[racket-dev] long double for racket

Could you formulate some test cases to check for this behavior?

Robby


On Sun, Dec 23, 2012 at 7:07 PM, Neil Toronto <neil.toronto at 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 ⊥
>
>
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