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authornsz <nsz@port70.net>2012-06-20 23:25:58 +0200
committernsz <nsz@port70.net>2012-06-20 23:25:58 +0200
commite5fb6820a42a1f675ba09c15273953e1ace65777 (patch)
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math: fix fma bug on x86 (found by Bruno Haible with gnulib)
The long double adjustment was wrong: The usual check is mant_bits & 0x7ff == 0x400 before doing a mant_bits++ or mant_bits-- adjustment since this is the only case when rounding an inexact ld80 into double can go wrong. (only in nearest rounding mode) After such a check the ++ and -- is ok (the mantissa will end in 0x401 or 0x3ff). fma is a bit different (we need to add 3 numbers with correct rounding: hi_xy + lo_xy + z so we should survive two roundings at different places without precision loss) The adjustment in fma only checks for zero low bits mant_bits & 0x3ff == 0 this way the adjusted value is correct when rounded to double or *less* precision. (this is an important piece in the fma puzzle) Unfortunately in this case the -- is not a correct adjustment because mant_bits might underflow so further checks are needed and this was the source of the bug.
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