Rmpfr product and inner product are not doubling the nominal precision. Small precision inner products are stored as 53-bit numeric.
library(Rmpfr) ## double with precBits=53 (5/17) * (5/17) ## 0.08650519 ## base 10 formatHex( (5/17) * (5/17) ) ## +0x1.6253443526171p-4 ## various precisions fs5 <- 5*mpfr(1, precBits=5)/17 fs6 <- 5*mpfr(1, precBits=6)/17 fs7 <- 5*mpfr(1, precBits=7)/17 fs8 <- 5*mpfr(1, precBits=8)/17 fs9 <- 5*mpfr(1, precBits=9)/17 ## product formatHex(fs5*fs5) ## +0x1.7p-4 ## All these are smaller formatHex(fs6*fs6) formatHex(fs7*fs7) formatHex(fs8*fs8) formatHex(fs9*fs9) ## and all round DOWN to +0x1.6p-4 formatHex(mpfr( fs6*fs6 , precBits=5)) formatHex(mpfr( fs7*fs7 , precBits=5)) formatHex(mpfr( fs8*fs8 , precBits=5)) formatHex(mpfr( fs9*fs9 , precBits=5)) ## inner product, for low precision, is stored as 53-bit numeric rounded to 6 bits formatHex(fs5 %*% fs5) ## +0x1.6900000000000p-4 class(fs5 %*% fs5) getPrec(fs5 %*% fs5) formatHex((fs5 %*% fs5)*(fs5 %*% fs5)) ## 12 bits ## +0x1.fd11000000000p-8 ## All these are smaller formatHex(fs6 %*% fs6) ## same formatHex(fs7 %*% fs7) formatHex(fs8 %*% fs8) formatHex(fs9 %*% fs9) ## and all round DOWN to +0x1.6p-4 formatHex(mpfr( fs6 %*% fs6 , precBits=5)) ## same formatHex(mpfr( fs7 %*% fs7 , precBits=5)) formatHex(mpfr( fs8 %*% fs8 , precBits=5)) formatHex(mpfr( fs9 %*% fs9 , precBits=5)) ## inner product, for high precision, stays at the specified precision fs65 <- 5*mpfr(1, precBits=65)/17 formatHex(fs65 * fs65) ## +0x1.62534435261707f8p-4 formatHex(fs65 %*% fs65) ## +0x1.62534435261707f8p-4 class(fs65 %*% fs65) getPrec(fs65 %*% fs65) fs130 <- 5*mpfr(1, precBits=130)/17 formatHex(fs130 * fs130) ## +0x1.62534435261707f8e9dacbbcad9e8f800p-4 formatHex(mpfr( fs130 * fs130 , precBits=65)) ## +0x1.62534435261707f9p-4 ## not the same as 65-bit inner product On Sat, Mar 14, 2020 at 4:51 PM J C Nash <profjcn...@gmail.com> wrote: > > The issue is to avoid the storage and operational penalty. 100 x 100 matrix > in 100 decimals vs 100 x 100 matrix in 50 > decimals for many operations like copy, scale, etc. But accumulation of inner > products, you want to avoid digit loss, > e.g., A and B are long vectors -- say 100000 long, with a few "large" > elements but most smaller. However 99000 "small" > numbers could add up and ... > > As with many such issues, it doesn't affect the vast majority of occurrences. > Indeed few of my own. IEEE arithmetic > usually does the job (I was one of the members of the original committee). > This particular > concern arose when trying to tease out a signal from a great deal of noise > from a spacecraft sensor. > > JN > > > On 2020-03-14 4:28 p.m., Jeff Newmiller wrote: > > Not sure I understand the concern. IEEE 754 double precision floating point > > was invented to allow for avoiding loss of precision when manipulating > > single precision floating point numbers... but then C just ignores single > > precision and you are expected to know that the precision of your answers > > may only be relied on at single precision for certain operations. > > > > Wouldn't you just set Rmpfr precision to double your actual desired > > precision and move on? Though I suppose you might consider more than > > doubling the desired precision to deal with exponentiation [1]. > > > > [1] https://en.m.wikipedia.org/wiki/Extended_precision#Working_range > > > > On March 14, 2020 1:10:19 PM PDT, J C Nash <profjcn...@gmail.com> wrote: > >> Rmpfr does "support" matrix algebra, but I have been trying for some > >> time to determine if it computes "double" precision (i.e., double the > >> set level of precision) inner products. I suspect that it does NOT, > >> which is unfortunate. However, I would be happy to be wrong about > >> this. > >> > >> JN > >> > >> On 2020-03-14 3:41 p.m., Bert Gunter wrote: > >>> Read its documentation yourself and unless you have good reason not > >> to, > >>> always cc the list (which I have done here). > >>> > >>> > >>> Bert Gunter > >>> > >>> "The trouble with having an open mind is that people keep coming > >> along and > >>> sticking things into it." > >>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) > >>> > >>> > >>> On Sat, Mar 14, 2020 at 12:28 PM 林伟璐 <13917987...@163.com> wrote: > >>> > >>>> Thanks. Does it support matrix algebra? > >>>> > >>>> > >>>> > >>>> 林伟璐 > >>>> 邮箱：13917987...@163.com > >>>> > >>>> > >> <https://maas.mail.163.com/dashi-web-extend/html/proSignature.html?iconUrl=http%3A%2F%2Fmail-online.nosdn.127.net%2F17c23bc1722125aa6261c33736f525c5.jpg&name=%E6%9E%97%E4%BC%9F%E7%92%90&uid=13917987541%40163.com&ftlId=1&items=%5B%22%E9%82%AE%E7%AE%B1%EF%BC%9A13917987541%40163.com%22%5D> > >>>> > >>>> 签名由 网易邮箱大师 <https://mail.163.com/dashi/dlpro.html?from=mail88> 定制 > >>>> > >>>> On 03/15/2020 03:18, Bert Gunter <bgunter.4...@gmail.com> wrote: > >>>> Use google instead, as I recommended. If that's impossible in China, > >> you > >>>> should state that and what you tried (Baidu) in your query. > >>>> > >>>> You'll get the Rmpfr package. > >>>> > >>>> Bert Gunter > >>>> > >>>> "The trouble with having an open mind is that people keep coming > >> along and > >>>> sticking things into it." > >>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) > >>>> > >>>> > >>>> On Sat, Mar 14, 2020 at 11:48 AM 林伟璐 <13917987...@163.com> wrote: > >>>> > >>>>> Thanks, I tried Baidu but get nothing > >>>>> > >>>>> > >>>>> > >>>>> 林伟璐 > >>>>> 邮箱：13917987...@163.com > >>>>> > >>>>> > >> <https://maas.mail.163.com/dashi-web-extend/html/proSignature.html?iconUrl=http%3A%2F%2Fmail-online.nosdn.127.net%2F17c23bc1722125aa6261c33736f525c5.jpg&name=%E6%9E%97%E4%BC%9F%E7%92%90&uid=13917987541%40163.com&ftlId=1&items=%5B%22%E9%82%AE%E7%AE%B1%EF%BC%9A13917987541%40163.com%22%5D> > >>>>> > >>>>> 签名由 网易邮箱大师 <https://mail.163.com/dashi/dlpro.html?from=mail88> 定制 > >>>>> > >>>>> On 03/15/2020 02:44, Bert Gunter <bgunter.4...@gmail.com> wrote: > >>>>> Here's a novel idea: > >>>>> Do a google search on "multiprecision computing package R" for an > >> answer. > >>>>> > >>>>> Bert Gunter > >>>>> > >>>>> "The trouble with having an open mind is that people keep coming > >> along > >>>>> and sticking things into it." > >>>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) > >>>>> > >>>>> > >>>>> On Sat, Mar 14, 2020 at 10:36 AM 林伟璐 <13917987...@163.com> wrote: > >>>>> > >>>>>> Dear all > >>>>>> > >>>>>> > >>>>>> I need a multiprecision computing package in R, if anyone in the > >> list > >>>>>> knows, please let me known... > >>>>>> > >>>>>> > >>>>>> Many thanks > >>>>>> > >>>>>> > >>>>>> Weilu Lin > >>>>>> [[alternative HTML version deleted]] > >>>>>> > >>>>>> ______________________________________________ > >>>>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > >>>>>> https://stat.ethz.ch/mailman/listinfo/r-help > >>>>>> PLEASE do read the posting guide > >>>>>> http://www.R-project.org/posting-guide.html > >>>>>> and provide commented, minimal, self-contained, reproducible code. > >>>>>> > >>>>> > >>> > >>> [[alternative HTML version deleted]] > >>> > >>> ______________________________________________ > >>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > >>> https://stat.ethz.ch/mailman/listinfo/r-help > >>> PLEASE do read the posting guide > >> http://www.R-project.org/posting-guide.html > >>> and provide commented, minimal, self-contained, reproducible code. > >>> > >> > >> ______________________________________________ > >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > >> https://stat.ethz.ch/mailman/listinfo/r-help > >> PLEASE do read the posting guide > >> http://www.R-project.org/posting-guide.html > >> and provide commented, minimal, self-contained, reproducible code. > > > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
