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same approach as in sqrt.
sqrtl was broken on aarch64, riscv64 and s390x targets because
of missing quad precision support and on m68k-sf because of
missing ld80 sqrtl.
this implementation is written for quad precision and then
edited to make it work for both m68k and x86 style ld80 formats
too, but it is not expected to be optimal for them.
note: using fp instructions for the initial estimate when such
instructions are available (e.g. double prec sqrt or rsqrt) is
avoided because of fenv correctness.
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for targets where long double is different from double.
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same method as in sqrt, this was tested on all inputs against
an sqrtf instruction. (the only difference found was that x86
sqrtf does not signal the x86 specific input-denormal exception
on negative subnormal inputs while the software sqrtf does,
this is fine as it was designed for ieee754 exceptions only.)
there is known faster method:
"Computing Floating-Point Square Roots via Bivariate Polynomial Evaluation"
that computes sqrtf directly via pipelined polynomial evaluation
which allows more parallelism, but the design does not generalize
easily to higher precisions.
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approximate 1/sqrt(x) and sqrt(x) with goldschmidt iterations.
this is known to be a fast method for computing sqrt, but it is
tricky to get right, so added detailed comments.
use a lookup table for the initial estimate, this adds 256bytes
rodata but it can be shared between sqrt, sqrtf and sqrtl.
this saves one iteration compared to a linear estimate.
this is for soft float targets, but it supports fenv by using a
floating-point operation to get the final result. the result
is correctly rounded in all rounding modes. if fenv support is
turned off then the nearest rounded result is computed and
inexact exception is not signaled.
assumes fast 32bit integer arithmetics and 32 to 64bit mul.
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prior to this change, the canonical name came from the first hosts
file line matching the requested family, so the canonical name for a
given hostname could differ depending on whether it was requested with
AF_UNSPEC or a particular family (AF_INET or AF_INET6). now, the
canonical name is deterministically the first one to appear with the
requested name as an alias.
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the existing code clobbered the canonical name already discovered
every time another matching line was found, which will necessarily be
the case when a hostname has both IPv4 and v6 definitions.
patch by Wolf.
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