<div dir="ltr"> <div class="gmail_extra"> <div class="gmail_quote">On Fri, Feb 8, 2013 at 7:53 PM, Tobias Hammer <<a href="mailto:tobias.hammer@dlr.de" target="_blank">tobias.hammer@dlr.de</a>> wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Tested it too and got an interesting result. On a 32bit linux its: +nan.0 +nan.0 +nan.0 +nan.0 +nan.0 +nan.0 +nan.0 +nan.0 </blockquote><div> </div><div>That's what I get too. And indeed my other machine was a 64bits Ubuntu and Racket. </div><div>Laurent </div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> so, completely wrong. But on a 64bit Linux its correct if i use the 64bit racket version. When i try the 32bit build i get the wrong results again. I think you can blame it on 32 implementation of racket/libc/compiler or whatever. Not on the actual cpu in use because the hardware was always the same (2 identical computers, identical OS + version, only 32bit in one, 64 in the other). Tobias On Fri, 08 Feb 2013 19:07:53 +0100, Neil Toronto <<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div> Back on list. A lot of things point to general sloppiness in either the FPU or C libraries, but I'd like more information just in case. Can you reply with the values of the following expressions on the Athlon? (flexpt -1001.0 -1.3407807929942596e+154) (flexpt -1001.0 1.3407807929942596e+154) (flexpt -0.1 -1.3407807929942596e+154) (flexpt -0.1 1.3407807929942596e+154) (flexpt -744.4400719213812 -1.3407807929942596e+154) (flexpt -744.4400719213812 1.3407807929942596e+154) (flexpt -1.0 -1.3407807929942596e+154) (flexpt -1.0 1.3407807929942596e+154) You should get these values: 0.0 +inf.0 +inf.0 0.0 0.0 +inf.0 1.0 1.0 I think these are cases Racket handles specially instead of handing off to C's `pow' on platforms where we know `pow' handles them wrongly. We might need to ask Matthew to expand that set of platforms. Small rounding errors like this: ((fl*/error -6.87181640380727e-156 2.3341566035927725e-153) 0.7079979032237692) which are only 1 bit off, are probably the cause of these errors: ((fl2log 1.5124390004859715e-308 0.0) 4294967296.220986) ((fl2log1p 3.799205740343036e+246 1.4492752004468653e+230) 549755813887.9473)) `fl2log' and `fl2log1p' are 103-ish-bit logarithm implementations used in certain tricky subdomains of a few special functions. They assume arithmetic is always correct and are very sensitive to rounding errors. You're getting about 65-bit output precision for certain inputs. We can almost certainly blame the FPU because IEEE 754 requires arithmetic to be implemented and correctly rounded. IEEE 754 only *recommends* typical irrational functions. When they're not implemented in hardware, C libraries compute them in software. So I don't know whether these and others are the FPU's or C library's fault: ((flsin 2.5489254492488616e+52) 22637349860729424.0) ((flcos 3.91520018229574e+49) 6369061509154398.0) ((fltan 1.6614020610450763e+21) 9158003261155244.0) ((flexp 16.938769136983012) 7.0) ((flexp 282.52374429474406) 102.0) ((flexp -10.0) 4.0) ((flexp -708.3964185322641) 124.0) These errors come from not doing argument reductions carefully enough. The trigonometric functions probably don't compute x % 2*pi using a high-precision 2*pi when x is large. They seem to be correct enough when x is small, though. The exponential function wasn't tested well at the boundaries of its domain: ((flexp 709.782712893384) +inf.0) 709.782712893384 is (fllog +max.0), and (flexp (fllog +max.0)) should be near +max.0, not (as I suspect) +inf.0. I don't know whether Racket should do anything about these errors. I don't think it would be too hard to do something like Java's StrictMath, but it would take time. In the meantime, don't use the Athlon for serious numerical computation. Neil ⊥ On 02/08/2013 12:13 AM, Laurent wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> Hi Neil, Interaction in a terminal is attached, using Racket 5.3.2.3. Some details about my machine: Linux 3.2.0-37-generic-pae #58-Ubuntu SMP Thu Jan 24 15:51:02 UTC 2013 i686 athlon i386 GNU/Linux In particular, I use a 32bits Ubuntu 12.04.2 on a 686 processor, if that's of any interest. Cheers, Laurent On Fri, Feb 8, 2013 at 1:15 AM, Neil Toronto <<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a> <mailto:<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a>>> wrote: On 02/07/2013 12:09 PM, Laurent wrote: On Thu, Feb 7, 2013 at 5:50 PM, Neil Toronto <<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a> <mailto:<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a>> <mailto:<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a> <mailto:<a href="mailto:neil.toronto@gmail.com" target="_blank">neil.toronto@gmail.com</a>>__>> wrote: Today is not that day, but thanks for asking about this anyway. :) On one machine with Ubuntu 12.10, I get no error, but on another machine with Ubuntu 12.04, I get more than 14000 errors, many of them being +inf.0 and other numbers with big exponents (is my machine really that bad?). Is this exactly the kind of reply you want to avoid for now or are you interested in a report? Alrighty, you've piqued my interest. Better send it off-list, though. :) Neil ⊥ </blockquote> </div></div><div> _________________________ Racket Developers list: <a href="http://lists.racket-lang.org/dev" target="_blank">http://lists.racket-lang.org/dev</a> </div></blockquote> -- --------------------------------------------------------- Tobias Hammer DLR / Institute of Robotics and Mechatronics Muenchner Str. 20, D-82234 Wessling Tel.: 08153/28-1487 Mail: <a href="mailto:tobias.hammer@dlr.de" target="_blank">tobias.hammer@dlr.de</a><div><div> _________________________ Racket Developers list: <a href="http://lists.racket-lang.org/dev" target="_blank">http://lists.racket-lang.org/dev</a> </div></div></blockquote></div> </div></div>