Date: Thu, 28 Feb 2008 16:22:36 +0000 (UTC) From: Bruce Evans <bde@FreeBSD.org> To: src-committers@FreeBSD.org, cvs-src@FreeBSD.org, cvs-all@FreeBSD.org Subject: cvs commit: src/lib/msun/src e_rem_pio2.c e_rem_pio2f.c Message-ID: <200802281622.m1SGMaMt050598@repoman.freebsd.org>
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bde 2008-02-28 16:22:36 UTC FreeBSD src repository Modified files: lib/msun/src e_rem_pio2.c e_rem_pio2f.c Log: 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. 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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