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Convert float and double with the library's own correctly rounded parser

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float, double, and long double where it is IEEE-754 binary64 (MSVC, Apple
arm64) are now converted by the library itself, correctly rounded and
independent of the locale and of the C and C++ libraries:

- The token is split into sign, significand w (at most 19 digits), and
  decimal exponent q, using the positions of the decimal point and the
  exponent that the scanners already recorded, so no character is
  classified again.
- Clinger's fast path where w and 10^|q| are exact.
- Eisel-Lemire otherwise, now templated for binary32 and binary64.
- For tokens with more than 19 digits whose w and w + 1 round differently,
  an exact big-integer comparison with the midpoint between the two
  candidates (the digit comparison of fast_float, simplified).

This replaces the separate token walks of Clinger's fast path and of
Eisel-Lemire, the significant-digit gate that avoided the former, and, for
float and double, std::from_chars and the locale-aware strtod. std::from_chars
and strtold remain only for other long double formats (x87, binary128,
double-double) and for types that are not IEEE-754. Values are bit-identical
to before wherever the previous conversion was correctly rounded; tokens
converted in a locale with a multi-byte decimal point are now also exact.
Overflow still gives out_of_range.406, underflow a signed zero.

convert_float() is the entry point for other parsers of JSON text: it
converts like the lexer, without allocation for binary32/binary64.

Tests: exact-bit tests for double and float (ties, subnormal and overflow
boundaries, huge exponents, more digits than any midpoint), Eisel-Lemire for
binary32, the round trips of 200,000 doubles and 100,000 floats without
declines, 508 generated hard cases with the expected bits of both formats
(float_hard_cases.hpp) through the converter and both scanners, and
JSON-level overflow/underflow checks for double and float. The locale tests
now check the values in a locale with a multi-byte decimal point.

Docs: the statements that parsing uses strtod/strtof/strtold; the fast_float
credit now names the digit comparison.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>
This commit is contained in:
Niels Lohmann
2026-09-30 13:45:23 +02:00
committed by GitHub
parent 6a073dbae4
commit 44ec53c77b
11 changed files with 2270 additions and 862 deletions
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391
tests/src/unit-class_lexer.cpp
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@@ -13,15 +13,18 @@
using nlohmann::json;
#include <array> // array
#include <cfloat> // FLT_EVAL_METHOD
#include <cstdint> // uint32_t, uint64_t
#include <cstdio> // snprintf
#include <cstdlib> // strtod
#include <cstring> // memcpy
#include <map> // map
#include <sstream> // stringstream
#include <string> // string
#include <utility> // pair
#include <vector> // vector
#include "float_hard_cases.hpp"
namespace
{
// shortcut to scan a string literal
@@ -257,7 +260,7 @@ TEST_CASE("lexer number fast path")
"123456789012345678901234567890", // huge -> float
"0.30000000000000004", "2.2250738585072014e-308", "1e308",
// high-precision / wide-exponent values that exercise the
// std::from_chars (Eisel-Lemire) path beyond the Clinger subset
// Eisel-Lemire path beyond the Clinger subset
"1.7976931348623157e308", "1.2345678901234567e-250",
"9007199254740993", "5e-324", "1e-320"
};
@@ -279,20 +282,18 @@ TEST_CASE("lexer number fast path")
}
}
SECTION("significant-digit gate for the Clinger fast path")
SECTION("significant digits around Clinger's fast path")
{
// Clinger's fast path needs a significand below 2^53, so it cannot
// succeed once the mantissa has 17 or more significant digits (the
// significand would be at least 10^16). The lexer skips the attempt
// there. That is only allowed to save work: every value must still come
// out bit-exactly, and both scanners must agree. In particular the gate
// must not fire for tokens whose leading zeros merely look like extra
// digits - "0.1234567890123456" has 16 significant digits, not 17.
// Clinger's fast path needs a significand of at most 2^53, which
// tokens with 17 or more significant digits exceed. The conversion
// splits the token at the positions the scanners recorded, so leading
// zeros must not count as digits - "0.1234567890123456" has 16
// significant digits, not 17 - and both scanners must agree.
const std::vector<std::string> numbers =
{
"1234567890123456", // 16 significant digits
"12345678901234567", // 17 -> attempt skipped
"123456789012345678", // 18 -> attempt skipped
"12345678901234567", // 17
"123456789012345678", // 18
"0.1234567890123456", // 16: the leading "0" is not significant
"0.12345678901234567", // 17
"0.00000000000000001", // 1, in a long token
@@ -663,46 +664,145 @@ TEST_CASE("lexer string fast path")
}
}
TEST_CASE("parse_float_fast declines what it cannot convert exactly")
namespace
{
// The lexer only hands well-formed numbers to parse_float_fast, so the
// malformed ones below can only be passed to it directly. Declining is
// always safe: the caller then falls back to a slower, exact conversion.
const auto fast = [](const std::string & s, double & out)
// the index of the decimal point (or npos) and of the end of the mantissa of a
// number token, which the lexer records while scanning it
std::pair<std::size_t, std::size_t> float_token_layout(const std::string& s)
{
std::size_t dot = std::string::npos;
std::size_t mantissa_end = s.size();
for (std::size_t i = 0; i < s.size(); ++i)
{
return nlohmann::detail::parse_float_fast(s.data(), s.data() + s.size(), out);
};
double out = 0;
if (s[i] == '.')
{
dot = i;
}
else if (s[i] == 'e' || s[i] == 'E')
{
mantissa_end = i;
break;
}
}
return {dot, mantissa_end};
}
#if defined(FLT_EVAL_METHOD) && FLT_EVAL_METHOD != 0
// without true double precision, the fast path declines everything
CHECK_FALSE(fast("1.5", out));
#else
CHECK(fast("1.5", out));
CHECK(out == 1.5);
CHECK(fast("+2.5e1", out));
CHECK(out == 25.0);
CHECK(fast("-25E-1", out));
CHECK(out == -2.5);
CHECK(fast("1e", out));
CHECK(out == 1.0);
#endif
template<typename FloatType>
FloatType parse_native(const std::string& s)
{
const auto layout = float_token_layout(s);
return nlohmann::detail::parse_float_native<FloatType>(s.data(), s.data() + s.size(), layout.first, layout.second);
}
// not a number
CHECK_FALSE(fast("", out));
CHECK_FALSE(fast("-", out));
CHECK_FALSE(fast(".", out));
CHECK_FALSE(fast("1.2.3", out));
CHECK_FALSE(fast("1x", out));
CHECK_FALSE(fast("1e+", out));
CHECK_FALSE(fast("1e1x", out));
std::uint64_t bits_of(double d)
{
std::uint64_t b = 0;
std::memcpy(&b, &d, sizeof(b));
return b;
}
// numbers that are not represented exactly on the fast path
CHECK_FALSE(fast("12345678901234567890", out));
CHECK_FALSE(fast("1e10000", out));
CHECK_FALSE(fast("9007199254740993", out));
CHECK_FALSE(fast("1e23", out));
CHECK_FALSE(fast("1e-23", out));
std::uint32_t bits_of(float f)
{
std::uint32_t b = 0;
std::memcpy(&b, &f, sizeof(b));
return b;
}
std::uint64_t native_bits64(const std::string& s)
{
return bits_of(parse_native<double>(s));
}
std::uint32_t native_bits32(const std::string& s)
{
return bits_of(parse_native<float>(s));
}
} // namespace
TEST_CASE("parse_float_native rounds correctly")
{
SECTION("double")
{
CHECK(native_bits64("1.5") == 0x3FF8000000000000u);
CHECK(native_bits64("0.1") == 0x3FB999999999999Au);
CHECK(native_bits64("-0.0") == 0x8000000000000000u);
CHECK(native_bits64("0e999999999999999999999") == 0u);
// 2^53 + 1 is exactly between two doubles: ties to even, unless more digits follow
CHECK(native_bits64("9007199254740993") == 0x4340000000000000u);
CHECK(native_bits64("9007199254740993.0000000000000000001") == 0x4340000000000001u);
CHECK(native_bits64("9007199254740992.9999999999999999999") == 0x4340000000000000u);
// 1 + 2^-53 exactly (a tie), and one unit in the 55th digit around it
CHECK(native_bits64("1.00000000000000011102230246251565404236316680908203125") == 0x3FF0000000000000u);
CHECK(native_bits64("1.00000000000000011102230246251565404236316680908203126") == 0x3FF0000000000001u);
CHECK(native_bits64("1.00000000000000011102230246251565404236316680908203124") == 0x3FF0000000000000u);
// subnormal and overflow boundaries
CHECK(native_bits64("2.4703282292062327e-324") == 0u);
CHECK(native_bits64("2.4703282292062328e-324") == 1u);
CHECK(native_bits64("2.2250738585072011e-308") == 0x000FFFFFFFFFFFFFu);
CHECK(native_bits64("2.2250738585072012e-308") == 0x0010000000000000u);
CHECK(native_bits64("1.7976931348623157e308") == 0x7FEFFFFFFFFFFFFFu);
CHECK(native_bits64("1.7976931348623159e308") == 0x7FF0000000000000u);
CHECK(native_bits64("-1e400") == 0xFFF0000000000000u);
CHECK(native_bits64("-1e-400") == 0x8000000000000000u);
// exponents and zeros far beyond the range cancel out
CHECK(native_bits64("0." + std::string(1000, '0') + "1e1001") == 0x3FF0000000000000u);
CHECK(native_bits64("1" + std::string(1000, '0') + "e-1000") == 0x3FF0000000000000u);
CHECK(native_bits64("1e-99999999999999999999999") == 0u);
CHECK(native_bits64("1E+99999999999999999999999") == 0x7FF0000000000000u);
// more digits than any midpoint has (769): only whether a nonzero digit follows matters
const std::string tie = "1.00000000000000011102230246251565404236316680908203125";
CHECK(native_bits64(tie + std::string(800, '0')) == 0x3FF0000000000000u);
CHECK(native_bits64(tie + std::string(800, '0') + "1") == 0x3FF0000000000001u);
}
SECTION("float")
{
CHECK(native_bits32("1.5") == 0x3FC00000u);
CHECK(native_bits32("0.1") == 0x3DCCCCCDu);
CHECK(native_bits32("-0.0") == 0x80000000u);
// 2^24 + 1 is exactly between two floats
CHECK(native_bits32("16777217") == 0x4B800000u);
CHECK(native_bits32("16777217.000000000000000000001") == 0x4B800001u);
CHECK(native_bits32("16777218.999999999999999999999") == 0x4B800001u);
CHECK(native_bits32("16777219") == 0x4B800002u);
// subnormal and overflow boundaries
CHECK(native_bits32("3.4028235677973366e38") == 0x7F7FFFFFu);
CHECK(native_bits32("3.4028235677973367e38") == 0x7F800000u);
CHECK(native_bits32("7.006492321624085e-46") == 0u);
CHECK(native_bits32("7.006492321624086e-46") == 1u);
CHECK(native_bits32("1.1754942e-38") == 0x007FFFFFu);
CHECK(native_bits32("-1.17549435e-38") == 0x80800000u);
CHECK(native_bits32("1e39") == 0x7F800000u);
CHECK(native_bits32("-1e-50") == 0x80000000u);
// not rounded through double: its double would round to another float
CHECK(native_bits32("1.00000005960464477539062500000000001") == 0x3F800001u);
CHECK(native_bits32("9007199254740993") == 0x5A000000u);
}
SECTION("the conversion shared with other parsers")
{
// convert_float() gives the lexer's results, for every type
const std::vector<std::string> tokens =
{
"0", "-0.0", "1.5", "0.1", "1e-400", "-2.5E+3", "123456789012345678901234567890",
"9007199254740993.0000000000000000001", "4.9406564584124654e-324"
};
using float_json = nlohmann::basic_json<std::map, std::vector, std::string, bool, std::int64_t, std::uint64_t, float>;
using long_double_json = nlohmann::basic_json<std::map, std::vector, std::string, bool, std::int64_t, std::uint64_t, long double>;
for (const auto& t : tokens)
{
CAPTURE(t);
const auto layout = float_token_layout(t);
const char* const first = t.data();
const char* const last = first + t.size();
const auto d = nlohmann::detail::convert_float<double>(first, last, layout.first, layout.second);
const auto f = nlohmann::detail::convert_float<float>(first, last, layout.first, layout.second);
const auto ld = nlohmann::detail::convert_float<long double>(first, last, layout.first, layout.second);
CHECK(bits_of(d) == bits_of(json::parse(t).get<double>()));
CHECK(bits_of(f) == bits_of(float_json::parse(t).get<float>()));
CHECK(ld == long_double_json::parse(t).get<long double>());
}
}
}
namespace
@@ -806,40 +906,6 @@ std::size_t big_bit_length(const big_uint& a)
}
return n;
}
std::uint64_t bits_of(double d)
{
std::uint64_t b = 0;
std::memcpy(&b, &d, sizeof(b));
return b;
}
bool eisel_lemire(const std::string& s, double& out)
{
return nlohmann::detail::parse_float_eisel_lemire(s.data(), s.data() + s.size(), out);
}
// significant digits of a token, without trailing zeros
std::size_t significant_digits(const std::string& s)
{
std::string digits;
for (const char c : s)
{
if (c == 'e' || c == 'E')
{
break;
}
if (c >= '0' && c <= '9' && !(digits.empty() && c == '0'))
{
digits += c;
}
}
while (!digits.empty() && digits.back() == '0')
{
digits.pop_back();
}
return digits.size();
}
} // namespace
TEST_CASE("Eisel-Lemire float conversion")
@@ -1237,26 +1303,33 @@ TEST_CASE("Eisel-Lemire float conversion")
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);
}
CHECK(native_bits64(c.first) == c.second);
}
}
SECTION("binary32")
{
using binary32 = nlohmann::detail::ieee_binary_format<24>;
CHECK(nlohmann::detail::eisel_lemire<binary32>(0, 1) == 0x3F800000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-1, 1) == 0x3DCCCCCDu);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-1, 15) == 0x3FC00000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(0, 16777217) == 0x4B800000u); // tie, to even
CHECK(nlohmann::detail::eisel_lemire<binary32>(0, 16777219) == 0x4B800002u); // tie, to even
CHECK(nlohmann::detail::eisel_lemire<binary32>(-45, 1) == 0x00000001u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-46, 7) == 0x00000000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-46, 8) == 0x00000001u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-65, 9999999999999999999u) == 0x00000000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(20, 3402823466385288598u) == 0x7F7FFFFFu);
CHECK(nlohmann::detail::eisel_lemire<binary32>(20, 3402823669209384635u) == 0x7F800000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(39, 1) == 0x7F800000u);
CHECK(nlohmann::detail::eisel_lemire<binary32>(-5, 0) == 0x00000000u);
}
SECTION("round trip")
{
// every double written by to_chars and read back, also with trailing
// digits that make the token longer than 19 digits
// every double written by to_chars and read back, and its 17-digit
// form 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;
@@ -1278,30 +1351,51 @@ TEST_CASE("Eisel-Lemire float conversion")
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);
CHECK(native_bits64(token) == 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;
// insert digits before the exponent of the 17-digit form: that
// form lies strictly inside the rounding interval of the double
// (the shortest one may lie on its boundary), and the digits move
// it by far less than the distance to the boundary, so the value
// must not change
std::array<char, 64> digits17{};
static_cast<void>(std::snprintf(digits17.data(), digits17.size(), "%.17g", d)); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
std::string longer = digits17.data();
const std::size_t e = longer.find('e');
const std::size_t dot = longer.find('.');
const std::string extra = dot == 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(native_bits64(longer) == b);
}
}
SECTION("round trip, binary32")
{
std::uint32_t state = 5295;
for (int i = 0; i < 100000; ++i)
{
state ^= state << 13u;
state ^= state >> 17u;
state ^= state << 5u;
std::uint32_t b = state;
if ((b & 0x7F800000u) == 0x7F800000u)
{
continue; // infinity or NaN
}
if (i % 4 == 0)
{
b &= 0x807FFFFFu; // subnormals
}
float f = 0;
std::memcpy(&f, &b, sizeof(f));
std::array<char, 64> buffer{};
const char* end = nlohmann::detail::to_chars(buffer.data(), buffer.data() + buffer.size(), f);
const std::string token(buffer.data(), static_cast<std::size_t>(end - buffer.data()));
CAPTURE(token);
CHECK(native_bits32(token) == b);
}
CHECK(declined < 1000); // 107 of the 200,000
}
SECTION("used by the lexer")
@@ -1315,3 +1409,76 @@ TEST_CASE("Eisel-Lemire float conversion")
"[json.exception.out_of_range.406] number overflow parsing '1.7976931348623159e308'", json::out_of_range&);
}
}
namespace
{
using float_json = nlohmann::basic_json<std::map, std::vector, std::string, bool, std::int64_t, std::uint64_t, float>;
// the bits of the float that parse() gives for a token, via both scanners;
// the value must be the same for both
template<typename Json, typename Bits>
void check_parse(const std::string& token, Bits expected, Bits infinity)
{
std::stringstream stream(token);
if ((expected & ~(Bits{1} << (8 * sizeof(Bits) - 1))) == infinity)
{
Json _;
CHECK_THROWS_WITH_AS(_ = Json::parse(token), ("[json.exception.out_of_range.406] number overflow parsing '" + token + "'").c_str(), typename Json::out_of_range&);
CHECK_THROWS_WITH_AS(_ = Json::parse(stream), ("[json.exception.out_of_range.406] number overflow parsing '" + token + "'").c_str(), typename Json::out_of_range&);
return;
}
const Json contiguous = Json::parse(token);
const Json streamed = Json::parse(stream);
if (contiguous.is_number_float()) // not an integer that fits
{
CHECK(bits_of(contiguous.template get<typename Json::number_float_t>()) == expected);
CHECK(bits_of(streamed.template get<typename Json::number_float_t>()) == expected);
}
else
{
CHECK(streamed.is_number_integer());
}
}
} // namespace
TEST_CASE("float conversion of hard cases")
{
// see float_hard_cases.hpp
for (const auto& c : float_hard_cases::cases())
{
const std::string token = c.token;
CAPTURE(token);
CHECK(native_bits64(token) == c.bits64);
CHECK(native_bits32(token) == c.bits32);
check_parse<json>(token, c.bits64, std::uint64_t{0x7FF0000000000000u});
check_parse<float_json>(token, c.bits32, std::uint32_t{0x7F800000u});
}
}
TEST_CASE("float overflow and underflow in the parser")
{
SECTION("double")
{
check_parse<json>("1.7976931348623157e308", std::uint64_t{0x7FEFFFFFFFFFFFFFu}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("1.7976931348623159e308", std::uint64_t{0x7FF0000000000000u}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("-1e309", std::uint64_t{0xFFF0000000000000u}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("1" + std::string(400, '0'), std::uint64_t{0x7FF0000000000000u}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("1e99999999999999999999", std::uint64_t{0x7FF0000000000000u}, std::uint64_t{0x7FF0000000000000u});
// an underflow gives a zero with the sign of the token
check_parse<json>("1e-400", std::uint64_t{0}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("-1e-400", std::uint64_t{0x8000000000000000u}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("-2.4703282292062327e-324", std::uint64_t{0x8000000000000000u}, std::uint64_t{0x7FF0000000000000u});
check_parse<json>("0." + std::string(400, '0') + "1", std::uint64_t{0}, std::uint64_t{0x7FF0000000000000u});
}
SECTION("float")
{
check_parse<float_json>("3.4028234e38", std::uint32_t{0x7F7FFFFFu}, std::uint32_t{0x7F800000u});
check_parse<float_json>("3.4028236e38", std::uint32_t{0x7F800000u}, std::uint32_t{0x7F800000u});
check_parse<float_json>("-1e39", std::uint32_t{0xFF800000u}, std::uint32_t{0x7F800000u});
check_parse<float_json>("1e-46", std::uint32_t{0}, std::uint32_t{0x7F800000u});
check_parse<float_json>("-1e-46", std::uint32_t{0x80000000u}, std::uint32_t{0x7F800000u});
check_parse<float_json>("-7.006492321624085e-46", std::uint32_t{0x80000000u}, std::uint32_t{0x7F800000u});
check_parse<float_json>("-7.006492321624086e-46", std::uint32_t{0x80000001u}, std::uint32_t{0x7F800000u});
}
}