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This makes little difference in float precision, but in double
precision gives a speedup of about 30% on amd64 (A64 CPU) and i386
(A64). This depends on fabs[f]() being inline and efficient. The
bit fiddling (or any use of SET_HIGH_WORD(), which libm does too
much because it was best on old 32-bit machines) always causes
packing overheads and sometimes causes stalls in the packing, since
it operates on only part of a variable in the double precision case.
It apparently did cause stalls in a critical path here.
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fabs(x+0.0)+fabs(y+0.0) when mixing NaNs. This improves
consistency of the result by making it harder for the compiler to reorder
the operands. (FP addition is not necessarily commutative because the
order of operands makes a difference on some machines iff the operands are
both NaNs.)
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precision in software useless, so hypotf() had some errors in the 1-2
ulp range unless there is extra precision in hardware (as happens on
i386).
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|x| or |y| and b is |y| or |x|) when mixing NaN arg(s).
hypot*() had its own foot shooting for mixing NaNs -- it swaps the
args so that |x| in bits is largest, but does this before quieting
signaling NaNs, so on amd64 (where the result of adding NaNs depends
on the order) it gets inconsistent results if setting the quiet bit
makes a difference, just like a similar ia64 and i387 hardware comparison.
The usual fix (see e_powf.c 1.13 for more details) of mixing using
(a+0.0)+-(b+0.0) doesn't work on amd64 if the args are swapped (since
the rder makes a difference with SSE). Fortunately, the original args
are unchanged and don't need to be swapped when we let the hardware
decide the mixing after quieting them, but we need to take their
absolute value.
hypotf() doesn't seem to have any real bugs masked by this non-bug.
On amd64, its maximum error in 2^32 trials on amd64 is now 0.8422 ulps,
and on i386 the maximum error is unchanged and about the same, except
with certain CFLAGS it magically drops to 0.5 (perfect rounding).
Convert to __FBSDID().
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- float ynf(int n, float x) /* wrapper ynf */
+float
+ynf(int n, float x) /* wrapper ynf */
This is because the __STDC__ stuff was indented.
Reviewed by: md5
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Reviewed by: md5
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float versions. Using sqrt() was inefficient.
Obtained from: NetBSD
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and small values:
hypotf(2.3819765e+38, 2.0416943e+38) was NaN instead of 3.1372484e+38
hypotf(-3.4028235e+38, 3.3886450e+38) was NaN instead of Inf
hypotf(-2.8025969e-45, -2.8025969e-45) was 0 instead of 4.2038954e-45
Found by: ucbtest
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This will make a number of things easier in the future, as well as (finally!)
avoiding the Id-smashing problem which has plagued developers for so long.
Boy, I'm glad we're not using sup anymore. This update would have been
insane otherwise.
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-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point. This doesn't help (performance)
much on the i386, but they are still nice to have.
The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code. After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments
Reviewed by: jkh
Submitted by: jtc
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