Could you formulate some test cases to check for this behavior? Robby
On Sun, Dec 23, 2012 at 7:07 PM, Neil Toronto <neil.toro...@gmail.com>wrote: > On 12/22/2012 10:24 AM, Michael Filonenko wrote: > >> Also, long double arithmetic requires setting "extended mode" flag on >> FPU, which forces the FPU to use 80-bit registers. The side effect on >> that flag is that the FPU gives slightly different (more accurate, but >> not IEEE-compliant) results for 64-bit operations. That is usually >> not a problem on machines who have SSE2 (introduced in Pentium 4 in >> 2001). In presense of SSE2, Racket performs 64-bit operations solely >> on 64-bit SSE2 registers (see MZ_USE_JIT_SSE and --mfpmath=sse), so the >> results are IEEE-compliant. 80-bit operations are done on FPU anyway >> as SSE2 can not do them. Therefore, by setting the "extended mode" on >> FPU, we introduce a subtle difference in ordinary flonums, but only on >> old machines that do not have SSE2. >> > > Where is a good place to read more about this? In particular, I'm > interested in how IEEE-compliant SSE2 implementations tend to be compared > to FPUs. > > About half the new flonum functions in the math library rely on perfectly > compliant rounding for good accuracy in difficult parts of their domains. A > few use double-double arithmetic to extend precision from 53-bit > significands to 106 in these subdomains; most use a combination of > precisions. > > If rounding isn't IEEE-compliant, these functions could suddenly become > much less precise: from just one least significant digit wrong to four or > five. That includes computations done *entirely in 80-bit registers*, which > seems like it should be more accurate. For example, there's a heavily used > macro that computes the result of `fl+' and its rounding error. If it were > done entirely in 80 bits and then rounded to 64, the error computation > would be totally bogus. > > I'd like to verify independently that this won't happen on machines with > an Intel FPU manufactured within the last 12 years or an AMD FPU > manufactured within the last 10 (i.e. those with SSE2). That would keep me > happy, since FPUs older than those tended to rounding incorrectly anyway. > > Thanks! > Neil ⊥ > > > _________________________ > Racket Developers list: > http://lists.racket-lang.org/**dev <http://lists.racket-lang.org/dev> >
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