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>

tests/src/unit-binary_formats.cpp

@@ -38,7 +38,7 @@ TEST_CASE("Binary Formats")
         const auto ubjson_2_size = json::to_ubjson(j, true).size();
         const auto ubjson_3_size = json::to_ubjson(j, true, true).size();
 
-        CHECK(json_size == 2090303);
+        CHECK(json_size == 2090234);
         CHECK(bjdata_1_size == 1112030);
         CHECK(bjdata_2_size == 1224148);
         CHECK(bjdata_3_size == 1224148);
@@ -51,16 +51,16 @@ TEST_CASE("Binary Formats")
         CHECK(ubjson_3_size == 1169069);
 
         CHECK((100.0 * double(json_size) / double(json_size)) == Approx(100.0));
-        CHECK((100.0 * double(bjdata_1_size) / double(json_size)) == Approx(53.199));
-        CHECK((100.0 * double(bjdata_2_size) / double(json_size)) == Approx(58.563));
-        CHECK((100.0 * double(bjdata_3_size) / double(json_size)) == Approx(58.563));
-        CHECK((100.0 * double(bon8_size) / double(json_size)) == Approx(50.509));
-        CHECK((100.0 * double(bson_size) / double(json_size)) == Approx(85.849));
-        CHECK((100.0 * double(cbor_size) / double(json_size)) == Approx(50.497));
-        CHECK((100.0 * double(msgpack_size) / double(json_size)) == Approx(50.526));
-        CHECK((100.0 * double(ubjson_1_size) / double(json_size)) == Approx(53.199));
-        CHECK((100.0 * double(ubjson_2_size) / double(json_size)) == Approx(58.563));
-        CHECK((100.0 * double(ubjson_3_size) / double(json_size)) == Approx(55.928));
+        CHECK((100.0 * double(bjdata_1_size) / double(json_size)) == Approx(53.201));
+        CHECK((100.0 * double(bjdata_2_size) / double(json_size)) == Approx(58.565));
+        CHECK((100.0 * double(bjdata_3_size) / double(json_size)) == Approx(58.565));
+        CHECK((100.0 * double(bon8_size) / double(json_size)) == Approx(50.511));
+        CHECK((100.0 * double(bson_size) / double(json_size)) == Approx(85.853));
+        CHECK((100.0 * double(cbor_size) / double(json_size)) == Approx(50.499));
+        CHECK((100.0 * double(msgpack_size) / double(json_size)) == Approx(50.528));
+        CHECK((100.0 * double(ubjson_1_size) / double(json_size)) == Approx(53.201));
+        CHECK((100.0 * double(ubjson_2_size) / double(json_size)) == Approx(58.565));
+        CHECK((100.0 * double(ubjson_3_size) / double(json_size)) == Approx(55.930));
     }
 
     SECTION("twitter.json")