> On Jul 3, 2015, at 11:05 PM, Duncan Murdoch <murdoch.dun...@gmail.com> wrote:
>
> On 04/07/2015 3:45 AM, David Winsemius wrote:
>>
>>> On Jul 3, 2015, at 5:08 PM, David Winsemius <dwinsem...@comcast.net> wrote:
>>>
>>>
>>>
>>> It doesn’t appear to me that mpfr was ever designed to handle expressions
>>> as the first argument.
>>
>> This could be a start. Obviously one would wnat to include code to do other
>> substitutions probably using the all.vars function to pull out the other
>> “constants” and ’numeric’ values to make them of equivalent precision. I’m
>> guessing you want to follow the parse-tree and then testing the numbers for
>> integer-ness and then replacing by paste0( “mpfr(“, val, “L, “, prec,”)” )
>>
>> Pre <- function(expr, prec){ sexpr <- deparse(substitute(expr) )
>
> Why deparse? That's almost never a good idea. I can't try your code (I
> don't have mpfr available), but it would be much better to modify the
> expression than the text representation of it. For example, I think
> your code would modify strings containing "pi", or variables with those
> letters in them, etc. If you used substitute(expr) without the
> deparse(), you could replace the symbol "pi" with the call to the Const
> function, and be more robust.
>
Really? I did try. I was fairly sure that someone could do better but I don’t
see an open path along the lines you suggest. I’m pretty sure I tried
`substitute(expr, list(pi= pi))` when `expr` had been the formal argument and
got disappointed because there is no `pi` in the expression `expr`. I _thought_
the problem was that `substitute` does not evaluate its first argument, but I
do admit to be pretty much of a klutz with this sort of programming. I don’t
think you need to have mpfr installed in order to demonstrate this.
testf <- function(expr) new <- substitute(expr, list(pi = 3.121450))
sth<-testf(exp(pi))
sth
#expr
—
David.
> Duncan Murdoch
>
>
>> spi <- paste0("Const('pi',",prec,”)”)
>> sexpr <- gsub("pi", spi, sexpr)
>> print( eval(parse(text=sexpr))) }
>>
>> # Very minimal testing
>>> Pre(pi,120)
>> 1 'mpfr' number of precision 120 bits
>> [1] 3.1415926535897932384626433832795028847
>>> Pre(exp(pi),120)
>> 1 'mpfr' number of precision 120 bits
>> [1] 23.140692632779269005729086367948547394
>>> Pre(log(exp(pi)),120)
>> 1 'mpfr' number of precision 120 bits
>> [1] 3.1415926535897932384626433832795028847
>>
>> At the moment it still needs to ahve other numbers mpfr-ified to succeed:
>>
>>> Pre(pi-4*atan(1),120)
>> 1 'mpfr' number of precision 120 bits
>> [1] 1.2246467991473531772315719253130892016e-16
>>> Pre(pi-4*atan(mpfr(1,120)),120)
>> 1 'mpfr' number of precision 120 bits
>> [1] 0
>>
>> Best;
>> David.
>>
>>>
>>
>>> —
>>> David
>>>
>>>> On Jul 3, 2015, at 12:01 PM, Ravi Varadhan <ravi.varad...@jhu.edu> wrote:
>>>>
>>>> Thank you all. I did think about declaring `pi' as a special constant,
>>>> but for some reason didn't actually try it.
>>>> Would it be easy to have the mpfr() written such that its argument is
>>>> automatically of extended precision? In other words, if I just called:
>>>> mpfr(exp(sqrt(163)*pi, 120), then all the constants, 163, pi, are
>>>> automatically of 120 bits precision.
>>>>
>>>> Is this easy to do?
>>>>
>>>> Best,
>>>> Ravi
>>>> ________________________________________
>>>> From: David Winsemius <dwinsem...@comcast.net>
>>>> Sent: Friday, July 3, 2015 2:06 PM
>>>> To: John Nash
>>>> Cc: r-help; Ravi Varadhan
>>>> Subject: Re: [R] : Ramanujan and the accuracy of floating point
>>>> computations - using Rmpfr in R
>>>>
>>>>> On Jul 3, 2015, at 8:08 AM, John Nash <john.n...@uottawa.ca> wrote:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> Third try -- I unsubscribed and re-subscribed. Sorry to Ravi for extra
>>>>> traffic.
>>>>>
>>>>> In case anyone gets a duplicate, R-help bounced my msg "from non-member"
>>>>> (I changed server, but not email yesterday,
>>>>> so possibly something changed enough). Trying again.
>>>>>
>>>>> JN
>>>>>
>>>>> I got the Wolfram answer as follows:
>>>>>
>>>>> library(Rmpfr)
>>>>> n163 <- mpfr(163, 500)
>>>>> n163
>>>>> pi500 <- mpfr(pi, 500)
>>>>> pi500
>>>>> pitan <- mpfr(4, 500)*atan(mpfr(1,500))
>>>>> pitan
>>>>> pitan-pi500
>>>>> r500 <- exp(sqrt(n163)*pitan)
>>>>> r500
>>>>> check <- "262537412640768743.99999999999925007259719818568887935385..."
>>>>> savehistory("jnramanujan.R")
>>>>>
>>>>> Note that I used 4*atan(1) to get pi.
>>>>
>>>> RK got it right by following the example in the help page for mpfr:
>>>>
>>>> Const("pi", 120)
>>>>
>>>> The R `pi` constant is not recognized by mpfr as being anything other than
>>>> another double .
>>>>
>>>>
>>>> There are four special values that mpfr recognizes.
>>>>
>>>> —
>>>> Best;
>>>> David
>>>>
>>>>
>>>>> It seems that may be important,
>>>>> rather than converting.
>>>>>
>>>>> JN
>>>>>
>>>>> On 15-07-03 06:00 AM, r-help-requ...@r-project.org wrote:
>>>>>
>>>>>> Message: 40
>>>>>> Date: Thu, 2 Jul 2015 22:38:45 +0000
>>>>>> From: Ravi Varadhan <ravi.varad...@jhu.edu>
>>>>>> To: "'Richard M. Heiberger'" <r...@temple.edu>, Aditya Singh
>>>>>> <aps...@yahoo.com>
>>>>>> Cc: r-help <r-help@r-project.org>
>>>>>> Subject: Re: [R] : Ramanujan and the accuracy of floating point
>>>>>> computations - using Rmpfr in R
>>>>>> Message-ID:
>>>>>> <14ad39aaf6a542849bbf3f62a0c2f...@dom-eb1-2013.win.ad.jhu.edu>
>>>>>> Content-Type: text/plain; charset="utf-8"
>>>>>>
>>>>>> Hi Rich,
>>>>>>
>>>>>> The Wolfram answer is correct.
>>>>>> http://mathworld.wolfram.com/RamanujanConstant.html
>>>>>>
>>>>>> There is no code for Wolfram alpha. You just go to their web engine and
>>>>>> plug in the expression and it will give you the answer.
>>>>>> http://www.wolframalpha.com/
>>>>>>
>>>>>> I am not sure that the precedence matters in Rmpfr. Even if it does,
>>>>>> the answer you get is still wrong as you showed.
>>>>>>
>>>>>> Thanks,
>>>>>> Ravi
>>>>>>
>>>>>> -----Original Message-----
>>>>>> From: Richard M. Heiberger [mailto:r...@temple.edu]
>>>>>> Sent: Thursday, July 02, 2015 6:30 PM
>>>>>> To: Aditya Singh
>>>>>> Cc: Ravi Varadhan; r-help
>>>>>> Subject: Re: [R] : Ramanujan and the accuracy of floating point
>>>>>> computations - using Rmpfr in R
>>>>>>
>>>>>> There is a precedence error in your R attempt. You need to convert
>>>>>> 163 to 120 bits first, before taking
>>>>>> its square root.
>>>>>>
>>>>>>>> exp(sqrt(mpfr(163, 120)) * mpfr(pi, 120))
>>>>>> 1 'mpfr' number of precision 120 bits
>>>>>> [1] 262537412640768333.51635812597335712954
>>>>>>
>>>>>> ## just the last four characters to the left of the decimal point.
>>>>>>>> tmp <- c(baseR=8256, Wolfram=8744, Rmpfr=8333, wrongRmpfr=7837)
>>>>>>>> tmp-tmp[2]
>>>>>> baseR Wolfram Rmpfr wrongRmpfr
>>>>>> -488 0 -411 -907
>>>>>> You didn't give the Wolfram alpha code you used. There is no way of
>>>>>> verifying the correct value from your email.
>>>>>> Please check that you didn't have a similar precedence error in that
>>>>>> code.
>>>>>>
>>>>>> Rich
>>>>>>
>>>>>>
>>>>>> On Thu, Jul 2, 2015 at 2:02 PM, Aditya Singh via R-help
>>>>>> <r-help@r-project.org> wrote:
>>>>>>>> Ravi
>>>>>>>>
>>>>>>>> I am a chemical engineer by training. Is there not something like law
>>>>>>>> of corresponding states in numerical analysis?
>>>>>>>>
>>>>>>>> Aditya
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> ------------------------------
>>>>>>>> On Thu 2 Jul, 2015 7:28 AM PDT Ravi Varadhan wrote:
>>>>>>>>
>>>>>>>>>> Hi,
>>>>>>>>>>
>>>>>>>>>> Ramanujan supposedly discovered that the number, 163, has this
>>>>>>>>>> interesting property that exp(sqrt(163)*pi), which is obviously a
>>>>>>>>>> transcendental number, is real close to an integer (close to
>>>>>>>>>> 10^(-12)).
>>>>>>>>>>
>>>>>>>>>> If I compute this using the Wolfram alpha engine, I get:
>>>>>>>>>> 262537412640768743.99999999999925007259719818568887935385...
>>>>>>>>>>
>>>>>>>>>> When I do this in R 3.1.1 (64-bit windows), I get:
>>>>>>>>>> 262537412640768256.0000
>>>>>>>>>>
>>>>>>>>>> The absolute error between the exact and R's value is 488, with a
>>>>>>>>>> relative error of about 1.9x10^(-15).
>>>>>>>>>>
>>>>>>>>>> In order to replicate Wolfram Alpha, I tried doing this in "Rmfpr"
>>>>>>>>>> but I am unable to get accurate results:
>>>>>>>>>>
>>>>>>>>>> library(Rmpfr)
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>> exp(sqrt(163) * mpfr(pi, 120))
>>>>>>>>>> 1 'mpfr' number of precision 120 bits
>>>>>>>>>>
>>>>>>>>>> [1] 262537412640767837.08771354274620169031
>>>>>>>>>>
>>>>>>>>>> The above answer is not only inaccurate, but it is actually worse
>>>>>>>>>> than the answer using the usual double precision. Any thoughts as
>>>>>>>>>> to what I am doing wrong?
>>>>>>>>>>
>>>>>>>>>> Thank you,
>>>>>>>>>> Ravi
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> [[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.
>>>>
>>>> David Winsemius, MD
>>>> Alameda, CA, USA
>>>>
>>>
>>> David Winsemius, MD
>>> Alameda, CA, USA
>>>
>>> ______________________________________________
>>> 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.
>>
>> David Winsemius, MD
>> Alameda, CA, USA
>>
>> ______________________________________________
>> 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.
>>
>
David Winsemius, MD
Alameda, CA, USA
______________________________________________
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