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* Use bit twiddling. This requires inclusion of math_private.h
and inclusion of float.h in s_roundl.c. Raise invalid exception.
* Use literal integer constants where possible. Let the compiler
do the appropriate conversion.
* In s_roundf.c, use an F suffix on float constants instead of
promoting float to double and then converting the result back
to float. In s_roundl.c, use an L suffix.
* In s_roundl.c, use the ENTERI and RETURNI macros. This requires
the inclusion of fpmath.h and on __i386__ class hardware ieeefp.h.
Reviewed by: bde
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- in round-towards-minus-infinity mode, on all machines, roundf(x) never
worked for 0 < |x| < 0.5 (2*0x3effffff cases in all, or almost half of
float space). It was -0 for 0 < x < 0.5 and 0 for -0.5 < x < 0, but
should be 0 and -0, respectively. This is because t = ceilf(|x|) = 1
for these args, and when we adjust t from 1 to 0 by subtracting 1, we
get -0 in this rounding mode, but we want and expected to get 0.
- in round-towards-minus-infinity, round towards zero and round-to-nearest
modes, on machines that evaluate float expressions in float precision
(most machines except i386's), roundf(x) never worked for |x| =
<float value immediately below 0.5> (2 cases in all). It was +-1 but
should have been +-0. This is because t = ceilf(|x|) = 1 for these
args, and when we try to classify |x| by subtracting it from 1 we
get an unexpected rounding error -- the result is 0.5 after rounding
to float in all 3 rounding modes, so we we have forgotten the
difference between |x| and 0.5 and end up returning the same value
as for +-0.5.
The fix is to use floorf() instead of ceilf() and to add 1 instead of
-1 in the adjustment. With floorf() all the expressions used are
always evaluated exactly so there are no rounding problems, and with
adjustments of +1 we don't go near -0 when adjusting.
Attempted to fix round() and roundl() by cloning the fix for roundf().
This has only been tested for round(), only on args representable as
floats. Double expressions are evaluated in double precision even on
i386's, so round(0.5-epsilon) was broken even on i386's. roundl()
must be completely broken on i386's since long double precision is not
really supported. There seem to be no other dependencies on the
precision.
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