Write doubles with the shortest digits (Żmij), digits in registers

Write doubles with the conversion of Zmij by Victor Zverovich (MIT),
ported to C++11 (detail/conversions/zmij.hpp). It finds the
shortest decimal that reads back as the same double, and the
closest one if there are several. Grisu2, used until now, is fast
but not always shortest: it sometimes writes a 17th digit where 16
suffice, or a last digit that is not the closest. The layout is
unchanged (1.5, 100.0, 1e+100, -0.0); float keeps Grisu2.

Digits are converted eight at a time with the BCD conversion of
Xiang JunBo, as in Zmij, and written with one byte swap per eight
digits and fixed-size moves instead of per-digit loops. Leading and
trailing zeros are counted from those bytes. to_chars() uses a
local buffer when the caller's is shorter than the 41 bytes this
may write. The powers of ten come from the number-parsing table,
adjusted where it holds values rounded up, and extended with Zmij's
compressed tables beyond 10^308.

write_shortest() converts its 16 digits in one vector register
(SSE2 on x86-64, NEON on 64-bit Arm, both baseline) and inserts the
decimal point inside the register, avoiding a store-forwarding
stall that cost about 25% of the time to write a double. dump()
writes floats and integers straight into the serializer's write
buffer instead of copying them from a member buffer, and small
integers eight digits at a time. read_eight_bytes() and
parse_eight_digits() are marked always-inline, which GCC had been
calling out of line in the number-parsing loops.

Of one million random doubles, about 0.14% are now written with
different digits, always to a value that still reads back as the
same double.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

include/nlohmann/detail/input/number_parse.hpp

@@ -249,8 +249,9 @@ template<typename FloatType>
 using native_float_t = typename std::conditional<std::numeric_limits<FloatType>::digits == 24, float, double>::type;
 
 /// the value of the eight ASCII digits in @a v (see read_eight_bytes()), three
-/// multiplications instead of eight (after simdjson and fast_float)
-inline std::uint32_t parse_eight_digits(std::uint64_t v) noexcept
+/// multiplications instead of eight (after simdjson and fast_float); always
+/// inlined, as GCC otherwise calls it in the number loops
+JSON_HEDLEY_ALWAYS_INLINE std::uint32_t parse_eight_digits(std::uint64_t v) noexcept
 {
     v = ((v & 0x0F0F0F0F0F0F0F0Fu) * 2561u) >> 8u;
     v = ((v & 0x00FF00FF00FF00FFu) * 6553601u) >> 16u;