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>
