cvs commit: src/lib/msun/src e_rem_pio2.c e_rem_pio2f.c
bde at FreeBSD.org
Thu Feb 28 16:22:37 UTC 2008
bde 2008-02-28 16:22:36 UTC
FreeBSD src repository
lib/msun/src e_rem_pio2.c e_rem_pio2f.c
Fix and improve some magic numbers for the "medium size" case.
This case goes up to about 2**20pi/2, but the comment about it said that
it goes up to about 2**19pi/2.
It went too far above 2**pi/2, giving a multiplier fn with 21 significant
bits in some cases. This would be harmful except for a numerical
accident. It happens that the terms of the approximation to pi/2,
when rounded to 33 bits so that multiplications by 20-bit fn's are
exact, happen to be rounded to 32 bits so multiplications by 21-bit
fn's are exact too, so the bug only complicates the error analysis (we
might lose a bit of accuracy but have bits to spare).
The bogus comment in e_rem_pio2.c was copied and the code was changed
to be bug-for-bug compatible with it, except the limit was made 90
ulps smaller than necessary. The approximation to pi/2 was not
modified except for discarding some of it.
The same rough error analysis that justifies the limit of 2**20pi/2
for double precision only justifies a limit of 2**18pi/2 for float
precision. We depended on exhaustive testing to check the magic numbers
for float precision. More exaustive testing shows that we can go up
to 2**28pi/2 using a 53+25 bit approximation to pi/2 for float precision,
with a the maximum error for cosf() and sinf() unchanged at 0.5009
ulps despite the maximum error in rem_pio2f being ~0.25 ulps. Implement
Revision Changes Path
1.18 +1 -1 src/lib/msun/src/e_rem_pio2.c
1.29 +3 -3 src/lib/msun/src/e_rem_pio2f.c
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