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authorbde <bde@FreeBSD.org>2008-02-28 16:22:36 +0000
committerbde <bde@FreeBSD.org>2008-02-28 16:22:36 +0000
commitd32d47f4d6b5747279a9f1453a813d65b719055c (patch)
treea61c5c489fa012672bf9a7437ba6c08d7df398bd /lib/libc/stdlib/lsearch.c
parent81520a3e82a451f4ad187ce4e86f9e5474afa811 (diff)
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Fix and improve some magic numbers for the "medium size" case.
e_rem_pio2.c: 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). e_rem_pio2f.c: 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 this.
Diffstat (limited to 'lib/libc/stdlib/lsearch.c')
0 files changed, 0 insertions, 0 deletions
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