From fa1f9822bc1ed0da2cffd20cd99e5a9ad16c266f Mon Sep 17 00:00:00 2001 From: Bill Date: Fri, 11 Nov 2022 03:14:50 +0800 Subject: [PATCH] WIP: rework exec-engine structure, GC, fast print --- Makefile | 14 +- README.md | 23 +- aquery_config.py | 1 + build.py | 16 +- msc-plugin/libaquery.vcxproj | 2 +- reconstruct/storage.py | 2 +- server/Makefile | 4 +- server/dragonbox/dragonbox.h | 2658 +++++++++++++++++++++++ server/dragonbox/dragonbox_to_chars.cpp | 519 +++++ server/dragonbox/dragonbox_to_chars.h | 108 + server/gc.h | 59 + server/jeaiii_to_text.h | 116 + server/{io.cpp => libaquery.cpp} | 164 +- server/libaquery.h | 11 +- server/monetdb_conn.cpp | 10 +- server/monetdb_conn.h | 1 + server/server.cpp | 127 +- server/utils.h | 20 +- 18 files changed, 3730 insertions(+), 125 deletions(-) create mode 100644 server/dragonbox/dragonbox.h create mode 100644 server/dragonbox/dragonbox_to_chars.cpp create mode 100644 server/dragonbox/dragonbox_to_chars.h create mode 100644 server/gc.h create mode 100644 server/jeaiii_to_text.h rename server/{io.cpp => libaquery.cpp} (68%) 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}, + {0x8c974f7383725573, 0x1e414218c73a13fc}, {0xafbd2350644eeacf, 0xe5d1929ef90898fb}, + {0xdbac6c247d62a583, 0xdf45f746b74abf3a}, {0x894bc396ce5da772, 0x6b8bba8c328eb784}, + {0xab9eb47c81f5114f, 0x066ea92f3f326565}, {0xd686619ba27255a2, 0xc80a537b0efefebe}, + {0x8613fd0145877585, 0xbd06742ce95f5f37}, {0xa798fc4196e952e7, 0x2c48113823b73705}, + {0xd17f3b51fca3a7a0, 0xf75a15862ca504c6}, {0x82ef85133de648c4, 0x9a984d73dbe722fc}, + {0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb}, {0xcc963fee10b7d1b3, 0x318df905079926a9}, + {0xffbbcfe994e5c61f, 0xfdf17746497f7053}, {0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634}, + {0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1}, {0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1}, + {0x9c1661a651213e2d, 0x06bea10ca65c084f}, {0xc31bfa0fe5698db8, 0x486e494fcff30a63}, + {0xf3e2f893dec3f126, 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0x76707543f4fa1f74}, {0x899504ae72497eba, 0x6a06494a791c53a9}, + {0xabfa45da0edbde69, 0x0487db9d17636893}, {0xd6f8d7509292d603, 0x45a9d2845d3c42b7}, + {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b3}, {0xa7f26836f282b732, 0x8e6cac7768d7141f}, + {0xd1ef0244af2364ff, 0x3207d795430cd927}, {0x8335616aed761f1f, 0x7f44e6bd49e807b9}, + {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a7}, {0xcd036837130890a1, 0x36dba887c37a8c10}, + {0x802221226be55a64, 0xc2494954da2c978a}, {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6d}, + {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::type; + +template inline char* to_text_from_integer(char* b, T i) +{ + u64 t = u64(i); + + if (i < T(0)) + t = u64(0) - t, b[0] = '-', ++b; + + u32 u = cond, unsigned char>, bool>(t); + + // if our input type fits in 32bits, or its value does, ctreat as 32bit (the line above ensures the compiler can still know the range limits of the input type) + // and optimize out cases for small integer types (if only c++ had a builtin way to get the unsigned type from a signed type) + if (sizeof(i) <= sizeof(u) || u == t) + return JEAIII_L09(JEAIII_K); + + u32 x = t % 100000000u; + u = u32(t /= 100000000u); + + // t / 10^8 (fits in 32 bit), t % 10^8 -> ~17.5 digits + if (u == t) + return JEAIII_L09(JEAIII_KX); + + // t / 10^16 (1-4 digits), t / 10^8 % 10^8, t % 10^8 + u32 y = t % 100000000u; + u = u32(t / 100000000u); + return JEAIII_L03(JEAIII_KYX); +} + +inline char* to_text(char text[], signed char i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], unsigned char i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], short i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], unsigned short i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], int i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], unsigned int i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], long i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], unsigned long i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], long long i) { return to_text_from_integer(text, i); } +inline char* to_text(char text[], unsigned long long i) { return to_text_from_integer(text, i); } + +// Copyright (c) 2022 Bill Sun +constexpr static __uint128_t _10_19 = 10000000000000000000ull, + _10_37 = _10_19*_10_19 / 10; + +template +char* jeaiii_i128(char* buf, T v){ + if (v < 0){ + *(buf++) = '0'; + v = -v; + } + if (v > _10_37){ + uint8_t vv = uint8_t(v/_10_37); + // vv <<= 1; + // if (vv < 20) + // *buf ++ = digits_00_99[vv + 1]; + // else{ + // *buf++ = digits_00_99[vv ]; + // *buf++ = digits_00_99[vv + 1]; + // } + + *(buf++) = vv%10 + '0'; + vv/=10; + if (vv) { + *buf = *(buf-1); + *(buf++-1) = vv + '0'; + } + } + + if (v > _10_19) + buf = to_text(buf, uint64_t((v/_10_19) % _10_19)); + + buf = to_text(buf, uint64_t(v % _10_19)); + return buf; +} \ No newline at end of file diff --git a/server/io.cpp b/server/libaquery.cpp similarity index 68% rename from server/io.cpp rename to server/libaquery.cpp index 878c0b6..2b3e802 100644 --- a/server/io.cpp +++ b/server/libaquery.cpp @@ -1,20 +1,20 @@ #include "pch_msc.hpp" #include "io.h" -#include "table.h" #include #include #include #include "utils.h" +#include "libaquery.h" #include char* gbuf = nullptr; void setgbuf(char* buf) { - static char* b = 0; - if (buf == 0) + static char* b = nullptr; + if (buf == nullptr) gbuf = b; else { gbuf = buf; @@ -63,6 +63,7 @@ T getInt(const char*& buf){ } return ret; } + template char* intToString(T val, char* buf){ @@ -275,6 +276,43 @@ inline const char* str(const bool& v) { return v ? "true" : "false"; } + +Context::Context() { + current.memory_map = new std::unordered_map; + init_session(); +} + +Context::~Context() { + auto memmap = (std::unordered_map*) this->current.memory_map; + delete memmap; +} + +void Context::init_session(){ + if (log_level == LOG_INFO){ + memset(&(this->current.stats), 0, sizeof(Session::Statistic)); + } + auto memmap = (std::unordered_map*) this->current.memory_map; + memmap->clear(); +} + +void Context::end_session(){ + auto memmap = (std::unordered_map*) this->current.memory_map; + for (auto& mem : *memmap) { + mem.second(mem.first); + } + memmap->clear(); +} + +void* Context::get_module_function(const char* fname){ + auto fmap = static_cast*> + (this->module_function_maps); + // printf("%p\n", fmap->find("mydiv")->second); + // for (const auto& [key, value] : *fmap){ + // printf("%s %p\n", key.c_str(), value); + // } + auto ret = fmap->find(fname); + return ret == fmap->end() ? nullptr : ret->second; +} // template // inline void vector_type<_Ty>::out(uint32_t n, const char* sep) const // { @@ -288,3 +326,123 @@ inline const char* str(const bool& v) { // } // std::cout << ')'; // } + +#include "gc.h" +#include +#include +#include +#include +#ifndef __AQ_USE_THREADEDGC__ + +struct gcmemory_t{ + void* memory; + void (*deallocator)(void*); +}; + +using memoryqueue_t = gcmemory_t*; +void GC::acquire_lock() { + auto this_tid = std::this_thread::get_id(); + while(lock != this_tid) + { + while(lock != this_tid && lock != std::thread::id()) { + std::this_thread::sleep_for(std::chrono::milliseconds(0)); + } + lock = this_tid; + } +} + +void GC::release_lock(){ + lock = std::thread::id(); +} + +void GC::gc() +{ + auto& _q = static_cast(q); + auto& _q_back = static_cast(q_back); + if (_q->size == 0) + return; + auto t = _q; + lock = true; + while(alive_cnt > 0); + _q = q_back; + uint32_t _slot = slot_pos; + slot_pos = 0; + current_size = 0; + lock = false; + _q_back = t; + + for(uint32_t i = 0; i < _slot; ++i){ + if (_q_back[i]->memory != nullptr && _q_back[i]->deallocator != nullptr) + _q_back[i]->deallocator(_q_back[i]->memory); + } + memset(_q_back, 0, sizeof(gcmemory_t) * _slot); + running = false; +} + +void GC::daemon() { + using namespace std::chrono; + + while (alive) { + if (running) { + if (current_size > max_size || + forceclean_timer > forced_clean) + { + gc(); + forceclean_timer = 0; + } + std::this_thread::sleep_for(microseconds(interval)); + forceclean_timer += interval; + } + else { + std::this_thread::sleep_for(10ms); + forceclean_timer += 10000; + } + } +} + +void GC::start_deamon() { + q = new gcmemory_t[max_slots << 1]; + q_back = new memoryqueue_t[max_slots << 1]; + lock = false; + slot_pos = 0; + current_size = 0; + alive_cnt = 0; + alive = true; + handle = new std::thread(&GC::daemon, this); +} + +void GC::terminate_daemon() { + running = false; + alive = false; + decltype(auto) _handle = static_cast(handle); + delete[] static_cast(q); + delete[] static_cast(q_back); + using namespace std::chrono; + std::this_thread::sleep_for(microseconds(1000 + std::max(static_cast(10000), interval))); + + if (_handle->joinable()) { + _handle->join(); + } + delete _handle; +} + +void GC::reg(void* v, uint32_t sz, void(*f)(void*)) { //~ 40ns expected v. free ~ 75ns + if (v == nullptr || f == nullptr) + return; + if (sz < threshould){ + f(v); + return; + } + auto _q = static_castq; + while(lock); + ++alive_cnt; + current_size += sz; + auto _slot = (slot_pos += 1); + q[_slot] = {v, f}; + --alive_cnt; + running = true; +} + +#endif + +static GC* GC::gc = nullptr; diff --git a/server/libaquery.h b/server/libaquery.h index 6227af9..1d6f864 100644 --- a/server/libaquery.h +++ b/server/libaquery.h @@ -1,6 +1,12 @@ #ifndef _AQUERY_H #define _AQUERY_H +#ifdef __INTELLISENSE__ + #define __AQUERY_ITC_USE_SEMPH__ + #define THREADING + #define __AQ_THREADED_GC__ +#endif + #include "table.h" #include #include @@ -55,7 +61,10 @@ struct Context{ #ifdef THREADING void* thread_pool; #endif - printf_type print = printf; +#ifdef __AQ_THREADED_GC__ + void* gc; +#endif + printf_type print = &printf; Context(); virtual ~Context(); template diff --git a/server/monetdb_conn.cpp b/server/monetdb_conn.cpp index c0e9d5b..644c1c4 100644 --- a/server/monetdb_conn.cpp +++ b/server/monetdb_conn.cpp @@ -6,6 +6,7 @@ #include "monetdb_conn.h" #include "monetdbe.h" #include "table.h" + #undef static_assert const char* monetdbe_type_str[] = { @@ -121,6 +122,8 @@ bool Server::haserror(){ return false; } } + + void Server::print_results(const char* sep, const char* end){ if (!haserror()){ @@ -138,6 +141,7 @@ void Server::print_results(const char* sep, const char* end){ std::string(types::printf_str[types::monetdbe_type_aqtypes[cols[i]->type]]) + (i < ncols - 1 ? sep : ""); puts(printf_string[i].c_str()); + puts(monetdbe_type_str[cols[i]->type]); col_data[i] = static_cast(cols[i]->data); szs [i] = monetdbe_type_szs[cols[i]->type]; header_string = header_string + cols[i]->name + sep + '|' + sep; @@ -179,7 +183,7 @@ void* Server::getCol(int col_idx){ auto _ret_col = static_cast(this->ret_col); cnt = _ret_col->count; printf("Dbg: Getting col %s, type: %s\n", - _ret_col->name, monetdbe_type_str[_ret_col->type]); + _ret_col->name, monetdbe_type_str[_ret_col->type]); return _ret_col->data; } else{ @@ -198,10 +202,10 @@ Server::~Server(){ bool Server::havehge() { #if defined(_MONETDBE_LIB_) and defined(HAVE_HGE) - puts("true"); + // puts("true"); return HAVE_HGE; #else - puts("false"); + // puts("false"); return false; #endif } diff --git a/server/monetdb_conn.h b/server/monetdb_conn.h index 3255342..9894218 100644 --- a/server/monetdb_conn.h +++ b/server/monetdb_conn.h @@ -24,6 +24,7 @@ struct Server{ static bool havehge(); void test(const char*); void print_results(const char* sep = " ", const char* end = "\n"); + friend void print_monetdb_results(Server* srv, const char* sep, const char* end, int limit); ~Server(); }; diff --git a/server/server.cpp b/server/server.cpp index e601019..ed97bc4 100644 --- a/server/server.cpp +++ b/server/server.cpp @@ -1,6 +1,5 @@ #include "pch_msc.hpp" -#include "../csv.h" #include #include #include @@ -10,28 +9,35 @@ #ifdef THREADING #include "threading.h" #endif + #ifdef _WIN32 #include "winhelper.h" #else #include #include #include + +// fast numeric to string conversion +#include "jeaiii_to_text.h" +#include "dragonbox/dragonbox_to_chars.h" + struct SharedMemory { std::atomic a; int hFileMap; void* pData; - SharedMemory(const char* fname) { + explicit SharedMemory(const char* fname) { hFileMap = open(fname, O_RDWR, 0); if (hFileMap != -1) - pData = mmap(NULL, 8, PROT_READ | PROT_WRITE, MAP_SHARED, hFileMap, 0); + pData = mmap(nullptr, 8, PROT_READ | PROT_WRITE, MAP_SHARED, hFileMap, 0); else - pData = 0; + pData = nullptr; } - void FreeMemoryMap() { - + void FreeMemoryMap() const { + // automatically unmapped in posix } }; + #ifndef __USE_STD_SEMAPHORE__ #ifdef __APPLE__ #include @@ -74,9 +80,10 @@ public: }; #endif #endif - #endif + #ifdef __USE_STD_SEMAPHORE__ +#define __AQUERY_ITC_USE_SEMPH__ #include class A_Semaphore { private: @@ -94,6 +101,7 @@ public: ~A_Semaphore() { } }; #endif + #ifdef __AQUERY_ITC_USE_SEMPH__ A_Semaphore prompt{ true }, engine{ false }; #define PROMPT_ACQUIRE() prompt.acquire() @@ -107,11 +115,9 @@ A_Semaphore prompt{ true }, engine{ false }; #define ENGINE_RELEASE() #endif -#include "aggregations.h" typedef int (*code_snippet)(void*); typedef void (*module_init_fn)(Context*); -int test_main(); int n_recv = 0; char** n_recvd = nullptr; @@ -119,6 +125,7 @@ char** n_recvd = nullptr; __AQEXPORT__(void) wait_engine(){ PROMPT_ACQUIRE(); } + __AQEXPORT__(void) wake_engine(){ ENGINE_RELEASE(); } @@ -152,42 +159,6 @@ __AQEXPORT__(bool) have_hge(){ #endif } -Context::Context() { - current.memory_map = new std::unordered_map; - init_session(); -} - -Context::~Context() { - auto memmap = (std::unordered_map*) this->current.memory_map; - delete memmap; -} - -void Context::init_session(){ - if (log_level == LOG_INFO){ - memset(&(this->current.stats), 0, sizeof(Session::Statistic)); - } - auto memmap = (std::unordered_map*) this->current.memory_map; - memmap->clear(); -} - -void Context::end_session(){ - auto memmap = (std::unordered_map*) this->current.memory_map; - for (auto& mem : *memmap) { - mem.second(mem.first); - } - memmap->clear(); -} - -void* Context::get_module_function(const char* fname){ - auto fmap = static_cast*> - (this->module_function_maps); - // printf("%p\n", fmap->find("mydiv")->second); - // for (const auto& [key, value] : *fmap){ - // printf("%s %p\n", key.c_str(), value); - // } - auto ret = fmap->find(fname); - return ret == fmap->end() ? nullptr : ret->second; -} void initialize_module(const char* module_name, void* module_handle, Context* cxt){ auto _init_module = reinterpret_cast(dlsym(module_handle, "init_session")); @@ -253,7 +224,7 @@ int dll_main(int argc, char** argv, Context* cxt){ timer.reset(); server->exec(n_recvd[i] + 1); cfg->stats.monet_time += timer.elapsed(); - printf("Exec Q%d: %s", i, n_recvd[i]); + // printf("Exec Q%d: %s", i, n_recvd[i]); } break; case 'P': // Postprocessing procedure @@ -313,7 +284,7 @@ int dll_main(int argc, char** argv, Context* cxt){ dlclose(handle); handle = nullptr; } - printf("%ld, %ld", cfg->stats.monet_time, cfg->stats.postproc_time); + printf("%lld, %lld", cfg->stats.monet_time, cfg->stats.postproc_time); cxt->end_session(); n_recv = 0; } @@ -370,20 +341,21 @@ extern "C" int __DLLEXPORT__ main(int argc, char** argv) { #ifdef __AQ_BUILD_LAUNCHER__ return launcher(argc, argv); #endif - puts("running"); + // puts("running"); Context* cxt = new Context(); - cxt->log("%d %s\n", argc, argv[1]); + // cxt->log("%d %s\n", argc, argv[1]); #ifdef THREADING auto tp = new ThreadPool(); cxt->thread_pool = tp; #endif +#ifdef __AQ_THREADED_GC__ + cxt->gc_thread = new std::thread(gc_thread, cxt); +#endif const char* shmname; if (argc < 0) return dll_main(argc, argv, cxt); - else if (argc <= 1) - return test_main(); else shmname = argv[1]; SharedMemory shm = SharedMemory(shmname); @@ -417,56 +389,3 @@ extern "C" int __DLLEXPORT__ main(int argc, char** argv) { return 0; } -#include "utils.h" -#include "table_ext_monetdb.hpp" -int test_main() -{ - Context* cxt = new Context(); - if (cxt->alt_server == 0) - cxt->alt_server = new Server(cxt); - Server* server = reinterpret_cast(cxt->alt_server); - - const char* qs[]= { - "QCREATE TABLE trade(stocksymbol INT, time INT, quantity INT, price INT);", - "QCOPY OFFSET 2 INTO trade FROM 'w:/gg/AQuery++/data/trade_numerical.csv' ON SERVER USING DELIMITERS ',';", - "QSELECT stocksymbol, (SUM((quantity * price)) / SUM(quantity)) AS weighted_average FROM trade GROUP BY stocksymbol ;", - "Pdll_5lYrMY", - "QSELECT stocksymbol, price FROM trade ORDER BY time ;", - "Pdll_4Sg6Ri", - "QSELECT stocksymbol, quantity, price FROM trade ORDER BY time ;", - "Pdll_5h4kL2", - "QSELECT stocksymbol, price FROM trade ORDER BY time ;", - "Pdll_7tEWCO", - "QSELECT query_c.weighted_moving_averages, query_c.stocksymbol FROM query_c;", - "Pdll_7FCPnF" - }; - n_recv = sizeof(qs)/(sizeof (char*)); - n_recvd = const_cast(qs); - void* handle = 0; - handle = dlopen("./dll.so", RTLD_LAZY); - cxt->init_session(); - for (int i = 0; i < n_recv; ++i) - { - //printf("%s, %d\n", n_recvd[i], n_recvd[i][0] == 'Q'); - switch (n_recvd[i][0]) { - case 'Q': // SQL query for monetdbe - { - server->exec(n_recvd[i] + 1); - printf("Exec Q%d: %s\n", i, n_recvd[i]); - } - break; - case 'P': // Postprocessing procedure - if (handle && !server->haserror()) { - code_snippet c = reinterpret_cast(dlsym(handle, n_recvd[i] + 1)); - c(cxt); - } - break; - } - } - n_recv = 0; - - //static_assert(std::is_same_v()), std::integer_sequence>, ""); - - return 0; -} - diff --git a/server/utils.h b/server/utils.h index 3cd7b2a..f96937f 100644 --- a/server/utils.h +++ b/server/utils.h @@ -1,5 +1,9 @@ #pragma once + #include +#include +#include + #if ((defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) || __cplusplus >= 201703L) constexpr static bool cpp_17 = true; #else @@ -10,5 +14,19 @@ inline const char* str(const T& v) { return ""; } -#include +template +constexpr char* aq_itoa(T t, char* buf){ + if constexpr (std::is_signed::value){ + if (t < 0){ + *buf++ = '-'; + t = -t; + } + } + while(t > 0){ + *buf++ = t%10 + '0'; + t /= 10; + } + return buf; +} + extern std::string base62uuid(int l = 6);