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| H A D | e_powf.c | diff 129950 Tue Jun 01 16:08:39 MDT 2004 bde Fixed 2 bugs in the computation /* t_h=ax+bp[k] High */. (1) The bit for the 1.0 part of bp[k] was right shifted by 4. This seems to have been caused by a typo in converting e_pow.c to e_powf.c. (2) The lower 12 bits of ax+bp[k] were not discarded, so t_h was actually plain ax+bp[k]. This seems to have been caused by a logic error in the conversion. These bugs gave wrong results like: powf(-1.1, 101.0) = -15158.703 (should be -15158.707) hex values: BF8CCCCD 42CA0000 C66CDAD0 C66CDAD4 Fixing (1) gives a result wrong in the opposite direction (hex C66CDAD8), and fixing (2) gives the correct result. ucbtest has been reporting this particular wrong result on i386 systems with unpatched libraries for 9 years. I finally figured out the extent of the bugs. On i386's they are normally hidden by extra precision. We use the trick of representing floats as a sum of 2 floats (one much smaller) to get extra precision in intermediate calculations without explicitly using more than float precision. This trick is just a pessimization when extra precision is available naturally (as it always is when dealing with IEEE single precision, so the float precision part of the library is mostly misimplemented). (1) and (2) break the trick in different ways, except on i386's it turns out that the intermediate calculations are done in enough precision to mask both the bugs and the limited precision of the float variables (as far as ucbtest can check). ucbtest detects the bugs because it forces float precision, but this is not a normal mode of operation so the bug normally has little effect on i386's. On systems that do float arithmetic in float precision, e.g., amd64's, there is no accidental extra precision and the bugs just give wrong results. |
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