mirror of
https://github.com/nlohmann/json.git
synced 2026-10-05 06:00:29 +00:00
Niels Lohmann
a04aa3d095
dump() writes doubles with the conversion of Zmij by Victor Zverovich (https://github.com/vitaut/zmij, MIT), ported to C++11 in detail/conversions/zmij.hpp: the shortest decimal in the rounding interval, the closest one if there are several. Grisu2 does not always find the shortest digits; about 0.14% of random doubles are now written differently (0.08% with fewer digits, 0.06% with the closest last digit); short decimals such as 0.1 or 2555.56 are not affected. float keeps Grisu2. The layout of doubles is unchanged, but written differently: the digits are converted eight at a time (the BCD conversion of Xiang JunBo, as in Zmij) and stored with one byte swap per eight digits; leading and trailing zeros are counted from those bytes; and the layouts of format_buffer() are written with fixed-size moves instead of per-digit loops and moves of the buffer (to_chars() uses a local buffer if the caller's is shorter than the 41 bytes this may write). The powers of ten come from the table for number parsing, adjusted where it holds them rounded up, and from the compressed tables of Zmij beyond 10^308. json::dump() gets faster on floats: canada -53%, numbers -46%, mesh -37%, marine_ik -30%. Tests: the powers of ten recomputed with a small big-integer; for random doubles, all powers of two and of ten and their neighbors, and boundary values: the output reads back as the same value, no decimal with one digit fewer does, the layout equals that of format_buffer() for the same digits, and (C++17) the digits equal those of std::to_chars. The size ratios of canada.json in unit-binary_formats.cpp and one expectation in unit-to_chars.cpp change with the shorter output. Signed-off-by: Niels Lohmann <mail@nlohmann.me>
1355 lines
47 KiB
C++
1355 lines
47 KiB
C++
// __ _____ _____ _____
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// __| | __| | | | JSON for Modern C++
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// | | |__ | | | | | | version 3.12.0
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// |_____|_____|_____|_|___| https://github.com/nlohmann/json
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//
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// SPDX-FileCopyrightText: 2009 Florian Loitsch <https://florian.loitsch.com/>
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// SPDX-FileCopyrightText: 2013-2026 Niels Lohmann <https://nlohmann.me>
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// SPDX-License-Identifier: MIT
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#pragma once
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#include <array> // array
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#include <cmath> // signbit, isfinite
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#include <cstddef> // size_t
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#include <cstdint> // intN_t, uintN_t
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#include <cstring> // memcpy, memmove
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#include <limits> // numeric_limits
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#include <type_traits> // conditional
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#ifdef _MSC_VER
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#include <cstdlib> // _byteswap_uint64
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#endif
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#include <nlohmann/detail/conversions/zmij.hpp>
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#include <nlohmann/detail/macro_scope.hpp>
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NLOHMANN_JSON_NAMESPACE_BEGIN
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namespace detail
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{
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/*!
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@brief implements the Grisu2 algorithm for binary to decimal floating-point
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conversion.
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This implementation is a slightly modified version of the reference
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implementation which may be obtained from
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http://florian.loitsch.com/publications (bench.tar.gz).
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The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.
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For a detailed description of the algorithm see:
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[1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with
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Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming
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Language Design and Implementation, PLDI 2010
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[2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
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Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language
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Design and Implementation, PLDI 1996
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*/
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namespace dtoa_impl
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{
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template<typename Target, typename Source>
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Target reinterpret_bits(const Source source)
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{
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static_assert(sizeof(Target) == sizeof(Source), "size mismatch");
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Target target;
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std::memcpy(&target, &source, sizeof(Source));
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return target;
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}
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struct diyfp // f * 2^e
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{
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static constexpr int kPrecision = 64; // = q
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std::uint64_t f = 0;
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int e = 0;
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constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {}
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/*!
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@brief returns x - y
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@pre x.e == y.e and x.f >= y.f
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*/
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static diyfp sub(const diyfp& x, const diyfp& y) noexcept
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{
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JSON_ASSERT(x.e == y.e);
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JSON_ASSERT(x.f >= y.f);
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return {x.f - y.f, x.e};
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}
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/*!
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@brief returns x * y
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@note The result is rounded. (Only the upper q bits are returned.)
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*/
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static diyfp mul(const diyfp& x, const diyfp& y) noexcept
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{
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static_assert(kPrecision == 64, "internal error");
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// Computes:
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// f = round((x.f * y.f) / 2^q)
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// e = x.e + y.e + q
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// Emulate the 64-bit * 64-bit multiplication:
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//
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// p = u * v
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// = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
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// = (u_lo v_lo ) + 2^32 ((u_lo v_hi ) + (u_hi v_lo )) + 2^64 (u_hi v_hi )
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// = (p0 ) + 2^32 ((p1 ) + (p2 )) + 2^64 (p3 )
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// = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3 )
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// = (p0_lo ) + 2^32 (p0_hi + p1_lo + p2_lo ) + 2^64 (p1_hi + p2_hi + p3)
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// = (p0_lo ) + 2^32 (Q ) + 2^64 (H )
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// = (p0_lo ) + 2^32 (Q_lo + 2^32 Q_hi ) + 2^64 (H )
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//
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// (Since Q might be larger than 2^32 - 1)
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//
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// = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
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//
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// (Q_hi + H does not overflow a 64-bit int)
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//
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// = p_lo + 2^64 p_hi
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const std::uint64_t u_lo = x.f & 0xFFFFFFFFu;
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const std::uint64_t u_hi = x.f >> 32u;
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const std::uint64_t v_lo = y.f & 0xFFFFFFFFu;
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const std::uint64_t v_hi = y.f >> 32u;
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const std::uint64_t p0 = u_lo * v_lo;
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const std::uint64_t p1 = u_lo * v_hi;
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const std::uint64_t p2 = u_hi * v_lo;
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const std::uint64_t p3 = u_hi * v_hi;
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const std::uint64_t p0_hi = p0 >> 32u;
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const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu;
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const std::uint64_t p1_hi = p1 >> 32u;
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const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu;
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const std::uint64_t p2_hi = p2 >> 32u;
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std::uint64_t Q = p0_hi + p1_lo + p2_lo;
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// The full product might now be computed as
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//
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// p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
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// p_lo = p0_lo + (Q << 32)
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//
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// But in this particular case here, the full p_lo is not required.
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// Effectively, we only need to add the highest bit in p_lo to p_hi (and
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// Q_hi + 1 does not overflow).
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Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up
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const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u);
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return {h, x.e + y.e + 64};
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}
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/*!
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@brief normalize x such that the significand is >= 2^(q-1)
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@pre x.f != 0
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*/
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static diyfp normalize(diyfp x) noexcept
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{
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JSON_ASSERT(x.f != 0);
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while ((x.f >> 63u) == 0)
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{
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x.f <<= 1u;
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x.e--;
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}
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return x;
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}
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/*!
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@brief normalize x such that the result has the exponent E
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@pre e >= x.e and the upper e - x.e bits of x.f must be zero.
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*/
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static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept
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{
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const int delta = x.e - target_exponent;
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JSON_ASSERT(delta >= 0);
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JSON_ASSERT(((x.f << delta) >> delta) == x.f);
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return {x.f << delta, target_exponent};
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}
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};
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struct boundaries
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{
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diyfp w;
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diyfp minus;
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diyfp plus;
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};
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/*!
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Compute the (normalized) diyfp representing the input number 'value' and its
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boundaries.
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@pre value must be finite and positive
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*/
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template<typename FloatType>
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boundaries compute_boundaries(FloatType value)
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{
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JSON_ASSERT(std::isfinite(value));
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JSON_ASSERT(value > 0);
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// Convert the IEEE representation into a diyfp.
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//
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// If v is denormal:
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// value = 0.F * 2^(1 - bias) = ( F) * 2^(1 - bias - (p-1))
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// If v is normalized:
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// value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))
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static_assert(std::numeric_limits<FloatType>::is_iec559,
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"internal error: dtoa_short requires an IEEE-754 floating-point implementation");
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constexpr int kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
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constexpr int kBias = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
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constexpr int kMinExp = 1 - kBias;
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constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)
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using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type;
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const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));
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const std::uint64_t E = bits >> (kPrecision - 1);
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const std::uint64_t F = bits & (kHiddenBit - 1);
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const bool is_denormal = E == 0;
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const diyfp v = is_denormal
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? diyfp(F, kMinExp)
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: diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);
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// Compute the boundaries m- and m+ of the floating-point value
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// v = f * 2^e.
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//
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// Determine v- and v+, the floating-point predecessor and successor of v,
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// respectively.
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//
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// v- = v - 2^e if f != 2^(p-1) or e == e_min (A)
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// = v - 2^(e-1) if f == 2^(p-1) and e > e_min (B)
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//
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// v+ = v + 2^e
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//
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// Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
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// between m- and m+ round to v, regardless of how the input rounding
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// algorithm breaks ties.
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//
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// ---+-------------+-------------+-------------+-------------+--- (A)
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// v- m- v m+ v+
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//
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// -----------------+------+------+-------------+-------------+--- (B)
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// v- m- v m+ v+
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const bool lower_boundary_is_closer = F == 0 && E > 1;
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const diyfp m_plus = diyfp((2 * v.f) + 1, v.e - 1);
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const diyfp m_minus = lower_boundary_is_closer
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? diyfp((4 * v.f) - 1, v.e - 2) // (B)
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: diyfp((2 * v.f) - 1, v.e - 1); // (A)
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// Determine the normalized w+ = m+.
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const diyfp w_plus = diyfp::normalize(m_plus);
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// Determine w- = m- such that e_(w-) = e_(w+).
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const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);
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return {diyfp::normalize(v), w_minus, w_plus};
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}
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// Given normalized diyfp w, Grisu needs to find a (normalized) cached
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// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
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// within a certain range [alpha, gamma] (Definition 3.2 from [1])
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//
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// alpha <= e = e_c + e_w + q <= gamma
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//
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// or
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//
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// f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q
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// <= f_c * f_w * 2^gamma
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//
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// Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies
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//
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// 2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma
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//
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// or
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//
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// 2^(q - 2 + alpha) <= c * w < 2^(q + gamma)
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//
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// The choice of (alpha,gamma) determines the size of the table and the form of
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// the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well
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// in practice:
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//
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// The idea is to cut the number c * w = f * 2^e into two parts, which can be
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// processed independently: An integral part p1, and a fractional part p2:
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//
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// f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e
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// = (f div 2^-e) + (f mod 2^-e) * 2^e
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// = p1 + p2 * 2^e
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//
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// The conversion of p1 into decimal form requires a series of divisions and
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// modulos by (a power of) 10. These operations are faster for 32-bit than for
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// 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be
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// achieved by choosing
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//
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// -e >= 32 or e <= -32 := gamma
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//
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// In order to convert the fractional part
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//
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// p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...
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//
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// into decimal form, the fraction is repeatedly multiplied by 10 and the digits
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// d[-i] are extracted in order:
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//
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// (10 * p2) div 2^-e = d[-1]
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// (10 * p2) mod 2^-e = d[-2] / 10^1 + ...
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//
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// The multiplication by 10 must not overflow. It is sufficient to choose
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//
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// 10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.
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//
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// Since p2 = f mod 2^-e < 2^-e,
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//
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// -e <= 60 or e >= -60 := alpha
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constexpr int kAlpha = -60;
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constexpr int kGamma = -32;
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struct cached_power // c = f * 2^e ~= 10^k
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{
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std::uint64_t f;
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int e;
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int k;
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};
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/*!
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For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached
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power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c
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satisfies (Definition 3.2 from [1])
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alpha <= e_c + e + q <= gamma.
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*/
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inline cached_power get_cached_power_for_binary_exponent(int e)
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{
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// Now
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//
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// alpha <= e_c + e + q <= gamma (1)
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// ==> f_c * 2^alpha <= c * 2^e * 2^q
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//
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// and since the c's are normalized, 2^(q-1) <= f_c,
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//
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// ==> 2^(q - 1 + alpha) <= c * 2^(e + q)
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// ==> 2^(alpha - e - 1) <= c
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//
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// If c were an exact power of ten, i.e. c = 10^k, one may determine k as
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//
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// k = ceil( log_10( 2^(alpha - e - 1) ) )
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// = ceil( (alpha - e - 1) * log_10(2) )
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//
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// From the paper:
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// "In theory the result of the procedure could be wrong since c is rounded,
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// and the computation itself is approximated [...]. In practice, however,
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// this simple function is sufficient."
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//
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// For IEEE double precision floating-point numbers converted into
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// normalized diyfp's w = f * 2^e, with q = 64,
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//
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// e >= -1022 (min IEEE exponent)
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// -52 (p - 1)
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// -52 (p - 1, possibly normalize denormal IEEE numbers)
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// -11 (normalize the diyfp)
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// = -1137
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//
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// and
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//
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// e <= +1023 (max IEEE exponent)
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// -52 (p - 1)
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// -11 (normalize the diyfp)
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// = 960
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//
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// This binary exponent range [-1137,960] results in a decimal exponent
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// range [-307,324]. One does not need to store a cached power for each
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// k in this range. For each such k it suffices to find a cached power
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// such that the exponent of the product lies in [alpha,gamma].
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// This implies that the difference of the decimal exponents of adjacent
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// table entries must be less than or equal to
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//
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// floor( (gamma - alpha) * log_10(2) ) = 8.
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//
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// (A smaller distance gamma-alpha would require a larger table.)
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// NB:
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// Actually, this function returns c, such that -60 <= e_c + e + 64 <= -34.
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constexpr int kCachedPowersMinDecExp = -300;
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constexpr int kCachedPowersDecStep = 8;
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static constexpr std::array<cached_power, 79> kCachedPowers =
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{
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{
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{ 0xAB70FE17C79AC6CA, -1060, -300 },
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{ 0xFF77B1FCBEBCDC4F, -1034, -292 },
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{ 0xBE5691EF416BD60C, -1007, -284 },
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{ 0x8DD01FAD907FFC3C, -980, -276 },
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{ 0xD3515C2831559A83, -954, -268 },
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{ 0x9D71AC8FADA6C9B5, -927, -260 },
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{ 0xEA9C227723EE8BCB, -901, -252 },
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{ 0xAECC49914078536D, -874, -244 },
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{ 0x823C12795DB6CE57, -847, -236 },
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{ 0xC21094364DFB5637, -821, -228 },
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{ 0x9096EA6F3848984F, -794, -220 },
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{ 0xD77485CB25823AC7, -768, -212 },
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{ 0xA086CFCD97BF97F4, -741, -204 },
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{ 0xEF340A98172AACE5, -715, -196 },
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{ 0xB23867FB2A35B28E, -688, -188 },
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{ 0x84C8D4DFD2C63F3B, -661, -180 },
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{ 0xC5DD44271AD3CDBA, -635, -172 },
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{ 0x936B9FCEBB25C996, -608, -164 },
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{ 0xDBAC6C247D62A584, -582, -156 },
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{ 0xA3AB66580D5FDAF6, -555, -148 },
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{ 0xF3E2F893DEC3F126, -529, -140 },
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{ 0xB5B5ADA8AAFF80B8, -502, -132 },
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{ 0x87625F056C7C4A8B, -475, -124 },
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{ 0xC9BCFF6034C13053, -449, -116 },
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{ 0x964E858C91BA2655, -422, -108 },
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{ 0xDFF9772470297EBD, -396, -100 },
|
|
{ 0xA6DFBD9FB8E5B88F, -369, -92 },
|
|
{ 0xF8A95FCF88747D94, -343, -84 },
|
|
{ 0xB94470938FA89BCF, -316, -76 },
|
|
{ 0x8A08F0F8BF0F156B, -289, -68 },
|
|
{ 0xCDB02555653131B6, -263, -60 },
|
|
{ 0x993FE2C6D07B7FAC, -236, -52 },
|
|
{ 0xE45C10C42A2B3B06, -210, -44 },
|
|
{ 0xAA242499697392D3, -183, -36 },
|
|
{ 0xFD87B5F28300CA0E, -157, -28 },
|
|
{ 0xBCE5086492111AEB, -130, -20 },
|
|
{ 0x8CBCCC096F5088CC, -103, -12 },
|
|
{ 0xD1B71758E219652C, -77, -4 },
|
|
{ 0x9C40000000000000, -50, 4 },
|
|
{ 0xE8D4A51000000000, -24, 12 },
|
|
{ 0xAD78EBC5AC620000, 3, 20 },
|
|
{ 0x813F3978F8940984, 30, 28 },
|
|
{ 0xC097CE7BC90715B3, 56, 36 },
|
|
{ 0x8F7E32CE7BEA5C70, 83, 44 },
|
|
{ 0xD5D238A4ABE98068, 109, 52 },
|
|
{ 0x9F4F2726179A2245, 136, 60 },
|
|
{ 0xED63A231D4C4FB27, 162, 68 },
|
|
{ 0xB0DE65388CC8ADA8, 189, 76 },
|
|
{ 0x83C7088E1AAB65DB, 216, 84 },
|
|
{ 0xC45D1DF942711D9A, 242, 92 },
|
|
{ 0x924D692CA61BE758, 269, 100 },
|
|
{ 0xDA01EE641A708DEA, 295, 108 },
|
|
{ 0xA26DA3999AEF774A, 322, 116 },
|
|
{ 0xF209787BB47D6B85, 348, 124 },
|
|
{ 0xB454E4A179DD1877, 375, 132 },
|
|
{ 0x865B86925B9BC5C2, 402, 140 },
|
|
{ 0xC83553C5C8965D3D, 428, 148 },
|
|
{ 0x952AB45CFA97A0B3, 455, 156 },
|
|
{ 0xDE469FBD99A05FE3, 481, 164 },
|
|
{ 0xA59BC234DB398C25, 508, 172 },
|
|
{ 0xF6C69A72A3989F5C, 534, 180 },
|
|
{ 0xB7DCBF5354E9BECE, 561, 188 },
|
|
{ 0x88FCF317F22241E2, 588, 196 },
|
|
{ 0xCC20CE9BD35C78A5, 614, 204 },
|
|
{ 0x98165AF37B2153DF, 641, 212 },
|
|
{ 0xE2A0B5DC971F303A, 667, 220 },
|
|
{ 0xA8D9D1535CE3B396, 694, 228 },
|
|
{ 0xFB9B7CD9A4A7443C, 720, 236 },
|
|
{ 0xBB764C4CA7A44410, 747, 244 },
|
|
{ 0x8BAB8EEFB6409C1A, 774, 252 },
|
|
{ 0xD01FEF10A657842C, 800, 260 },
|
|
{ 0x9B10A4E5E9913129, 827, 268 },
|
|
{ 0xE7109BFBA19C0C9D, 853, 276 },
|
|
{ 0xAC2820D9623BF429, 880, 284 },
|
|
{ 0x80444B5E7AA7CF85, 907, 292 },
|
|
{ 0xBF21E44003ACDD2D, 933, 300 },
|
|
{ 0x8E679C2F5E44FF8F, 960, 308 },
|
|
{ 0xD433179D9C8CB841, 986, 316 },
|
|
{ 0x9E19DB92B4E31BA9, 1013, 324 },
|
|
}
|
|
};
|
|
|
|
// This computation gives exactly the same results for k as
|
|
// k = ceil((kAlpha - e - 1) * 0.30102999566398114)
|
|
// for |e| <= 1500, but doesn't require floating-point operations.
|
|
// NB: log_10(2) ~= 78913 / 2^18
|
|
JSON_ASSERT(e >= -1500);
|
|
JSON_ASSERT(e <= 1500);
|
|
const int f = kAlpha - e - 1;
|
|
const int k = ((f * 78913) / (1 << 18)) + static_cast<int>(f > 0);
|
|
|
|
const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
|
|
JSON_ASSERT(index >= 0);
|
|
JSON_ASSERT(static_cast<std::size_t>(index) < kCachedPowers.size());
|
|
|
|
const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)];
|
|
JSON_ASSERT(kAlpha <= cached.e + e + 64);
|
|
JSON_ASSERT(kGamma >= cached.e + e + 64);
|
|
|
|
return cached;
|
|
}
|
|
|
|
/*!
|
|
For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
|
|
For n == 0, returns 1 and sets pow10 := 1.
|
|
*/
|
|
inline int find_largest_pow10(const std::uint32_t n, std::uint32_t& pow10)
|
|
{
|
|
// LCOV_EXCL_START
|
|
if (n >= 1000000000)
|
|
{
|
|
pow10 = 1000000000;
|
|
return 10;
|
|
}
|
|
// LCOV_EXCL_STOP
|
|
if (n >= 100000000)
|
|
{
|
|
pow10 = 100000000;
|
|
return 9;
|
|
}
|
|
if (n >= 10000000)
|
|
{
|
|
pow10 = 10000000;
|
|
return 8;
|
|
}
|
|
if (n >= 1000000)
|
|
{
|
|
pow10 = 1000000;
|
|
return 7;
|
|
}
|
|
if (n >= 100000)
|
|
{
|
|
pow10 = 100000;
|
|
return 6;
|
|
}
|
|
if (n >= 10000)
|
|
{
|
|
pow10 = 10000;
|
|
return 5;
|
|
}
|
|
if (n >= 1000)
|
|
{
|
|
pow10 = 1000;
|
|
return 4;
|
|
}
|
|
if (n >= 100)
|
|
{
|
|
pow10 = 100;
|
|
return 3;
|
|
}
|
|
if (n >= 10)
|
|
{
|
|
pow10 = 10;
|
|
return 2;
|
|
}
|
|
|
|
pow10 = 1;
|
|
return 1;
|
|
}
|
|
|
|
inline void grisu2_round(char* buf, int len, std::uint64_t dist, std::uint64_t delta,
|
|
std::uint64_t rest, std::uint64_t ten_k)
|
|
{
|
|
JSON_ASSERT(len >= 1);
|
|
JSON_ASSERT(dist <= delta);
|
|
JSON_ASSERT(rest <= delta);
|
|
JSON_ASSERT(ten_k > 0);
|
|
|
|
// <--------------------------- delta ---->
|
|
// <---- dist --------->
|
|
// --------------[------------------+-------------------]--------------
|
|
// M- w M+
|
|
//
|
|
// ten_k
|
|
// <------>
|
|
// <---- rest ---->
|
|
// --------------[------------------+----+--------------]--------------
|
|
// w V
|
|
// = buf * 10^k
|
|
//
|
|
// ten_k represents a unit-in-the-last-place in the decimal representation
|
|
// stored in buf.
|
|
// Decrement buf by ten_k while this takes buf closer to w.
|
|
|
|
// The tests are written in this order to avoid overflow in unsigned
|
|
// integer arithmetic.
|
|
|
|
while (rest < dist
|
|
&& delta - rest >= ten_k
|
|
&& (rest + ten_k < dist || dist - rest > rest + ten_k - dist))
|
|
{
|
|
JSON_ASSERT(buf[len - 1] != '0');
|
|
buf[len - 1]--;
|
|
rest += ten_k;
|
|
}
|
|
}
|
|
|
|
/*!
|
|
Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
|
|
M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
|
|
*/
|
|
inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,
|
|
diyfp M_minus, diyfp w, diyfp M_plus)
|
|
{
|
|
static_assert(kAlpha >= -60, "internal error");
|
|
static_assert(kGamma <= -32, "internal error");
|
|
|
|
// Generates the digits (and the exponent) of a decimal floating-point
|
|
// number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
|
|
// w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
|
|
//
|
|
// <--------------------------- delta ---->
|
|
// <---- dist --------->
|
|
// --------------[------------------+-------------------]--------------
|
|
// M- w M+
|
|
//
|
|
// Grisu2 generates the digits of M+ from left to right and stops as soon as
|
|
// V is in [M-,M+].
|
|
|
|
JSON_ASSERT(M_plus.e >= kAlpha);
|
|
JSON_ASSERT(M_plus.e <= kGamma);
|
|
|
|
std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
|
|
std::uint64_t dist = diyfp::sub(M_plus, w ).f; // (significand of (M+ - w ), implicit exponent is e)
|
|
|
|
// Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
|
|
//
|
|
// M+ = f * 2^e
|
|
// = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
|
|
// = ((p1 ) * 2^-e + (p2 )) * 2^e
|
|
// = p1 + p2 * 2^e
|
|
|
|
const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e);
|
|
|
|
auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
|
|
std::uint64_t p2 = M_plus.f & (one.f - 1); // p2 = f mod 2^-e
|
|
|
|
// 1)
|
|
//
|
|
// Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]
|
|
|
|
JSON_ASSERT(p1 > 0);
|
|
|
|
std::uint32_t pow10{};
|
|
const int k = find_largest_pow10(p1, pow10);
|
|
|
|
// 10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
|
|
//
|
|
// p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
|
|
// = (d[k-1] ) * 10^(k-1) + (p1 mod 10^(k-1))
|
|
//
|
|
// M+ = p1 + p2 * 2^e
|
|
// = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1)) + p2 * 2^e
|
|
// = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
|
|
// = d[k-1] * 10^(k-1) + ( rest) * 2^e
|
|
//
|
|
// Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
|
|
//
|
|
// p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]
|
|
//
|
|
// but stop as soon as
|
|
//
|
|
// rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e
|
|
|
|
int n = k;
|
|
while (n > 0)
|
|
{
|
|
// Invariants:
|
|
// M+ = buffer * 10^n + (p1 + p2 * 2^e) (buffer = 0 for n = k)
|
|
// pow10 = 10^(n-1) <= p1 < 10^n
|
|
//
|
|
const std::uint32_t d = p1 / pow10; // d = p1 div 10^(n-1)
|
|
const std::uint32_t r = p1 % pow10; // r = p1 mod 10^(n-1)
|
|
//
|
|
// M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e
|
|
// = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)
|
|
//
|
|
JSON_ASSERT(d <= 9);
|
|
buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
|
|
//
|
|
// M+ = buffer * 10^(n-1) + (r + p2 * 2^e)
|
|
//
|
|
p1 = r;
|
|
n--;
|
|
//
|
|
// M+ = buffer * 10^n + (p1 + p2 * 2^e)
|
|
// pow10 = 10^n
|
|
//
|
|
|
|
// Now check if enough digits have been generated.
|
|
// Compute
|
|
//
|
|
// p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e
|
|
//
|
|
// Note:
|
|
// Since rest and delta share the same exponent e, it suffices to
|
|
// compare the significands.
|
|
const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2;
|
|
if (rest <= delta)
|
|
{
|
|
// V = buffer * 10^n, with M- <= V <= M+.
|
|
|
|
decimal_exponent += n;
|
|
|
|
// We may now just stop. But instead, it looks as if the buffer
|
|
// could be decremented to bring V closer to w.
|
|
//
|
|
// pow10 = 10^n is now 1 ulp in the decimal representation V.
|
|
// The rounding procedure works with diyfp's with an implicit
|
|
// exponent of e.
|
|
//
|
|
// 10^n = (10^n * 2^-e) * 2^e = ulp * 2^e
|
|
//
|
|
const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e;
|
|
grisu2_round(buffer, length, dist, delta, rest, ten_n);
|
|
|
|
return;
|
|
}
|
|
|
|
pow10 /= 10;
|
|
//
|
|
// pow10 = 10^(n-1) <= p1 < 10^n
|
|
// Invariants restored.
|
|
}
|
|
|
|
// 2)
|
|
//
|
|
// The digits of the integral part have been generated:
|
|
//
|
|
// M+ = d[k-1]...d[1]d[0] + p2 * 2^e
|
|
// = buffer + p2 * 2^e
|
|
//
|
|
// Now generate the digits of the fractional part p2 * 2^e.
|
|
//
|
|
// Note:
|
|
// No decimal point is generated: the exponent is adjusted instead.
|
|
//
|
|
// p2 actually represents the fraction
|
|
//
|
|
// p2 * 2^e
|
|
// = p2 / 2^-e
|
|
// = d[-1] / 10^1 + d[-2] / 10^2 + ...
|
|
//
|
|
// Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)
|
|
//
|
|
// p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m
|
|
// + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)
|
|
//
|
|
// using
|
|
//
|
|
// 10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)
|
|
// = ( d) * 2^-e + ( r)
|
|
//
|
|
// or
|
|
// 10^m * p2 * 2^e = d + r * 2^e
|
|
//
|
|
// i.e.
|
|
//
|
|
// M+ = buffer + p2 * 2^e
|
|
// = buffer + 10^-m * (d + r * 2^e)
|
|
// = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e
|
|
//
|
|
// and stop as soon as 10^-m * r * 2^e <= delta * 2^e
|
|
|
|
JSON_ASSERT(p2 > delta);
|
|
|
|
int m = 0;
|
|
for (;;)
|
|
{
|
|
// Invariant:
|
|
// M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e
|
|
// = buffer * 10^-m + 10^-m * (p2 ) * 2^e
|
|
// = buffer * 10^-m + 10^-m * (1/10 * (10 * p2) ) * 2^e
|
|
// = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e
|
|
//
|
|
JSON_ASSERT(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10);
|
|
p2 *= 10;
|
|
const std::uint64_t d = p2 >> -one.e; // d = (10 * p2) div 2^-e
|
|
const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e
|
|
//
|
|
// M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e
|
|
// = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))
|
|
// = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e
|
|
//
|
|
JSON_ASSERT(d <= 9);
|
|
buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
|
|
//
|
|
// M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e
|
|
//
|
|
p2 = r;
|
|
m++;
|
|
//
|
|
// M+ = buffer * 10^-m + 10^-m * p2 * 2^e
|
|
// Invariant restored.
|
|
|
|
// Check if enough digits have been generated.
|
|
//
|
|
// 10^-m * p2 * 2^e <= delta * 2^e
|
|
// p2 * 2^e <= 10^m * delta * 2^e
|
|
// p2 <= 10^m * delta
|
|
delta *= 10;
|
|
dist *= 10;
|
|
if (p2 <= delta)
|
|
{
|
|
break;
|
|
}
|
|
}
|
|
|
|
// V = buffer * 10^-m, with M- <= V <= M+.
|
|
|
|
decimal_exponent -= m;
|
|
|
|
// 1 ulp in the decimal representation is now 10^-m.
|
|
// Since delta and dist are now scaled by 10^m, we need to do the
|
|
// same with ulp in order to keep the units in sync.
|
|
//
|
|
// 10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e
|
|
//
|
|
const std::uint64_t ten_m = one.f;
|
|
grisu2_round(buffer, length, dist, delta, p2, ten_m);
|
|
|
|
// By construction this algorithm generates the shortest possible decimal
|
|
// number (Loitsch, Theorem 6.2) which rounds back to w.
|
|
// For an input number of precision p, at least
|
|
//
|
|
// N = 1 + ceil(p * log_10(2))
|
|
//
|
|
// decimal digits are sufficient to identify all binary floating-point
|
|
// numbers (Matula, "In-and-Out conversions").
|
|
// This implies that the algorithm does not produce more than N decimal
|
|
// digits.
|
|
//
|
|
// N = 17 for p = 53 (IEEE double precision)
|
|
// N = 9 for p = 24 (IEEE single precision)
|
|
}
|
|
|
|
/*!
|
|
v = buf * 10^decimal_exponent
|
|
len is the length of the buffer (number of decimal digits)
|
|
The buffer must be large enough, i.e. >= max_digits10.
|
|
*/
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
inline void grisu2(char* buf, int& len, int& decimal_exponent,
|
|
diyfp m_minus, diyfp v, diyfp m_plus)
|
|
{
|
|
JSON_ASSERT(m_plus.e == m_minus.e);
|
|
JSON_ASSERT(m_plus.e == v.e);
|
|
|
|
// --------(-----------------------+-----------------------)-------- (A)
|
|
// m- v m+
|
|
//
|
|
// --------------------(-----------+-----------------------)-------- (B)
|
|
// m- v m+
|
|
//
|
|
// First scale v (and m- and m+) such that the exponent is in the range
|
|
// [alpha, gamma].
|
|
|
|
const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);
|
|
|
|
const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k
|
|
|
|
// The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
|
|
const diyfp w = diyfp::mul(v, c_minus_k);
|
|
const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
|
|
const diyfp w_plus = diyfp::mul(m_plus, c_minus_k);
|
|
|
|
// ----(---+---)---------------(---+---)---------------(---+---)----
|
|
// w- w w+
|
|
// = c*m- = c*v = c*m+
|
|
//
|
|
// diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
|
|
// w+ are now off by a small amount.
|
|
// In fact:
|
|
//
|
|
// w - v * 10^k < 1 ulp
|
|
//
|
|
// To account for this inaccuracy, add resp. subtract 1 ulp.
|
|
//
|
|
// --------+---[---------------(---+---)---------------]---+--------
|
|
// w- M- w M+ w+
|
|
//
|
|
// Now any number in [M-, M+] (bounds included) will round to w when input,
|
|
// regardless of how the input rounding algorithm breaks ties.
|
|
//
|
|
// And digit_gen generates the shortest possible such number in [M-, M+].
|
|
// Note that this does not mean that Grisu2 always generates the shortest
|
|
// possible number in the interval (m-, m+).
|
|
const diyfp M_minus(w_minus.f + 1, w_minus.e);
|
|
const diyfp M_plus (w_plus.f - 1, w_plus.e );
|
|
|
|
decimal_exponent = -cached.k; // = -(-k) = k
|
|
|
|
grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
|
|
}
|
|
|
|
/*!
|
|
v = buf * 10^decimal_exponent
|
|
len is the length of the buffer (number of decimal digits)
|
|
The buffer must be large enough, i.e. >= max_digits10.
|
|
*/
|
|
template<typename FloatType>
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
void grisu2(char* buf, int& len, int& decimal_exponent, FloatType value)
|
|
{
|
|
static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3,
|
|
"internal error: not enough precision");
|
|
|
|
JSON_ASSERT(std::isfinite(value));
|
|
JSON_ASSERT(value > 0);
|
|
|
|
// If the neighbors (and boundaries) of 'value' are always computed for double-precision
|
|
// numbers, all float's can be recovered using strtod (and strtof). However, the resulting
|
|
// decimal representations are not exactly "short".
|
|
//
|
|
// The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars)
|
|
// says "value is converted to a string as if by std::sprintf in the default ("C") locale"
|
|
// and since sprintf promotes floats to doubles, I think this is exactly what 'std::to_chars'
|
|
// does.
|
|
// On the other hand, the documentation for 'std::to_chars' requires that "parsing the
|
|
// representation using the corresponding std::from_chars function recovers value exactly". That
|
|
// indicates that single precision floating-point numbers should be recovered using
|
|
// 'std::strtof'.
|
|
//
|
|
// NB: If the neighbors are computed for single-precision numbers, there is a single float
|
|
// (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision
|
|
// value is off by 1 ulp.
|
|
#if 0 // NOLINT(readability-avoid-unconditional-preprocessor-if)
|
|
const boundaries w = compute_boundaries(static_cast<double>(value));
|
|
#else
|
|
const boundaries w = compute_boundaries(value);
|
|
#endif
|
|
|
|
grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);
|
|
}
|
|
|
|
/*!
|
|
@brief the shortest digits of a positive finite float (other than double): Grisu2
|
|
*/
|
|
template<typename FloatType>
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
void shortest_digits(char* buf, int& len, int& decimal_exponent, FloatType value)
|
|
{
|
|
grisu2(buf, len, decimal_exponent, value);
|
|
}
|
|
|
|
/*!
|
|
@brief the shortest digits of a positive finite double: the conversion of
|
|
Zmij (see zmij.hpp), which always finds the shortest digits that read back as
|
|
the same value (Grisu2 does not for about one double in a thousand), and the
|
|
closest of them if there are several
|
|
|
|
v = buf * 10^decimal_exponent, as for grisu2()
|
|
*/
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
inline void shortest_digits(char* buf, int& len, int& decimal_exponent, double value)
|
|
{
|
|
static_assert(std::numeric_limits<double>::is_iec559 && std::numeric_limits<double>::digits == 53,
|
|
"internal error: the conversion of Zmij needs IEEE 754 binary64 doubles");
|
|
JSON_ASSERT(std::isfinite(value));
|
|
JSON_ASSERT(value > 0);
|
|
|
|
std::uint64_t bits = 0;
|
|
std::memcpy(&bits, &value, sizeof(bits));
|
|
zmij::decimal d = zmij::to_decimal(bits);
|
|
// without trailing zeros (up to 16): 8, 4, 2, 1 at a time
|
|
while (d.significand % 100000000 == 0)
|
|
{
|
|
d.significand /= 100000000;
|
|
d.exponent += 8;
|
|
}
|
|
if (d.significand % 10000 == 0)
|
|
{
|
|
d.significand /= 10000;
|
|
d.exponent += 4;
|
|
}
|
|
if (d.significand % 100 == 0)
|
|
{
|
|
d.significand /= 100;
|
|
d.exponent += 2;
|
|
}
|
|
if (d.significand % 10 == 0)
|
|
{
|
|
d.significand /= 10;
|
|
d.exponent += 1;
|
|
}
|
|
// at most 17 digits, written from the back two at a time
|
|
static constexpr const char* pairs =
|
|
"00010203040506070809101112131415161718192021222324252627282930313233343536373839"
|
|
"40414243444546474849505152535455565758596061626364656667686970717273747576777879"
|
|
"8081828384858687888990919293949596979899";
|
|
std::array<char, 20> digits{};
|
|
std::size_t n = digits.size();
|
|
while (d.significand >= 100)
|
|
{
|
|
const auto i = static_cast<std::size_t>(d.significand % 100) * 2;
|
|
d.significand /= 100;
|
|
n -= 2;
|
|
digits[n] = pairs[i];
|
|
digits[n + 1] = pairs[i + 1];
|
|
}
|
|
if (d.significand >= 10)
|
|
{
|
|
const auto i = static_cast<std::size_t>(d.significand) * 2;
|
|
n -= 2;
|
|
digits[n] = pairs[i];
|
|
digits[n + 1] = pairs[i + 1];
|
|
}
|
|
else
|
|
{
|
|
digits[--n] = static_cast<char>('0' + d.significand);
|
|
}
|
|
len = static_cast<int>(digits.size() - n);
|
|
std::memcpy(buf, digits.data() + n, static_cast<std::size_t>(len));
|
|
decimal_exponent = d.exponent;
|
|
}
|
|
|
|
/*!
|
|
@brief appends a decimal representation of e to buf
|
|
@return a pointer to the element following the exponent.
|
|
@pre -1000 < e < 1000
|
|
*/
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
inline char* append_exponent(char* buf, int e)
|
|
{
|
|
JSON_ASSERT(e > -1000);
|
|
JSON_ASSERT(e < 1000);
|
|
|
|
if (e < 0)
|
|
{
|
|
e = -e;
|
|
*buf++ = '-';
|
|
}
|
|
else
|
|
{
|
|
*buf++ = '+';
|
|
}
|
|
|
|
auto k = static_cast<std::uint32_t>(e);
|
|
if (k < 10)
|
|
{
|
|
// Always print at least two digits in the exponent.
|
|
// This is for compatibility with printf("%g").
|
|
*buf++ = '0';
|
|
*buf++ = static_cast<char>('0' + k);
|
|
}
|
|
else if (k < 100)
|
|
{
|
|
*buf++ = static_cast<char>('0' + (k / 10));
|
|
k %= 10;
|
|
*buf++ = static_cast<char>('0' + k);
|
|
}
|
|
else
|
|
{
|
|
*buf++ = static_cast<char>('0' + (k / 100));
|
|
k %= 100;
|
|
*buf++ = static_cast<char>('0' + (k / 10));
|
|
k %= 10;
|
|
*buf++ = static_cast<char>('0' + k);
|
|
}
|
|
|
|
return buf;
|
|
}
|
|
|
|
/*!
|
|
@brief prettify v = buf * 10^decimal_exponent
|
|
|
|
If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point
|
|
notation. Otherwise it will be printed in exponential notation.
|
|
|
|
@pre min_exp < 0
|
|
@pre max_exp > 0
|
|
*/
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
inline char* format_buffer(char* buf, int len, int decimal_exponent,
|
|
int min_exp, int max_exp)
|
|
{
|
|
JSON_ASSERT(min_exp < 0);
|
|
JSON_ASSERT(max_exp > 0);
|
|
|
|
const int k = len;
|
|
const int n = len + decimal_exponent;
|
|
|
|
// v = buf * 10^(n-k)
|
|
// k is the length of the buffer (number of decimal digits)
|
|
// n is the position of the decimal point relative to the start of the buffer.
|
|
|
|
if (k <= n && n <= max_exp)
|
|
{
|
|
// digits[000]
|
|
// len <= max_exp + 2
|
|
|
|
std::memset(buf + k, '0', static_cast<size_t>(n) - static_cast<size_t>(k));
|
|
// Make it look like a floating-point number (#362, #378)
|
|
buf[n + 0] = '.';
|
|
buf[n + 1] = '0';
|
|
return buf + (static_cast<size_t>(n) + 2);
|
|
}
|
|
|
|
if (0 < n && n <= max_exp)
|
|
{
|
|
// dig.its
|
|
// len <= max_digits10 + 1
|
|
|
|
JSON_ASSERT(k > n);
|
|
|
|
std::memmove(buf + (static_cast<size_t>(n) + 1), buf + n, static_cast<size_t>(k) - static_cast<size_t>(n));
|
|
buf[n] = '.';
|
|
return buf + (static_cast<size_t>(k) + 1U);
|
|
}
|
|
|
|
if (min_exp < n && n <= 0)
|
|
{
|
|
// 0.[000]digits
|
|
// len <= 2 + (-min_exp - 1) + max_digits10
|
|
|
|
std::memmove(buf + (2 + static_cast<size_t>(-n)), buf, static_cast<size_t>(k));
|
|
buf[0] = '0';
|
|
buf[1] = '.';
|
|
std::memset(buf + 2, '0', static_cast<size_t>(-n));
|
|
return buf + (2U + static_cast<size_t>(-n) + static_cast<size_t>(k));
|
|
}
|
|
|
|
if (k == 1)
|
|
{
|
|
// dE+123
|
|
// len <= 1 + 5
|
|
|
|
buf += 1;
|
|
}
|
|
else
|
|
{
|
|
// d.igitsE+123
|
|
// len <= max_digits10 + 1 + 5
|
|
|
|
std::memmove(buf + 2, buf + 1, static_cast<size_t>(k) - 1);
|
|
buf[1] = '.';
|
|
buf += 1 + static_cast<size_t>(k);
|
|
}
|
|
|
|
*buf++ = 'e';
|
|
return append_exponent(buf, n - 1);
|
|
}
|
|
|
|
/// eight decimal digits (a value below 10^8) as bytes 0..9, the first digit
|
|
/// in the most significant byte: three steps that divide all lanes at once
|
|
/// by a multiplication (the conversion of Xiang JunBo, as in Zmij)
|
|
inline std::uint64_t eight_digit_bytes(std::uint64_t abcdefgh) noexcept
|
|
{
|
|
const std::uint64_t abcd_efgh = abcdefgh + (((std::uint64_t{1} << 32u) - 10000u) * ((abcdefgh * (((std::uint64_t{1} << 40u) / 10000u) + 1u)) >> 40u));
|
|
const std::uint64_t ab_cd_ef_gh = abcd_efgh + (((std::uint64_t{1} << 16u) - 100u) * (((abcd_efgh * (((std::uint64_t{1} << 19u) / 100u) + 1u)) >> 19u) & 0x7F0000007Fu));
|
|
return ab_cd_ef_gh + (((std::uint64_t{1} << 8u) - 10u) * (((ab_cd_ef_gh * (((std::uint64_t{1} << 10u) / 10u) + 1u)) >> 10u) & 0x000F000F000F000Fu));
|
|
}
|
|
|
|
/// store the bytes of v, the most significant one first (one byte swap and
|
|
/// one store where the byte order is known: compilers do not reliably merge
|
|
/// the byte stores once this is inlined)
|
|
inline void store_msb_first(char* p, std::uint64_t v) noexcept
|
|
{
|
|
#if defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
|
|
v = __builtin_bswap64(v);
|
|
std::memcpy(p, &v, sizeof(v));
|
|
#elif defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__) && __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
|
|
std::memcpy(p, &v, sizeof(v));
|
|
#elif defined(_MSC_VER) // (little-endian on all its targets)
|
|
v = _byteswap_uint64(v);
|
|
std::memcpy(p, &v, sizeof(v));
|
|
#else
|
|
for (unsigned i = 0; i < 8; ++i)
|
|
{
|
|
p[i] = static_cast<char>(v >> (56u - (8u * i)));
|
|
}
|
|
#endif
|
|
}
|
|
|
|
/*!
|
|
@brief digits * 10^exp for a double, in the layout of format_buffer()
|
|
|
|
The layout is that of format_buffer() with min_exp -4 and max_exp 15 (the
|
|
digits10 of double). The digits are converted eight at a time and placed
|
|
with fixed-size moves instead of per-digit loops and moves of the buffer.
|
|
|
|
@param[in] digits the digits (not 0, at most 17 digits; trailing zeros allowed)
|
|
@param[in] exp the decimal exponent of the last digit
|
|
@return a pointer past the text; up to 41 bytes at @a first are written
|
|
(some beyond the returned end)
|
|
*/
|
|
JSON_HEDLEY_NON_NULL(1)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
inline char* write_decimal(char* first, std::uint64_t digits, int exp) noexcept
|
|
{
|
|
JSON_ASSERT(digits != 0 && digits < 100000000000000000u);
|
|
const std::uint64_t upper = digits / 100000000u;
|
|
const std::uint64_t b0 = upper / 100000000u; // (one digit: it is its own byte)
|
|
const std::uint64_t b1 = eight_digit_bytes(upper % 100000000u);
|
|
const std::uint64_t b2 = eight_digit_bytes(digits % 100000000u);
|
|
// leading and trailing zero digits: zero bytes, counted without division
|
|
int leading = 16;
|
|
int zeros = 16;
|
|
if (b0 != 0)
|
|
{
|
|
leading = count_leading_zeros(b0) / 8;
|
|
}
|
|
else if (b1 != 0)
|
|
{
|
|
leading = 8 + (count_leading_zeros(b1) / 8);
|
|
}
|
|
else
|
|
{
|
|
leading += count_leading_zeros(b2) / 8;
|
|
}
|
|
if (b2 != 0)
|
|
{
|
|
zeros = count_trailing_zeros(b2) / 8;
|
|
}
|
|
else if (b1 != 0)
|
|
{
|
|
zeros = 8 + (count_trailing_zeros(b1) / 8);
|
|
}
|
|
// (else: 16, b0 is the one digit that is not 0)
|
|
// the digits as text at text + leading, then '0's, so that fixed-size
|
|
// moves need not check how many digits there are
|
|
std::array<char, 64> text; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
|
|
store_msb_first(text.data(), b0 + 0x3030303030303030u);
|
|
store_msb_first(text.data() + 8, b1 + 0x3030303030303030u);
|
|
store_msb_first(text.data() + 16, b2 + 0x3030303030303030u);
|
|
std::memset(text.data() + 24, '0', 40);
|
|
const int k = 24 - leading - zeros; // significant digits
|
|
const int n = k + exp + zeros; // position of the decimal point after the first digit
|
|
const char* const s0 = text.data() + leading;
|
|
|
|
if (-4 < n && n <= 15)
|
|
{
|
|
// "0.[000]digits" (n <= 0) is the digits after 1 - n leading '0's
|
|
// with the point after the first; "digits[000].0" (n >= k) and
|
|
// "dig.its" put the point after n characters
|
|
const int pad = n <= 0 ? 1 - n : 0;
|
|
const char* const s = s0 - pad;
|
|
const int len = k + pad;
|
|
const int point = n + pad;
|
|
std::memcpy(first, s, 16);
|
|
std::memcpy(first + point + 1, s + point, 24);
|
|
first[point] = '.';
|
|
return first + (point >= len ? point + 2 : len + 1);
|
|
}
|
|
|
|
// d.igitse+XX, with at least two exponent digits (as append_exponent())
|
|
std::memcpy(first, s0, 16);
|
|
std::memcpy(first + 2, s0 + 1, 16);
|
|
first[1] = '.';
|
|
char* const end = first + (k == 1 ? 1 : k + 1);
|
|
const int e = n - 1;
|
|
const auto ea = static_cast<unsigned>(e < 0 ? -e : e);
|
|
const bool three = ea >= 100;
|
|
end[0] = 'e';
|
|
end[1] = e < 0 ? '-' : '+';
|
|
end[2] = static_cast<char>('0' + (three ? ea / 100 : (ea / 10) % 10));
|
|
end[3] = static_cast<char>('0' + (three ? (ea / 10) % 10 : ea % 10));
|
|
end[4] = static_cast<char>('0' + (ea % 10));
|
|
return end + (three ? 5 : 4);
|
|
}
|
|
|
|
/// a positive finite float (other than double): Grisu2 and format_buffer()
|
|
template<typename FloatType>
|
|
JSON_HEDLEY_NON_NULL(1, 2)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
char* write_positive(char* first, const char* last, FloatType value)
|
|
{
|
|
JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10);
|
|
|
|
// Compute v = buffer * 10^decimal_exponent.
|
|
// The decimal digits are stored in the buffer, which needs to be interpreted
|
|
// as an unsigned decimal integer.
|
|
// len is the length of the buffer, i.e., the number of decimal digits.
|
|
int len = 0;
|
|
int decimal_exponent = 0;
|
|
shortest_digits(first, len, decimal_exponent, value);
|
|
|
|
JSON_ASSERT(len <= std::numeric_limits<FloatType>::max_digits10);
|
|
|
|
// Format the buffer like printf("%.*g", prec, value)
|
|
constexpr int kMinExp = -4;
|
|
// Use digits10 here to increase compatibility with version 2.
|
|
constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;
|
|
|
|
JSON_ASSERT(last - first >= kMaxExp + 2);
|
|
JSON_ASSERT(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10);
|
|
JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6);
|
|
|
|
return format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);
|
|
}
|
|
|
|
/// a positive finite double: the shortest digits (Zmij), laid out by
|
|
/// write_decimal() (through a local buffer if [first, last) is shorter than
|
|
/// the 41 bytes it may write)
|
|
JSON_HEDLEY_NON_NULL(1, 2)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
inline char* write_positive(char* first, const char* last, double value)
|
|
{
|
|
static_assert(std::numeric_limits<double>::is_iec559 && std::numeric_limits<double>::digits == 53,
|
|
"internal error: the conversion of Zmij needs IEEE 754 binary64 doubles");
|
|
std::uint64_t bits = 0;
|
|
std::memcpy(&bits, &value, sizeof(bits));
|
|
const zmij::decimal d = zmij::to_decimal(bits);
|
|
if (JSON_HEDLEY_LIKELY(last - first >= 41))
|
|
{
|
|
return write_decimal(first, d.significand, d.exponent);
|
|
}
|
|
std::array<char, 64> buf; // NOLINT(cppcoreguidelines-pro-type-member-init,hicpp-member-init): written before read
|
|
const auto len = static_cast<std::size_t>(write_decimal(buf.data(), d.significand, d.exponent) - buf.data());
|
|
JSON_ASSERT(static_cast<std::size_t>(last - first) >= len);
|
|
std::memcpy(first, buf.data(), len);
|
|
return first + len;
|
|
}
|
|
|
|
} // namespace dtoa_impl
|
|
|
|
/*!
|
|
@brief generates a decimal representation of the floating-point number value in [first, last).
|
|
|
|
The format of the resulting decimal representation is similar to printf's %g
|
|
format. Returns an iterator pointing past-the-end of the decimal representation.
|
|
|
|
@note The input number must be finite, i.e. NaN's and Inf's are not supported.
|
|
@note The buffer must be large enough.
|
|
@note The result is NOT null-terminated.
|
|
*/
|
|
template<typename FloatType>
|
|
JSON_HEDLEY_NON_NULL(1, 2)
|
|
JSON_HEDLEY_RETURNS_NON_NULL
|
|
char* to_chars(char* first, const char* last, FloatType value)
|
|
{
|
|
JSON_ASSERT(std::isfinite(value));
|
|
|
|
// Use signbit(value) instead of (value < 0) since signbit works for -0.
|
|
if (std::signbit(value))
|
|
{
|
|
value = -value;
|
|
*first++ = '-';
|
|
}
|
|
|
|
#ifdef __GNUC__
|
|
JSON_HEDLEY_DIAGNOSTIC_PUSH
|
|
JSON_HEDLEY_PRAGMA(GCC diagnostic ignored "-Wfloat-equal")
|
|
#endif
|
|
if (value == 0) // +-0
|
|
{
|
|
*first++ = '0';
|
|
// Make it look like a floating-point number (#362, #378)
|
|
*first++ = '.';
|
|
*first++ = '0';
|
|
return first;
|
|
}
|
|
#ifdef __GNUC__
|
|
JSON_HEDLEY_DIAGNOSTIC_POP
|
|
#endif
|
|
|
|
return dtoa_impl::write_positive(first, last, value);
|
|
}
|
|
|
|
} // namespace detail
|
|
NLOHMANN_JSON_NAMESPACE_END
|