when upscaling, even the very last digit is needed in cases where the
input is exact; no digits can be discarded. but when downscaling, any
digits less significant than the mantissa bits are destined for the
great bitbucket; the only influence they can have is their presence
(being nonzero). thus, we simply throw them away early. the result is
nearly a 4x performance improvement for processing huge values.
the particular threshold LD_B1B_DIG+3 is not chosen sharply; it's
simply a "safe" distance past the significant bits. it would be nice
to replace it with a sharp bound, but i suspect performance will be
comparable (within a few percent) anyway.
now that this is the first operation, it can rely on the circular
buffer contents not being wrapped when it begins. we limit the number
of digits read slightly in the initial parsing loops too so that this
code does not have to consider the case where it might cause the
circular buffer to wrap; this is perfectly fine because KMAX is chosen
as a power of two for circular-buffer purposes and is much larger than
it otherwise needs to be, anyway.
these changes should not affect performance at all.
upscaling by even one step too much creates 3-29 extra iterations for
the next loop. this is still suboptimal since it always goes by 2^29
rather than using a smaller upscale factor when nearing the target,
but performance on common, small-magnitude, few-digit values has
already more than doubled with this change.
more optimizations on the way...
for example, "1000000000" was being read as "1" due to this loop
exiting early. it's necessary to actually update z and zero the
entries so that the subsequent rounding code does not get confused;
before i did that, spurious inexact exceptions were being raised.
note that there's no need for a precise cutoff, because exponents this
large will always result in overflow or underflow (it's impossible to
read enough digits to compensate for the exponent magnitude; even at a
few nanoseconds per digit it would take hundreds of years).
the immediate benefit is a significant debloating of the float parsing
code by moving the responsibility for keeping track of the number of
characters read to a different module.
by linking shgetc with the stdio buffer logic, counting logic is
defered to buffer refill time, keeping the calls to shgetc fast and
light.
in the future, shgetc will also be useful for integrating the new
float code with scanf, which needs to not only count the characters
consumed, but also limit the number of characters read based on field
width specifiers.
shgetc may also become a useful tool for simplifying the integer
parsing code.
this version is intended to be fully conformant to the ISO C, POSIX,
and IEEE standards for conversion of decimal/hex floating point
strings to float, double, and long double (ld64 or ld80 only at
present) values. in particular, all results are intended to be rounded
correctly according to the current rounding mode. further, this
implementation aims to set the floating point underflow, overflow, and
inexact flags to reflect the conversion performed.
a moderate amount of testing has been performed (by nsz and myself)
prior to integration of the code in musl, but it still may have bugs.
so far, only strto(d|ld|f) use the new code. scanf integration will be
done as a separate commit, and i will add implementations of the wide
character functions later.
the buffer in getaddrinfo really only matters when /etc/hosts is huge,
but in that case, the huge number of syscalls resulting from a tiny
buffer would seriously impact the performance of every name lookup.
the buffer in __dns.c has also been enlarged a bit so that typical
resolv.conf files will fit fully in the buffer. there's no need to
make it so large as to dominate the syscall overhead for large files,
because resolv.conf should never be large.
special care is made to avoid any inexact computations when either arg
is zero (in which case the exact absolute value of the other arg
should be returned) and to support the special condition that
hypot(±inf,nan) yields inf.
hypotl is not yet implemented since avoiding overflow is nontrivial.
the error status is required to be sticky after failure of dlopen or
dlsym until cleared by dlerror. applications and especially libraries
should never rely on this since it is not thread-safe and subject to
race conditions, but glib does anyway.
the old formula atan2(1,sqrt((1+x)/(1-x))) was faster but
could give nan result at x=1 when the rounding mode is
FE_DOWNWARD (so 1-1 == -0 and 2/-0 == -inf), the new formula
gives -0 at x=+-1 with downward rounding.
this has not been tested heavily, but it's known to at least assemble
and run in basic usage cases. it's nearly identical to the
corresponding i386 code, and thus expected to be just as correct or
just as incorrect.
the main practical results of this change are
1. the regex code is no longer subject to LGPL; it's now 2-clause BSD
2. most (all?) popular nonstandard regex extensions are supported
I hesitate to call this a "sync" since both the old and new code are
heavily modified. in one sense, the old code was "more severely"
modified, in that it was actively hostile to non-strictly-conforming
expressions. on the other hand, the new code has eliminated the
useless translation of the entire regex string to wchar_t prior to
compiling, and now only converts multibyte character literals as
needed.
in the future i may use this modified TRE as a basis for writing the
long-planned new regex engine that will avoid multibyte-to-wide
character conversion entirely by compiling multibyte bracket
expressions specific to UTF-8.
old code saved/restored the fenv (the new code is only as slow
as that when inexact is not set before the call, but some other
flag is set and the rounding is inexact, which is rare)
before:
bench_nearbyint_exact 5000000 N 261 ns/op
bench_nearbyint_inexact_set 5000000 N 262 ns/op
bench_nearbyint_inexact_unset 5000000 N 261 ns/op
after:
bench_nearbyint_exact 10000000 N 94.99 ns/op
bench_nearbyint_inexact_set 25000000 N 65.81 ns/op
bench_nearbyint_inexact_unset 10000000 N 94.97 ns/op
the fscale instruction is slow everywhere, probably because it
involves a costly and unnecessary integer truncation operation that
ends up being a no-op in common usages. instead, construct a floating
point scale value with integer arithmetic and simply multiply by it,
when possible.
for float and double, this is always possible by going to the
next-larger type. we use some cheap but effective saturating
arithmetic tricks to make sure even very large-magnitude exponents
fit. for long double, if the scaling exponent is too large to fit in
the exponent of a long double value, we simply fallback to the
expensive fscale method.
on atom cpu, these changes speed up scalbn by over 30%. (min rdtsc
timing dropped from 110 cycles to 70 cycles.)
exponents (base 2) near 16383 were broken due to (1) wrong cutoff, and
(2) inability to fit the necessary range of scalings into a long
double value.
as a solution, we fall back to using frndint/fscale for insanely large
exponents, and also have to special-case infinities here to avoid
inf-inf generating nan.
thankfully the costly code never runs in normal usage cases.
zero, one, two, half are replaced by const literals
The policy was to use the f suffix for float consts (1.0f),
but don't use suffix for long double consts (these consts
can be exactly represented as double).
Underflow exception is only raised when the result is
invalid, but fmod is always exact. x87 has a denormalization
exception, but that's nonstandard. And the superflous *1.0
will be optimized away by any compiler that does not honor
signaling nans.
Some code assumed ldexp(x, 1) is faster than 2.0*x,
but ldexp is a wrapper around scalbn which uses
multiplications inside, so this optimization is
wrong.
This commit also fixes fmal which accidentally
used ldexp instead of ldexpl loosing precision.
There are various additional changes from the
work-in-progress const cleanups.
Rich Felker
nsz