, y.low());
+ return {high + high_low.high(), high_low.low()};
+ }
+
+ // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit
+ // unsigned integer.
+ inline std::uint64_t umul96_lower64(std::uint32_t x, std::uint64_t y) noexcept {
+ return x * y;
+ }
+ }
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Some simple utilities for constexpr computation.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ template
+ constexpr Int compute_power(Int a) noexcept {
+ static_assert(k >= 0);
+ Int p = 1;
+ for (int i = 0; i < k; ++i) {
+ p *= a;
+ }
+ return p;
+ }
+
+ template
+ constexpr int count_factors(UInt n) noexcept {
+ static_assert(a > 1);
+ int c = 0;
+ while (n % a == 0) {
+ n /= a;
+ ++c;
+ }
+ return c;
+ }
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Utilities for fast/constexpr log computation.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace log {
+ static_assert((-1 >> 1) == -1, "right-shift for signed integers must be arithmetic");
+
+ // Compute floor(e * c - s).
+ enum class multiply : std::uint32_t {};
+ enum class subtract : std::uint32_t {};
+ enum class shift : std::size_t {};
+ enum class min_exponent : std::int32_t {};
+ enum class max_exponent : std::int32_t {};
+
+ template
+ constexpr int compute(int e) noexcept {
+ assert(std::int32_t(e_min) <= e && e <= std::int32_t(e_max));
+ return int((std::int32_t(e) * std::int32_t(m) - std::int32_t(f)) >> std::size_t(k));
+ }
+
+ // For constexpr computation.
+ // Returns -1 when n = 0.
+ template
+ constexpr int floor_log2(UInt n) noexcept {
+ int count = -1;
+ while (n != 0) {
+ ++count;
+ n >>= 1;
+ }
+ return count;
+ }
+
+ static constexpr int floor_log10_pow2_min_exponent = -2620;
+ static constexpr int floor_log10_pow2_max_exponent = 2620;
+ constexpr int floor_log10_pow2(int e) noexcept {
+ using namespace log;
+ return compute(e);
+ }
+
+ static constexpr int floor_log2_pow10_min_exponent = -1233;
+ static constexpr int floor_log2_pow10_max_exponent = 1233;
+ constexpr int floor_log2_pow10(int e) noexcept {
+ using namespace log;
+ return compute(e);
+ }
+
+ static constexpr int floor_log10_pow2_minus_log10_4_over_3_min_exponent = -2985;
+ static constexpr int floor_log10_pow2_minus_log10_4_over_3_max_exponent = 2936;
+ constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) noexcept {
+ using namespace log;
+ return compute(e);
+ }
+
+ static constexpr int floor_log5_pow2_min_exponent = -1831;
+ static constexpr int floor_log5_pow2_max_exponent = 1831;
+ constexpr int floor_log5_pow2(int e) noexcept {
+ using namespace log;
+ return compute(e);
+ }
+
+ static constexpr int floor_log5_pow2_minus_log5_3_min_exponent = -3543;
+ static constexpr int floor_log5_pow2_minus_log5_3_max_exponent = 2427;
+ constexpr int floor_log5_pow2_minus_log5_3(int e) noexcept {
+ using namespace log;
+ return compute(e);
+ }
+ }
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Utilities for fast divisibility tests.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace div {
+ // Replace n by floor(n / 10^N).
+ // Returns true if and only if n is divisible by 10^N.
+ // Precondition: n <= 10^(N+1)
+ // !!It takes an in-out parameter!!
+ template
+ struct divide_by_pow10_info;
+
+ template <>
+ struct divide_by_pow10_info<1> {
+ static constexpr std::uint32_t magic_number = 6554;
+ static constexpr int shift_amount = 16;
+ };
+
+ template <>
+ struct divide_by_pow10_info<2> {
+ static constexpr std::uint32_t magic_number = 656;
+ static constexpr int shift_amount = 16;
+ };
+
+ template
+ constexpr bool check_divisibility_and_divide_by_pow10(std::uint32_t& n) noexcept {
+ // Make sure the computation for max_n does not overflow.
+ static_assert(N + 1 <= log::floor_log10_pow2(31));
+ assert(n <= compute_power(std::uint32_t(10)));
+
+ using info = divide_by_pow10_info;
+ n *= info::magic_number;
+
+ constexpr auto mask = std::uint32_t(std::uint32_t(1) << info::shift_amount) - 1;
+ bool result = ((n & mask) < info::magic_number);
+
+ n >>= info::shift_amount;
+ return result;
+ }
+
+ // Compute floor(n / 10^N) for small n and N.
+ // Precondition: n <= 10^(N+1)
+ template
+ constexpr std::uint32_t small_division_by_pow10(std::uint32_t n) noexcept {
+ // Make sure the computation for max_n does not overflow.
+ static_assert(N + 1 <= log::floor_log10_pow2(31));
+ assert(n <= compute_power(std::uint32_t(10)));
+
+ return (n * divide_by_pow10_info::magic_number) >>
+ divide_by_pow10_info::shift_amount;
+ }
+
+ // Compute floor(n / 10^N) for small N.
+ // Precondition: n <= n_max
+ template
+ constexpr UInt divide_by_pow10(UInt n) noexcept {
+ static_assert(N >= 0);
+
+ // Specialize for 32-bit division by 100.
+ // Compiler is supposed to generate the identical code for just writing
+ // "n / 100", but for some reason MSVC generates an inefficient code
+ // (mul + mov for no apparent reason, instead of single imul),
+ // so we does this manually.
+ if constexpr (std::is_same_v && N == 2) {
+ return std::uint32_t(wuint::umul64(n, std::uint32_t(1374389535)) >> 37);
+ }
+ // Specialize for 64-bit division by 1000.
+ // Ensure that the correctness condition is met.
+ if constexpr (std::is_same_v && N == 3 &&
+ n_max <= std::uint64_t(15534100272597517998ull)) {
+ return wuint::umul128_upper64(n, std::uint64_t(2361183241434822607ull)) >> 7;
+ }
+ else {
+ constexpr auto divisor = compute_power(UInt(10));
+ return n / divisor;
+ }
+ }
+ }
+ }
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Return types for the main interface function.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ template
+ struct decimal_fp;
+
+ template
+ struct decimal_fp {
+ using carrier_uint = UInt;
+
+ carrier_uint significand;
+ int exponent;
+ };
+
+ template
+ struct decimal_fp {
+ using carrier_uint = UInt;
+
+ carrier_uint significand;
+ int exponent;
+ bool is_negative;
+ };
+
+ template
+ struct decimal_fp {
+ using carrier_uint = UInt;
+
+ carrier_uint significand;
+ int exponent;
+ bool may_have_trailing_zeros;
+ };
+
+ template
+ struct decimal_fp {
+ using carrier_uint = UInt;
+
+ carrier_uint significand;
+ int exponent;
+ bool is_negative;
+ bool may_have_trailing_zeros;
+ };
+
+ template
+ using unsigned_decimal_fp = decimal_fp;
+
+ template
+ using signed_decimal_fp = decimal_fp;
+
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Computed cache entries.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace detail {
+ template
+ struct cache_holder;
+
+ template <>
+ struct cache_holder {
+ using cache_entry_type = std::uint64_t;
+ static constexpr int cache_bits = 64;
+ static constexpr int min_k = -31;
+ static constexpr int max_k = 46;
+ static constexpr cache_entry_type cache[] = {
+ 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};
+ };
+
+ template <>
+ struct cache_holder {
+ using cache_entry_type = wuint::uint128;
+ static constexpr int cache_bits = 128;
+ static constexpr int min_k = -292;
+ static constexpr int max_k = 326;
+ static constexpr cache_entry_type cache[] = {
+ {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},
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+ {0xc83553c5c8965d3d, 0x6f92829494e5acc8}, {0xfa42a8b73abbf48c, 0xcb772339ba1f17fa},
+ {0x9c69a97284b578d7, 0xff2a760414536efc}, {0xc38413cf25e2d70d, 0xfef5138519684abb},
+ {0xf46518c2ef5b8cd1, 0x7eb258665fc25d6a}, {0x98bf2f79d5993802, 0xef2f773ffbd97a62},
+ {0xbeeefb584aff8603, 0xaafb550ffacfd8fb}, {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf39},
+ {0x952ab45cfa97a0b2, 0xdd945a747bf26184}, {0xba756174393d88df, 0x94f971119aeef9e5},
+ {0xe912b9d1478ceb17, 0x7a37cd5601aab85e}, {0x91abb422ccb812ee, 0xac62e055c10ab33b},
+ {0xb616a12b7fe617aa, 0x577b986b314d600a}, {0xe39c49765fdf9d94, 0xed5a7e85fda0b80c},
+ {0x8e41ade9fbebc27d, 0x14588f13be847308}, {0xb1d219647ae6b31c, 0x596eb2d8ae258fc9},
+ {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bc}, {0x8aec23d680043bee, 0x25de7bb9480d5855},
+ {0xada72ccc20054ae9, 0xaf561aa79a10ae6b}, {0xd910f7ff28069da4, 0x1b2ba1518094da05},
+ {0x87aa9aff79042286, 0x90fb44d2f05d0843}, {0xa99541bf57452b28, 0x353a1607ac744a54},
+ {0xd3fa922f2d1675f2, 0x42889b8997915ce9}, {0x847c9b5d7c2e09b7, 0x69956135febada12},
+ {0xa59bc234db398c25, 0x43fab9837e699096}, {0xcf02b2c21207ef2e, 0x94f967e45e03f4bc},
+ {0x8161afb94b44f57d, 0x1d1be0eebac278f6}, {0xa1ba1ba79e1632dc, 0x6462d92a69731733},
+ {0xca28a291859bbf93, 0x7d7b8f7503cfdcff}, {0xfcb2cb35e702af78, 0x5cda735244c3d43f},
+ {0x9defbf01b061adab, 0x3a0888136afa64a8}, {0xc56baec21c7a1916, 0x088aaa1845b8fdd1},
+ {0xf6c69a72a3989f5b, 0x8aad549e57273d46}, {0x9a3c2087a63f6399, 0x36ac54e2f678864c},
+ {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7de}, {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d6},
+ {0x969eb7c47859e743, 0x9f644ae5a4b1b326}, {0xbc4665b596706114, 0x873d5d9f0dde1fef},
+ {0xeb57ff22fc0c7959, 0xa90cb506d155a7eb}, {0x9316ff75dd87cbd8, 0x09a7f12442d588f3},
+ {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb30}, {0xe5d3ef282a242e81, 0x8f1668c8a86da5fb},
+ {0x8fa475791a569d10, 0xf96e017d694487bd}, {0xb38d92d760ec4455, 0x37c981dcc395a9ad},
+ {0xe070f78d3927556a, 0x85bbe253f47b1418}, {0x8c469ab843b89562, 0x93956d7478ccec8f},
+ {0xaf58416654a6babb, 0x387ac8d1970027b3}, {0xdb2e51bfe9d0696a, 0x06997b05fcc0319f},
+ {0x88fcf317f22241e2, 0x441fece3bdf81f04}, {0xab3c2fddeeaad25a, 0xd527e81cad7626c4},
+ {0xd60b3bd56a5586f1, 0x8a71e223d8d3b075}, {0x85c7056562757456, 0xf6872d5667844e4a},
+ {0xa738c6bebb12d16c, 0xb428f8ac016561dc}, {0xd106f86e69d785c7, 0xe13336d701beba53},
+ {0x82a45b450226b39c, 0xecc0024661173474}, {0xa34d721642b06084, 0x27f002d7f95d0191},
+ {0xcc20ce9bd35c78a5, 0x31ec038df7b441f5}, {0xff290242c83396ce, 0x7e67047175a15272},
+ {0x9f79a169bd203e41, 0x0f0062c6e984d387}, {0xc75809c42c684dd1, 0x52c07b78a3e60869},
+ {0xf92e0c3537826145, 0xa7709a56ccdf8a83}, {0x9bbcc7a142b17ccb, 0x88a66076400bb692},
+ {0xc2abf989935ddbfe, 0x6acff893d00ea436}, {0xf356f7ebf83552fe, 0x0583f6b8c4124d44},
+ {0x98165af37b2153de, 0xc3727a337a8b704b}, {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5d},
+ {0xeda2ee1c7064130c, 0x1162def06f79df74}, {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba9},
+ {0xb9a74a0637ce2ee1, 0x6d953e2bd7173693}, {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0438},
+ {0x910ab1d4db9914a0, 0x1d9c9892400a22a3}, {0xb54d5e4a127f59c8, 0x2503beb6d00cab4c},
+ {0xe2a0b5dc971f303a, 0x2e44ae64840fd61e}, {0x8da471a9de737e24, 0x5ceaecfed289e5d3},
+ {0xb10d8e1456105dad, 0x7425a83e872c5f48}, {0xdd50f1996b947518, 0xd12f124e28f7771a},
+ {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa70}, {0xace73cbfdc0bfb7b, 0x636cc64d1001550c},
+ {0xd8210befd30efa5a, 0x3c47f7e05401aa4f}, {0x8714a775e3e95c78, 0x65acfaec34810a72},
+ {0xa8d9d1535ce3b396, 0x7f1839a741a14d0e}, {0xd31045a8341ca07c, 0x1ede48111209a051},
+ {0x83ea2b892091e44d, 0x934aed0aab460433}, {0xa4e4b66b68b65d60, 0xf81da84d56178540},
+ {0xce1de40642e3f4b9, 0x36251260ab9d668f}, {0x80d2ae83e9ce78f3, 0xc1d72b7c6b42601a},
+ {0xa1075a24e4421730, 0xb24cf65b8612f820}, {0xc94930ae1d529cfc, 0xdee033f26797b628},
+ {0xfb9b7cd9a4a7443c, 0x169840ef017da3b2}, {0x9d412e0806e88aa5, 0x8e1f289560ee864f},
+ {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e3}, {0xf5b5d7ec8acb58a2, 0xae10af696774b1dc},
+ {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef2a}, {0xbff610b0cc6edd3f, 0x17fd090a58d32af4},
+ {0xeff394dcff8a948e, 0xddfc4b4cef07f5b1}, {0x95f83d0a1fb69cd9, 0x4abdaf101564f98f},
+ {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f2}, {0xea53df5fd18d5513, 0x84c86189216dc5ee},
+ {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb5}, {0xb7118682dbb66a77, 0x3fbc8c33221dc2a2},
+ {0xe4d5e82392a40515, 0x0fabaf3feaa5334b}, {0x8f05b1163ba6832d, 0x29cb4d87f2a7400f},
+ {0xb2c71d5bca9023f8, 0x743e20e9ef511013}, {0xdf78e4b2bd342cf6, 0x914da9246b255417},
+ {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548f}, {0xae9672aba3d0c320, 0xa184ac2473b529b2},
+ {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741f}, {0x8865899617fb1871, 0x7e2fa67c7a658893},
+ {0xaa7eebfb9df9de8d, 0xddbb901b98feeab8}, {0xd51ea6fa85785631, 0x552a74227f3ea566},
+ {0x8533285c936b35de, 0xd53a88958f872760}, {0xa67ff273b8460356, 0x8a892abaf368f138},
+ {0xd01fef10a657842c, 0x2d2b7569b0432d86}, {0x8213f56a67f6b29b, 0x9c3b29620e29fc74},
+ {0xa298f2c501f45f42, 0x8349f3ba91b47b90}, {0xcb3f2f7642717713, 0x241c70a936219a74},
+ {0xfe0efb53d30dd4d7, 0xed238cd383aa0111}, {0x9ec95d1463e8a506, 0xf4363804324a40ab},
+ {0xc67bb4597ce2ce48, 0xb143c6053edcd0d6}, {0xf81aa16fdc1b81da, 0xdd94b7868e94050b},
+ {0x9b10a4e5e9913128, 0xca7cf2b4191c8327}, {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f1},
+ {0xf24a01a73cf2dccf, 0xbc633b39673c8ced}, {0x976e41088617ca01, 0xd5be0503e085d814},
+ {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e19}, {0xec9c459d51852ba2, 0xddf8e7d60ed1219f},
+ {0x93e1ab8252f33b45, 0xcabb90e5c942b504}, {0xb8da1662e7b00a17, 0x3d6a751f3b936244},
+ {0xe7109bfba19c0c9d, 0x0cc512670a783ad5}, {0x906a617d450187e2, 0x27fb2b80668b24c6},
+ {0xb484f9dc9641e9da, 0xb1f9f660802dedf7}, {0xe1a63853bbd26451, 0x5e7873f8a0396974},
+ {0x8d07e33455637eb2, 0xdb0b487b6423e1e9}, {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda63},
+ {0xdc5c5301c56b75f7, 0x7641a140cc7810fc}, {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9e},
+ {0xac2820d9623bf429, 0x546345fa9fbdcd45}, {0xd732290fbacaf133, 0xa97c177947ad4096},
+ {0x867f59a9d4bed6c0, 0x49ed8eabcccc485e}, {0xa81f301449ee8c70, 0x5c68f256bfff5a75},
+ {0xd226fc195c6a2f8c, 0x73832eec6fff3112}, {0x83585d8fd9c25db7, 0xc831fd53c5ff7eac},
+ {0xa42e74f3d032f525, 0xba3e7ca8b77f5e56}, {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35ec},
+ {0x80444b5e7aa7cf85, 0x7980d163cf5b81b4}, {0xa0555e361951c366, 0xd7e105bcc3326220},
+ {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa8}, {0xfa856334878fc150, 0xb14f98f6f0feb952},
+ {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d4}, {0xc3b8358109e84f07, 0x0a862f80ec4700c9},
+ {0xf4a642e14c6262c8, 0xcd27bb612758c0fb}, {0x98e7e9cccfbd7dbd, 0x8038d51cb897789d},
+ {0xbf21e44003acdd2c, 0xe0470a63e6bd56c4}, {0xeeea5d5004981478, 0x1858ccfce06cac75},
+ {0x95527a5202df0ccb, 0x0f37801e0c43ebc9}, {0xbaa718e68396cffd, 0xd30560258f54e6bb},
+ {0xe950df20247c83fd, 0x47c6b82ef32a206a}, {0x91d28b7416cdd27e, 0x4cdc331d57fa5442},
+ {0xb6472e511c81471d, 0xe0133fe4adf8e953}, {0xe3d8f9e563a198e5, 0x58180fddd97723a7},
+ {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7649}, {0xb201833b35d63f73, 0x2cd2cc6551e513db},
+ {0xde81e40a034bcf4f, 0xf8077f7ea65e58d2}, {0x8b112e86420f6191, 0xfb04afaf27faf783},
+ {0xadd57a27d29339f6, 0x79c5db9af1f9b564}, {0xd94ad8b1c7380874, 0x18375281ae7822bd},
+ {0x87cec76f1c830548, 0x8f2293910d0b15b6}, {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb23},
+ {0xd433179d9c8cb841, 0x5fa60692a46151ec}, {0x849feec281d7f328, 0xdbc7c41ba6bcd334},
+ {0xa5c7ea73224deff3, 0x12b9b522906c0801}, {0xcf39e50feae16bef, 0xd768226b34870a01},
+ {0x81842f29f2cce375, 0xe6a1158300d46641}, {0xa1e53af46f801c53, 0x60495ae3c1097fd1},
+ {0xca5e89b18b602368, 0x385bb19cb14bdfc5}, {0xfcf62c1dee382c42, 0x46729e03dd9ed7b6},
+ {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d2}, {0xc5a05277621be293, 0xc7098b7305241886},
+ {0xf70867153aa2db38, 0xb8cbee4fc66d1ea8}};
+ };
+
+ // Compressed cache for double
+ struct compressed_cache_detail {
+ static constexpr int compression_ratio = 27;
+ static constexpr std::size_t compressed_table_size =
+ (cache_holder::max_k - cache_holder::min_k +
+ compression_ratio) /
+ compression_ratio;
+
+ struct cache_holder_t {
+ wuint::uint128 table[compressed_table_size];
+ };
+ static constexpr cache_holder_t cache = [] {
+ cache_holder_t res{};
+ for (std::size_t i = 0; i < compressed_table_size; ++i) {
+ res.table[i] = cache_holder::cache[i * compression_ratio];
+ }
+ return res;
+ }();
+
+ struct pow5_holder_t {
+ std::uint64_t table[compression_ratio];
+ };
+ static constexpr pow5_holder_t pow5 = [] {
+ pow5_holder_t res{};
+ std::uint64_t p = 1;
+ for (std::size_t i = 0; i < compression_ratio; ++i) {
+ res.table[i] = p;
+ p *= 5;
+ }
+ return res;
+ }();
+ };
+ }
+
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Policies.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace detail {
+ // Forward declare the implementation class.
+ template >
+ struct impl;
+
+ namespace policy_impl {
+ // Sign policies.
+ namespace sign {
+ struct base {};
+
+ struct ignore : base {
+ using sign_policy = ignore;
+ static constexpr bool return_has_sign = false;
+
+ template
+ static constexpr void handle_sign(SignedSignificandBits, ReturnType&) noexcept {
+ }
+ };
+
+ struct return_sign : base {
+ using sign_policy = return_sign;
+ static constexpr bool return_has_sign = true;
+
+ template
+ static constexpr void handle_sign(SignedSignificandBits s,
+ ReturnType& r) noexcept {
+ r.is_negative = s.is_negative();
+ }
+ };
+ }
+
+ // Trailing zero policies.
+ namespace trailing_zero {
+ struct base {};
+
+ struct ignore : base {
+ using trailing_zero_policy = ignore;
+ static constexpr bool report_trailing_zeros = false;
+
+ template
+ static constexpr void on_trailing_zeros(ReturnType&) noexcept {}
+
+ template
+ static constexpr void no_trailing_zeros(ReturnType&) noexcept {}
+ };
+
+ struct remove : base {
+ using trailing_zero_policy = remove;
+ static constexpr bool report_trailing_zeros = false;
+
+ template
+ JKJ_FORCEINLINE static constexpr void
+ on_trailing_zeros(ReturnType& r) noexcept {
+ r.exponent += Impl::remove_trailing_zeros(r.significand);
+ }
+
+ template
+ static constexpr void no_trailing_zeros(ReturnType&) noexcept {}
+ };
+
+ struct report : base {
+ using trailing_zero_policy = report;
+ static constexpr bool report_trailing_zeros = true;
+
+ template
+ static constexpr void on_trailing_zeros(ReturnType& r) noexcept {
+ r.may_have_trailing_zeros = true;
+ }
+
+ template
+ static constexpr void no_trailing_zeros(ReturnType& r) noexcept {
+ r.may_have_trailing_zeros = false;
+ }
+ };
+ }
+
+ // Decimal-to-binary rounding mode policies.
+ namespace decimal_to_binary_rounding {
+ struct base {};
+
+ enum class tag_t { to_nearest, left_closed_directed, right_closed_directed };
+ namespace interval_type {
+ struct symmetric_boundary {
+ static constexpr bool is_symmetric = true;
+ bool is_closed;
+ constexpr bool include_left_endpoint() const noexcept { return is_closed; }
+ constexpr bool include_right_endpoint() const noexcept { return is_closed; }
+ };
+ struct asymmetric_boundary {
+ static constexpr bool is_symmetric = false;
+ bool is_left_closed;
+ constexpr bool include_left_endpoint() const noexcept {
+ return is_left_closed;
+ }
+ constexpr bool include_right_endpoint() const noexcept {
+ return !is_left_closed;
+ }
+ };
+ struct closed {
+ static constexpr bool is_symmetric = true;
+ static constexpr bool include_left_endpoint() noexcept { return true; }
+ static constexpr bool include_right_endpoint() noexcept { return true; }
+ };
+ struct open {
+ static constexpr bool is_symmetric = true;
+ static constexpr bool include_left_endpoint() noexcept { return false; }
+ static constexpr bool include_right_endpoint() noexcept { return false; }
+ };
+ struct left_closed_right_open {
+ static constexpr bool is_symmetric = false;
+ static constexpr bool include_left_endpoint() noexcept { return true; }
+ static constexpr bool include_right_endpoint() noexcept { return false; }
+ };
+ struct right_closed_left_open {
+ static constexpr bool is_symmetric = false;
+ static constexpr bool include_left_endpoint() noexcept { return false; }
+ static constexpr bool include_right_endpoint() noexcept { return true; }
+ };
+ }
+
+ struct nearest_to_even : base {
+ using decimal_to_binary_rounding_policy = nearest_to_even;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::symmetric_boundary;
+ using shorter_interval_type = interval_type::closed;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_to_even{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(s.has_even_significand_bits());
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+ struct nearest_to_odd : base {
+ using decimal_to_binary_rounding_policy = nearest_to_odd;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::symmetric_boundary;
+ using shorter_interval_type = interval_type::open;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_to_odd{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(!s.has_even_significand_bits());
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+ struct nearest_toward_plus_infinity : base {
+ using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::asymmetric_boundary;
+ using shorter_interval_type = interval_type::asymmetric_boundary;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_toward_plus_infinity{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(!s.is_negative());
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(!s.is_negative());
+ }
+ };
+ struct nearest_toward_minus_infinity : base {
+ using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::asymmetric_boundary;
+ using shorter_interval_type = interval_type::asymmetric_boundary;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_toward_minus_infinity{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(s.is_negative());
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept {
+ return f(s.is_negative());
+ }
+ };
+ struct nearest_toward_zero : base {
+ using decimal_to_binary_rounding_policy = nearest_toward_zero;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::right_closed_left_open;
+ using shorter_interval_type = interval_type::right_closed_left_open;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_toward_zero{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+ struct nearest_away_from_zero : base {
+ using decimal_to_binary_rounding_policy = nearest_away_from_zero;
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::left_closed_right_open;
+ using shorter_interval_type = interval_type::left_closed_right_open;
+
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(nearest_away_from_zero{});
+ }
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+
+ namespace detail {
+ struct nearest_always_closed {
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::closed;
+ using shorter_interval_type = interval_type::closed;
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+ struct nearest_always_open {
+ static constexpr auto tag = tag_t::to_nearest;
+ using normal_interval_type = interval_type::open;
+ using shorter_interval_type = interval_type::open;
+
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ template
+ JKJ_FORCEINLINE static constexpr auto
+ invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept {
+ return f();
+ }
+ };
+ }
+
+ struct nearest_to_even_static_boundary : base {
+ using decimal_to_binary_rounding_policy = nearest_to_even_static_boundary;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.has_even_significand_bits()) {
+ return f(detail::nearest_always_closed{});
+ }
+ else {
+ return f(detail::nearest_always_open{});
+ }
+ }
+ };
+ struct nearest_to_odd_static_boundary : base {
+ using decimal_to_binary_rounding_policy = nearest_to_odd_static_boundary;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.has_even_significand_bits()) {
+ return f(detail::nearest_always_open{});
+ }
+ else {
+ return f(detail::nearest_always_closed{});
+ }
+ }
+ };
+ struct nearest_toward_plus_infinity_static_boundary : base {
+ using decimal_to_binary_rounding_policy =
+ nearest_toward_plus_infinity_static_boundary;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.is_negative()) {
+ return f(nearest_toward_zero{});
+ }
+ else {
+ return f(nearest_away_from_zero{});
+ }
+ }
+ };
+ struct nearest_toward_minus_infinity_static_boundary : base {
+ using decimal_to_binary_rounding_policy =
+ nearest_toward_minus_infinity_static_boundary;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.is_negative()) {
+ return f(nearest_away_from_zero{});
+ }
+ else {
+ return f(nearest_toward_zero{});
+ }
+ }
+ };
+
+ namespace detail {
+ struct left_closed_directed {
+ static constexpr auto tag = tag_t::left_closed_directed;
+ };
+ struct right_closed_directed {
+ static constexpr auto tag = tag_t::right_closed_directed;
+ };
+ }
+
+ struct toward_plus_infinity : base {
+ using decimal_to_binary_rounding_policy = toward_plus_infinity;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.is_negative()) {
+ return f(detail::left_closed_directed{});
+ }
+ else {
+ return f(detail::right_closed_directed{});
+ }
+ }
+ };
+ struct toward_minus_infinity : base {
+ using decimal_to_binary_rounding_policy = toward_minus_infinity;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits s,
+ Func&& f) noexcept {
+ if (s.is_negative()) {
+ return f(detail::right_closed_directed{});
+ }
+ else {
+ return f(detail::left_closed_directed{});
+ }
+ }
+ };
+ struct toward_zero : base {
+ using decimal_to_binary_rounding_policy = toward_zero;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(detail::left_closed_directed{});
+ }
+ };
+ struct away_from_zero : base {
+ using decimal_to_binary_rounding_policy = away_from_zero;
+ template
+ JKJ_FORCEINLINE static auto delegate(SignedSignificandBits, Func&& f) noexcept {
+ return f(detail::right_closed_directed{});
+ }
+ };
+ }
+
+ // Binary-to-decimal rounding policies.
+ // (Always assumes nearest rounding modes.)
+ namespace binary_to_decimal_rounding {
+ struct base {};
+
+ enum class tag_t { do_not_care, to_even, to_odd, away_from_zero, toward_zero };
+
+ struct do_not_care : base {
+ using binary_to_decimal_rounding_policy = do_not_care;
+ static constexpr auto tag = tag_t::do_not_care;
+
+ template
+ static constexpr bool prefer_round_down(ReturnType const&) noexcept {
+ return false;
+ }
+ };
+
+ struct to_even : base {
+ using binary_to_decimal_rounding_policy = to_even;
+ static constexpr auto tag = tag_t::to_even;
+
+ template
+ static constexpr bool prefer_round_down(ReturnType const& r) noexcept {
+ return r.significand % 2 != 0;
+ }
+ };
+
+ struct to_odd : base {
+ using binary_to_decimal_rounding_policy = to_odd;
+ static constexpr auto tag = tag_t::to_odd;
+
+ template
+ static constexpr bool prefer_round_down(ReturnType const& r) noexcept {
+ return r.significand % 2 == 0;
+ }
+ };
+
+ struct away_from_zero : base {
+ using binary_to_decimal_rounding_policy = away_from_zero;
+ static constexpr auto tag = tag_t::away_from_zero;
+
+ template
+ static constexpr bool prefer_round_down(ReturnType const&) noexcept {
+ return false;
+ }
+ };
+
+ struct toward_zero : base {
+ using binary_to_decimal_rounding_policy = toward_zero;
+ static constexpr auto tag = tag_t::toward_zero;
+
+ template
+ static constexpr bool prefer_round_down(ReturnType const&) noexcept {
+ return true;
+ }
+ };
+ }
+
+ // Cache policies.
+ namespace cache {
+ struct base {};
+
+ struct full : base {
+ using cache_policy = full;
+ template
+ static constexpr typename cache_holder::cache_entry_type
+ get_cache(int k) noexcept {
+ assert(k >= cache_holder::min_k &&
+ k <= cache_holder::max_k);
+ return cache_holder::cache[std::size_t(
+ k - cache_holder::min_k)];
+ }
+ };
+
+ struct compact : base {
+ using cache_policy = compact;
+ template
+ static constexpr typename cache_holder::cache_entry_type
+ get_cache(int k) noexcept {
+ assert(k >= cache_holder::min_k &&
+ k <= cache_holder::max_k);
+
+ if constexpr (std::is_same_v) {
+ // Compute the base index.
+ auto const cache_index =
+ int(std::uint32_t(k - cache_holder::min_k) /
+ compressed_cache_detail::compression_ratio);
+ auto const kb =
+ cache_index * compressed_cache_detail::compression_ratio +
+ cache_holder::min_k;
+ auto const offset = k - kb;
+
+ // Get the base cache.
+ auto const base_cache =
+ compressed_cache_detail::cache.table[cache_index];
+
+ if (offset == 0) {
+ return base_cache;
+ }
+ else {
+ // Compute the required amount of bit-shift.
+ auto const alpha = log::floor_log2_pow10(kb + offset) -
+ log::floor_log2_pow10(kb) - offset;
+ assert(alpha > 0 && alpha < 64);
+
+ // Try to recover the real cache.
+ auto const pow5 = compressed_cache_detail::pow5.table[offset];
+ auto recovered_cache = wuint::umul128(base_cache.high(), pow5);
+ auto const middle_low = wuint::umul128(base_cache.low(), pow5);
+
+ recovered_cache += middle_low.high();
+
+ auto const high_to_middle = recovered_cache.high() << (64 - alpha);
+ auto const middle_to_low = recovered_cache.low() << (64 - alpha);
+
+ recovered_cache = wuint::uint128{
+ (recovered_cache.low() >> alpha) | high_to_middle,
+ ((middle_low.low() >> alpha) | middle_to_low)};
+
+ assert(recovered_cache.low() + 1 != 0);
+ recovered_cache = {recovered_cache.high(),
+ recovered_cache.low() + 1};
+
+ return recovered_cache;
+ }
+ }
+ else {
+ // Just use the full cache for anything other than binary64
+ return cache_holder::cache[std::size_t(
+ k - cache_holder::min_k)];
+ }
+ }
+ };
+ }
+ }
+ }
+
+ namespace policy {
+ namespace sign {
+ inline constexpr auto ignore = detail::policy_impl::sign::ignore{};
+ inline constexpr auto return_sign = detail::policy_impl::sign::return_sign{};
+ }
+
+ namespace trailing_zero {
+ inline constexpr auto ignore = detail::policy_impl::trailing_zero::ignore{};
+ inline constexpr auto remove = detail::policy_impl::trailing_zero::remove{};
+ inline constexpr auto report = detail::policy_impl::trailing_zero::report{};
+ }
+
+ namespace decimal_to_binary_rounding {
+ inline constexpr auto nearest_to_even =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_to_even{};
+ inline constexpr auto nearest_to_odd =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd{};
+ inline constexpr auto nearest_toward_plus_infinity =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_toward_plus_infinity{};
+ inline constexpr auto nearest_toward_minus_infinity =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_toward_minus_infinity{};
+ inline constexpr auto nearest_toward_zero =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_toward_zero{};
+ inline constexpr auto nearest_away_from_zero =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_away_from_zero{};
+
+ inline constexpr auto nearest_to_even_static_boundary =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_to_even_static_boundary{};
+ inline constexpr auto nearest_to_odd_static_boundary =
+ detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd_static_boundary{};
+ inline constexpr auto nearest_toward_plus_infinity_static_boundary =
+ detail::policy_impl::decimal_to_binary_rounding::
+ nearest_toward_plus_infinity_static_boundary{};
+ inline constexpr auto nearest_toward_minus_infinity_static_boundary =
+ detail::policy_impl::decimal_to_binary_rounding::
+ nearest_toward_minus_infinity_static_boundary{};
+
+ inline constexpr auto toward_plus_infinity =
+ detail::policy_impl::decimal_to_binary_rounding::toward_plus_infinity{};
+ inline constexpr auto toward_minus_infinity =
+ detail::policy_impl::decimal_to_binary_rounding::toward_minus_infinity{};
+ inline constexpr auto toward_zero =
+ detail::policy_impl::decimal_to_binary_rounding::toward_zero{};
+ inline constexpr auto away_from_zero =
+ detail::policy_impl::decimal_to_binary_rounding::away_from_zero{};
+ }
+
+ namespace binary_to_decimal_rounding {
+ inline constexpr auto do_not_care =
+ detail::policy_impl::binary_to_decimal_rounding::do_not_care{};
+ inline constexpr auto to_even =
+ detail::policy_impl::binary_to_decimal_rounding::to_even{};
+ inline constexpr auto to_odd =
+ detail::policy_impl::binary_to_decimal_rounding::to_odd{};
+ inline constexpr auto away_from_zero =
+ detail::policy_impl::binary_to_decimal_rounding::away_from_zero{};
+ inline constexpr auto toward_zero =
+ detail::policy_impl::binary_to_decimal_rounding::toward_zero{};
+ }
+
+ namespace cache {
+ inline constexpr auto full = detail::policy_impl::cache::full{};
+ inline constexpr auto compact = detail::policy_impl::cache::compact{};
+ }
+ }
+
+ namespace detail {
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // The main algorithm.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ template
+ struct impl : private FloatTraits, private FloatTraits::format {
+ using format = typename FloatTraits::format;
+ using carrier_uint = typename FloatTraits::carrier_uint;
+
+ using FloatTraits::carrier_bits;
+ using format::significand_bits;
+ using format::min_exponent;
+ using format::max_exponent;
+ using format::exponent_bias;
+ using format::decimal_digits;
+
+ static constexpr int kappa = std::is_same_v ? 1 : 2;
+ static_assert(kappa >= 1);
+ static_assert(carrier_bits >= significand_bits + 2 + log::floor_log2_pow10(kappa + 1));
+
+ static constexpr int min_k = [] {
+ constexpr auto a = -log::floor_log10_pow2_minus_log10_4_over_3(
+ int(max_exponent - significand_bits));
+ constexpr auto b =
+ -log::floor_log10_pow2(int(max_exponent - significand_bits)) + kappa;
+ return a < b ? a : b;
+ }();
+ static_assert(min_k >= cache_holder::min_k);
+
+ static constexpr int max_k = [] {
+ // We do invoke shorter_interval_case for exponent == min_exponent case,
+ // so we should not add 1 here.
+ constexpr auto a = -log::floor_log10_pow2_minus_log10_4_over_3(
+ int(min_exponent - significand_bits /*+ 1*/));
+ constexpr auto b =
+ -log::floor_log10_pow2(int(min_exponent - significand_bits)) + kappa;
+ return a > b ? a : b;
+ }();
+ static_assert(max_k <= cache_holder::max_k);
+
+ using cache_entry_type = typename cache_holder::cache_entry_type;
+ static constexpr auto cache_bits = cache_holder::cache_bits;
+
+ static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2;
+ static constexpr int case_shorter_interval_left_endpoint_upper_threshold =
+ 2 +
+ log::floor_log2(
+ compute_power<
+ count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) /
+ 3);
+
+ static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0;
+ static constexpr int case_shorter_interval_right_endpoint_upper_threshold =
+ 2 +
+ log::floor_log2(
+ compute_power<
+ count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) /
+ 3);
+
+ static constexpr int shorter_interval_tie_lower_threshold =
+ -log::floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits;
+ static constexpr int shorter_interval_tie_upper_threshold =
+ -log::floor_log5_pow2(significand_bits + 2) - 2 - significand_bits;
+
+ struct compute_mul_result {
+ carrier_uint result;
+ bool is_integer;
+ };
+ struct compute_mul_parity_result {
+ bool parity;
+ bool is_integer;
+ };
+
+ //// The main algorithm assumes the input is a normal/subnormal finite number
+
+ template
+ JKJ_SAFEBUFFERS static ReturnType
+ compute_nearest_normal(carrier_uint const two_fc, int const exponent,
+ AdditionalArgs... additional_args) noexcept {
+ //////////////////////////////////////////////////////////////////////
+ // Step 1: Schubfach multiplier calculation
+ //////////////////////////////////////////////////////////////////////
+
+ ReturnType ret_value;
+ IntervalType interval_type{additional_args...};
+
+ // Compute k and beta.
+ int const minus_k = log::floor_log10_pow2(exponent) - kappa;
+ auto const cache = CachePolicy::template get_cache(-minus_k);
+ int const beta = exponent + log::floor_log2_pow10(-minus_k);
+
+ // Compute zi and deltai.
+ // 10^kappa <= deltai < 10^(kappa + 1)
+ auto const deltai = compute_delta(cache, beta);
+ // For the case of binary32, the result of integer check is not correct for
+ // 29711844 * 2^-82
+ // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
+ // and 29711844 * 2^-81
+ // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17,
+ // and they are the unique counterexamples. However, since 29711844 is even,
+ // this does not cause any problem for the endpoints calculations; it can only
+ // cause a problem when we need to perform integer check for the center.
+ // Fortunately, with these inputs, that branch is never executed, so we are fine.
+ auto const [zi, is_z_integer] = compute_mul((two_fc | 1) << beta, cache);
+
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 2: Try larger divisor; remove trailing zeros if necessary
+ //////////////////////////////////////////////////////////////////////
+
+ constexpr auto big_divisor = compute_power(std::uint32_t(10));
+ constexpr auto small_divisor = compute_power(std::uint32_t(10));
+
+ // Using an upper bound on zi, we might be able to optimize the division
+ // better than the compiler; we are computing zi / big_divisor here.
+ ret_value.significand =
+ div::divide_by_pow10(zi);
+ auto r = std::uint32_t(zi - big_divisor * ret_value.significand);
+
+ if (r < deltai) {
+ // Exclude the right endpoint if necessary.
+ if (r == 0 && (is_z_integer & !interval_type.include_right_endpoint())) {
+ if constexpr (BinaryToDecimalRoundingPolicy::tag ==
+ policy_impl::binary_to_decimal_rounding::tag_t::do_not_care) {
+ ret_value.significand *= 10;
+ ret_value.exponent = minus_k + kappa;
+ --ret_value.significand;
+ TrailingZeroPolicy::template no_trailing_zeros(ret_value);
+ return ret_value;
+ }
+ else {
+ --ret_value.significand;
+ r = big_divisor;
+ goto small_divisor_case_label;
+ }
+ }
+ }
+ else if (r > deltai) {
+ goto small_divisor_case_label;
+ }
+ else {
+ // r == deltai; compare fractional parts.
+ auto const [xi_parity, x_is_integer] =
+ compute_mul_parity(two_fc - 1, cache, beta);
+
+ if (!(xi_parity | (x_is_integer & interval_type.include_left_endpoint()))) {
+ goto small_divisor_case_label;
+ }
+ }
+ ret_value.exponent = minus_k + kappa + 1;
+
+ // We may need to remove trailing zeros.
+ TrailingZeroPolicy::template on_trailing_zeros(ret_value);
+ return ret_value;
+
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 3: Find the significand with the smaller divisor
+ //////////////////////////////////////////////////////////////////////
+
+ small_divisor_case_label:
+ TrailingZeroPolicy::template no_trailing_zeros(ret_value);
+ ret_value.significand *= 10;
+ ret_value.exponent = minus_k + kappa;
+
+ if constexpr (BinaryToDecimalRoundingPolicy::tag ==
+ policy_impl::binary_to_decimal_rounding::tag_t::do_not_care) {
+ // Normally, we want to compute
+ // ret_value.significand += r / small_divisor
+ // and return, but we need to take care of the case that the resulting
+ // value is exactly the right endpoint, while that is not included in the
+ // interval.
+ if (!interval_type.include_right_endpoint()) {
+ // Is r divisible by 10^kappa?
+ if (is_z_integer && div::check_divisibility_and_divide_by_pow10(r)) {
+ // This should be in the interval.
+ ret_value.significand += r - 1;
+ }
+ else {
+ ret_value.significand += r;
+ }
+ }
+ else {
+ ret_value.significand += div::small_division_by_pow10(r);
+ }
+ }
+ else {
+ auto dist = r - (deltai / 2) + (small_divisor / 2);
+ bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0;
+
+ // Is dist divisible by 10^kappa?
+ bool const divisible_by_small_divisor =
+ div::check_divisibility_and_divide_by_pow10(dist);
+
+ // Add dist / 10^kappa to the significand.
+ ret_value.significand += dist;
+
+ if (divisible_by_small_divisor) {
+ // Check z^(f) >= epsilon^(f).
+ // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
+ // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f).
+ // Since there are only 2 possibilities, we only need to care about the
+ // parity. Also, zi and r should have the same parity since the divisor is
+ // an even number.
+ auto const [yi_parity, is_y_integer] =
+ compute_mul_parity(two_fc, cache, beta);
+ if (yi_parity != approx_y_parity) {
+ --ret_value.significand;
+ }
+ else {
+ // If z^(f) >= epsilon^(f), we might have a tie
+ // when z^(f) == epsilon^(f), or equivalently, when y is an integer.
+ // For tie-to-up case, we can just choose the upper one.
+ if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) &
+ is_y_integer) {
+ --ret_value.significand;
+ }
+ }
+ }
+ }
+ return ret_value;
+ }
+
+ template
+ JKJ_SAFEBUFFERS static ReturnType
+ compute_nearest_shorter(int const exponent,
+ AdditionalArgs... additional_args) noexcept {
+ ReturnType ret_value;
+ IntervalType interval_type{additional_args...};
+
+ // Compute k and beta.
+ int const minus_k = log::floor_log10_pow2_minus_log10_4_over_3(exponent);
+ int const beta = exponent + log::floor_log2_pow10(-minus_k);
+
+ // Compute xi and zi.
+ auto const cache = CachePolicy::template get_cache(-minus_k);
+
+ auto xi = compute_left_endpoint_for_shorter_interval_case(cache, beta);
+ auto zi = compute_right_endpoint_for_shorter_interval_case(cache, beta);
+
+ // If we don't accept the right endpoint and
+ // if the right endpoint is an integer, decrease it.
+ if (!interval_type.include_right_endpoint() &&
+ is_right_endpoint_integer_shorter_interval(exponent)) {
+ --zi;
+ }
+ // If we don't accept the left endpoint or
+ // if the left endpoint is not an integer, increase it.
+ if (!interval_type.include_left_endpoint() ||
+ !is_left_endpoint_integer_shorter_interval(exponent)) {
+ ++xi;
+ }
+
+ // Try bigger divisor.
+ ret_value.significand = zi / 10;
+
+ // If succeed, remove trailing zeros if necessary and return.
+ if (ret_value.significand * 10 >= xi) {
+ ret_value.exponent = minus_k + 1;
+ TrailingZeroPolicy::template on_trailing_zeros(ret_value);
+ return ret_value;
+ }
+
+ // Otherwise, compute the round-up of y.
+ TrailingZeroPolicy::template no_trailing_zeros(ret_value);
+ ret_value.significand = compute_round_up_for_shorter_interval_case(cache, beta);
+ ret_value.exponent = minus_k;
+
+ // When tie occurs, choose one of them according to the rule.
+ if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) &&
+ exponent >= shorter_interval_tie_lower_threshold &&
+ exponent <= shorter_interval_tie_upper_threshold) {
+ --ret_value.significand;
+ }
+ else if (ret_value.significand < xi) {
+ ++ret_value.significand;
+ }
+ return ret_value;
+ }
+
+ template
+ JKJ_SAFEBUFFERS static ReturnType
+ compute_left_closed_directed(carrier_uint const two_fc, int exponent) noexcept {
+ //////////////////////////////////////////////////////////////////////
+ // Step 1: Schubfach multiplier calculation
+ //////////////////////////////////////////////////////////////////////
+
+ ReturnType ret_value;
+
+ // Compute k and beta.
+ int const minus_k = log::floor_log10_pow2(exponent) - kappa;
+ auto const cache = CachePolicy::template get_cache(-minus_k);
+ int const beta = exponent + log::floor_log2_pow10(-minus_k);
+
+ // Compute xi and deltai.
+ // 10^kappa <= deltai < 10^(kappa + 1)
+ auto const deltai = compute_delta(cache, beta);
+ auto [xi, is_x_integer] = compute_mul(two_fc << beta, cache);
+
+ // Deal with the unique exceptional cases
+ // 29711844 * 2^-82
+ // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
+ // and 29711844 * 2^-81
+ // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17
+ // for binary32.
+ if constexpr (std::is_same_v) {
+ if (exponent <= -80) {
+ is_x_integer = false;
+ }
+ }
+
+ if (!is_x_integer) {
+ ++xi;
+ }
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 2: Try larger divisor; remove trailing zeros if necessary
+ //////////////////////////////////////////////////////////////////////
+
+ constexpr auto big_divisor = compute_power(std::uint32_t(10));
+
+ // Using an upper bound on xi, we might be able to optimize the division
+ // better than the compiler; we are computing xi / big_divisor here.
+ ret_value.significand =
+ div::divide_by_pow10(xi);
+ auto r = std::uint32_t(xi - big_divisor * ret_value.significand);
+
+ if (r != 0) {
+ ++ret_value.significand;
+ r = big_divisor - r;
+ }
+
+ if (r > deltai) {
+ goto small_divisor_case_label;
+ }
+ else if (r == deltai) {
+ // Compare the fractional parts.
+ // This branch is never taken for the exceptional cases
+ // 2f_c = 29711482, e = -81
+ // (6.1442649164096937243516663440523473127541365101933479309082... * 10^-18)
+ // and 2f_c = 29711482, e = -80
+ // (1.2288529832819387448703332688104694625508273020386695861816... * 10^-17).
+ auto const [zi_parity, is_z_integer] =
+ compute_mul_parity(two_fc + 2, cache, beta);
+ if (zi_parity || is_z_integer) {
+ goto small_divisor_case_label;
+ }
+ }
+
+ // The ceiling is inside, so we are done.
+ ret_value.exponent = minus_k + kappa + 1;
+ TrailingZeroPolicy::template on_trailing_zeros(ret_value);
+ return ret_value;
+
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 3: Find the significand with the smaller divisor
+ //////////////////////////////////////////////////////////////////////
+
+ small_divisor_case_label:
+ ret_value.significand *= 10;
+ ret_value.significand -= div::small_division_by_pow10(r);
+ ret_value.exponent = minus_k + kappa;
+ TrailingZeroPolicy::template no_trailing_zeros(ret_value);
+ return ret_value;
+ }
+
+ template
+ JKJ_SAFEBUFFERS static ReturnType
+ compute_right_closed_directed(carrier_uint const two_fc, int const exponent,
+ bool shorter_interval) noexcept {
+ //////////////////////////////////////////////////////////////////////
+ // Step 1: Schubfach multiplier calculation
+ //////////////////////////////////////////////////////////////////////
+
+ ReturnType ret_value;
+
+ // Compute k and beta.
+ int const minus_k =
+ log::floor_log10_pow2(exponent - (shorter_interval ? 1 : 0)) - kappa;
+ auto const cache = CachePolicy::template get_cache(-minus_k);
+ int const beta = exponent + log::floor_log2_pow10(-minus_k);
+
+ // Compute zi and deltai.
+ // 10^kappa <= deltai < 10^(kappa + 1)
+ auto const deltai =
+ shorter_interval ? compute_delta(cache, beta - 1) : compute_delta(cache, beta);
+ carrier_uint const zi = compute_mul(two_fc << beta, cache).result;
+
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 2: Try larger divisor; remove trailing zeros if necessary
+ //////////////////////////////////////////////////////////////////////
+
+ constexpr auto big_divisor = compute_power(std::uint32_t(10));
+
+ // Using an upper bound on zi, we might be able to optimize the division better than
+ // the compiler; we are computing zi / big_divisor here.
+ ret_value.significand =
+ div::divide_by_pow10(zi);
+ auto const r = std::uint32_t(zi - big_divisor * ret_value.significand);
+
+ if (r > deltai) {
+ goto small_divisor_case_label;
+ }
+ else if (r == deltai) {
+ // Compare the fractional parts.
+ if (!compute_mul_parity(two_fc - (shorter_interval ? 1 : 2), cache, beta)
+ .parity) {
+ goto small_divisor_case_label;
+ }
+ }
+
+ // The floor is inside, so we are done.
+ ret_value.exponent = minus_k + kappa + 1;
+ TrailingZeroPolicy::template on_trailing_zeros(ret_value);
+ return ret_value;
+
+
+ //////////////////////////////////////////////////////////////////////
+ // Step 3: Find the significand with the small divisor
+ //////////////////////////////////////////////////////////////////////
+
+ small_divisor_case_label:
+ ret_value.significand *= 10;
+ ret_value.significand += div::small_division_by_pow10(r);
+ ret_value.exponent = minus_k + kappa;
+ TrailingZeroPolicy::template no_trailing_zeros(ret_value);
+ return ret_value;
+ }
+
+ // Remove trailing zeros from n and return the number of zeros removed.
+ JKJ_FORCEINLINE static int remove_trailing_zeros(carrier_uint& n) noexcept {
+ assert(n != 0);
+
+ if constexpr (std::is_same_v) {
+ constexpr auto mod_inv_5 = std::uint32_t(0xcccc'cccd);
+ constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
+
+ int s = 0;
+ while (true) {
+ auto q = bits::rotr(n * mod_inv_25, 2);
+ if (q <= std::numeric_limits::max() / 100) {
+ n = q;
+ s += 2;
+ }
+ else {
+ break;
+ }
+ }
+ auto q = bits::rotr(n * mod_inv_5, 1);
+ if (q <= std::numeric_limits::max() / 10) {
+ n = q;
+ s |= 1;
+ }
+
+ return s;
+ }
+ else {
+ static_assert(std::is_same_v);
+
+ // Divide by 10^8 and reduce to 32-bits if divisible.
+ // Since ret_value.significand <= (2^53 * 1000 - 1) / 1000 < 10^16,
+ // n is at most of 16 digits.
+
+ // This magic number is ceil(2^90 / 10^8).
+ constexpr auto magic_number = std::uint64_t(12379400392853802749ull);
+ auto nm = wuint::umul128(n, magic_number);
+
+ // Is n is divisible by 10^8?
+ if ((nm.high() & ((std::uint64_t(1) << (90 - 64)) - 1)) == 0 &&
+ nm.low() < magic_number) {
+ // If yes, work with the quotient.
+ auto n32 = std::uint32_t(nm.high() >> (90 - 64));
+
+ constexpr auto mod_inv_5 = std::uint32_t(0xcccc'cccd);
+ constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
+
+ int s = 8;
+ while (true) {
+ auto q = bits::rotr(n32 * mod_inv_25, 2);
+ if (q <= std::numeric_limits::max() / 100) {
+ n32 = q;
+ s += 2;
+ }
+ else {
+ break;
+ }
+ }
+ auto q = bits::rotr(n32 * mod_inv_5, 1);
+ if (q <= std::numeric_limits::max() / 10) {
+ n32 = q;
+ s |= 1;
+ }
+
+ n = n32;
+ return s;
+ }
+
+ // If n is not divisible by 10^8, work with n itself.
+ constexpr auto mod_inv_5 = std::uint64_t(0xcccc'cccc'cccc'cccd);
+ constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
+
+ int s = 0;
+ while (true) {
+ auto q = bits::rotr(n * mod_inv_25, 2);
+ if (q <= std::numeric_limits::max() / 100) {
+ n = q;
+ s += 2;
+ }
+ else {
+ break;
+ }
+ }
+ auto q = bits::rotr(n * mod_inv_5, 1);
+ if (q <= std::numeric_limits::max() / 10) {
+ n = q;
+ s |= 1;
+ }
+
+ return s;
+ }
+ }
+
+ static compute_mul_result compute_mul(carrier_uint u,
+ cache_entry_type const& cache) noexcept {
+ if constexpr (std::is_same_v) {
+ auto r = wuint::umul96_upper64(u, cache);
+ return {carrier_uint(r >> 32), carrier_uint(r) == 0};
+ }
+ else {
+ static_assert(std::is_same_v);
+ auto r = wuint::umul192_upper128(u, cache);
+ return {r.high(), r.low() == 0};
+ }
+ }
+
+ static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
+ int beta) noexcept {
+ if constexpr (std::is_same_v) {
+ return std::uint32_t(cache >> (cache_bits - 1 - beta));
+ }
+ else {
+ static_assert(std::is_same_v);
+ return std::uint32_t(cache.high() >> (carrier_bits - 1 - beta));
+ }
+ }
+
+ static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
+ cache_entry_type const& cache,
+ int beta) noexcept {
+ assert(beta >= 1);
+ assert(beta < 64);
+
+ if constexpr (std::is_same_v) {
+ auto r = wuint::umul96_lower64(two_f, cache);
+ return {((r >> (64 - beta)) & 1) != 0, std::uint32_t(r >> (32 - beta)) == 0};
+ }
+ else {
+ static_assert(std::is_same_v);
+ auto r = wuint::umul192_lower128(two_f, cache);
+ return {((r.high() >> (64 - beta)) & 1) != 0,
+ ((r.high() << beta) | (r.low() >> (64 - beta))) == 0};
+ }
+ }
+
+ static constexpr carrier_uint
+ compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache,
+ int beta) noexcept {
+ if constexpr (std::is_same_v) {
+ return carrier_uint((cache - (cache >> (significand_bits + 2))) >>
+ (cache_bits - significand_bits - 1 - beta));
+ }
+ else {
+ static_assert(std::is_same_v);
+ return (cache.high() - (cache.high() >> (significand_bits + 2))) >>
+ (carrier_bits - significand_bits - 1 - beta);
+ }
+ }
+
+ static constexpr carrier_uint
+ compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache,
+ int beta) noexcept {
+ if constexpr (std::is_same_v) {
+ return carrier_uint((cache + (cache >> (significand_bits + 1))) >>
+ (cache_bits - significand_bits - 1 - beta));
+ }
+ else {
+ static_assert(std::is_same_v);
+ return (cache.high() + (cache.high() >> (significand_bits + 1))) >>
+ (carrier_bits - significand_bits - 1 - beta);
+ }
+ }
+
+ static constexpr carrier_uint
+ compute_round_up_for_shorter_interval_case(cache_entry_type const& cache,
+ int beta) noexcept {
+ if constexpr (std::is_same_v) {
+ return (carrier_uint(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) /
+ 2;
+ }
+ else {
+ static_assert(std::is_same_v);
+ return ((cache.high() >> (carrier_bits - significand_bits - 2 - beta)) + 1) / 2;
+ }
+ }
+
+ static constexpr bool
+ is_right_endpoint_integer_shorter_interval(int exponent) noexcept {
+ return exponent >= case_shorter_interval_right_endpoint_lower_threshold &&
+ exponent <= case_shorter_interval_right_endpoint_upper_threshold;
+ }
+
+ static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept {
+ return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
+ exponent <= case_shorter_interval_left_endpoint_upper_threshold;
+ }
+ };
+
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // Policy holder.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ namespace policy_impl {
+ // The library will specify a list of accepted kinds of policies and their defaults, and
+ // the user will pass a list of policies. The aim of helper classes/functions here is to
+ // do the following:
+ // 1. Check if the policy parameters given by the user are all valid; that means,
+ // each of them should be of the kinds specified by the library.
+ // If that's not the case, then the compilation fails.
+ // 2. Check if multiple policy parameters for the same kind is specified by the user.
+ // If that's the case, then the compilation fails.
+ // 3. Build a class deriving from all policies the user have given, and also from
+ // the default policies if the user did not specify one for some kinds.
+ // A policy belongs to a certain kind if it is deriving from a base class.
+
+ // For a given kind, find a policy belonging to that kind.
+ // Check if there are more than one such policies.
+ enum class policy_found_info { not_found, unique, repeated };
+ template
+ struct found_policy_pair {
+ using policy = Policy;
+ static constexpr auto found_info = info;
+ };
+
+ template
+ struct base_default_pair {
+ using base = Base;
+
+ template
+ static constexpr FoundPolicyInfo get_policy_impl(FoundPolicyInfo) {
+ return {};
+ }
+ template
+ static constexpr auto get_policy_impl(FoundPolicyInfo, FirstPolicy,
+ RemainingPolicies... remainings) {
+ if constexpr (std::is_base_of_v) {
+ if constexpr (FoundPolicyInfo::found_info == policy_found_info::not_found) {
+ return get_policy_impl(
+ found_policy_pair{},
+ remainings...);
+ }
+ else {
+ return get_policy_impl(
+ found_policy_pair{},
+ remainings...);
+ }
+ }
+ else {
+ return get_policy_impl(FoundPolicyInfo{}, remainings...);
+ }
+ }
+
+ template
+ static constexpr auto get_policy(Policies... policies) {
+ return get_policy_impl(
+ found_policy_pair{},
+ policies...);
+ }
+ };
+ template
+ struct base_default_pair_list {};
+
+ // Check if a given policy belongs to one of the kinds specified by the library.
+ template
+ constexpr bool check_policy_validity(Policy, base_default_pair_list<>) {
+ return false;
+ }
+ template
+ constexpr bool check_policy_validity(
+ Policy,
+ base_default_pair_list) {
+ return std::is_base_of_v ||
+ check_policy_validity(
+ Policy{}, base_default_pair_list{});
+ }
+
+ template
+ constexpr bool check_policy_list_validity(BaseDefaultPairList) {
+ return true;
+ }
+
+ template
+ constexpr bool check_policy_list_validity(BaseDefaultPairList, FirstPolicy,
+ RemainingPolicies... remaining_policies) {
+ return check_policy_validity(FirstPolicy{}, BaseDefaultPairList{}) &&
+ check_policy_list_validity(BaseDefaultPairList{}, remaining_policies...);
+ }
+
+ // Build policy_holder.
+ template
+ struct found_policy_pair_list {
+ static constexpr bool repeated = repeated_;
+ };
+
+ template
+ struct policy_holder : Policies... {};
+
+ template
+ constexpr auto
+ make_policy_holder_impl(base_default_pair_list<>,
+ found_policy_pair_list,
+ Policies...) {
+ return found_policy_pair_list{};
+ }
+
+ template
+ constexpr auto make_policy_holder_impl(
+ base_default_pair_list,
+ found_policy_pair_list, Policies... policies) {
+ using new_found_policy_pair =
+ decltype(FirstBaseDefaultPair::get_policy(policies...));
+
+ return make_policy_holder_impl(
+ base_default_pair_list{},
+ found_policy_pair_list < repeated ||
+ new_found_policy_pair::found_info == policy_found_info::repeated,
+ new_found_policy_pair, FoundPolicyPairs... > {}, policies...);
+ }
+
+ template
+ constexpr auto convert_to_policy_holder(found_policy_pair_list,
+ RawPolicies...) {
+ return policy_holder{};
+ }
+
+ template
+ constexpr auto
+ convert_to_policy_holder(found_policy_pair_list,
+ RawPolicies... policies) {
+ return convert_to_policy_holder(
+ found_policy_pair_list{},
+ typename FirstFoundPolicyPair::policy{}, policies...);
+ }
+
+ template
+ constexpr auto make_policy_holder(BaseDefaultPairList, Policies... policies) {
+ static_assert(check_policy_list_validity(BaseDefaultPairList{}, Policies{}...),
+ "jkj::dragonbox: an invalid policy is specified");
+
+ using policy_pair_list = decltype(make_policy_holder_impl(
+ BaseDefaultPairList{}, found_policy_pair_list{}, policies...));
+
+ static_assert(!policy_pair_list::repeated,
+ "jkj::dragonbox: each policy should be specified at most once");
+
+ return convert_to_policy_holder(policy_pair_list{});
+ }
+ }
+ }
+
+
+ ////////////////////////////////////////////////////////////////////////////////////////
+ // The interface function.
+ ////////////////////////////////////////////////////////////////////////////////////////
+
+ template , class... Policies>
+ JKJ_FORCEINLINE JKJ_SAFEBUFFERS auto
+ to_decimal(signed_significand_bits signed_significand_bits,
+ unsigned int exponent_bits, Policies... policies) noexcept {
+ // Build policy holder type.
+ using namespace detail::policy_impl;
+ using policy_holder = decltype(make_policy_holder(
+ base_default_pair_list,
+ base_default_pair,
+ base_default_pair,
+ base_default_pair,
+ base_default_pair>{},
+ policies...));
+
+ using return_type =
+ decimal_fp;
+
+ return_type ret = policy_holder::delegate(
+ signed_significand_bits,
+ [exponent_bits, signed_significand_bits](auto interval_type_provider) {
+ using format = typename FloatTraits::format;
+ constexpr auto tag = decltype(interval_type_provider)::tag;
+
+ auto two_fc = signed_significand_bits.remove_sign_bit_and_shift();
+ auto exponent = int(exponent_bits);
+
+ if constexpr (tag == decimal_to_binary_rounding::tag_t::to_nearest) {
+ // Is the input a normal number?
+ if (exponent != 0) {
+ exponent += format::exponent_bias - format::significand_bits;
+
+ // Shorter interval case; proceed like Schubfach.
+ // One might think this condition is wrong, since when exponent_bits == 1
+ // and two_fc == 0, the interval is actually regular. However, it turns out
+ // that this seemingly wrong condition is actually fine, because the end
+ // result is anyway the same.
+ //
+ // [binary32]
+ // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38
+ // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38
+ // fc * 2^e = 1.175'494'35... * 10^-38
+ // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38
+ //
+ // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38.
+ // 1.175'494'3 * 10^-38 is also a correct shortest representation that will
+ // be rejected if we assume shorter interval, but 1.175'494'4 * 10^-38 is
+ // closer to the true value so it doesn't matter.
+ //
+ // [binary64]
+ // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308
+ // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308
+ // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308
+ // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308
+ //
+ // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 *
+ // 10^-308. This is indeed of the shortest length, and it is the unique one
+ // closest to the true value among valid representations of the same length.
+ static_assert(std::is_same_v ||
+ std::is_same_v);
+
+ if (two_fc == 0) {
+ return decltype(interval_type_provider)::invoke_shorter_interval_case(
+ signed_significand_bits, [exponent](auto... additional_args) {
+ return detail::impl::
+ template compute_nearest_shorter<
+ return_type,
+ typename decltype(interval_type_provider)::
+ shorter_interval_type,
+ typename policy_holder::trailing_zero_policy,
+ typename policy_holder::
+ binary_to_decimal_rounding_policy,
+ typename policy_holder::cache_policy>(
+ exponent, additional_args...);
+ });
+ }
+
+ two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
+ }
+ // Is the input a subnormal number?
+ else {
+ exponent = format::min_exponent - format::significand_bits;
+ }
+
+ return decltype(interval_type_provider)::invoke_normal_interval_case(
+ signed_significand_bits, [two_fc, exponent](auto... additional_args) {
+ return detail::impl::
+ template compute_nearest_normal<
+ return_type,
+ typename decltype(interval_type_provider)::normal_interval_type,
+ typename policy_holder::trailing_zero_policy,
+ typename policy_holder::binary_to_decimal_rounding_policy,
+ typename policy_holder::cache_policy>(two_fc, exponent,
+ additional_args...);
+ });
+ }
+ else if constexpr (tag == decimal_to_binary_rounding::tag_t::left_closed_directed) {
+ // Is the input a normal number?
+ if (exponent != 0) {
+ exponent += format::exponent_bias - format::significand_bits;
+ two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
+ }
+ // Is the input a subnormal number?
+ else {
+ exponent = format::min_exponent - format::significand_bits;
+ }
+
+ return detail::impl::template compute_left_closed_directed<
+ return_type, typename policy_holder::trailing_zero_policy,
+ typename policy_holder::cache_policy>(two_fc, exponent);
+ }
+ else {
+ static_assert(tag == decimal_to_binary_rounding::tag_t::right_closed_directed);
+
+ bool shorter_interval = false;
+
+ // Is the input a normal number?
+ if (exponent != 0) {
+ if (two_fc == 0 && exponent != 1) {
+ shorter_interval = true;
+ }
+ exponent += format::exponent_bias - format::significand_bits;
+ two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
+ }
+ // Is the input a subnormal number?
+ else {
+ exponent = format::min_exponent - format::significand_bits;
+ }
+
+ return detail::impl::template compute_right_closed_directed<
+ return_type, typename policy_holder::trailing_zero_policy,
+ typename policy_holder::cache_policy>(two_fc, exponent, shorter_interval);
+ }
+ });
+
+ policy_holder::handle_sign(signed_significand_bits, ret);
+ return ret;
+ }
+
+ template , class... Policies>
+ JKJ_FORCEINLINE JKJ_SAFEBUFFERS auto to_decimal(Float x, Policies... policies) noexcept {
+ auto const br = float_bits(x);
+ auto const exponent_bits = br.extract_exponent_bits();
+ auto const s = br.remove_exponent_bits(exponent_bits);
+ assert(br.is_finite());
+
+ return to_decimal(s, exponent_bits, policies...);
+ }
+}
+
+#undef JKJ_FORCEINLINE
+#undef JKJ_SAFEBUFFERS
+#undef JKJ_DRAGONBOX_HAS_BUILTIN
+
+#endif
diff --git a/server/dragonbox/dragonbox_to_chars.cpp b/server/dragonbox/dragonbox_to_chars.cpp
new file mode 100644
index 0000000..75b82b6
--- /dev/null
+++ b/server/dragonbox/dragonbox_to_chars.cpp
@@ -0,0 +1,519 @@
+// 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_to_chars.h"
+
+#if defined(__GNUC__) || defined(__clang__)
+ #define JKJ_FORCEINLINE inline __attribute__((always_inline))
+#elif defined(_MSC_VER)
+ #define JKJ_FORCEINLINE __forceinline
+#else
+ #define JKJ_FORCEINLINE inline
+#endif
+
+namespace jkj::dragonbox {
+ namespace to_chars_detail {
+ // These "//"'s are to prevent clang-format to ruin this nice alignment.
+ // Thanks to reddit user u/mcmcc:
+ // https://www.reddit.com/r/cpp/comments/so3wx9/dragonbox_110_is_released_a_fast_floattostring/hw8z26r/?context=3
+ static constexpr char radix_100_table[] = {
+ '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', //
+ '0', '5', '0', '6', '0', '7', '0', '8', '0', '9', //
+ '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', //
+ '1', '5', '1', '6', '1', '7', '1', '8', '1', '9', //
+ '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', //
+ '2', '5', '2', '6', '2', '7', '2', '8', '2', '9', //
+ '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', //
+ '3', '5', '3', '6', '3', '7', '3', '8', '3', '9', //
+ '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', //
+ '4', '5', '4', '6', '4', '7', '4', '8', '4', '9', //
+ '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', //
+ '5', '5', '5', '6', '5', '7', '5', '8', '5', '9', //
+ '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', //
+ '6', '5', '6', '6', '6', '7', '6', '8', '6', '9', //
+ '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', //
+ '7', '5', '7', '6', '7', '7', '7', '8', '7', '9', //
+ '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', //
+ '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', //
+ '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', //
+ '9', '5', '9', '6', '9', '7', '9', '8', '9', '9' //
+ };
+ static constexpr char radix_100_head_table[] = {
+ '0', '.', '1', '.', '2', '.', '3', '.', '4', '.', //
+ '5', '.', '6', '.', '7', '.', '8', '.', '9', '.', //
+ '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', //
+ '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', //
+ '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', //
+ '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', //
+ '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', //
+ '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', //
+ '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', //
+ '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', //
+ '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', //
+ '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', //
+ '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', //
+ '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', //
+ '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', //
+ '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', //
+ '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', //
+ '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', //
+ '9', '.', '9', '.', '9', '.', '9', '.', '9', '.', //
+ '9', '.', '9', '.', '9', '.', '9', '.', '9', '.' //
+ };
+
+ // These digit generation routines are inspired by James Anhalt's itoa algorithm:
+ // https://github.com/jeaiii/itoa
+ // The main idea is for given n, find y such that floor(10^k * y / 2^32) = n holds,
+ // where k is an appropriate integer depending on the length of n.
+ // For example, if n = 1234567, we set k = 6. In this case, we have
+ // floor(y / 2^32) = 1,
+ // floor(10^2 * ((10^0 * y) mod 2^32) / 2^32) = 23,
+ // floor(10^2 * ((10^2 * y) mod 2^32) / 2^32) = 45, and
+ // floor(10^2 * ((10^4 * y) mod 2^32) / 2^32) = 67.
+ // See https://jk-jeon.github.io/posts/2022/02/jeaiii-algorithm/ for more explanation.
+
+ JKJ_FORCEINLINE static void print_9_digits(std::uint32_t s32, int& exponent,
+ char*& buffer) noexcept {
+ // -- IEEE-754 binary32
+ // Since we do not cut trailing zeros in advance, s32 must be of 6~9 digits
+ // unless the original input was subnormal.
+ // In particular, when it is of 9 digits it shouldn't have any trailing zeros.
+ // -- IEEE-754 binary64
+ // In this case, s32 must be of 7~9 digits unless the input is subnormal,
+ // and it shouldn't have any trailing zeros if it is of 9 digits.
+ if (s32 >= 1'0000'0000) {
+ // 9 digits.
+ // 1441151882 = ceil(2^57 / 1'0000'0000) + 1
+ auto prod = s32 * std::uint64_t(1441151882);
+ prod >>= 25;
+ std::memcpy(buffer, radix_100_head_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 8, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ exponent += 8;
+ buffer += 10;
+ }
+ else if (s32 >= 100'0000) {
+ // 7 or 8 digits.
+ // 281474978 = ceil(2^48 / 100'0000) + 1
+ auto prod = s32 * std::uint64_t(281474978);
+ prod >>= 16;
+ auto two_digits = std::uint32_t(prod >> 32);
+ // If s32 is of 8 digits, increase the exponent by 7.
+ // Otherwise, increase it by 6.
+ exponent += (6 + unsigned(two_digits >= 10));
+
+ // Write the first digit and the decimal point.
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ // This third character may be overwritten later but we don't care.
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ // Remaining 6 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100'0000)) {
+ // The number of characters actually written is:
+ // 1, if only the first digit is nonzero, which means that either s32 is of 7
+ // digits or it is of 8 digits but the second digit is zero, or
+ // 3, otherwise.
+ // Note that buffer[2] is never zero if s32 is of 7 digits, because the input is
+ // never zero.
+ buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2);
+ }
+ else {
+ // At least one of the remaining 6 digits are nonzero.
+ // After this adjustment, now the first destination becomes buffer + 2.
+ buffer += unsigned(two_digits >= 10);
+
+ // Obtain the next two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 4 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) {
+ buffer += (3 + unsigned(buffer[3] > '0'));
+ }
+ else {
+ // At least one of the remaining 4 digits are nonzero.
+
+ // Obtain the next two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 2 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) {
+ buffer += (5 + unsigned(buffer[5] > '0'));
+ }
+ else {
+ // Obtain the last two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 6, radix_100_table + two_digits * 2, 2);
+
+ buffer += (7 + unsigned(buffer[7] > '0'));
+ }
+ }
+ }
+ }
+ else if (s32 >= 1'0000) {
+ // 5 or 6 digits.
+ // 429497 = ceil(2^32 / 1'0000)
+ auto prod = s32 * std::uint64_t(429497);
+ auto two_digits = std::uint32_t(prod >> 32);
+
+ // If s32 is of 6 digits, increase the exponent by 5.
+ // Otherwise, increase it by 4.
+ exponent += (4 + unsigned(two_digits >= 10));
+
+ // Write the first digit and the decimal point.
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ // This third character may be overwritten later but we don't care.
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ // Remaining 4 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) {
+ // The number of characters actually written is 1 or 3, similarly to the case of
+ // 7 or 8 digits.
+ buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2);
+ }
+ else {
+ // At least one of the remaining 4 digits are nonzero.
+ // After this adjustment, now the first destination becomes buffer + 2.
+ buffer += unsigned(two_digits >= 10);
+
+ // Obtain the next two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 2 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) {
+ buffer += (3 + unsigned(buffer[3] > '0'));
+ }
+ else {
+ // Obtain the last two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2);
+
+ buffer += (5 + unsigned(buffer[5] > '0'));
+ }
+ }
+ }
+ else if (s32 >= 100) {
+ // 3 or 4 digits.
+ // 42949673 = ceil(2^32 / 100)
+ auto prod = s32 * std::uint64_t(42949673);
+ auto two_digits = std::uint32_t(prod >> 32);
+
+ // If s32 is of 4 digits, increase the exponent by 3.
+ // Otherwise, increase it by 2.
+ exponent += (2 + int(two_digits >= 10));
+
+ // Write the first digit and the decimal point.
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ // This third character may be overwritten later but we don't care.
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ // Remaining 2 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100)) {
+ // The number of characters actually written is 1 or 3, similarly to the case of
+ // 7 or 8 digits.
+ buffer += (1 + (unsigned(two_digits >= 10) & unsigned(buffer[2] > '0')) * 2);
+ }
+ else {
+ // At least one of the remaining 2 digits are nonzero.
+ // After this adjustment, now the first destination becomes buffer + 2.
+ buffer += unsigned(two_digits >= 10);
+
+ // Obtain the last two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2);
+
+ buffer += (3 + unsigned(buffer[3] > '0'));
+ }
+ }
+ else {
+ // 1 or 2 digits.
+ // If s32 is of 2 digits, increase the exponent by 1.
+ exponent += int(s32 >= 10);
+
+ // Write the first digit and the decimal point.
+ std::memcpy(buffer, radix_100_head_table + s32 * 2, 2);
+ // This third character may be overwritten later but we don't care.
+ buffer[2] = radix_100_table[s32 * 2 + 1];
+
+ // The number of characters actually written is 1 or 3, similarly to the case of
+ // 7 or 8 digits.
+ buffer += (1 + (unsigned(s32 >= 10) & unsigned(buffer[2] > '0')) * 2);
+ }
+ }
+
+ template <>
+ char* to_chars>(std::uint32_t s32, int exponent,
+ char* buffer) noexcept {
+ // Print significand.
+ print_9_digits(s32, exponent, buffer);
+
+ // Print exponent and return
+ if (exponent < 0) {
+ std::memcpy(buffer, "E-", 2);
+ buffer += 2;
+ exponent = -exponent;
+ }
+ else if (exponent > 0) {
+ buffer[0] = 'E';
+ buffer += 1;
+ }
+ else {
+ return buffer;
+ }
+
+ if (exponent >= 10) {
+ std::memcpy(buffer, &radix_100_table[exponent * 2], 2);
+ buffer += 2;
+ }
+ else {
+ buffer[0] = char('0' + exponent);
+ buffer += 1;
+ }
+
+ return buffer;
+ }
+
+ template <>
+ char* to_chars>(std::uint64_t const significand,
+ int exponent, char* buffer) noexcept {
+ // Print significand by decomposing it into a 9-digit block and a 8-digit block.
+ std::uint32_t first_block, second_block;
+ bool no_second_block;
+
+ if (significand >= 1'0000'0000) {
+ first_block = std::uint32_t(significand / 1'0000'0000);
+ second_block = std::uint32_t(significand) - first_block * 1'0000'0000;
+ exponent += 8;
+ no_second_block = (second_block == 0);
+ }
+ else {
+ first_block = std::uint32_t(significand);
+ no_second_block = true;
+ }
+
+ if (no_second_block) {
+ print_9_digits(first_block, exponent, buffer);
+ }
+ else {
+ // We proceed similarly to print_9_digits(), but since we do not need to remove
+ // trailing zeros, the procedure is a bit simpler.
+ if (first_block >= 1'0000'0000) {
+ // The input is of 17 digits, thus there should be no trailing zero at all.
+ // The first block is of 9 digits.
+ // 1441151882 = ceil(2^57 / 1'0000'0000) + 1
+ auto prod = first_block * std::uint64_t(1441151882);
+ prod >>= 25;
+ std::memcpy(buffer, radix_100_head_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 8, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ // The second block is of 8 digits.
+ // 281474978 = ceil(2^48 / 100'0000) + 1
+ prod = second_block * std::uint64_t(281474978);
+ prod >>= 16;
+ prod += 1;
+ std::memcpy(buffer + 10, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 12, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 14, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 16, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ exponent += 8;
+ buffer += 18;
+ }
+ else {
+ if (first_block >= 100'0000) {
+ // 7 or 8 digits.
+ // 281474978 = ceil(2^48 / 100'0000) + 1
+ auto prod = first_block * std::uint64_t(281474978);
+ prod >>= 16;
+ auto two_digits = std::uint32_t(prod >> 32);
+
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ exponent += (6 + unsigned(two_digits >= 10));
+ buffer += unsigned(two_digits >= 10);
+
+ // Print remaining 6 digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 6, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ buffer += 8;
+ }
+ else if (first_block >= 1'0000) {
+ // 5 or 6 digits.
+ // 429497 = ceil(2^32 / 1'0000)
+ auto prod = first_block * std::uint64_t(429497);
+ auto two_digits = std::uint32_t(prod >> 32);
+
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ exponent += (4 + unsigned(two_digits >= 10));
+ buffer += unsigned(two_digits >= 10);
+
+ // Print remaining 4 digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 4, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ buffer += 6;
+ }
+ else if (first_block >= 100) {
+ // 3 or 4 digits.
+ // 42949673 = ceil(2^32 / 100)
+ auto prod = first_block * std::uint64_t(42949673);
+ auto two_digits = std::uint32_t(prod >> 32);
+
+ std::memcpy(buffer, radix_100_head_table + two_digits * 2, 2);
+ buffer[2] = radix_100_table[two_digits * 2 + 1];
+
+ exponent += (2 + unsigned(two_digits >= 10));
+ buffer += unsigned(two_digits >= 10);
+
+ // Print remaining 2 digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ std::memcpy(buffer + 2, radix_100_table + std::uint32_t(prod >> 32) * 2, 2);
+
+ buffer += 4;
+ }
+ else {
+ // 1 or 2 digits.
+ std::memcpy(buffer, radix_100_head_table + first_block * 2, 2);
+ buffer[2] = radix_100_table[first_block * 2 + 1];
+
+ exponent += unsigned(first_block >= 10);
+ buffer += (2 + unsigned(first_block >= 10));
+ }
+
+ // Next, print the second block.
+ // The second block is of 8 digits, but we may have trailing zeros.
+ // 281474978 = ceil(2^48 / 100'0000) + 1
+ auto prod = second_block * std::uint64_t(281474978);
+ prod >>= 16;
+ prod += 1;
+ auto two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 6 digits are all zero?
+ if (std::uint32_t(prod) <= std::uint32_t((std::uint64_t(1) << 32) / 100'0000)) {
+ buffer += (1 + unsigned(buffer[1] > '0'));
+ }
+ else {
+ // Obtain the next two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 2, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 4 digits are all zero?
+ if (std::uint32_t(prod) <=
+ std::uint32_t((std::uint64_t(1) << 32) / 1'0000)) {
+ buffer += (3 + unsigned(buffer[3] > '0'));
+ }
+ else {
+ // Obtain the next two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 4, radix_100_table + two_digits * 2, 2);
+
+ // Remaining 2 digits are all zero?
+ if (std::uint32_t(prod) <=
+ std::uint32_t((std::uint64_t(1) << 32) / 100)) {
+ buffer += (5 + unsigned(buffer[5] > '0'));
+ }
+ else {
+ // Obtain the last two digits.
+ prod = std::uint32_t(prod) * std::uint64_t(100);
+ two_digits = std::uint32_t(prod >> 32);
+ std::memcpy(buffer + 6, radix_100_table + two_digits * 2, 2);
+ buffer += (7 + unsigned(buffer[7] > '0'));
+ }
+ }
+ }
+ }
+ }
+
+ // Print exponent and return
+ if (exponent < 0) {
+ std::memcpy(buffer, "E-", 2);
+ buffer += 2;
+ exponent = -exponent;
+ }
+ else if (exponent > 0) {
+ buffer[0] = 'E';
+ buffer += 1;
+ }
+ else {
+ return buffer;
+ }
+
+ if (exponent >= 100) {
+ // d1 = exponent / 10; d2 = exponent % 10;
+ // 6554 = ceil(2^16 / 10)
+ auto prod = std::uint32_t(exponent) * std::uint32_t(6554);
+ auto d1 = prod >> 16;
+ prod = std::uint16_t(prod) * std::uint32_t(5); // * 10
+ auto d2 = prod >> 15; // >> 16
+ std::memcpy(buffer, &radix_100_table[d1 * 2], 2);
+ buffer[2] = char('0' + d2);
+ buffer += 3;
+ }
+ else if (exponent >= 10) {
+ std::memcpy(buffer, &radix_100_table[exponent * 2], 2);
+ buffer += 2;
+ }
+ else {
+ buffer[0] = char('0' + exponent);
+ buffer += 1;
+ }
+
+ return buffer;
+ }
+ }
+}
diff --git a/server/dragonbox/dragonbox_to_chars.h b/server/dragonbox/dragonbox_to_chars.h
new file mode 100644
index 0000000..e22a2b4
--- /dev/null
+++ b/server/dragonbox/dragonbox_to_chars.h
@@ -0,0 +1,108 @@
+// 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.
+
+#ifndef JKJ_HEADER_DRAGONBOX_TO_CHARS
+#define JKJ_HEADER_DRAGONBOX_TO_CHARS
+
+#include "dragonbox.h"
+
+namespace jkj::dragonbox {
+ namespace to_chars_detail {
+ template
+ extern char* to_chars(typename FloatTraits::carrier_uint significand, int exponent,
+ char* buffer) noexcept;
+
+ // Avoid needless ABI overhead incurred by tag dispatch.
+ template
+ char* to_chars_n_impl(float_bits br, char* buffer) noexcept {
+ auto const exponent_bits = br.extract_exponent_bits();
+ auto const s = br.remove_exponent_bits(exponent_bits);
+
+ if (br.is_finite(exponent_bits)) {
+ if (s.is_negative()) {
+ *buffer = '-';
+ ++buffer;
+ }
+ if (br.is_nonzero()) {
+ auto result = to_decimal(
+ s, exponent_bits, policy::sign::ignore, policy::trailing_zero::ignore,
+ typename PolicyHolder::decimal_to_binary_rounding_policy{},
+ typename PolicyHolder::binary_to_decimal_rounding_policy{},
+ typename PolicyHolder::cache_policy{});
+ return to_chars_detail::to_chars(result.significand,
+ result.exponent, buffer);
+ }
+ else {
+ std::memcpy(buffer, "0E0", 3);
+ return buffer + 3;
+ }
+ }
+ else {
+ if (s.has_all_zero_significand_bits()) {
+ if (s.is_negative()) {
+ *buffer = '-';
+ ++buffer;
+ }
+ std::memcpy(buffer, "Infinity", 8);
+ return buffer + 8;
+ }
+ else {
+ std::memcpy(buffer, "NaN", 3);
+ return buffer + 3;
+ }
+ }
+ }
+ }
+
+ // Returns the next-to-end position
+ template , class... Policies>
+ char* to_chars_n(Float x, char* buffer, Policies... policies) noexcept {
+ using namespace jkj::dragonbox::detail::policy_impl;
+ using policy_holder = decltype(make_policy_holder(
+ base_default_pair_list,
+ base_default_pair,
+ base_default_pair>{},
+ policies...));
+
+ return to_chars_detail::to_chars_n_impl(float_bits(x),
+ buffer);
+ }
+
+ // Null-terminate and bypass the return value of fp_to_chars_n
+ template , class... Policies>
+ char* to_chars(Float x, char* buffer, Policies... policies) noexcept {
+ auto ptr = to_chars_n(x, buffer, policies...);
+ *ptr = '\0';
+ return ptr;
+ }
+
+ // Maximum required buffer size (excluding null-terminator)
+ template
+ inline constexpr std::size_t max_output_string_length =
+ std::is_same_v
+ ?
+ // sign(1) + significand(9) + decimal_point(1) + exp_marker(1) + exp_sign(1) + exp(2)
+ (1 + 9 + 1 + 1 + 1 + 2)
+ :
+ // format == ieee754_format::binary64
+ // sign(1) + significand(17) + decimal_point(1) + exp_marker(1) + exp_sign(1) + exp(3)
+ (1 + 17 + 1 + 1 + 1 + 3);
+}
+
+#endif
diff --git a/server/gc.h b/server/gc.h
new file mode 100644
index 0000000..b2eff44
--- /dev/null
+++ b/server/gc.h
@@ -0,0 +1,59 @@
+#ifndef __AQ_USE_THREADEDGC__
+#include
+class GC {
+private:;
+
+ size_t max_size, max_slots,
+ interval, forced_clean,
+ forceclean_timer = 0;
+ bool running, alive;
+// ptr, dealloc, ref, sz
+ void *q, *q_back;
+ void* handle;
+ std::atomic slot_pos;
+ std::atomic alive_cnt;
+ std::atomic current_size;
+ volatile bool lock;
+ // maybe use volatile std::thread::id instead
+protected:
+ void acquire_lock();
+ void release_lock();
+ void gc();
+ void daemon();
+ void start_deamon();
+ void terminate_daemon();
+
+public:
+ void reg(void* v, uint32_t sz = 1,
+ void(*f)(void*) = free
+ );
+
+ GC(
+ uint32_t max_size = 0xfffffff, uint32_t max_slots = 4096,
+ uint32_t interval = 10000, uint32_t forced_clean = 1000000 //one seconds
+ ) : max_size(max_size), max_slots(max_slots),
+ interval(interval), forced_clean(forced_clean){
+
+ start_deamon();
+ GC::gc = this;
+ } // 256 MB
+
+ ~GC(){
+ terminate_daemon();
+ }
+ static GC* gc;
+ constexpr static void(*_free) (void*) = free;
+};
+
+#else
+class GC {
+public:
+ GC(uint32_t) = default;
+ void reg(
+ void* v, uint32_t = 0,
+ void(*f)(void*) = free
+ ) const { f(v); }
+ static GC* gc;
+ constexpr static void(*_free) (void*) = free;
+}
+#endif
diff --git a/server/jeaiii_to_text.h b/server/jeaiii_to_text.h
new file mode 100644
index 0000000..a4f1a53
--- /dev/null
+++ b/server/jeaiii_to_text.h
@@ -0,0 +1,116 @@
+
+// Copyright (c) 2022 James Edward Anhalt III - https://github.com/jeaiii/itoa
+using u32 = decltype(0xffffffff);
+using u64 = decltype(0xffffffffffffffff);
+
+static_assert(u32(-1) > 0, "u32 must be unsigned");
+static_assert(u32(0xffffffff) + u32(1) == u32(0), "u32 must be 32 bits");
+static_assert(u64(-1) > 0, "u64 must be unsigned");
+static_assert(u64(0xffffffffffffffff) + u32(1) == u32(0), "u64 must be 64 bits");
+
+constexpr auto digits_00_99 =
+ "00010203040506070809" "10111213141516171819" "20212223242526272829" "30313233343536373839" "40414243444546474849"
+ "50515253545556575859" "60616263646566676869" "70717273747576777879" "80818283848586878889" "90919293949596979899";
+
+struct pair { char t, o; };
+
+#define JEAIII_W(I, U) *(pair*)&b[I] = *(pair*)&digits_00_99[(U) * 2]
+#define JEAIII_A(I, N) t = (u64(1) << (32 + N / 5 * N * 53 / 16)) / u32(1e##N) + 1 + N / 6 - N / 8, t *= u, t >>= N / 5 * N * 53 / 16, t += N / 6 * 4, JEAIII_W(I, t >> 32)
+#define JEAIII_S(I) b[I] = char(u64(10) * u32(t) >> 32) + '0'
+#define JEAIII_D(I) t = u64(100) * u32(t), JEAIII_W(I, t >> 32)
+
+#define JEAIII_C0(I) b[I] = char(u) + '0'
+#define JEAIII_C1(I) JEAIII_W(I, u)
+#define JEAIII_C2(I) JEAIII_A(I, 1), JEAIII_S(I + 2)
+#define JEAIII_C3(I) JEAIII_A(I, 2), JEAIII_D(I + 2)
+#define JEAIII_C4(I) JEAIII_A(I, 3), JEAIII_D(I + 2), JEAIII_S(I + 4)
+#define JEAIII_C5(I) JEAIII_A(I, 4), JEAIII_D(I + 2), JEAIII_D(I + 4)
+#define JEAIII_C6(I) JEAIII_A(I, 5), JEAIII_D(I + 2), JEAIII_D(I + 4), JEAIII_S(I + 6)
+#define JEAIII_C7(I) JEAIII_A(I, 6), JEAIII_D(I + 2), JEAIII_D(I + 4), JEAIII_D(I + 6)
+#define JEAIII_C8(I) JEAIII_A(I, 7), JEAIII_D(I + 2), JEAIII_D(I + 4), JEAIII_D(I + 6), JEAIII_S(I + 8)
+#define JEAIII_C9(I) JEAIII_A(I, 8), JEAIII_D(I + 2), JEAIII_D(I + 4), JEAIII_D(I + 6), JEAIII_D(I + 8)
+
+#define JEAIII_L(N, A, B) u < u32(1e##N) ? A : B
+#define JEAIII_L09(F) JEAIII_L(2, JEAIII_L(1, F(0), F(1)), JEAIII_L(6, JEAIII_L(4, JEAIII_L(3, F(2), F(3)), JEAIII_L(5, F(4), F(5))), JEAIII_L(8, JEAIII_L(7, F(6), F(7)), JEAIII_L(9, F(8), F(9)))))
+#define JEAIII_L03(F) JEAIII_L(2, JEAIII_L(1, F(0), F(1)), JEAIII_L(3, F(2), F(3)))
+
+#define JEAIII_K(N) (JEAIII_C##N(0), b + N + 1)
+#define JEAIII_KX(N) (JEAIII_C##N(0), u = x, JEAIII_C7(N + 1), b + N + 9)
+#define JEAIII_KYX(N) (JEAIII_C##N(0), u = y, JEAIII_C7(N + 1), u = x, JEAIII_C7(N + 9), b + N + 17)
+
+template struct _cond { using type = F; };
+template struct _cond { using type = T; };
+template using cond = typename _cond