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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>