Hi
(If you're wondering, this is a Project Euler question :))
If I wanted to calculate the sum of the digits in the decimal representation
of 2^1000, what would be a good way to go about that? I've tried the
following methods:
# Calculate the sum of digits in the decimal representation of 2^n
# Only works for smaller values of n
bsum <- function(n) {
s <- 0
e <- floor(log10(2^n))
for (i in seq(e,0,-1)) {
s <- s + (((2^n) %/% 10^i) %% 10)
}
s
}
The above doesnt work, as I am using an integer modulus which has
insufficient precision. so I tried to coerce R to produce a full-precision
integer and sum the digits of that:
bsum2 <- function(n) {
s <- 0
strn <- formatC(2^n, format="fg")
sum(as.numeric(strsplit(strn,"")[[1]]))
}
This also doesnt seem to work. Is there another way I can do this in R?
Cheers
Rory
--
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One way of "doing it in R" is to use the 'bc' command that is on most UNIX/LINUX systems and is also on cygwin for Windows. Here are decimal digits for 2^1000 /cygdrive/c/jph/consulting/2008-03-30: bc bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. 2^1000 10715086071862673209484250490600018105614048117055336074437503883703\ 51051124936122493198378815695858127594672917553146825187145285692314\ 04359845775746985748039345677748242309854210746050623711418779541821\ 53046474983581941267398767559165543946077062914571196477686542167660\ 429831652624386837205668069376 So you can 'shell' the command from R, collect the digits and then sum them. On Fri, Apr 4, 2008 at 10:43 AM, Rory Winston <rory.winston at gmail.com> wrote:> > Hi > > (If you're wondering, this is a Project Euler question :)) > > If I wanted to calculate the sum of the digits in the decimal representation > of 2^1000, what would be a good way to go about that? I've tried the > following methods: > > # Calculate the sum of digits in the decimal representation of 2^n > # Only works for smaller values of n > bsum <- function(n) { > s <- 0 > e <- floor(log10(2^n)) > for (i in seq(e,0,-1)) { > s <- s + (((2^n) %/% 10^i) %% 10) > } > s > } > > The above doesnt work, as I am using an integer modulus which has > insufficient precision. so I tried to coerce R to produce a full-precision > integer and sum the digits of that: > > bsum2 <- function(n) { > s <- 0 > strn <- formatC(2^n, format="fg") > sum(as.numeric(strsplit(strn,"")[[1]])) > } > > This also doesnt seem to work. Is there another way I can do this in R? > Cheers > Rory > -- > View this message in context: http://www.nabble.com/Arbitrary-Precision-Numbers-tp16492549p16492549.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help at r-project.org mailing list > 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. >-- Jim Holtman Cincinnati, OH +1 513 646 9390 What is the problem you are trying to solve?
Have a look at the Ryacas package which interfaces R to yacas. yacas can do exact arithmetic. On Fri, Apr 4, 2008 at 11:43 AM, Rory Winston <rory.winston at gmail.com> wrote:> > Hi > > (If you're wondering, this is a Project Euler question :)) > > If I wanted to calculate the sum of the digits in the decimal representation > of 2^1000, what would be a good way to go about that? I've tried the > following methods: > > # Calculate the sum of digits in the decimal representation of 2^n > # Only works for smaller values of n > bsum <- function(n) { > s <- 0 > e <- floor(log10(2^n)) > for (i in seq(e,0,-1)) { > s <- s + (((2^n) %/% 10^i) %% 10) > } > s > } > > The above doesnt work, as I am using an integer modulus which has > insufficient precision. so I tried to coerce R to produce a full-precision > integer and sum the digits of that: > > bsum2 <- function(n) { > s <- 0 > strn <- formatC(2^n, format="fg") > sum(as.numeric(strsplit(strn,"")[[1]])) > } > > This also doesnt seem to work. Is there another way I can do this in R? > Cheers > Rory > -- > View this message in context: http://www.nabble.com/Arbitrary-Precision-Numbers-tp16492549p16492549.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help at r-project.org mailing list > 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. >
Probably not helpful for your particular problem, but the package rcdd
also has a fairly limited interface to the GNU MP Bignum library.
It does arithmetic on arbitrary precision rationals. Also exact linear
programming and computational geometry using arbitrary precision rationals.
library(rcdd)
?ArithmeticGMP
--
Charles Geyer
Professor, School of Statistics
University of Minnesota
charlie at stat.umn.edu
"Rory Winston" <rory.winston at gmail.com> wrote in message news:16492549.post at talk.nabble.com...> (If you're wondering, this is a Project Euler question :)) > > If I wanted to calculate the sum of the digits in the decimal > representation > of 2^1000, what would be a good way to go about that?Try this:> library(gmp) > for (N in c(10,16,32,100,1000))+ { + s <- as.character(pow.bigz(2,N)) + t <- as.numeric(unlist(strsplit(s,""))) + cat(N, s, sum(t), "\n") + } 10 1024 7 16 65536 25 32 4294967296 58 100 1267650600228229401496703205376 115 1000 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 1366 The first few can be verified manually. -- efg Earl F. Glynn Bioinformatics Stowers Institute for Medical Research