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Convert floats with Eisel-Lemire when std::from_chars is unavailable
Float tokens that Clinger's fast path cannot convert (e.g. the 17-digit coordinates of canada.json) went to strtod unless std::from_chars was available. It is not used in C++11/14, and not with libc++, which does not define __cpp_lib_to_chars. The Eisel-Lemire algorithm (after fast_float's compute_float) now converts them with integer arithmetic, correctly rounded for any token with at most 19 significant digits. Longer tokens are truncated; the result is used if w and w + 1 round alike, else strtod decides as before. Overflow still yields infinity (out_of_range.406). The table of powers of five (fast_float's) lives in pow5_table.hpp; a unit test recomputes every entry with big-integer arithmetic. Further tests: known values generated with Python (whose float() is correctly rounded), 200,000 round trips through to_chars, and the 128-bit multiplication and leading-zero count against big-integer references (both with and without a 128-bit type). Checked against strtod on 6.5 million tokens, among them 60,000 exact halfway cases: no difference. json::parse on canada.json: -8.6% (C++11), -7.6% (C++17, Apple clang); other files unchanged. Compile time of a TU including json.hpp: +0.7%. Signed-off-by: Niels Lohmann <mail@nlohmann.me>
This commit is contained in:
Niels Lohmann
@@ -12,10 +12,14 @@
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#include <nlohmann/json.hpp>
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using nlohmann::json;
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#include <array> // array
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#include <cfloat> // FLT_EVAL_METHOD
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#include <cstdint> // uint32_t, uint64_t
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#include <cstdlib> // strtod
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#include <cstring> // memcpy
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#include <sstream> // stringstream
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#include <string> // string
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#include <utility> // pair
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#include <vector> // vector
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namespace
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@@ -700,3 +704,612 @@ TEST_CASE("parse_float_fast declines what it cannot convert exactly")
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CHECK_FALSE(fast("1e23", out));
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CHECK_FALSE(fast("1e-23", out));
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}
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namespace
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{
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// arbitrary-precision unsigned integers, just enough to recompute the table of
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// powers of five (little-endian 32-bit limbs)
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using big_uint = std::vector<std::uint32_t>;
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void big_trim(big_uint& a)
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{
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while (!a.empty() && a.back() == 0)
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{
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a.pop_back();
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}
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}
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big_uint big_from(std::uint64_t high, std::uint64_t low)
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{
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big_uint a = {static_cast<std::uint32_t>(low), static_cast<std::uint32_t>(low >> 32u),
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static_cast<std::uint32_t>(high), static_cast<std::uint32_t>(high >> 32u)
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};
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big_trim(a);
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return a;
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}
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big_uint big_mul(const big_uint& a, const big_uint& b)
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{
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big_uint r(a.size() + b.size(), 0);
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for (std::size_t i = 0; i < a.size(); ++i)
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{
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std::uint64_t carry = 0;
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for (std::size_t j = 0; j < b.size(); ++j)
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{
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const std::uint64_t t = (static_cast<std::uint64_t>(a[i]) * b[j]) + r[i + j] + carry;
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r[i + j] = static_cast<std::uint32_t>(t);
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carry = t >> 32u;
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}
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r[i + b.size()] = static_cast<std::uint32_t>(carry);
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}
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big_trim(r);
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return r;
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}
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big_uint big_shl(const big_uint& a, std::size_t s)
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{
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big_uint r(s / 32, 0);
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std::uint32_t carry = 0;
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for (const std::uint32_t x : a)
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{
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const std::uint64_t t = static_cast<std::uint64_t>(x) << (s % 32);
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r.push_back(static_cast<std::uint32_t>(t) | carry);
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carry = static_cast<std::uint32_t>(t >> 32u);
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}
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r.push_back(carry);
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big_trim(r);
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return r;
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}
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// a + 1 (add) or a - 1 (!add, a > 0)
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big_uint big_step(big_uint a, bool add)
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{
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for (auto& x : a)
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{
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const std::uint32_t old = x;
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x = add ? x + 1 : x - 1;
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if ((add && x > old) || (!add && x < old))
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{
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break;
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}
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}
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if (add && (a.empty() || a.back() == 0))
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{
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a.push_back(1);
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}
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big_trim(a);
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return a;
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}
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bool big_less_equal(const big_uint& a, const big_uint& b)
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{
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if (a.size() != b.size())
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{
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return a.size() < b.size();
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}
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for (std::size_t i = a.size(); i-- > 0;)
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{
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if (a[i] != b[i])
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{
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return a[i] < b[i];
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}
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}
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return true;
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}
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std::size_t big_bit_length(const big_uint& a)
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{
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std::size_t n = a.size() * 32;
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for (std::uint32_t top = a.back(); (top & 0x80000000u) == 0; top <<= 1u)
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{
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--n;
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}
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return n;
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}
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std::uint64_t bits_of(double d)
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{
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std::uint64_t b = 0;
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std::memcpy(&b, &d, sizeof(b));
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return b;
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}
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bool eisel_lemire(const std::string& s, double& out)
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{
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return nlohmann::detail::parse_float_eisel_lemire(s.data(), s.data() + s.size(), out);
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}
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// significant digits of a token, without trailing zeros
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std::size_t significant_digits(const std::string& s)
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{
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std::string digits;
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for (const char c : s)
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{
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if (c == 'e' || c == 'E')
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{
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break;
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}
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if (c >= '0' && c <= '9' && !(digits.empty() && c == '0'))
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{
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digits += c;
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}
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}
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while (!digits.empty() && digits.back() == '0')
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{
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digits.pop_back();
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}
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return digits.size();
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}
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} // namespace
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TEST_CASE("Eisel-Lemire float conversion")
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{
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SECTION("the table of powers of five")
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{
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// Recompute every entry the way fast_float's table_generation.py
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// defines it, using only multiplications and comparisons: for q >= 0
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// the most significant 128 bits of 5^q; for q < 0 floor(2^b / 5^-q) + 1
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// for b = z + 127 (q >= -27), or that value for b = 2z + 128 cut to
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// its most significant 128 bits (q < -27), where z is the bit length
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// of 5^-q.
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const auto& table = nlohmann::detail::pow5_128();
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big_uint power5 = {1};
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for (std::int64_t q = 0; q <= nlohmann::detail::pow5_128_largest_power; ++q)
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{
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const auto index = static_cast<std::size_t>(2 * (q - nlohmann::detail::pow5_128_smallest_power));
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const big_uint entry = big_from(table[index], table[index + 1]);
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const std::size_t bits = big_bit_length(power5);
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if (bits <= 128)
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{
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CHECK(entry == big_shl(power5, 128 - bits));
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}
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else
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{
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// floor(5^q / 2^(bits - 128))
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CHECK(big_less_equal(big_shl(entry, bits - 128), power5));
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CHECK_FALSE(big_less_equal(big_shl(big_step(entry, true), bits - 128), power5));
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}
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power5 = big_mul(power5, {5});
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}
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power5 = {5};
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for (std::int64_t q = -1; q >= nlohmann::detail::pow5_128_smallest_power; --q)
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{
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const auto index = static_cast<std::size_t>(2 * (q - nlohmann::detail::pow5_128_smallest_power));
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const big_uint entry = big_from(table[index], table[index + 1]);
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CHECK(big_bit_length(entry) == 128);
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const std::size_t z = big_bit_length(power5);
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const big_uint two_b = big_shl({1}, q >= -27 ? z + 127 : (2 * z) + 128);
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// c = floor(2^b / p) + 1, stored as floor(c / 2^s):
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// (entry * 2^s - 1) * p <= 2^b < ((entry + 1) * 2^s - 1) * p
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const std::size_t s = q >= -27 ? 0 : z + 1;
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CHECK(big_less_equal(big_mul(big_step(big_shl(entry, s), false), power5), two_b));
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CHECK_FALSE(big_less_equal(big_mul(big_step(big_shl(big_step(entry, true), s), false), power5), two_b));
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power5 = big_mul(power5, {5});
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}
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}
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SECTION("128-bit products and leading zeros")
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{
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// whichever implementation the compiler gets (with or without a
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// 128-bit integer type or a builtin)
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std::uint64_t state = 42;
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for (int i = 0; i < 10000; ++i)
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{
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state ^= state << 13u;
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state ^= state >> 7u;
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state ^= state << 17u;
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const std::uint64_t a = state;
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const std::uint64_t b = (state * 0x9E3779B97F4A7C15u) >> (i % 64);
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const auto product = nlohmann::detail::full_multiplication(a, b);
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CHECK(big_from(product.high, product.low) == big_mul(big_from(0, a), big_from(0, b)));
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const int k = i % 64;
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const std::uint64_t x = (std::uint64_t{1} << k) | (a & ((std::uint64_t{1} << k) - 1));
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CHECK(nlohmann::detail::count_leading_zeros(x) == 63 - k);
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}
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}
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SECTION("known values")
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{
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// Generated with Python, whose float() is correctly rounded:
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// cases = [<hard cases>, 2**53 + 2k + 1, 2**54 + 4k + 2, and exact midpoints
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// between neighbouring doubles, also 1e-60 above and below them]
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// print('{"%s", 0x%016xu},' % (s, struct.unpack('<Q', struct.pack('<d', float(s)))[0]))
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const std::vector<std::pair<std::string, std::uint64_t>> known =
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{
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{"0", 0x0000000000000000u},
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{"-0", 0x8000000000000000u},
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{"0.0", 0x0000000000000000u},
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{"-0.0", 0x8000000000000000u},
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{"0e5", 0x0000000000000000u},
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{"0.000e-9", 0x0000000000000000u},
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{"1", 0x3ff0000000000000u},
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{"-1", 0xbff0000000000000u},
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{"0.1", 0x3fb999999999999au},
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{"0.3", 0x3fd3333333333333u},
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{"1.5", 0x3ff8000000000000u},
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{"-2.5e-3", 0xbf647ae147ae147bu},
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{"1e23", 0x44b52d02c7e14af6u},
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{"1e22", 0x4480f0cf064dd592u},
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{"8.98846567431158e307", 0x7fe0000000000000u},
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{"2.2250738585072011e-308", 0x000fffffffffffffu},
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{"2.2250738585072012e-308", 0x0010000000000000u},
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{"2.2250738585072014e-308", 0x0010000000000000u},
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{"4.9406564584124654e-324", 0x0000000000000001u},
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{"2.4703282292062327e-324", 0x0000000000000000u},
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{"2.4703282292062328e-324", 0x0000000000000001u},
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{"1e-324", 0x0000000000000000u},
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{"3e-324", 0x0000000000000001u},
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{"1.7976931348623157e308", 0x7fefffffffffffffu},
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{"1.7976931348623158e308", 0x7fefffffffffffffu},
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{"1.7976931348623159e308", 0x7ff0000000000000u},
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{"1e308", 0x7fe1ccf385ebc8a0u},
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{"1e309", 0x7ff0000000000000u},
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{"-1e400", 0xfff0000000000000u},
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{"1e-400", 0x0000000000000000u},
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{"9007199254740991", 0x433fffffffffffffu},
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{"9007199254740992", 0x4340000000000000u},
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{"9007199254740993", 0x4340000000000000u},
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{"9007199254740995", 0x4340000000000002u},
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{"18014398509481986", 0x4350000000000000u},
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{"18014398509481990", 0x4350000000000002u},
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{"7.2057594037927933e16", 0x4370000000000000u},
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{"123456789012345678901234567890", 0x45f8ee90ff6c373eu},
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{"1.000000000000000111", 0x3ff0000000000000u},
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{"1.0000000000000001110223", 0x3ff0000000000000u},
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{"1.00000000000000011102230246251565404236316680908203125", 0x3ff0000000000000u},
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{"1.00000000000000011102230246251565404236316680908203126", 0x3ff0000000000001u},
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{"0.00000000000000000000000000000000000000000000000000000000000001", 0x3310747ddddf22a8u},
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{"100000000000000000000000000000000000000000000", 0x4911efc659cf7d4cu},
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{"1234567890123456789", 0x43b12210f47de981u},
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{"12345678901234567890", 0x43e56a95319d63e1u},
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{"1234567890123456789.5", 0x43b12210f47de981u},
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{"0.1234567890123456789012345", 0x3fbf9add3746f65fu},
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{"4.4501477170144023e-308", 0x001fffffffffffffu},
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{"2.4406961166466664e-309", 0x0001c14ae5310a48u},
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{"5e-324", 0x0000000000000001u},
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{"1.0e-307", 0x0031fa182c40c60du},
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{"179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368", 0x7fefffffffffffffu},
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{"4.9e-324", 0x0000000000000001u},
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{"9007199254740993", 0x4340000000000000u},
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{"18014398509481986", 0x4350000000000000u},
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{"9007199254740995", 0x4340000000000002u},
|
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{"18014398509481990", 0x4350000000000002u},
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{"9007199254740997", 0x4340000000000002u},
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{"18014398509481994", 0x4350000000000002u},
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{"9007199254740999", 0x4340000000000004u},
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{"18014398509481998", 0x4350000000000004u},
|
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{"9007199254741001", 0x4340000000000004u},
|
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{"18014398509482002", 0x4350000000000004u},
|
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{"9007199254741003", 0x4340000000000006u},
|
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{"18014398509482006", 0x4350000000000006u},
|
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{"9007199254741005", 0x4340000000000006u},
|
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{"18014398509482010", 0x4350000000000006u},
|
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{"9007199254741007", 0x4340000000000008u},
|
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{"18014398509482014", 0x4350000000000008u},
|
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{"9007199254741009", 0x4340000000000008u},
|
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{"18014398509482018", 0x4350000000000008u},
|
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{"9007199254741011", 0x434000000000000au},
|
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{"18014398509482022", 0x435000000000000au},
|
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{"9007199254741013", 0x434000000000000au},
|
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{"18014398509482026", 0x435000000000000au},
|
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{"9007199254741015", 0x434000000000000cu},
|
||||
{"18014398509482030", 0x435000000000000cu},
|
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{"9007199254741017", 0x434000000000000cu},
|
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{"18014398509482034", 0x435000000000000cu},
|
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{"9007199254741019", 0x434000000000000eu},
|
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{"18014398509482038", 0x435000000000000eu},
|
||||
{"9007199254741021", 0x434000000000000eu},
|
||||
{"18014398509482042", 0x435000000000000eu},
|
||||
{"9007199254741023", 0x4340000000000010u},
|
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{"18014398509482046", 0x4350000000000010u},
|
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{"9007199254741025", 0x4340000000000010u},
|
||||
{"18014398509482050", 0x4350000000000010u},
|
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{"9007199254741027", 0x4340000000000012u},
|
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{"18014398509482054", 0x4350000000000012u},
|
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{"9007199254741029", 0x4340000000000012u},
|
||||
{"18014398509482058", 0x4350000000000012u},
|
||||
{"9007199254741031", 0x4340000000000014u},
|
||||
{"18014398509482062", 0x4350000000000014u},
|
||||
{"9007199254741033", 0x4340000000000014u},
|
||||
{"18014398509482066", 0x4350000000000014u},
|
||||
{"9007199254741035", 0x4340000000000016u},
|
||||
{"18014398509482070", 0x4350000000000016u},
|
||||
{"9007199254741037", 0x4340000000000016u},
|
||||
{"18014398509482074", 0x4350000000000016u},
|
||||
{"9007199254741039", 0x4340000000000018u},
|
||||
{"18014398509482078", 0x4350000000000018u},
|
||||
{"9007199254741041", 0x4340000000000018u},
|
||||
{"18014398509482082", 0x4350000000000018u},
|
||||
{"9007199254741043", 0x434000000000001au},
|
||||
{"18014398509482086", 0x435000000000001au},
|
||||
{"9007199254741045", 0x434000000000001au},
|
||||
{"18014398509482090", 0x435000000000001au},
|
||||
{"9007199254741047", 0x434000000000001cu},
|
||||
{"18014398509482094", 0x435000000000001cu},
|
||||
{"9007199254741049", 0x434000000000001cu},
|
||||
{"18014398509482098", 0x435000000000001cu},
|
||||
{"9007199254741051", 0x434000000000001eu},
|
||||
{"18014398509482102", 0x435000000000001eu},
|
||||
{"9007199254741053", 0x434000000000001eu},
|
||||
{"18014398509482106", 0x435000000000001eu},
|
||||
{"9007199254741055", 0x4340000000000020u},
|
||||
{"18014398509482110", 0x4350000000000020u},
|
||||
{"9007199254741057", 0x4340000000000020u},
|
||||
{"18014398509482114", 0x4350000000000020u},
|
||||
{"9007199254741059", 0x4340000000000022u},
|
||||
{"18014398509482118", 0x4350000000000022u},
|
||||
{"9007199254741061", 0x4340000000000022u},
|
||||
{"18014398509482122", 0x4350000000000022u},
|
||||
{"9007199254741063", 0x4340000000000024u},
|
||||
{"18014398509482126", 0x4350000000000024u},
|
||||
{"9007199254741065", 0x4340000000000024u},
|
||||
{"18014398509482130", 0x4350000000000024u},
|
||||
{"9007199254741067", 0x4340000000000026u},
|
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|
||||
{"0.0000000216458400594294836451424756990254139044083103726734407246112823486328125", 0x3e573df694e72fb8u},
|
||||
{"0.00000002164584005942948364514247569902541390440831037267344072461128234863281251", 0x3e573df694e72fb9u},
|
||||
{"0.0000000216458400594294836451424756990254139044083103726734407246112723486328125", 0x3e573df694e72fb8u},
|
||||
{"5107.79271041116453488939441740512847900390625", 0x40b3f3caef11cb26u},
|
||||
{"5107.792710411164534889394417405128479003906251", 0x40b3f3caef11cb27u},
|
||||
{"5107.792710411164534889394417405128479003906249999999999999999", 0x40b3f3caef11cb26u},
|
||||
{"734059.8035226609208621084690093994140625", 0x412666d79b67527cu},
|
||||
{"734059.80352266092086210846900939941406251", 0x412666d79b67527du},
|
||||
{"734059.8035226609208621084690093994140624999999999999999999999", 0x412666d79b67527cu},
|
||||
{"61431562016722684", 0x436b47f5c40021e0u},
|
||||
{"614315620167226841", 0x43a10cf99a80152cu},
|
||||
{"61431562016722683.99999999999999999999999999999999999999999999", 0x436b47f5c40021dfu},
|
||||
{"2.0060840449445034305853141631814651191234588623046875", 0x40000c75cab08326u},
|
||||
{"2.00608404494450343058531416318146511912345886230468751", 0x40000c75cab08326u},
|
||||
{"2.006084044944503430585314163181465119123458862304687499999999", 0x40000c75cab08325u},
|
||||
{"0.0000001760623599453036952716420489480075861621344301966018974781036376953125", 0x3e87a174e55262cau},
|
||||
{"0.00000017606235994530369527164204894800758616213443019660189747810363769531251", 0x3e87a174e55262cbu},
|
||||
{"0.0000001760623599453036952716420489480075861621344301966018974781035376953125", 0x3e87a174e55262cau},
|
||||
{"0.833085849636964581588216560703585855662822723388671875", 0x3feaa8a3a7de6fb6u},
|
||||
{"0.8330858496369645815882165607035858556628227233886718751", 0x3feaa8a3a7de6fb6u},
|
||||
{"0.8330858496369645815882165607035858556628227233886718749999999", 0x3feaa8a3a7de6fb5u},
|
||||
{"45031428.4182307310402393341064453125", 0x418579002358895au},
|
||||
{"45031428.41823073104023933410644531251", 0x418579002358895bu},
|
||||
{"45031428.41823073104023933410644531249999999999999999999999999", 0x418579002358895au},
|
||||
{"5003361733758455296", 0x43d15be0bf39dd24u},
|
||||
{"50033617337584552961", 0x4405b2d8ef08546cu},
|
||||
{"5003361733758455295.999999999999999999999999999999999999999999", 0x43d15be0bf39dd23u},
|
||||
};
|
||||
|
||||
for (const auto& c : known)
|
||||
{
|
||||
CAPTURE(c.first);
|
||||
double out = 0;
|
||||
if (eisel_lemire(c.first, out))
|
||||
{
|
||||
CHECK(bits_of(out) == c.second);
|
||||
}
|
||||
else
|
||||
{
|
||||
// only tokens with more than 19 significant digits are left to
|
||||
// strtod: those whose value lies too close to a tie
|
||||
CHECK(significant_digits(c.first) > 19);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
SECTION("round trip")
|
||||
{
|
||||
// every double written by to_chars and read back, also with trailing
|
||||
// digits that make the token longer than 19 digits
|
||||
std::uint64_t state = 5295;
|
||||
std::size_t declined = 0;
|
||||
for (int i = 0; i < 200000; ++i)
|
||||
{
|
||||
state ^= state << 13u;
|
||||
state ^= state >> 7u;
|
||||
state ^= state << 17u;
|
||||
std::uint64_t b = state;
|
||||
if ((b & 0x7FF0000000000000u) == 0x7FF0000000000000u)
|
||||
{
|
||||
continue; // infinity or NaN
|
||||
}
|
||||
if (i % 4 == 0)
|
||||
{
|
||||
b &= 0x800FFFFFFFFFFFFFu; // subnormals
|
||||
}
|
||||
double d = 0;
|
||||
std::memcpy(&d, &b, sizeof(d));
|
||||
|
||||
std::array<char, 64> buffer{};
|
||||
const char* end = nlohmann::detail::to_chars(buffer.data(), buffer.data() + buffer.size(), d);
|
||||
const std::string token(buffer.data(), static_cast<std::size_t>(end - buffer.data()));
|
||||
CAPTURE(token);
|
||||
double out = 0;
|
||||
REQUIRE(eisel_lemire(token, out));
|
||||
CHECK(bits_of(out) == b);
|
||||
|
||||
// insert digits before the exponent: the value moves by far less
|
||||
// than the distance to the rounding boundary, so it must not change
|
||||
std::string longer = token;
|
||||
const std::size_t e = longer.find('e');
|
||||
const std::string extra = longer.find('.') == std::string::npos ? ".000000000000000000001" : "000000000000000000001";
|
||||
longer.insert(e == std::string::npos ? longer.size() : e, extra);
|
||||
CAPTURE(longer);
|
||||
if (eisel_lemire(longer, out))
|
||||
{
|
||||
CHECK(bits_of(out) == b);
|
||||
}
|
||||
else
|
||||
{
|
||||
// w and w + 1 round differently: only when the value is very
|
||||
// close to a rounding boundary
|
||||
++declined;
|
||||
}
|
||||
}
|
||||
CHECK(declined < 1000); // 107 of the 200,000
|
||||
}
|
||||
|
||||
SECTION("used by the lexer")
|
||||
{
|
||||
// 17 significant digits: beyond Clinger's fast path
|
||||
CHECK(bits_of(json::parse("-65.613616999999977").get<double>()) == bits_of(-65.613616999999977));
|
||||
CHECK(bits_of(json::parse("2.2250738585072011e-308").get<double>()) == 0x000FFFFFFFFFFFFFu);
|
||||
CHECK(bits_of(json::parse("4.9406564584124654e-324").get<double>()) == 1u);
|
||||
CHECK_THROWS_WITH_AS(json::parse("1.7976931348623159e308"),
|
||||
"[json.exception.out_of_range.406] number overflow parsing '1.7976931348623159e308'", json::out_of_range&);
|
||||
}
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user