2636 lines
102 KiB
C++
2636 lines
102 KiB
C++
// Formatting library for C++ - implementation
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//
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// Copyright (c) 2012 - 2016, Victor Zverovich
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// All rights reserved.
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//
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// For the license information refer to format.h.
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#ifndef FMT_FORMAT_INL_H_
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#define FMT_FORMAT_INL_H_
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#include <algorithm>
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#include <cctype>
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#include <cerrno> // errno
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#include <climits>
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#include <cmath>
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#include <cstdarg>
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#include <cstring> // std::memmove
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#include <cwchar>
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#include <exception>
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#ifndef FMT_STATIC_THOUSANDS_SEPARATOR
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# include <locale>
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#endif
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#ifdef _WIN32
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# include <io.h> // _isatty
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#endif
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#include "format.h"
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FMT_BEGIN_NAMESPACE
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namespace detail {
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FMT_FUNC void assert_fail(const char* file, int line, const char* message) {
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// Use unchecked std::fprintf to avoid triggering another assertion when
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// writing to stderr fails
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std::fprintf(stderr, "%s:%d: assertion failed: %s", file, line, message);
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// Chosen instead of std::abort to satisfy Clang in CUDA mode during device
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// code pass.
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std::terminate();
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}
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#ifndef _MSC_VER
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# define FMT_SNPRINTF snprintf
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#else // _MSC_VER
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inline int fmt_snprintf(char* buffer, size_t size, const char* format, ...) {
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va_list args;
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va_start(args, format);
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int result = vsnprintf_s(buffer, size, _TRUNCATE, format, args);
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va_end(args);
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return result;
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}
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# define FMT_SNPRINTF fmt_snprintf
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#endif // _MSC_VER
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FMT_FUNC void format_error_code(detail::buffer<char>& out, int error_code,
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string_view message) FMT_NOEXCEPT {
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// Report error code making sure that the output fits into
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// inline_buffer_size to avoid dynamic memory allocation and potential
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// bad_alloc.
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out.try_resize(0);
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static const char SEP[] = ": ";
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static const char ERROR_STR[] = "error ";
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// Subtract 2 to account for terminating null characters in SEP and ERROR_STR.
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size_t error_code_size = sizeof(SEP) + sizeof(ERROR_STR) - 2;
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auto abs_value = static_cast<uint32_or_64_or_128_t<int>>(error_code);
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if (detail::is_negative(error_code)) {
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abs_value = 0 - abs_value;
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++error_code_size;
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}
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error_code_size += detail::to_unsigned(detail::count_digits(abs_value));
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auto it = buffer_appender<char>(out);
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if (message.size() <= inline_buffer_size - error_code_size)
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format_to(it, FMT_STRING("{}{}"), message, SEP);
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format_to(it, FMT_STRING("{}{}"), ERROR_STR, error_code);
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FMT_ASSERT(out.size() <= inline_buffer_size, "");
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}
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FMT_FUNC void report_error(format_func func, int error_code,
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const char* message) FMT_NOEXCEPT {
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memory_buffer full_message;
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func(full_message, error_code, message);
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// Don't use fwrite_fully because the latter may throw.
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if (std::fwrite(full_message.data(), full_message.size(), 1, stderr) > 0)
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std::fputc('\n', stderr);
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}
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// A wrapper around fwrite that throws on error.
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inline void fwrite_fully(const void* ptr, size_t size, size_t count,
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FILE* stream) {
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size_t written = std::fwrite(ptr, size, count, stream);
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if (written < count) FMT_THROW(system_error(errno, "cannot write to file"));
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}
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#ifndef FMT_STATIC_THOUSANDS_SEPARATOR
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template <typename Locale>
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locale_ref::locale_ref(const Locale& loc) : locale_(&loc) {
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static_assert(std::is_same<Locale, std::locale>::value, "");
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}
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template <typename Locale> Locale locale_ref::get() const {
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static_assert(std::is_same<Locale, std::locale>::value, "");
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return locale_ ? *static_cast<const std::locale*>(locale_) : std::locale();
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}
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template <typename Char> FMT_FUNC std::string grouping_impl(locale_ref loc) {
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return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>()).grouping();
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}
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template <typename Char> FMT_FUNC Char thousands_sep_impl(locale_ref loc) {
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return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>())
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.thousands_sep();
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}
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template <typename Char> FMT_FUNC Char decimal_point_impl(locale_ref loc) {
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return std::use_facet<std::numpunct<Char>>(loc.get<std::locale>())
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.decimal_point();
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}
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#else
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template <typename Char> FMT_FUNC std::string grouping_impl(locale_ref) {
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return "\03";
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}
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template <typename Char> FMT_FUNC Char thousands_sep_impl(locale_ref) {
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return FMT_STATIC_THOUSANDS_SEPARATOR;
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}
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template <typename Char> FMT_FUNC Char decimal_point_impl(locale_ref) {
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return '.';
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}
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#endif
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} // namespace detail
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#if !FMT_MSC_VER
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FMT_API FMT_FUNC format_error::~format_error() FMT_NOEXCEPT = default;
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#endif
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FMT_FUNC std::system_error vsystem_error(int error_code, string_view format_str,
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format_args args) {
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auto ec = std::error_code(error_code, std::generic_category());
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return std::system_error(ec, vformat(format_str, args));
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}
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namespace detail {
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template <> FMT_FUNC int count_digits<4>(detail::fallback_uintptr n) {
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// fallback_uintptr is always stored in little endian.
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int i = static_cast<int>(sizeof(void*)) - 1;
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while (i > 0 && n.value[i] == 0) --i;
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auto char_digits = std::numeric_limits<unsigned char>::digits / 4;
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return i >= 0 ? i * char_digits + count_digits<4, unsigned>(n.value[i]) : 1;
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}
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#if __cplusplus < 201703L
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template <typename T>
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constexpr const typename basic_data<T>::digit_pair basic_data<T>::digits[];
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template <typename T> constexpr const char basic_data<T>::hex_digits[];
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template <typename T> constexpr const char basic_data<T>::signs[];
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template <typename T> constexpr const unsigned basic_data<T>::prefixes[];
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template <typename T> constexpr const char basic_data<T>::left_padding_shifts[];
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template <typename T>
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constexpr const char basic_data<T>::right_padding_shifts[];
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#endif
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template <typename T> struct bits {
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static FMT_CONSTEXPR_DECL const int value =
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static_cast<int>(sizeof(T) * std::numeric_limits<unsigned char>::digits);
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};
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class fp;
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template <int SHIFT = 0> fp normalize(fp value);
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// Lower (upper) boundary is a value half way between a floating-point value
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// and its predecessor (successor). Boundaries have the same exponent as the
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// value so only significands are stored.
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struct boundaries {
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uint64_t lower;
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uint64_t upper;
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};
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// A handmade floating-point number f * pow(2, e).
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class fp {
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private:
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using significand_type = uint64_t;
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template <typename Float>
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using is_supported_float = bool_constant<sizeof(Float) == sizeof(uint64_t) ||
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sizeof(Float) == sizeof(uint32_t)>;
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public:
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significand_type f;
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int e;
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// All sizes are in bits.
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// Subtract 1 to account for an implicit most significant bit in the
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// normalized form.
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static FMT_CONSTEXPR_DECL const int double_significand_size =
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std::numeric_limits<double>::digits - 1;
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static FMT_CONSTEXPR_DECL const uint64_t implicit_bit =
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1ULL << double_significand_size;
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static FMT_CONSTEXPR_DECL const int significand_size =
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bits<significand_type>::value;
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fp() : f(0), e(0) {}
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fp(uint64_t f_val, int e_val) : f(f_val), e(e_val) {}
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// Constructs fp from an IEEE754 double. It is a template to prevent compile
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// errors on platforms where double is not IEEE754.
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template <typename Double> explicit fp(Double d) { assign(d); }
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// Assigns d to this and return true iff predecessor is closer than successor.
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template <typename Float, FMT_ENABLE_IF(is_supported_float<Float>::value)>
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bool assign(Float d) {
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// Assume float is in the format [sign][exponent][significand].
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using limits = std::numeric_limits<Float>;
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const int float_significand_size = limits::digits - 1;
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const int exponent_size =
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bits<Float>::value - float_significand_size - 1; // -1 for sign
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const uint64_t float_implicit_bit = 1ULL << float_significand_size;
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const uint64_t significand_mask = float_implicit_bit - 1;
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const uint64_t exponent_mask = (~0ULL >> 1) & ~significand_mask;
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const int exponent_bias = (1 << exponent_size) - limits::max_exponent - 1;
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constexpr bool is_double = sizeof(Float) == sizeof(uint64_t);
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auto u = bit_cast<conditional_t<is_double, uint64_t, uint32_t>>(d);
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f = u & significand_mask;
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int biased_e =
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static_cast<int>((u & exponent_mask) >> float_significand_size);
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// Predecessor is closer if d is a normalized power of 2 (f == 0) other than
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// the smallest normalized number (biased_e > 1).
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bool is_predecessor_closer = f == 0 && biased_e > 1;
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if (biased_e != 0)
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f += float_implicit_bit;
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else
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biased_e = 1; // Subnormals use biased exponent 1 (min exponent).
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e = biased_e - exponent_bias - float_significand_size;
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return is_predecessor_closer;
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}
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template <typename Float, FMT_ENABLE_IF(!is_supported_float<Float>::value)>
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bool assign(Float) {
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*this = fp();
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return false;
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}
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};
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// Normalizes the value converted from double and multiplied by (1 << SHIFT).
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template <int SHIFT> fp normalize(fp value) {
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// Handle subnormals.
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const auto shifted_implicit_bit = fp::implicit_bit << SHIFT;
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while ((value.f & shifted_implicit_bit) == 0) {
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value.f <<= 1;
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--value.e;
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}
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// Subtract 1 to account for hidden bit.
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const auto offset =
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fp::significand_size - fp::double_significand_size - SHIFT - 1;
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value.f <<= offset;
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value.e -= offset;
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return value;
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}
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inline bool operator==(fp x, fp y) { return x.f == y.f && x.e == y.e; }
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// Computes lhs * rhs / pow(2, 64) rounded to nearest with half-up tie breaking.
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inline uint64_t multiply(uint64_t lhs, uint64_t rhs) {
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#if FMT_USE_INT128
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auto product = static_cast<__uint128_t>(lhs) * rhs;
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auto f = static_cast<uint64_t>(product >> 64);
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return (static_cast<uint64_t>(product) & (1ULL << 63)) != 0 ? f + 1 : f;
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#else
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// Multiply 32-bit parts of significands.
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uint64_t mask = (1ULL << 32) - 1;
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uint64_t a = lhs >> 32, b = lhs & mask;
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uint64_t c = rhs >> 32, d = rhs & mask;
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uint64_t ac = a * c, bc = b * c, ad = a * d, bd = b * d;
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// Compute mid 64-bit of result and round.
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uint64_t mid = (bd >> 32) + (ad & mask) + (bc & mask) + (1U << 31);
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return ac + (ad >> 32) + (bc >> 32) + (mid >> 32);
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#endif
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}
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inline fp operator*(fp x, fp y) { return {multiply(x.f, y.f), x.e + y.e + 64}; }
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// Returns a cached power of 10 `c_k = c_k.f * pow(2, c_k.e)` such that its
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// (binary) exponent satisfies `min_exponent <= c_k.e <= min_exponent + 28`.
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inline fp get_cached_power(int min_exponent, int& pow10_exponent) {
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// Normalized 64-bit significands of pow(10, k), for k = -348, -340, ..., 340.
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// These are generated by support/compute-powers.py.
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static constexpr const uint64_t pow10_significands[] = {
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0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76,
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0xcf42894a5dce35ea, 0x9a6bb0aa55653b2d, 0xe61acf033d1a45df,
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0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f, 0xbe5691ef416bd60c,
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0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5,
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0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57,
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0xc21094364dfb5637, 0x9096ea6f3848984f, 0xd77485cb25823ac7,
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0xa086cfcd97bf97f4, 0xef340a98172aace5, 0xb23867fb2a35b28e,
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0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996,
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0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126,
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0xb5b5ada8aaff80b8, 0x87625f056c7c4a8b, 0xc9bcff6034c13053,
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0x964e858c91ba2655, 0xdff9772470297ebd, 0xa6dfbd9fb8e5b88f,
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0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b,
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0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06,
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0xaa242499697392d3, 0xfd87b5f28300ca0e, 0xbce5086492111aeb,
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0x8cbccc096f5088cc, 0xd1b71758e219652c, 0x9c40000000000000,
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0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984,
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0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068,
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0x9f4f2726179a2245, 0xed63a231d4c4fb27, 0xb0de65388cc8ada8,
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0x83c7088e1aab65db, 0xc45d1df942711d9a, 0x924d692ca61be758,
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0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85,
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0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d,
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0x952ab45cfa97a0b3, 0xde469fbd99a05fe3, 0xa59bc234db398c25,
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0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece, 0x88fcf317f22241e2,
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0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a,
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0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410,
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0x8bab8eefb6409c1a, 0xd01fef10a657842c, 0x9b10a4e5e9913129,
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0xe7109bfba19c0c9d, 0xac2820d9623bf429, 0x80444b5e7aa7cf85,
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0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841,
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0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b,
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};
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// Binary exponents of pow(10, k), for k = -348, -340, ..., 340, corresponding
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// to significands above.
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static constexpr const int16_t pow10_exponents[] = {
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-1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954,
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-927, -901, -874, -847, -821, -794, -768, -741, -715, -688, -661,
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-635, -608, -582, -555, -529, -502, -475, -449, -422, -396, -369,
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-343, -316, -289, -263, -236, -210, -183, -157, -130, -103, -77,
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-50, -24, 3, 30, 56, 83, 109, 136, 162, 189, 216,
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242, 269, 295, 322, 348, 375, 402, 428, 455, 481, 508,
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534, 561, 588, 614, 641, 667, 694, 720, 747, 774, 800,
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827, 853, 880, 907, 933, 960, 986, 1013, 1039, 1066};
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const int shift = 32;
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const auto significand = static_cast<int64_t>(data::log10_2_significand);
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int index = static_cast<int>(
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((min_exponent + fp::significand_size - 1) * (significand >> shift) +
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((int64_t(1) << shift) - 1)) // ceil
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>> 32 // arithmetic shift
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);
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// Decimal exponent of the first (smallest) cached power of 10.
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const int first_dec_exp = -348;
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// Difference between 2 consecutive decimal exponents in cached powers of 10.
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const int dec_exp_step = 8;
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index = (index - first_dec_exp - 1) / dec_exp_step + 1;
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pow10_exponent = first_dec_exp + index * dec_exp_step;
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return {pow10_significands[index], pow10_exponents[index]};
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}
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// A simple accumulator to hold the sums of terms in bigint::square if uint128_t
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// is not available.
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struct accumulator {
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uint64_t lower;
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uint64_t upper;
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accumulator() : lower(0), upper(0) {}
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explicit operator uint32_t() const { return static_cast<uint32_t>(lower); }
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void operator+=(uint64_t n) {
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lower += n;
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if (lower < n) ++upper;
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}
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void operator>>=(int shift) {
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FMT_ASSERT(shift == 32, "");
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(void)shift;
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lower = (upper << 32) | (lower >> 32);
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upper >>= 32;
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}
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};
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class bigint {
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private:
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// A bigint is stored as an array of bigits (big digits), with bigit at index
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// 0 being the least significant one.
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using bigit = uint32_t;
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using double_bigit = uint64_t;
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enum { bigits_capacity = 32 };
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basic_memory_buffer<bigit, bigits_capacity> bigits_;
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int exp_;
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bigit operator[](int index) const { return bigits_[to_unsigned(index)]; }
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bigit& operator[](int index) { return bigits_[to_unsigned(index)]; }
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static FMT_CONSTEXPR_DECL const int bigit_bits = bits<bigit>::value;
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friend struct formatter<bigint>;
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void subtract_bigits(int index, bigit other, bigit& borrow) {
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auto result = static_cast<double_bigit>((*this)[index]) - other - borrow;
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(*this)[index] = static_cast<bigit>(result);
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borrow = static_cast<bigit>(result >> (bigit_bits * 2 - 1));
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}
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void remove_leading_zeros() {
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int num_bigits = static_cast<int>(bigits_.size()) - 1;
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while (num_bigits > 0 && (*this)[num_bigits] == 0) --num_bigits;
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bigits_.resize(to_unsigned(num_bigits + 1));
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}
|
|
|
|
// Computes *this -= other assuming aligned bigints and *this >= other.
|
|
void subtract_aligned(const bigint& other) {
|
|
FMT_ASSERT(other.exp_ >= exp_, "unaligned bigints");
|
|
FMT_ASSERT(compare(*this, other) >= 0, "");
|
|
bigit borrow = 0;
|
|
int i = other.exp_ - exp_;
|
|
for (size_t j = 0, n = other.bigits_.size(); j != n; ++i, ++j)
|
|
subtract_bigits(i, other.bigits_[j], borrow);
|
|
while (borrow > 0) subtract_bigits(i, 0, borrow);
|
|
remove_leading_zeros();
|
|
}
|
|
|
|
void multiply(uint32_t value) {
|
|
const double_bigit wide_value = value;
|
|
bigit carry = 0;
|
|
for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
|
|
double_bigit result = bigits_[i] * wide_value + carry;
|
|
bigits_[i] = static_cast<bigit>(result);
|
|
carry = static_cast<bigit>(result >> bigit_bits);
|
|
}
|
|
if (carry != 0) bigits_.push_back(carry);
|
|
}
|
|
|
|
void multiply(uint64_t value) {
|
|
const bigit mask = ~bigit(0);
|
|
const double_bigit lower = value & mask;
|
|
const double_bigit upper = value >> bigit_bits;
|
|
double_bigit carry = 0;
|
|
for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
|
|
double_bigit result = bigits_[i] * lower + (carry & mask);
|
|
carry =
|
|
bigits_[i] * upper + (result >> bigit_bits) + (carry >> bigit_bits);
|
|
bigits_[i] = static_cast<bigit>(result);
|
|
}
|
|
while (carry != 0) {
|
|
bigits_.push_back(carry & mask);
|
|
carry >>= bigit_bits;
|
|
}
|
|
}
|
|
|
|
public:
|
|
bigint() : exp_(0) {}
|
|
explicit bigint(uint64_t n) { assign(n); }
|
|
~bigint() { FMT_ASSERT(bigits_.capacity() <= bigits_capacity, ""); }
|
|
|
|
bigint(const bigint&) = delete;
|
|
void operator=(const bigint&) = delete;
|
|
|
|
void assign(const bigint& other) {
|
|
auto size = other.bigits_.size();
|
|
bigits_.resize(size);
|
|
auto data = other.bigits_.data();
|
|
std::copy(data, data + size, make_checked(bigits_.data(), size));
|
|
exp_ = other.exp_;
|
|
}
|
|
|
|
void assign(uint64_t n) {
|
|
size_t num_bigits = 0;
|
|
do {
|
|
bigits_[num_bigits++] = n & ~bigit(0);
|
|
n >>= bigit_bits;
|
|
} while (n != 0);
|
|
bigits_.resize(num_bigits);
|
|
exp_ = 0;
|
|
}
|
|
|
|
int num_bigits() const { return static_cast<int>(bigits_.size()) + exp_; }
|
|
|
|
FMT_NOINLINE bigint& operator<<=(int shift) {
|
|
FMT_ASSERT(shift >= 0, "");
|
|
exp_ += shift / bigit_bits;
|
|
shift %= bigit_bits;
|
|
if (shift == 0) return *this;
|
|
bigit carry = 0;
|
|
for (size_t i = 0, n = bigits_.size(); i < n; ++i) {
|
|
bigit c = bigits_[i] >> (bigit_bits - shift);
|
|
bigits_[i] = (bigits_[i] << shift) + carry;
|
|
carry = c;
|
|
}
|
|
if (carry != 0) bigits_.push_back(carry);
|
|
return *this;
|
|
}
|
|
|
|
template <typename Int> bigint& operator*=(Int value) {
|
|
FMT_ASSERT(value > 0, "");
|
|
multiply(uint32_or_64_or_128_t<Int>(value));
|
|
return *this;
|
|
}
|
|
|
|
friend int compare(const bigint& lhs, const bigint& rhs) {
|
|
int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits();
|
|
if (num_lhs_bigits != num_rhs_bigits)
|
|
return num_lhs_bigits > num_rhs_bigits ? 1 : -1;
|
|
int i = static_cast<int>(lhs.bigits_.size()) - 1;
|
|
int j = static_cast<int>(rhs.bigits_.size()) - 1;
|
|
int end = i - j;
|
|
if (end < 0) end = 0;
|
|
for (; i >= end; --i, --j) {
|
|
bigit lhs_bigit = lhs[i], rhs_bigit = rhs[j];
|
|
if (lhs_bigit != rhs_bigit) return lhs_bigit > rhs_bigit ? 1 : -1;
|
|
}
|
|
if (i != j) return i > j ? 1 : -1;
|
|
return 0;
|
|
}
|
|
|
|
// Returns compare(lhs1 + lhs2, rhs).
|
|
friend int add_compare(const bigint& lhs1, const bigint& lhs2,
|
|
const bigint& rhs) {
|
|
int max_lhs_bigits = (std::max)(lhs1.num_bigits(), lhs2.num_bigits());
|
|
int num_rhs_bigits = rhs.num_bigits();
|
|
if (max_lhs_bigits + 1 < num_rhs_bigits) return -1;
|
|
if (max_lhs_bigits > num_rhs_bigits) return 1;
|
|
auto get_bigit = [](const bigint& n, int i) -> bigit {
|
|
return i >= n.exp_ && i < n.num_bigits() ? n[i - n.exp_] : 0;
|
|
};
|
|
double_bigit borrow = 0;
|
|
int min_exp = (std::min)((std::min)(lhs1.exp_, lhs2.exp_), rhs.exp_);
|
|
for (int i = num_rhs_bigits - 1; i >= min_exp; --i) {
|
|
double_bigit sum =
|
|
static_cast<double_bigit>(get_bigit(lhs1, i)) + get_bigit(lhs2, i);
|
|
bigit rhs_bigit = get_bigit(rhs, i);
|
|
if (sum > rhs_bigit + borrow) return 1;
|
|
borrow = rhs_bigit + borrow - sum;
|
|
if (borrow > 1) return -1;
|
|
borrow <<= bigit_bits;
|
|
}
|
|
return borrow != 0 ? -1 : 0;
|
|
}
|
|
|
|
// Assigns pow(10, exp) to this bigint.
|
|
void assign_pow10(int exp) {
|
|
FMT_ASSERT(exp >= 0, "");
|
|
if (exp == 0) return assign(1);
|
|
// Find the top bit.
|
|
int bitmask = 1;
|
|
while (exp >= bitmask) bitmask <<= 1;
|
|
bitmask >>= 1;
|
|
// pow(10, exp) = pow(5, exp) * pow(2, exp). First compute pow(5, exp) by
|
|
// repeated squaring and multiplication.
|
|
assign(5);
|
|
bitmask >>= 1;
|
|
while (bitmask != 0) {
|
|
square();
|
|
if ((exp & bitmask) != 0) *this *= 5;
|
|
bitmask >>= 1;
|
|
}
|
|
*this <<= exp; // Multiply by pow(2, exp) by shifting.
|
|
}
|
|
|
|
void square() {
|
|
int num_bigits = static_cast<int>(bigits_.size());
|
|
int num_result_bigits = 2 * num_bigits;
|
|
basic_memory_buffer<bigit, bigits_capacity> n(std::move(bigits_));
|
|
bigits_.resize(to_unsigned(num_result_bigits));
|
|
using accumulator_t = conditional_t<FMT_USE_INT128, uint128_t, accumulator>;
|
|
auto sum = accumulator_t();
|
|
for (int bigit_index = 0; bigit_index < num_bigits; ++bigit_index) {
|
|
// Compute bigit at position bigit_index of the result by adding
|
|
// cross-product terms n[i] * n[j] such that i + j == bigit_index.
|
|
for (int i = 0, j = bigit_index; j >= 0; ++i, --j) {
|
|
// Most terms are multiplied twice which can be optimized in the future.
|
|
sum += static_cast<double_bigit>(n[i]) * n[j];
|
|
}
|
|
(*this)[bigit_index] = static_cast<bigit>(sum);
|
|
sum >>= bits<bigit>::value; // Compute the carry.
|
|
}
|
|
// Do the same for the top half.
|
|
for (int bigit_index = num_bigits; bigit_index < num_result_bigits;
|
|
++bigit_index) {
|
|
for (int j = num_bigits - 1, i = bigit_index - j; i < num_bigits;)
|
|
sum += static_cast<double_bigit>(n[i++]) * n[j--];
|
|
(*this)[bigit_index] = static_cast<bigit>(sum);
|
|
sum >>= bits<bigit>::value;
|
|
}
|
|
--num_result_bigits;
|
|
remove_leading_zeros();
|
|
exp_ *= 2;
|
|
}
|
|
|
|
// If this bigint has a bigger exponent than other, adds trailing zero to make
|
|
// exponents equal. This simplifies some operations such as subtraction.
|
|
void align(const bigint& other) {
|
|
int exp_difference = exp_ - other.exp_;
|
|
if (exp_difference <= 0) return;
|
|
int num_bigits = static_cast<int>(bigits_.size());
|
|
bigits_.resize(to_unsigned(num_bigits + exp_difference));
|
|
for (int i = num_bigits - 1, j = i + exp_difference; i >= 0; --i, --j)
|
|
bigits_[j] = bigits_[i];
|
|
std::uninitialized_fill_n(bigits_.data(), exp_difference, 0);
|
|
exp_ -= exp_difference;
|
|
}
|
|
|
|
// Divides this bignum by divisor, assigning the remainder to this and
|
|
// returning the quotient.
|
|
int divmod_assign(const bigint& divisor) {
|
|
FMT_ASSERT(this != &divisor, "");
|
|
if (compare(*this, divisor) < 0) return 0;
|
|
FMT_ASSERT(divisor.bigits_[divisor.bigits_.size() - 1u] != 0, "");
|
|
align(divisor);
|
|
int quotient = 0;
|
|
do {
|
|
subtract_aligned(divisor);
|
|
++quotient;
|
|
} while (compare(*this, divisor) >= 0);
|
|
return quotient;
|
|
}
|
|
};
|
|
|
|
enum class round_direction { unknown, up, down };
|
|
|
|
// Given the divisor (normally a power of 10), the remainder = v % divisor for
|
|
// some number v and the error, returns whether v should be rounded up, down, or
|
|
// whether the rounding direction can't be determined due to error.
|
|
// error should be less than divisor / 2.
|
|
inline round_direction get_round_direction(uint64_t divisor, uint64_t remainder,
|
|
uint64_t error) {
|
|
FMT_ASSERT(remainder < divisor, ""); // divisor - remainder won't overflow.
|
|
FMT_ASSERT(error < divisor, ""); // divisor - error won't overflow.
|
|
FMT_ASSERT(error < divisor - error, ""); // error * 2 won't overflow.
|
|
// Round down if (remainder + error) * 2 <= divisor.
|
|
if (remainder <= divisor - remainder && error * 2 <= divisor - remainder * 2)
|
|
return round_direction::down;
|
|
// Round up if (remainder - error) * 2 >= divisor.
|
|
if (remainder >= error &&
|
|
remainder - error >= divisor - (remainder - error)) {
|
|
return round_direction::up;
|
|
}
|
|
return round_direction::unknown;
|
|
}
|
|
|
|
namespace digits {
|
|
enum result {
|
|
more, // Generate more digits.
|
|
done, // Done generating digits.
|
|
error // Digit generation cancelled due to an error.
|
|
};
|
|
}
|
|
|
|
inline uint64_t power_of_10_64(int exp) {
|
|
static constexpr const uint64_t data[] = {1, FMT_POWERS_OF_10(1),
|
|
FMT_POWERS_OF_10(1000000000ULL),
|
|
10000000000000000000ULL};
|
|
return data[exp];
|
|
}
|
|
|
|
// Generates output using the Grisu digit-gen algorithm.
|
|
// error: the size of the region (lower, upper) outside of which numbers
|
|
// definitely do not round to value (Delta in Grisu3).
|
|
template <typename Handler>
|
|
FMT_ALWAYS_INLINE digits::result grisu_gen_digits(fp value, uint64_t error,
|
|
int& exp, Handler& handler) {
|
|
const fp one(1ULL << -value.e, value.e);
|
|
// The integral part of scaled value (p1 in Grisu) = value / one. It cannot be
|
|
// zero because it contains a product of two 64-bit numbers with MSB set (due
|
|
// to normalization) - 1, shifted right by at most 60 bits.
|
|
auto integral = static_cast<uint32_t>(value.f >> -one.e);
|
|
FMT_ASSERT(integral != 0, "");
|
|
FMT_ASSERT(integral == value.f >> -one.e, "");
|
|
// The fractional part of scaled value (p2 in Grisu) c = value % one.
|
|
uint64_t fractional = value.f & (one.f - 1);
|
|
exp = count_digits(integral); // kappa in Grisu.
|
|
// Divide by 10 to prevent overflow.
|
|
auto result = handler.on_start(power_of_10_64(exp - 1) << -one.e,
|
|
value.f / 10, error * 10, exp);
|
|
if (result != digits::more) return result;
|
|
// Generate digits for the integral part. This can produce up to 10 digits.
|
|
do {
|
|
uint32_t digit = 0;
|
|
auto divmod_integral = [&](uint32_t divisor) {
|
|
digit = integral / divisor;
|
|
integral %= divisor;
|
|
};
|
|
// This optimization by Milo Yip reduces the number of integer divisions by
|
|
// one per iteration.
|
|
switch (exp) {
|
|
case 10:
|
|
divmod_integral(1000000000);
|
|
break;
|
|
case 9:
|
|
divmod_integral(100000000);
|
|
break;
|
|
case 8:
|
|
divmod_integral(10000000);
|
|
break;
|
|
case 7:
|
|
divmod_integral(1000000);
|
|
break;
|
|
case 6:
|
|
divmod_integral(100000);
|
|
break;
|
|
case 5:
|
|
divmod_integral(10000);
|
|
break;
|
|
case 4:
|
|
divmod_integral(1000);
|
|
break;
|
|
case 3:
|
|
divmod_integral(100);
|
|
break;
|
|
case 2:
|
|
divmod_integral(10);
|
|
break;
|
|
case 1:
|
|
digit = integral;
|
|
integral = 0;
|
|
break;
|
|
default:
|
|
FMT_ASSERT(false, "invalid number of digits");
|
|
}
|
|
--exp;
|
|
auto remainder = (static_cast<uint64_t>(integral) << -one.e) + fractional;
|
|
result = handler.on_digit(static_cast<char>('0' + digit),
|
|
power_of_10_64(exp) << -one.e, remainder, error,
|
|
exp, true);
|
|
if (result != digits::more) return result;
|
|
} while (exp > 0);
|
|
// Generate digits for the fractional part.
|
|
for (;;) {
|
|
fractional *= 10;
|
|
error *= 10;
|
|
char digit = static_cast<char>('0' + (fractional >> -one.e));
|
|
fractional &= one.f - 1;
|
|
--exp;
|
|
result = handler.on_digit(digit, one.f, fractional, error, exp, false);
|
|
if (result != digits::more) return result;
|
|
}
|
|
}
|
|
|
|
// The fixed precision digit handler.
|
|
struct fixed_handler {
|
|
char* buf;
|
|
int size;
|
|
int precision;
|
|
int exp10;
|
|
bool fixed;
|
|
|
|
digits::result on_start(uint64_t divisor, uint64_t remainder, uint64_t error,
|
|
int& exp) {
|
|
// Non-fixed formats require at least one digit and no precision adjustment.
|
|
if (!fixed) return digits::more;
|
|
// Adjust fixed precision by exponent because it is relative to decimal
|
|
// point.
|
|
precision += exp + exp10;
|
|
// Check if precision is satisfied just by leading zeros, e.g.
|
|
// format("{:.2f}", 0.001) gives "0.00" without generating any digits.
|
|
if (precision > 0) return digits::more;
|
|
if (precision < 0) return digits::done;
|
|
auto dir = get_round_direction(divisor, remainder, error);
|
|
if (dir == round_direction::unknown) return digits::error;
|
|
buf[size++] = dir == round_direction::up ? '1' : '0';
|
|
return digits::done;
|
|
}
|
|
|
|
digits::result on_digit(char digit, uint64_t divisor, uint64_t remainder,
|
|
uint64_t error, int, bool integral) {
|
|
FMT_ASSERT(remainder < divisor, "");
|
|
buf[size++] = digit;
|
|
if (!integral && error >= remainder) return digits::error;
|
|
if (size < precision) return digits::more;
|
|
if (!integral) {
|
|
// Check if error * 2 < divisor with overflow prevention.
|
|
// The check is not needed for the integral part because error = 1
|
|
// and divisor > (1 << 32) there.
|
|
if (error >= divisor || error >= divisor - error) return digits::error;
|
|
} else {
|
|
FMT_ASSERT(error == 1 && divisor > 2, "");
|
|
}
|
|
auto dir = get_round_direction(divisor, remainder, error);
|
|
if (dir != round_direction::up)
|
|
return dir == round_direction::down ? digits::done : digits::error;
|
|
++buf[size - 1];
|
|
for (int i = size - 1; i > 0 && buf[i] > '9'; --i) {
|
|
buf[i] = '0';
|
|
++buf[i - 1];
|
|
}
|
|
if (buf[0] > '9') {
|
|
buf[0] = '1';
|
|
if (fixed)
|
|
buf[size++] = '0';
|
|
else
|
|
++exp10;
|
|
}
|
|
return digits::done;
|
|
}
|
|
};
|
|
|
|
// A 128-bit integer type used internally,
|
|
struct uint128_wrapper {
|
|
uint128_wrapper() = default;
|
|
|
|
#if FMT_USE_INT128
|
|
uint128_t internal_;
|
|
|
|
constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT
|
|
: internal_{static_cast<uint128_t>(low) |
|
|
(static_cast<uint128_t>(high) << 64)} {}
|
|
|
|
constexpr uint128_wrapper(uint128_t u) : internal_{u} {}
|
|
|
|
constexpr uint64_t high() const FMT_NOEXCEPT {
|
|
return uint64_t(internal_ >> 64);
|
|
}
|
|
constexpr uint64_t low() const FMT_NOEXCEPT { return uint64_t(internal_); }
|
|
|
|
uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT {
|
|
internal_ += n;
|
|
return *this;
|
|
}
|
|
#else
|
|
uint64_t high_;
|
|
uint64_t low_;
|
|
|
|
constexpr uint128_wrapper(uint64_t high, uint64_t low) FMT_NOEXCEPT
|
|
: high_{high},
|
|
low_{low} {}
|
|
|
|
constexpr uint64_t high() const FMT_NOEXCEPT { return high_; }
|
|
constexpr uint64_t low() const FMT_NOEXCEPT { return low_; }
|
|
|
|
uint128_wrapper& operator+=(uint64_t n) FMT_NOEXCEPT {
|
|
# if defined(_MSC_VER) && defined(_M_X64)
|
|
unsigned char carry = _addcarry_u64(0, low_, n, &low_);
|
|
_addcarry_u64(carry, high_, 0, &high_);
|
|
return *this;
|
|
# else
|
|
uint64_t sum = low_ + n;
|
|
high_ += (sum < low_ ? 1 : 0);
|
|
low_ = sum;
|
|
return *this;
|
|
# endif
|
|
}
|
|
#endif
|
|
};
|
|
|
|
// Implementation of Dragonbox algorithm: https://github.com/jk-jeon/dragonbox.
|
|
namespace dragonbox {
|
|
// Computes 128-bit result of multiplication of two 64-bit unsigned integers.
|
|
inline uint128_wrapper umul128(uint64_t x, uint64_t y) FMT_NOEXCEPT {
|
|
#if FMT_USE_INT128
|
|
return static_cast<uint128_t>(x) * static_cast<uint128_t>(y);
|
|
#elif defined(_MSC_VER) && defined(_M_X64)
|
|
uint128_wrapper result;
|
|
result.low_ = _umul128(x, y, &result.high_);
|
|
return result;
|
|
#else
|
|
const uint64_t mask = (uint64_t(1) << 32) - uint64_t(1);
|
|
|
|
uint64_t a = x >> 32;
|
|
uint64_t b = x & mask;
|
|
uint64_t c = y >> 32;
|
|
uint64_t d = y & mask;
|
|
|
|
uint64_t ac = a * c;
|
|
uint64_t bc = b * c;
|
|
uint64_t ad = a * d;
|
|
uint64_t bd = b * d;
|
|
|
|
uint64_t intermediate = (bd >> 32) + (ad & mask) + (bc & mask);
|
|
|
|
return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32),
|
|
(intermediate << 32) + (bd & mask)};
|
|
#endif
|
|
}
|
|
|
|
// Computes upper 64 bits of multiplication of two 64-bit unsigned integers.
|
|
inline uint64_t umul128_upper64(uint64_t x, uint64_t y) FMT_NOEXCEPT {
|
|
#if FMT_USE_INT128
|
|
auto p = static_cast<uint128_t>(x) * static_cast<uint128_t>(y);
|
|
return static_cast<uint64_t>(p >> 64);
|
|
#elif defined(_MSC_VER) && defined(_M_X64)
|
|
return __umulh(x, y);
|
|
#else
|
|
return umul128(x, y).high();
|
|
#endif
|
|
}
|
|
|
|
// Computes upper 64 bits of multiplication of a 64-bit unsigned integer and a
|
|
// 128-bit unsigned integer.
|
|
inline uint64_t umul192_upper64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT {
|
|
uint128_wrapper g0 = umul128(x, y.high());
|
|
g0 += umul128_upper64(x, y.low());
|
|
return g0.high();
|
|
}
|
|
|
|
// Computes upper 32 bits of multiplication of a 32-bit unsigned integer and a
|
|
// 64-bit unsigned integer.
|
|
inline uint32_t umul96_upper32(uint32_t x, uint64_t y) FMT_NOEXCEPT {
|
|
return static_cast<uint32_t>(umul128_upper64(x, y));
|
|
}
|
|
|
|
// Computes middle 64 bits of multiplication of a 64-bit unsigned integer and a
|
|
// 128-bit unsigned integer.
|
|
inline uint64_t umul192_middle64(uint64_t x, uint128_wrapper y) FMT_NOEXCEPT {
|
|
uint64_t g01 = x * y.high();
|
|
uint64_t g10 = umul128_upper64(x, y.low());
|
|
return g01 + g10;
|
|
}
|
|
|
|
// Computes lower 64 bits of multiplication of a 32-bit unsigned integer and a
|
|
// 64-bit unsigned integer.
|
|
inline uint64_t umul96_lower64(uint32_t x, uint64_t y) FMT_NOEXCEPT {
|
|
return x * y;
|
|
}
|
|
|
|
// Computes floor(log10(pow(2, e))) for e in [-1700, 1700] using the method from
|
|
// https://fmt.dev/papers/Grisu-Exact.pdf#page=5, section 3.4.
|
|
inline int floor_log10_pow2(int e) FMT_NOEXCEPT {
|
|
FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent");
|
|
const int shift = 22;
|
|
return (e * static_cast<int>(data::log10_2_significand >> (64 - shift))) >>
|
|
shift;
|
|
}
|
|
|
|
// Various fast log computations.
|
|
inline int floor_log2_pow10(int e) FMT_NOEXCEPT {
|
|
FMT_ASSERT(e <= 1233 && e >= -1233, "too large exponent");
|
|
const uint64_t log2_10_integer_part = 3;
|
|
const uint64_t log2_10_fractional_digits = 0x5269e12f346e2bf9;
|
|
const int shift_amount = 19;
|
|
return (e * static_cast<int>(
|
|
(log2_10_integer_part << shift_amount) |
|
|
(log2_10_fractional_digits >> (64 - shift_amount)))) >>
|
|
shift_amount;
|
|
}
|
|
inline int floor_log10_pow2_minus_log10_4_over_3(int e) FMT_NOEXCEPT {
|
|
FMT_ASSERT(e <= 1700 && e >= -1700, "too large exponent");
|
|
const uint64_t log10_4_over_3_fractional_digits = 0x1ffbfc2bbc780375;
|
|
const int shift_amount = 22;
|
|
return (e * static_cast<int>(data::log10_2_significand >>
|
|
(64 - shift_amount)) -
|
|
static_cast<int>(log10_4_over_3_fractional_digits >>
|
|
(64 - shift_amount))) >>
|
|
shift_amount;
|
|
}
|
|
|
|
// Returns true iff x is divisible by pow(2, exp).
|
|
inline bool divisible_by_power_of_2(uint32_t x, int exp) FMT_NOEXCEPT {
|
|
FMT_ASSERT(exp >= 1, "");
|
|
FMT_ASSERT(x != 0, "");
|
|
#ifdef FMT_BUILTIN_CTZ
|
|
return FMT_BUILTIN_CTZ(x) >= exp;
|
|
#else
|
|
return exp < num_bits<uint32_t>() && x == ((x >> exp) << exp);
|
|
#endif
|
|
}
|
|
inline bool divisible_by_power_of_2(uint64_t x, int exp) FMT_NOEXCEPT {
|
|
FMT_ASSERT(exp >= 1, "");
|
|
FMT_ASSERT(x != 0, "");
|
|
#ifdef FMT_BUILTIN_CTZLL
|
|
return FMT_BUILTIN_CTZLL(x) >= exp;
|
|
#else
|
|
return exp < num_bits<uint64_t>() && x == ((x >> exp) << exp);
|
|
#endif
|
|
}
|
|
|
|
// Table entry type for divisibility test.
|
|
template <typename T> struct divtest_table_entry {
|
|
T mod_inv;
|
|
T max_quotient;
|
|
};
|
|
|
|
// Returns true iff x is divisible by pow(5, exp).
|
|
inline bool divisible_by_power_of_5(uint32_t x, int exp) FMT_NOEXCEPT {
|
|
FMT_ASSERT(exp <= 10, "too large exponent");
|
|
static constexpr const divtest_table_entry<uint32_t> divtest_table[] = {
|
|
{0x00000001, 0xffffffff}, {0xcccccccd, 0x33333333},
|
|
{0xc28f5c29, 0x0a3d70a3}, {0x26e978d5, 0x020c49ba},
|
|
{0x3afb7e91, 0x0068db8b}, {0x0bcbe61d, 0x0014f8b5},
|
|
{0x68c26139, 0x000431bd}, {0xae8d46a5, 0x0000d6bf},
|
|
{0x22e90e21, 0x00002af3}, {0x3a2e9c6d, 0x00000897},
|
|
{0x3ed61f49, 0x000001b7}};
|
|
return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient;
|
|
}
|
|
inline bool divisible_by_power_of_5(uint64_t x, int exp) FMT_NOEXCEPT {
|
|
FMT_ASSERT(exp <= 23, "too large exponent");
|
|
static constexpr const divtest_table_entry<uint64_t> divtest_table[] = {
|
|
{0x0000000000000001, 0xffffffffffffffff},
|
|
{0xcccccccccccccccd, 0x3333333333333333},
|
|
{0x8f5c28f5c28f5c29, 0x0a3d70a3d70a3d70},
|
|
{0x1cac083126e978d5, 0x020c49ba5e353f7c},
|
|
{0xd288ce703afb7e91, 0x0068db8bac710cb2},
|
|
{0x5d4e8fb00bcbe61d, 0x0014f8b588e368f0},
|
|
{0x790fb65668c26139, 0x000431bde82d7b63},
|
|
{0xe5032477ae8d46a5, 0x0000d6bf94d5e57a},
|
|
{0xc767074b22e90e21, 0x00002af31dc46118},
|
|
{0x8e47ce423a2e9c6d, 0x0000089705f4136b},
|
|
{0x4fa7f60d3ed61f49, 0x000001b7cdfd9d7b},
|
|
{0x0fee64690c913975, 0x00000057f5ff85e5},
|
|
{0x3662e0e1cf503eb1, 0x000000119799812d},
|
|
{0xa47a2cf9f6433fbd, 0x0000000384b84d09},
|
|
{0x54186f653140a659, 0x00000000b424dc35},
|
|
{0x7738164770402145, 0x0000000024075f3d},
|
|
{0xe4a4d1417cd9a041, 0x000000000734aca5},
|
|
{0xc75429d9e5c5200d, 0x000000000170ef54},
|
|
{0xc1773b91fac10669, 0x000000000049c977},
|
|
{0x26b172506559ce15, 0x00000000000ec1e4},
|
|
{0xd489e3a9addec2d1, 0x000000000002f394},
|
|
{0x90e860bb892c8d5d, 0x000000000000971d},
|
|
{0x502e79bf1b6f4f79, 0x0000000000001e39},
|
|
{0xdcd618596be30fe5, 0x000000000000060b}};
|
|
return x * divtest_table[exp].mod_inv <= divtest_table[exp].max_quotient;
|
|
}
|
|
|
|
// Replaces n by floor(n / pow(5, N)) returning true if and only if n is
|
|
// divisible by pow(5, N).
|
|
// Precondition: n <= 2 * pow(5, N + 1).
|
|
template <int N>
|
|
bool check_divisibility_and_divide_by_pow5(uint32_t& n) FMT_NOEXCEPT {
|
|
static constexpr struct {
|
|
uint32_t magic_number;
|
|
int bits_for_comparison;
|
|
uint32_t threshold;
|
|
int shift_amount;
|
|
} infos[] = {{0xcccd, 16, 0x3333, 18}, {0xa429, 8, 0x0a, 20}};
|
|
constexpr auto info = infos[N - 1];
|
|
n *= info.magic_number;
|
|
const uint32_t comparison_mask = (1u << info.bits_for_comparison) - 1;
|
|
bool result = (n & comparison_mask) <= info.threshold;
|
|
n >>= info.shift_amount;
|
|
return result;
|
|
}
|
|
|
|
// Computes floor(n / pow(10, N)) for small n and N.
|
|
// Precondition: n <= pow(10, N + 1).
|
|
template <int N> uint32_t small_division_by_pow10(uint32_t n) FMT_NOEXCEPT {
|
|
static constexpr struct {
|
|
uint32_t magic_number;
|
|
int shift_amount;
|
|
uint32_t divisor_times_10;
|
|
} infos[] = {{0xcccd, 19, 100}, {0xa3d8, 22, 1000}};
|
|
constexpr auto info = infos[N - 1];
|
|
FMT_ASSERT(n <= info.divisor_times_10, "n is too large");
|
|
return n * info.magic_number >> info.shift_amount;
|
|
}
|
|
|
|
// Computes floor(n / 10^(kappa + 1)) (float)
|
|
inline uint32_t divide_by_10_to_kappa_plus_1(uint32_t n) FMT_NOEXCEPT {
|
|
return n / float_info<float>::big_divisor;
|
|
}
|
|
// Computes floor(n / 10^(kappa + 1)) (double)
|
|
inline uint64_t divide_by_10_to_kappa_plus_1(uint64_t n) FMT_NOEXCEPT {
|
|
return umul128_upper64(n, 0x83126e978d4fdf3c) >> 9;
|
|
}
|
|
|
|
// Various subroutines using pow10 cache
|
|
template <class T> struct cache_accessor;
|
|
|
|
template <> struct cache_accessor<float> {
|
|
using carrier_uint = float_info<float>::carrier_uint;
|
|
using cache_entry_type = uint64_t;
|
|
|
|
static uint64_t get_cached_power(int k) FMT_NOEXCEPT {
|
|
FMT_ASSERT(k >= float_info<float>::min_k && k <= float_info<float>::max_k,
|
|
"k is out of range");
|
|
constexpr const uint64_t pow10_significands[] = {
|
|
0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f,
|
|
0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, 0xc612062576589ddb,
|
|
0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28,
|
|
0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb,
|
|
0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a,
|
|
0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810,
|
|
0xe12e13424bb40e14, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff,
|
|
0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd,
|
|
0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424,
|
|
0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b,
|
|
0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000,
|
|
0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000,
|
|
0xc350000000000000, 0xf424000000000000, 0x9896800000000000,
|
|
0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000,
|
|
0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000,
|
|
0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000,
|
|
0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000,
|
|
0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000,
|
|
0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0,
|
|
0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984,
|
|
0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296,
|
|
0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6,
|
|
0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20,
|
|
0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd,
|
|
0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719,
|
|
0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e};
|
|
return pow10_significands[k - float_info<float>::min_k];
|
|
}
|
|
|
|
static carrier_uint compute_mul(carrier_uint u,
|
|
const cache_entry_type& cache) FMT_NOEXCEPT {
|
|
return umul96_upper32(u, cache);
|
|
}
|
|
|
|
static uint32_t compute_delta(const cache_entry_type& cache,
|
|
int beta_minus_1) FMT_NOEXCEPT {
|
|
return static_cast<uint32_t>(cache >> (64 - 1 - beta_minus_1));
|
|
}
|
|
|
|
static bool compute_mul_parity(carrier_uint two_f,
|
|
const cache_entry_type& cache,
|
|
int beta_minus_1) FMT_NOEXCEPT {
|
|
FMT_ASSERT(beta_minus_1 >= 1, "");
|
|
FMT_ASSERT(beta_minus_1 < 64, "");
|
|
|
|
return ((umul96_lower64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0;
|
|
}
|
|
|
|
static carrier_uint compute_left_endpoint_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return static_cast<carrier_uint>(
|
|
(cache - (cache >> (float_info<float>::significand_bits + 2))) >>
|
|
(64 - float_info<float>::significand_bits - 1 - beta_minus_1));
|
|
}
|
|
|
|
static carrier_uint compute_right_endpoint_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return static_cast<carrier_uint>(
|
|
(cache + (cache >> (float_info<float>::significand_bits + 1))) >>
|
|
(64 - float_info<float>::significand_bits - 1 - beta_minus_1));
|
|
}
|
|
|
|
static carrier_uint compute_round_up_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return (static_cast<carrier_uint>(
|
|
cache >>
|
|
(64 - float_info<float>::significand_bits - 2 - beta_minus_1)) +
|
|
1) /
|
|
2;
|
|
}
|
|
};
|
|
|
|
template <> struct cache_accessor<double> {
|
|
using carrier_uint = float_info<double>::carrier_uint;
|
|
using cache_entry_type = uint128_wrapper;
|
|
|
|
static uint128_wrapper get_cached_power(int k) FMT_NOEXCEPT {
|
|
FMT_ASSERT(k >= float_info<double>::min_k && k <= float_info<double>::max_k,
|
|
"k is out of range");
|
|
|
|
static constexpr const uint128_wrapper pow10_significands[] = {
|
|
#if FMT_USE_FULL_CACHE_DRAGONBOX
|
|
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b},
|
|
{0x9faacf3df73609b1, 0x77b191618c54e9ad},
|
|
{0xc795830d75038c1d, 0xd59df5b9ef6a2418},
|
|
{0xf97ae3d0d2446f25, 0x4b0573286b44ad1e},
|
|
{0x9becce62836ac577, 0x4ee367f9430aec33},
|
|
{0xc2e801fb244576d5, 0x229c41f793cda740},
|
|
{0xf3a20279ed56d48a, 0x6b43527578c11110},
|
|
{0x9845418c345644d6, 0x830a13896b78aaaa},
|
|
{0xbe5691ef416bd60c, 0x23cc986bc656d554},
|
|
{0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9},
|
|
{0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa},
|
|
{0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54},
|
|
{0xe858ad248f5c22c9, 0xd1b3400f8f9cff69},
|
|
{0x91376c36d99995be, 0x23100809b9c21fa2},
|
|
{0xb58547448ffffb2d, 0xabd40a0c2832a78b},
|
|
{0xe2e69915b3fff9f9, 0x16c90c8f323f516d},
|
|
{0x8dd01fad907ffc3b, 0xae3da7d97f6792e4},
|
|
{0xb1442798f49ffb4a, 0x99cd11cfdf41779d},
|
|
{0xdd95317f31c7fa1d, 0x40405643d711d584},
|
|
{0x8a7d3eef7f1cfc52, 0x482835ea666b2573},
|
|
{0xad1c8eab5ee43b66, 0xda3243650005eed0},
|
|
{0xd863b256369d4a40, 0x90bed43e40076a83},
|
|
{0x873e4f75e2224e68, 0x5a7744a6e804a292},
|
|
{0xa90de3535aaae202, 0x711515d0a205cb37},
|
|
{0xd3515c2831559a83, 0x0d5a5b44ca873e04},
|
|
{0x8412d9991ed58091, 0xe858790afe9486c3},
|
|
{0xa5178fff668ae0b6, 0x626e974dbe39a873},
|
|
{0xce5d73ff402d98e3, 0xfb0a3d212dc81290},
|
|
{0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a},
|
|
{0xa139029f6a239f72, 0x1c1fffc1ebc44e81},
|
|
{0xc987434744ac874e, 0xa327ffb266b56221},
|
|
{0xfbe9141915d7a922, 0x4bf1ff9f0062baa9},
|
|
{0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa},
|
|
{0xc4ce17b399107c22, 0xcb550fb4384d21d4},
|
|
{0xf6019da07f549b2b, 0x7e2a53a146606a49},
|
|
{0x99c102844f94e0fb, 0x2eda7444cbfc426e},
|
|
{0xc0314325637a1939, 0xfa911155fefb5309},
|
|
{0xf03d93eebc589f88, 0x793555ab7eba27cb},
|
|
{0x96267c7535b763b5, 0x4bc1558b2f3458df},
|
|
{0xbbb01b9283253ca2, 0x9eb1aaedfb016f17},
|
|
{0xea9c227723ee8bcb, 0x465e15a979c1cadd},
|
|
{0x92a1958a7675175f, 0x0bfacd89ec191eca},
|
|
{0xb749faed14125d36, 0xcef980ec671f667c},
|
|
{0xe51c79a85916f484, 0x82b7e12780e7401b},
|
|
{0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811},
|
|
{0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16},
|
|
{0xdfbdcece67006ac9, 0x67a791e093e1d49b},
|
|
{0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1},
|
|
{0xaecc49914078536d, 0x58fae9f773886e19},
|
|
{0xda7f5bf590966848, 0xaf39a475506a899f},
|
|
{0x888f99797a5e012d, 0x6d8406c952429604},
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|
|
{0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e},
|
|
{0x8865899617fb1871, 0x7e2fa67c7a658892},
|
|
{0xaa7eebfb9df9de8d, 0xddbb901b98feeab7},
|
|
{0xd51ea6fa85785631, 0x552a74227f3ea565},
|
|
{0x8533285c936b35de, 0xd53a88958f87275f},
|
|
{0xa67ff273b8460356, 0x8a892abaf368f137},
|
|
{0xd01fef10a657842c, 0x2d2b7569b0432d85},
|
|
{0x8213f56a67f6b29b, 0x9c3b29620e29fc73},
|
|
{0xa298f2c501f45f42, 0x8349f3ba91b47b8f},
|
|
{0xcb3f2f7642717713, 0x241c70a936219a73},
|
|
{0xfe0efb53d30dd4d7, 0xed238cd383aa0110},
|
|
{0x9ec95d1463e8a506, 0xf4363804324a40aa},
|
|
{0xc67bb4597ce2ce48, 0xb143c6053edcd0d5},
|
|
{0xf81aa16fdc1b81da, 0xdd94b7868e94050a},
|
|
{0x9b10a4e5e9913128, 0xca7cf2b4191c8326},
|
|
{0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0},
|
|
{0xf24a01a73cf2dccf, 0xbc633b39673c8cec},
|
|
{0x976e41088617ca01, 0xd5be0503e085d813},
|
|
{0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18},
|
|
{0xec9c459d51852ba2, 0xddf8e7d60ed1219e},
|
|
{0x93e1ab8252f33b45, 0xcabb90e5c942b503},
|
|
{0xb8da1662e7b00a17, 0x3d6a751f3b936243},
|
|
{0xe7109bfba19c0c9d, 0x0cc512670a783ad4},
|
|
{0x906a617d450187e2, 0x27fb2b80668b24c5},
|
|
{0xb484f9dc9641e9da, 0xb1f9f660802dedf6},
|
|
{0xe1a63853bbd26451, 0x5e7873f8a0396973},
|
|
{0x8d07e33455637eb2, 0xdb0b487b6423e1e8},
|
|
{0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62},
|
|
{0xdc5c5301c56b75f7, 0x7641a140cc7810fb},
|
|
{0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d},
|
|
{0xac2820d9623bf429, 0x546345fa9fbdcd44},
|
|
{0xd732290fbacaf133, 0xa97c177947ad4095},
|
|
{0x867f59a9d4bed6c0, 0x49ed8eabcccc485d},
|
|
{0xa81f301449ee8c70, 0x5c68f256bfff5a74},
|
|
{0xd226fc195c6a2f8c, 0x73832eec6fff3111},
|
|
{0x83585d8fd9c25db7, 0xc831fd53c5ff7eab},
|
|
{0xa42e74f3d032f525, 0xba3e7ca8b77f5e55},
|
|
{0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb},
|
|
{0x80444b5e7aa7cf85, 0x7980d163cf5b81b3},
|
|
{0xa0555e361951c366, 0xd7e105bcc332621f},
|
|
{0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7},
|
|
{0xfa856334878fc150, 0xb14f98f6f0feb951},
|
|
{0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3},
|
|
{0xc3b8358109e84f07, 0x0a862f80ec4700c8},
|
|
{0xf4a642e14c6262c8, 0xcd27bb612758c0fa},
|
|
{0x98e7e9cccfbd7dbd, 0x8038d51cb897789c},
|
|
{0xbf21e44003acdd2c, 0xe0470a63e6bd56c3},
|
|
{0xeeea5d5004981478, 0x1858ccfce06cac74},
|
|
{0x95527a5202df0ccb, 0x0f37801e0c43ebc8},
|
|
{0xbaa718e68396cffd, 0xd30560258f54e6ba},
|
|
{0xe950df20247c83fd, 0x47c6b82ef32a2069},
|
|
{0x91d28b7416cdd27e, 0x4cdc331d57fa5441},
|
|
{0xb6472e511c81471d, 0xe0133fe4adf8e952},
|
|
{0xe3d8f9e563a198e5, 0x58180fddd97723a6},
|
|
{0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648},
|
|
{0xb201833b35d63f73, 0x2cd2cc6551e513da},
|
|
{0xde81e40a034bcf4f, 0xf8077f7ea65e58d1},
|
|
{0x8b112e86420f6191, 0xfb04afaf27faf782},
|
|
{0xadd57a27d29339f6, 0x79c5db9af1f9b563},
|
|
{0xd94ad8b1c7380874, 0x18375281ae7822bc},
|
|
{0x87cec76f1c830548, 0x8f2293910d0b15b5},
|
|
{0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22},
|
|
{0xd433179d9c8cb841, 0x5fa60692a46151eb},
|
|
{0x849feec281d7f328, 0xdbc7c41ba6bcd333},
|
|
{0xa5c7ea73224deff3, 0x12b9b522906c0800},
|
|
{0xcf39e50feae16bef, 0xd768226b34870a00},
|
|
{0x81842f29f2cce375, 0xe6a1158300d46640},
|
|
{0xa1e53af46f801c53, 0x60495ae3c1097fd0},
|
|
{0xca5e89b18b602368, 0x385bb19cb14bdfc4},
|
|
{0xfcf62c1dee382c42, 0x46729e03dd9ed7b5},
|
|
{0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1},
|
|
{0xc5a05277621be293, 0xc7098b7305241885},
|
|
{ 0xf70867153aa2db38,
|
|
0xb8cbee4fc66d1ea7 }
|
|
#else
|
|
{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b},
|
|
{0xce5d73ff402d98e3, 0xfb0a3d212dc81290},
|
|
{0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f},
|
|
{0x86a8d39ef77164bc, 0xae5dff9c02033198},
|
|
{0xd98ddaee19068c76, 0x3badd624dd9b0958},
|
|
{0xafbd2350644eeacf, 0xe5d1929ef90898fb},
|
|
{0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2},
|
|
{0xe55990879ddcaabd, 0xcc420a6a101d0516},
|
|
{0xb94470938fa89bce, 0xf808e40e8d5b3e6a},
|
|
{0x95a8637627989aad, 0xdde7001379a44aa9},
|
|
{0xf1c90080baf72cb1, 0x5324c68b12dd6339},
|
|
{0xc350000000000000, 0x0000000000000000},
|
|
{0x9dc5ada82b70b59d, 0xf020000000000000},
|
|
{0xfee50b7025c36a08, 0x02f236d04753d5b4},
|
|
{0xcde6fd5e09abcf26, 0xed4c0226b55e6f86},
|
|
{0xa6539930bf6bff45, 0x84db8346b786151c},
|
|
{0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2},
|
|
{0xd910f7ff28069da4, 0x1b2ba1518094da04},
|
|
{0xaf58416654a6babb, 0x387ac8d1970027b2},
|
|
{0x8da471a9de737e24, 0x5ceaecfed289e5d2},
|
|
{0xe4d5e82392a40515, 0x0fabaf3feaa5334a},
|
|
{0xb8da1662e7b00a17, 0x3d6a751f3b936243},
|
|
{ 0x95527a5202df0ccb,
|
|
0x0f37801e0c43ebc8 }
|
|
#endif
|
|
};
|
|
|
|
#if FMT_USE_FULL_CACHE_DRAGONBOX
|
|
return pow10_significands[k - float_info<double>::min_k];
|
|
#else
|
|
static constexpr const uint64_t powers_of_5_64[] = {
|
|
0x0000000000000001, 0x0000000000000005, 0x0000000000000019,
|
|
0x000000000000007d, 0x0000000000000271, 0x0000000000000c35,
|
|
0x0000000000003d09, 0x000000000001312d, 0x000000000005f5e1,
|
|
0x00000000001dcd65, 0x00000000009502f9, 0x0000000002e90edd,
|
|
0x000000000e8d4a51, 0x0000000048c27395, 0x000000016bcc41e9,
|
|
0x000000071afd498d, 0x0000002386f26fc1, 0x000000b1a2bc2ec5,
|
|
0x000003782dace9d9, 0x00001158e460913d, 0x000056bc75e2d631,
|
|
0x0001b1ae4d6e2ef5, 0x000878678326eac9, 0x002a5a058fc295ed,
|
|
0x00d3c21bcecceda1, 0x0422ca8b0a00a425, 0x14adf4b7320334b9};
|
|
|
|
static constexpr const uint32_t pow10_recovery_errors[] = {
|
|
0x50001400, 0x54044100, 0x54014555, 0x55954415, 0x54115555, 0x00000001,
|
|
0x50000000, 0x00104000, 0x54010004, 0x05004001, 0x55555544, 0x41545555,
|
|
0x54040551, 0x15445545, 0x51555514, 0x10000015, 0x00101100, 0x01100015,
|
|
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x04450514, 0x45414110,
|
|
0x55555145, 0x50544050, 0x15040155, 0x11054140, 0x50111514, 0x11451454,
|
|
0x00400541, 0x00000000, 0x55555450, 0x10056551, 0x10054011, 0x55551014,
|
|
0x69514555, 0x05151109, 0x00155555};
|
|
|
|
static const int compression_ratio = 27;
|
|
|
|
// Compute base index.
|
|
int cache_index = (k - float_info<double>::min_k) / compression_ratio;
|
|
int kb = cache_index * compression_ratio + float_info<double>::min_k;
|
|
int offset = k - kb;
|
|
|
|
// Get base cache.
|
|
uint128_wrapper base_cache = pow10_significands[cache_index];
|
|
if (offset == 0) return base_cache;
|
|
|
|
// Compute the required amount of bit-shift.
|
|
int alpha = floor_log2_pow10(kb + offset) - floor_log2_pow10(kb) - offset;
|
|
FMT_ASSERT(alpha > 0 && alpha < 64, "shifting error detected");
|
|
|
|
// Try to recover the real cache.
|
|
uint64_t pow5 = powers_of_5_64[offset];
|
|
uint128_wrapper recovered_cache = umul128(base_cache.high(), pow5);
|
|
uint128_wrapper middle_low =
|
|
umul128(base_cache.low() - (kb < 0 ? 1u : 0u), pow5);
|
|
|
|
recovered_cache += middle_low.high();
|
|
|
|
uint64_t high_to_middle = recovered_cache.high() << (64 - alpha);
|
|
uint64_t middle_to_low = recovered_cache.low() << (64 - alpha);
|
|
|
|
recovered_cache =
|
|
uint128_wrapper{(recovered_cache.low() >> alpha) | high_to_middle,
|
|
((middle_low.low() >> alpha) | middle_to_low)};
|
|
|
|
if (kb < 0) recovered_cache += 1;
|
|
|
|
// Get error.
|
|
int error_idx = (k - float_info<double>::min_k) / 16;
|
|
uint32_t error = (pow10_recovery_errors[error_idx] >>
|
|
((k - float_info<double>::min_k) % 16) * 2) &
|
|
0x3;
|
|
|
|
// Add the error back.
|
|
FMT_ASSERT(recovered_cache.low() + error >= recovered_cache.low(), "");
|
|
return {recovered_cache.high(), recovered_cache.low() + error};
|
|
#endif
|
|
}
|
|
|
|
static carrier_uint compute_mul(carrier_uint u,
|
|
const cache_entry_type& cache) FMT_NOEXCEPT {
|
|
return umul192_upper64(u, cache);
|
|
}
|
|
|
|
static uint32_t compute_delta(cache_entry_type const& cache,
|
|
int beta_minus_1) FMT_NOEXCEPT {
|
|
return static_cast<uint32_t>(cache.high() >> (64 - 1 - beta_minus_1));
|
|
}
|
|
|
|
static bool compute_mul_parity(carrier_uint two_f,
|
|
const cache_entry_type& cache,
|
|
int beta_minus_1) FMT_NOEXCEPT {
|
|
FMT_ASSERT(beta_minus_1 >= 1, "");
|
|
FMT_ASSERT(beta_minus_1 < 64, "");
|
|
|
|
return ((umul192_middle64(two_f, cache) >> (64 - beta_minus_1)) & 1) != 0;
|
|
}
|
|
|
|
static carrier_uint compute_left_endpoint_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return (cache.high() -
|
|
(cache.high() >> (float_info<double>::significand_bits + 2))) >>
|
|
(64 - float_info<double>::significand_bits - 1 - beta_minus_1);
|
|
}
|
|
|
|
static carrier_uint compute_right_endpoint_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return (cache.high() +
|
|
(cache.high() >> (float_info<double>::significand_bits + 1))) >>
|
|
(64 - float_info<double>::significand_bits - 1 - beta_minus_1);
|
|
}
|
|
|
|
static carrier_uint compute_round_up_for_shorter_interval_case(
|
|
const cache_entry_type& cache, int beta_minus_1) FMT_NOEXCEPT {
|
|
return ((cache.high() >>
|
|
(64 - float_info<double>::significand_bits - 2 - beta_minus_1)) +
|
|
1) /
|
|
2;
|
|
}
|
|
};
|
|
|
|
// Various integer checks
|
|
template <class T>
|
|
bool is_left_endpoint_integer_shorter_interval(int exponent) FMT_NOEXCEPT {
|
|
return exponent >=
|
|
float_info<
|
|
T>::case_shorter_interval_left_endpoint_lower_threshold &&
|
|
exponent <=
|
|
float_info<T>::case_shorter_interval_left_endpoint_upper_threshold;
|
|
}
|
|
template <class T>
|
|
bool is_endpoint_integer(typename float_info<T>::carrier_uint two_f,
|
|
int exponent, int minus_k) FMT_NOEXCEPT {
|
|
if (exponent < float_info<T>::case_fc_pm_half_lower_threshold) return false;
|
|
// For k >= 0.
|
|
if (exponent <= float_info<T>::case_fc_pm_half_upper_threshold) return true;
|
|
// For k < 0.
|
|
if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false;
|
|
return divisible_by_power_of_5(two_f, minus_k);
|
|
}
|
|
|
|
template <class T>
|
|
bool is_center_integer(typename float_info<T>::carrier_uint two_f, int exponent,
|
|
int minus_k) FMT_NOEXCEPT {
|
|
// Exponent for 5 is negative.
|
|
if (exponent > float_info<T>::divisibility_check_by_5_threshold) return false;
|
|
if (exponent > float_info<T>::case_fc_upper_threshold)
|
|
return divisible_by_power_of_5(two_f, minus_k);
|
|
// Both exponents are nonnegative.
|
|
if (exponent >= float_info<T>::case_fc_lower_threshold) return true;
|
|
// Exponent for 2 is negative.
|
|
return divisible_by_power_of_2(two_f, minus_k - exponent + 1);
|
|
}
|
|
|
|
// Remove trailing zeros from n and return the number of zeros removed (float)
|
|
FMT_ALWAYS_INLINE int remove_trailing_zeros(uint32_t& n) FMT_NOEXCEPT {
|
|
#ifdef FMT_BUILTIN_CTZ
|
|
int t = FMT_BUILTIN_CTZ(n);
|
|
#else
|
|
int t = ctz(n);
|
|
#endif
|
|
if (t > float_info<float>::max_trailing_zeros)
|
|
t = float_info<float>::max_trailing_zeros;
|
|
|
|
const uint32_t mod_inv1 = 0xcccccccd;
|
|
const uint32_t max_quotient1 = 0x33333333;
|
|
const uint32_t mod_inv2 = 0xc28f5c29;
|
|
const uint32_t max_quotient2 = 0x0a3d70a3;
|
|
|
|
int s = 0;
|
|
for (; s < t - 1; s += 2) {
|
|
if (n * mod_inv2 > max_quotient2) break;
|
|
n *= mod_inv2;
|
|
}
|
|
if (s < t && n * mod_inv1 <= max_quotient1) {
|
|
n *= mod_inv1;
|
|
++s;
|
|
}
|
|
n >>= s;
|
|
return s;
|
|
}
|
|
|
|
// Removes trailing zeros and returns the number of zeros removed (double)
|
|
FMT_ALWAYS_INLINE int remove_trailing_zeros(uint64_t& n) FMT_NOEXCEPT {
|
|
#ifdef FMT_BUILTIN_CTZLL
|
|
int t = FMT_BUILTIN_CTZLL(n);
|
|
#else
|
|
int t = ctzll(n);
|
|
#endif
|
|
if (t > float_info<double>::max_trailing_zeros)
|
|
t = float_info<double>::max_trailing_zeros;
|
|
// Divide by 10^8 and reduce to 32-bits
|
|
// Since ret_value.significand <= (2^64 - 1) / 1000 < 10^17,
|
|
// both of the quotient and the r should fit in 32-bits
|
|
|
|
const uint32_t mod_inv1 = 0xcccccccd;
|
|
const uint32_t max_quotient1 = 0x33333333;
|
|
const uint64_t mod_inv8 = 0xc767074b22e90e21;
|
|
const uint64_t max_quotient8 = 0x00002af31dc46118;
|
|
|
|
// If the number is divisible by 1'0000'0000, work with the quotient
|
|
if (t >= 8) {
|
|
auto quotient_candidate = n * mod_inv8;
|
|
|
|
if (quotient_candidate <= max_quotient8) {
|
|
auto quotient = static_cast<uint32_t>(quotient_candidate >> 8);
|
|
|
|
int s = 8;
|
|
for (; s < t; ++s) {
|
|
if (quotient * mod_inv1 > max_quotient1) break;
|
|
quotient *= mod_inv1;
|
|
}
|
|
quotient >>= (s - 8);
|
|
n = quotient;
|
|
return s;
|
|
}
|
|
}
|
|
|
|
// Otherwise, work with the remainder
|
|
auto quotient = static_cast<uint32_t>(n / 100000000);
|
|
auto remainder = static_cast<uint32_t>(n - 100000000 * quotient);
|
|
|
|
if (t == 0 || remainder * mod_inv1 > max_quotient1) {
|
|
return 0;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 1 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 1) + quotient * 10000000ull;
|
|
return 1;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 2 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 2) + quotient * 1000000ull;
|
|
return 2;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 3 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 3) + quotient * 100000ull;
|
|
return 3;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 4 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 4) + quotient * 10000ull;
|
|
return 4;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 5 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 5) + quotient * 1000ull;
|
|
return 5;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
if (t == 6 || remainder * mod_inv1 > max_quotient1) {
|
|
n = (remainder >> 6) + quotient * 100ull;
|
|
return 6;
|
|
}
|
|
remainder *= mod_inv1;
|
|
|
|
n = (remainder >> 7) + quotient * 10ull;
|
|
return 7;
|
|
}
|
|
|
|
// The main algorithm for shorter interval case
|
|
template <class T>
|
|
FMT_ALWAYS_INLINE decimal_fp<T> shorter_interval_case(int exponent)
|
|
FMT_NOEXCEPT {
|
|
decimal_fp<T> ret_value;
|
|
// Compute k and beta
|
|
const int minus_k = floor_log10_pow2_minus_log10_4_over_3(exponent);
|
|
const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k);
|
|
|
|
// Compute xi and zi
|
|
using cache_entry_type = typename cache_accessor<T>::cache_entry_type;
|
|
const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k);
|
|
|
|
auto xi = cache_accessor<T>::compute_left_endpoint_for_shorter_interval_case(
|
|
cache, beta_minus_1);
|
|
auto zi = cache_accessor<T>::compute_right_endpoint_for_shorter_interval_case(
|
|
cache, beta_minus_1);
|
|
|
|
// If the left endpoint is not an integer, increase it
|
|
if (!is_left_endpoint_integer_shorter_interval<T>(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;
|
|
ret_value.exponent += remove_trailing_zeros(ret_value.significand);
|
|
return ret_value;
|
|
}
|
|
|
|
// Otherwise, compute the round-up of y
|
|
ret_value.significand =
|
|
cache_accessor<T>::compute_round_up_for_shorter_interval_case(
|
|
cache, beta_minus_1);
|
|
ret_value.exponent = minus_k;
|
|
|
|
// When tie occurs, choose one of them according to the rule
|
|
if (exponent >= float_info<T>::shorter_interval_tie_lower_threshold &&
|
|
exponent <= float_info<T>::shorter_interval_tie_upper_threshold) {
|
|
ret_value.significand = ret_value.significand % 2 == 0
|
|
? ret_value.significand
|
|
: ret_value.significand - 1;
|
|
} else if (ret_value.significand < xi) {
|
|
++ret_value.significand;
|
|
}
|
|
return ret_value;
|
|
}
|
|
|
|
template <typename T> decimal_fp<T> to_decimal(T x) FMT_NOEXCEPT {
|
|
// Step 1: integer promotion & Schubfach multiplier calculation.
|
|
|
|
using carrier_uint = typename float_info<T>::carrier_uint;
|
|
using cache_entry_type = typename cache_accessor<T>::cache_entry_type;
|
|
auto br = bit_cast<carrier_uint>(x);
|
|
|
|
// Extract significand bits and exponent bits.
|
|
const carrier_uint significand_mask =
|
|
(static_cast<carrier_uint>(1) << float_info<T>::significand_bits) - 1;
|
|
carrier_uint significand = (br & significand_mask);
|
|
int exponent = static_cast<int>((br & exponent_mask<T>()) >>
|
|
float_info<T>::significand_bits);
|
|
|
|
if (exponent != 0) { // Check if normal.
|
|
exponent += float_info<T>::exponent_bias - float_info<T>::significand_bits;
|
|
|
|
// Shorter interval case; proceed like Schubfach.
|
|
if (significand == 0) return shorter_interval_case<T>(exponent);
|
|
|
|
significand |=
|
|
(static_cast<carrier_uint>(1) << float_info<T>::significand_bits);
|
|
} else {
|
|
// Subnormal case; the interval is always regular.
|
|
if (significand == 0) return {0, 0};
|
|
exponent = float_info<T>::min_exponent - float_info<T>::significand_bits;
|
|
}
|
|
|
|
const bool include_left_endpoint = (significand % 2 == 0);
|
|
const bool include_right_endpoint = include_left_endpoint;
|
|
|
|
// Compute k and beta.
|
|
const int minus_k = floor_log10_pow2(exponent) - float_info<T>::kappa;
|
|
const cache_entry_type cache = cache_accessor<T>::get_cached_power(-minus_k);
|
|
const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k);
|
|
|
|
// Compute zi and deltai
|
|
// 10^kappa <= deltai < 10^(kappa + 1)
|
|
const uint32_t deltai = cache_accessor<T>::compute_delta(cache, beta_minus_1);
|
|
const carrier_uint two_fc = significand << 1;
|
|
const carrier_uint two_fr = two_fc | 1;
|
|
const carrier_uint zi =
|
|
cache_accessor<T>::compute_mul(two_fr << beta_minus_1, cache);
|
|
|
|
// Step 2: Try larger divisor; remove trailing zeros if necessary
|
|
|
|
// 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
|
|
decimal_fp<T> ret_value;
|
|
ret_value.significand = divide_by_10_to_kappa_plus_1(zi);
|
|
uint32_t r = static_cast<uint32_t>(zi - float_info<T>::big_divisor *
|
|
ret_value.significand);
|
|
|
|
if (r > deltai) {
|
|
goto small_divisor_case_label;
|
|
} else if (r < deltai) {
|
|
// Exclude the right endpoint if necessary
|
|
if (r == 0 && !include_right_endpoint &&
|
|
is_endpoint_integer<T>(two_fr, exponent, minus_k)) {
|
|
--ret_value.significand;
|
|
r = float_info<T>::big_divisor;
|
|
goto small_divisor_case_label;
|
|
}
|
|
} else {
|
|
// r == deltai; compare fractional parts
|
|
// Check conditions in the order different from the paper
|
|
// to take advantage of short-circuiting
|
|
const carrier_uint two_fl = two_fc - 1;
|
|
if ((!include_left_endpoint ||
|
|
!is_endpoint_integer<T>(two_fl, exponent, minus_k)) &&
|
|
!cache_accessor<T>::compute_mul_parity(two_fl, cache, beta_minus_1)) {
|
|
goto small_divisor_case_label;
|
|
}
|
|
}
|
|
ret_value.exponent = minus_k + float_info<T>::kappa + 1;
|
|
|
|
// We may need to remove trailing zeros
|
|
ret_value.exponent += remove_trailing_zeros(ret_value.significand);
|
|
return ret_value;
|
|
|
|
// Step 3: Find the significand with the smaller divisor
|
|
|
|
small_divisor_case_label:
|
|
ret_value.significand *= 10;
|
|
ret_value.exponent = minus_k + float_info<T>::kappa;
|
|
|
|
const uint32_t mask = (1u << float_info<T>::kappa) - 1;
|
|
auto dist = r - (deltai / 2) + (float_info<T>::small_divisor / 2);
|
|
|
|
// Is dist divisible by 2^kappa?
|
|
if ((dist & mask) == 0) {
|
|
const bool approx_y_parity =
|
|
((dist ^ (float_info<T>::small_divisor / 2)) & 1) != 0;
|
|
dist >>= float_info<T>::kappa;
|
|
|
|
// Is dist divisible by 5^kappa?
|
|
if (check_divisibility_and_divide_by_pow5<float_info<T>::kappa>(dist)) {
|
|
ret_value.significand += dist;
|
|
|
|
// 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
|
|
if (cache_accessor<T>::compute_mul_parity(two_fc, cache, beta_minus_1) !=
|
|
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
|
|
if (is_center_integer<T>(two_fc, exponent, minus_k)) {
|
|
ret_value.significand = ret_value.significand % 2 == 0
|
|
? ret_value.significand
|
|
: ret_value.significand - 1;
|
|
}
|
|
}
|
|
}
|
|
// Is dist not divisible by 5^kappa?
|
|
else {
|
|
ret_value.significand += dist;
|
|
}
|
|
}
|
|
// Is dist not divisible by 2^kappa?
|
|
else {
|
|
// Since we know dist is small, we might be able to optimize the division
|
|
// better than the compiler; we are computing dist / small_divisor here
|
|
ret_value.significand +=
|
|
small_division_by_pow10<float_info<T>::kappa>(dist);
|
|
}
|
|
return ret_value;
|
|
}
|
|
} // namespace dragonbox
|
|
|
|
// Formats value using a variation of the Fixed-Precision Positive
|
|
// Floating-Point Printout ((FPP)^2) algorithm by Steele & White:
|
|
// https://fmt.dev/papers/p372-steele.pdf.
|
|
template <typename Double>
|
|
void fallback_format(Double d, int num_digits, bool binary32, buffer<char>& buf,
|
|
int& exp10) {
|
|
bigint numerator; // 2 * R in (FPP)^2.
|
|
bigint denominator; // 2 * S in (FPP)^2.
|
|
// lower and upper are differences between value and corresponding boundaries.
|
|
bigint lower; // (M^- in (FPP)^2).
|
|
bigint upper_store; // upper's value if different from lower.
|
|
bigint* upper = nullptr; // (M^+ in (FPP)^2).
|
|
fp value;
|
|
// Shift numerator and denominator by an extra bit or two (if lower boundary
|
|
// is closer) to make lower and upper integers. This eliminates multiplication
|
|
// by 2 during later computations.
|
|
const bool is_predecessor_closer =
|
|
binary32 ? value.assign(static_cast<float>(d)) : value.assign(d);
|
|
int shift = is_predecessor_closer ? 2 : 1;
|
|
uint64_t significand = value.f << shift;
|
|
if (value.e >= 0) {
|
|
numerator.assign(significand);
|
|
numerator <<= value.e;
|
|
lower.assign(1);
|
|
lower <<= value.e;
|
|
if (shift != 1) {
|
|
upper_store.assign(1);
|
|
upper_store <<= value.e + 1;
|
|
upper = &upper_store;
|
|
}
|
|
denominator.assign_pow10(exp10);
|
|
denominator <<= shift;
|
|
} else if (exp10 < 0) {
|
|
numerator.assign_pow10(-exp10);
|
|
lower.assign(numerator);
|
|
if (shift != 1) {
|
|
upper_store.assign(numerator);
|
|
upper_store <<= 1;
|
|
upper = &upper_store;
|
|
}
|
|
numerator *= significand;
|
|
denominator.assign(1);
|
|
denominator <<= shift - value.e;
|
|
} else {
|
|
numerator.assign(significand);
|
|
denominator.assign_pow10(exp10);
|
|
denominator <<= shift - value.e;
|
|
lower.assign(1);
|
|
if (shift != 1) {
|
|
upper_store.assign(1ULL << 1);
|
|
upper = &upper_store;
|
|
}
|
|
}
|
|
// Invariant: value == (numerator / denominator) * pow(10, exp10).
|
|
if (num_digits < 0) {
|
|
// Generate the shortest representation.
|
|
if (!upper) upper = &lower;
|
|
bool even = (value.f & 1) == 0;
|
|
num_digits = 0;
|
|
char* data = buf.data();
|
|
for (;;) {
|
|
int digit = numerator.divmod_assign(denominator);
|
|
bool low = compare(numerator, lower) - even < 0; // numerator <[=] lower.
|
|
// numerator + upper >[=] pow10:
|
|
bool high = add_compare(numerator, *upper, denominator) + even > 0;
|
|
data[num_digits++] = static_cast<char>('0' + digit);
|
|
if (low || high) {
|
|
if (!low) {
|
|
++data[num_digits - 1];
|
|
} else if (high) {
|
|
int result = add_compare(numerator, numerator, denominator);
|
|
// Round half to even.
|
|
if (result > 0 || (result == 0 && (digit % 2) != 0))
|
|
++data[num_digits - 1];
|
|
}
|
|
buf.try_resize(to_unsigned(num_digits));
|
|
exp10 -= num_digits - 1;
|
|
return;
|
|
}
|
|
numerator *= 10;
|
|
lower *= 10;
|
|
if (upper != &lower) *upper *= 10;
|
|
}
|
|
}
|
|
// Generate the given number of digits.
|
|
exp10 -= num_digits - 1;
|
|
if (num_digits == 0) {
|
|
buf.try_resize(1);
|
|
denominator *= 10;
|
|
buf[0] = add_compare(numerator, numerator, denominator) > 0 ? '1' : '0';
|
|
return;
|
|
}
|
|
buf.try_resize(to_unsigned(num_digits));
|
|
for (int i = 0; i < num_digits - 1; ++i) {
|
|
int digit = numerator.divmod_assign(denominator);
|
|
buf[i] = static_cast<char>('0' + digit);
|
|
numerator *= 10;
|
|
}
|
|
int digit = numerator.divmod_assign(denominator);
|
|
auto result = add_compare(numerator, numerator, denominator);
|
|
if (result > 0 || (result == 0 && (digit % 2) != 0)) {
|
|
if (digit == 9) {
|
|
const auto overflow = '0' + 10;
|
|
buf[num_digits - 1] = overflow;
|
|
// Propagate the carry.
|
|
for (int i = num_digits - 1; i > 0 && buf[i] == overflow; --i) {
|
|
buf[i] = '0';
|
|
++buf[i - 1];
|
|
}
|
|
if (buf[0] == overflow) {
|
|
buf[0] = '1';
|
|
++exp10;
|
|
}
|
|
return;
|
|
}
|
|
++digit;
|
|
}
|
|
buf[num_digits - 1] = static_cast<char>('0' + digit);
|
|
}
|
|
|
|
template <typename T>
|
|
int format_float(T value, int precision, float_specs specs, buffer<char>& buf) {
|
|
static_assert(!std::is_same<T, float>::value, "");
|
|
FMT_ASSERT(value >= 0, "value is negative");
|
|
|
|
const bool fixed = specs.format == float_format::fixed;
|
|
if (value <= 0) { // <= instead of == to silence a warning.
|
|
if (precision <= 0 || !fixed) {
|
|
buf.push_back('0');
|
|
return 0;
|
|
}
|
|
buf.try_resize(to_unsigned(precision));
|
|
std::uninitialized_fill_n(buf.data(), precision, '0');
|
|
return -precision;
|
|
}
|
|
|
|
if (!specs.use_grisu) return snprintf_float(value, precision, specs, buf);
|
|
|
|
if (precision < 0) {
|
|
// Use Dragonbox for the shortest format.
|
|
if (specs.binary32) {
|
|
auto dec = dragonbox::to_decimal(static_cast<float>(value));
|
|
write<char>(buffer_appender<char>(buf), dec.significand);
|
|
return dec.exponent;
|
|
}
|
|
auto dec = dragonbox::to_decimal(static_cast<double>(value));
|
|
write<char>(buffer_appender<char>(buf), dec.significand);
|
|
return dec.exponent;
|
|
}
|
|
|
|
// Use Grisu + Dragon4 for the given precision:
|
|
// https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf.
|
|
int exp = 0;
|
|
const int min_exp = -60; // alpha in Grisu.
|
|
int cached_exp10 = 0; // K in Grisu.
|
|
fp normalized = normalize(fp(value));
|
|
const auto cached_pow = get_cached_power(
|
|
min_exp - (normalized.e + fp::significand_size), cached_exp10);
|
|
normalized = normalized * cached_pow;
|
|
// Limit precision to the maximum possible number of significant digits in an
|
|
// IEEE754 double because we don't need to generate zeros.
|
|
const int max_double_digits = 767;
|
|
if (precision > max_double_digits) precision = max_double_digits;
|
|
fixed_handler handler{buf.data(), 0, precision, -cached_exp10, fixed};
|
|
if (grisu_gen_digits(normalized, 1, exp, handler) == digits::error) {
|
|
exp += handler.size - cached_exp10 - 1;
|
|
fallback_format(value, handler.precision, specs.binary32, buf, exp);
|
|
} else {
|
|
exp += handler.exp10;
|
|
buf.try_resize(to_unsigned(handler.size));
|
|
}
|
|
if (!fixed && !specs.showpoint) {
|
|
// Remove trailing zeros.
|
|
auto num_digits = buf.size();
|
|
while (num_digits > 0 && buf[num_digits - 1] == '0') {
|
|
--num_digits;
|
|
++exp;
|
|
}
|
|
buf.try_resize(num_digits);
|
|
}
|
|
return exp;
|
|
} // namespace detail
|
|
|
|
template <typename T>
|
|
int snprintf_float(T value, int precision, float_specs specs,
|
|
buffer<char>& buf) {
|
|
// Buffer capacity must be non-zero, otherwise MSVC's vsnprintf_s will fail.
|
|
FMT_ASSERT(buf.capacity() > buf.size(), "empty buffer");
|
|
static_assert(!std::is_same<T, float>::value, "");
|
|
|
|
// Subtract 1 to account for the difference in precision since we use %e for
|
|
// both general and exponent format.
|
|
if (specs.format == float_format::general ||
|
|
specs.format == float_format::exp)
|
|
precision = (precision >= 0 ? precision : 6) - 1;
|
|
|
|
// Build the format string.
|
|
enum { max_format_size = 7 }; // The longest format is "%#.*Le".
|
|
char format[max_format_size];
|
|
char* format_ptr = format;
|
|
*format_ptr++ = '%';
|
|
if (specs.showpoint && specs.format == float_format::hex) *format_ptr++ = '#';
|
|
if (precision >= 0) {
|
|
*format_ptr++ = '.';
|
|
*format_ptr++ = '*';
|
|
}
|
|
if (std::is_same<T, long double>()) *format_ptr++ = 'L';
|
|
*format_ptr++ = specs.format != float_format::hex
|
|
? (specs.format == float_format::fixed ? 'f' : 'e')
|
|
: (specs.upper ? 'A' : 'a');
|
|
*format_ptr = '\0';
|
|
|
|
// Format using snprintf.
|
|
auto offset = buf.size();
|
|
for (;;) {
|
|
auto begin = buf.data() + offset;
|
|
auto capacity = buf.capacity() - offset;
|
|
#ifdef FMT_FUZZ
|
|
if (precision > 100000)
|
|
throw std::runtime_error(
|
|
"fuzz mode - avoid large allocation inside snprintf");
|
|
#endif
|
|
// Suppress the warning about a nonliteral format string.
|
|
// Cannot use auto because of a bug in MinGW (#1532).
|
|
int (*snprintf_ptr)(char*, size_t, const char*, ...) = FMT_SNPRINTF;
|
|
int result = precision >= 0
|
|
? snprintf_ptr(begin, capacity, format, precision, value)
|
|
: snprintf_ptr(begin, capacity, format, value);
|
|
if (result < 0) {
|
|
// The buffer will grow exponentially.
|
|
buf.try_reserve(buf.capacity() + 1);
|
|
continue;
|
|
}
|
|
auto size = to_unsigned(result);
|
|
// Size equal to capacity means that the last character was truncated.
|
|
if (size >= capacity) {
|
|
buf.try_reserve(size + offset + 1); // Add 1 for the terminating '\0'.
|
|
continue;
|
|
}
|
|
auto is_digit = [](char c) { return c >= '0' && c <= '9'; };
|
|
if (specs.format == float_format::fixed) {
|
|
if (precision == 0) {
|
|
buf.try_resize(size);
|
|
return 0;
|
|
}
|
|
// Find and remove the decimal point.
|
|
auto end = begin + size, p = end;
|
|
do {
|
|
--p;
|
|
} while (is_digit(*p));
|
|
int fraction_size = static_cast<int>(end - p - 1);
|
|
std::memmove(p, p + 1, to_unsigned(fraction_size));
|
|
buf.try_resize(size - 1);
|
|
return -fraction_size;
|
|
}
|
|
if (specs.format == float_format::hex) {
|
|
buf.try_resize(size + offset);
|
|
return 0;
|
|
}
|
|
// Find and parse the exponent.
|
|
auto end = begin + size, exp_pos = end;
|
|
do {
|
|
--exp_pos;
|
|
} while (*exp_pos != 'e');
|
|
char sign = exp_pos[1];
|
|
FMT_ASSERT(sign == '+' || sign == '-', "");
|
|
int exp = 0;
|
|
auto p = exp_pos + 2; // Skip 'e' and sign.
|
|
do {
|
|
FMT_ASSERT(is_digit(*p), "");
|
|
exp = exp * 10 + (*p++ - '0');
|
|
} while (p != end);
|
|
if (sign == '-') exp = -exp;
|
|
int fraction_size = 0;
|
|
if (exp_pos != begin + 1) {
|
|
// Remove trailing zeros.
|
|
auto fraction_end = exp_pos - 1;
|
|
while (*fraction_end == '0') --fraction_end;
|
|
// Move the fractional part left to get rid of the decimal point.
|
|
fraction_size = static_cast<int>(fraction_end - begin - 1);
|
|
std::memmove(begin + 1, begin + 2, to_unsigned(fraction_size));
|
|
}
|
|
buf.try_resize(to_unsigned(fraction_size) + offset + 1);
|
|
return exp - fraction_size;
|
|
}
|
|
}
|
|
|
|
struct stringifier {
|
|
template <typename T> FMT_INLINE std::string operator()(T value) const {
|
|
return to_string(value);
|
|
}
|
|
std::string operator()(basic_format_arg<format_context>::handle h) const {
|
|
memory_buffer buf;
|
|
format_parse_context parse_ctx({});
|
|
format_context format_ctx(buffer_appender<char>(buf), {}, {});
|
|
h.format(parse_ctx, format_ctx);
|
|
return to_string(buf);
|
|
}
|
|
};
|
|
} // namespace detail
|
|
|
|
template <> struct formatter<detail::bigint> {
|
|
FMT_CONSTEXPR format_parse_context::iterator parse(
|
|
format_parse_context& ctx) {
|
|
return ctx.begin();
|
|
}
|
|
|
|
format_context::iterator format(const detail::bigint& n,
|
|
format_context& ctx) {
|
|
auto out = ctx.out();
|
|
bool first = true;
|
|
for (auto i = n.bigits_.size(); i > 0; --i) {
|
|
auto value = n.bigits_[i - 1u];
|
|
if (first) {
|
|
out = format_to(out, FMT_STRING("{:x}"), value);
|
|
first = false;
|
|
continue;
|
|
}
|
|
out = format_to(out, FMT_STRING("{:08x}"), value);
|
|
}
|
|
if (n.exp_ > 0)
|
|
out = format_to(out, FMT_STRING("p{}"),
|
|
n.exp_ * detail::bigint::bigit_bits);
|
|
return out;
|
|
}
|
|
};
|
|
|
|
FMT_FUNC detail::utf8_to_utf16::utf8_to_utf16(string_view s) {
|
|
for_each_codepoint(s, [this](uint32_t cp, int error) {
|
|
if (error != 0) FMT_THROW(std::runtime_error("invalid utf8"));
|
|
if (cp <= 0xFFFF) {
|
|
buffer_.push_back(static_cast<wchar_t>(cp));
|
|
} else {
|
|
cp -= 0x10000;
|
|
buffer_.push_back(static_cast<wchar_t>(0xD800 + (cp >> 10)));
|
|
buffer_.push_back(static_cast<wchar_t>(0xDC00 + (cp & 0x3FF)));
|
|
}
|
|
});
|
|
buffer_.push_back(0);
|
|
}
|
|
|
|
FMT_FUNC void format_system_error(detail::buffer<char>& out, int error_code,
|
|
const char* message) FMT_NOEXCEPT {
|
|
FMT_TRY {
|
|
auto ec = std::error_code(error_code, std::generic_category());
|
|
write(std::back_inserter(out), std::system_error(ec, message).what());
|
|
return;
|
|
}
|
|
FMT_CATCH(...) {}
|
|
format_error_code(out, error_code, message);
|
|
}
|
|
|
|
FMT_FUNC void detail::error_handler::on_error(const char* message) {
|
|
FMT_THROW(format_error(message));
|
|
}
|
|
|
|
FMT_FUNC void report_system_error(int error_code,
|
|
const char* message) FMT_NOEXCEPT {
|
|
report_error(format_system_error, error_code, message);
|
|
}
|
|
|
|
FMT_FUNC std::string vformat(string_view fmt, format_args args) {
|
|
if (fmt.size() == 2 && detail::equal2(fmt.data(), "{}")) {
|
|
auto arg = args.get(0);
|
|
if (!arg) detail::error_handler().on_error("argument not found");
|
|
return visit_format_arg(detail::stringifier(), arg);
|
|
}
|
|
memory_buffer buffer;
|
|
detail::vformat_to(buffer, fmt, args);
|
|
return to_string(buffer);
|
|
}
|
|
|
|
#ifdef _WIN32
|
|
namespace detail {
|
|
using dword = conditional_t<sizeof(long) == 4, unsigned long, unsigned>;
|
|
extern "C" __declspec(dllimport) int __stdcall WriteConsoleW( //
|
|
void*, const void*, dword, dword*, void*);
|
|
} // namespace detail
|
|
#endif
|
|
|
|
FMT_FUNC void vprint(std::FILE* f, string_view format_str, format_args args) {
|
|
memory_buffer buffer;
|
|
detail::vformat_to(buffer, format_str, args);
|
|
#ifdef _WIN32
|
|
auto fd = _fileno(f);
|
|
if (_isatty(fd)) {
|
|
detail::utf8_to_utf16 u16(string_view(buffer.data(), buffer.size()));
|
|
auto written = detail::dword();
|
|
if (detail::WriteConsoleW(reinterpret_cast<void*>(_get_osfhandle(fd)),
|
|
u16.c_str(), static_cast<uint32_t>(u16.size()),
|
|
&written, nullptr)) {
|
|
return;
|
|
}
|
|
// Fallback to fwrite on failure. It can happen if the output has been
|
|
// redirected to NUL.
|
|
}
|
|
#endif
|
|
detail::fwrite_fully(buffer.data(), 1, buffer.size(), f);
|
|
}
|
|
|
|
#ifdef _WIN32
|
|
// Print assuming legacy (non-Unicode) encoding.
|
|
FMT_FUNC void detail::vprint_mojibake(std::FILE* f, string_view format_str,
|
|
format_args args) {
|
|
memory_buffer buffer;
|
|
detail::vformat_to(buffer, format_str,
|
|
basic_format_args<buffer_context<char>>(args));
|
|
fwrite_fully(buffer.data(), 1, buffer.size(), f);
|
|
}
|
|
#endif
|
|
|
|
FMT_FUNC void vprint(string_view format_str, format_args args) {
|
|
vprint(stdout, format_str, args);
|
|
}
|
|
|
|
FMT_END_NAMESPACE
|
|
|
|
#endif // FMT_FORMAT_INL_H_
|