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I am trying to calculate the value of exp(1000) or more in R. I looked at the solution provided in Calculate the exponentials of big negative value and followed it to replicate the code for negative values first, but I have the following output.
a <- mpfr(exp(-1000),precBits = 64)
a
1 'mpfr' number of precision 64 bits
[1] 0
I do not understand why my output would be different from the provided solution. I understand this particular solution is for negative values and that I am looking for positive exponents. Regardless, it should work for both ways.
You need to convert to extended precision before you exponentiate, otherwise R will try to compute exp(-1000) with its usual precision and underflow will occur (as you found out).
> a <- exp(mpfr(-1000, precBits = 64))
> a
1 'mpfr' number of precision 64 bits
[1] 5.07595889754945676548e-435
There is an option in R to get control over digit display. For example:
options(digits=10)
is supposed to give the calculation results in 10 digits till the end of R session. In the help file of R, the definition for digits parameter is as follows:
digits: controls the number of digits
to print when printing numeric values.
It is a suggestion only. Valid values
are 1...22 with default 7
So, it says this is a suggestion only. What if I like to always display 10 digits, not more or less?
My second question is, what if I like to display more than 22 digits, i.e. for more precise calculations like 100 digits? Is it possible with base R, or do I need an additional package/function for that?
Edit: Thanks to jmoy's suggestion, I tried sprintf("%.100f",pi) and it gave
[1] "3.1415926535897931159979634685441851615905761718750000000000000000000000000000000000000000000000000000"
which has 48 decimals. Is this the maximum limit R can handle?
The reason it is only a suggestion is that you could quite easily write a print function that ignored the options value. The built-in printing and formatting functions do use the options value as a default.
As to the second question, since R uses finite precision arithmetic, your answers aren't accurate beyond 15 or 16 decimal places, so in general, more aren't required. The gmp and rcdd packages deal with multiple precision arithmetic (via an interace to the gmp library), but this is mostly related to big integers rather than more decimal places for your doubles.
Mathematica or Maple will allow you to give as many decimal places as your heart desires.
EDIT:
It might be useful to think about the difference between decimal places and significant figures. If you are doing statistical tests that rely on differences beyond the 15th significant figure, then your analysis is almost certainly junk.
On the other hand, if you are just dealing with very small numbers, that is less of a problem, since R can handle number as small as .Machine$double.xmin (usually 2e-308).
Compare these two analyses.
x1 <- rnorm(50, 1, 1e-15)
y1 <- rnorm(50, 1 + 1e-15, 1e-15)
t.test(x1, y1) #Should throw an error
x2 <- rnorm(50, 0, 1e-15)
y2 <- rnorm(50, 1e-15, 1e-15)
t.test(x2, y2) #ok
In the first case, differences between numbers only occur after many significant figures, so the data are "nearly constant". In the second case, Although the size of the differences between numbers are the same, compared to the magnitude of the numbers themselves they are large.
As mentioned by e3bo, you can use multiple-precision floating point numbers using the Rmpfr package.
mpfr("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825")
These are slower and more memory intensive to use than regular (double precision) numeric vectors, but can be useful if you have a poorly conditioned problem or unstable algorithm.
If you are producing the entire output yourself, you can use sprintf(), e.g.
> sprintf("%.10f",0.25)
[1] "0.2500000000"
specifies that you want to format a floating point number with ten decimal points (in %.10f the f is for float and the .10 specifies ten decimal points).
I don't know of any way of forcing R's higher level functions to print an exact number of digits.
Displaying 100 digits does not make sense if you are printing R's usual numbers, since the best accuracy you can get using 64-bit doubles is around 16 decimal digits (look at .Machine$double.eps on your system). The remaining digits will just be junk.
One more solution able to control the how many decimal digits to print out based on needs (if you don't want to print redundant zero(s))
For example, if you have a vector as elements and would like to get sum of it
elements <- c(-1e-05, -2e-04, -3e-03, -4e-02, -5e-01, -6e+00, -7e+01, -8e+02)
sum(elements)
## -876.5432
Apparently, the last digital as 1 been truncated, the ideal result should be -876.54321, but if set as fixed printing decimal option, e.g sprintf("%.10f", sum(elements)), redundant zero(s) generate as -876.5432100000
Following the tutorial here: printing decimal numbers, if able to identify how many decimal digits in the certain numeric number, like here in -876.54321, there are 5 decimal digits need to print, then we can set up a parameter for format function as below:
decimal_length <- 5
formatC(sum(elements), format = "f", digits = decimal_length)
## -876.54321
We can change the decimal_length based on each time query, so it can satisfy different decimal printing requirement.
If you work primarily with tibbles, there is a function that enforces digits: num().
Here is an example:
library(tidyverse)
data <- tribble(
~ weight, ~ weight_selfreport,
81.5,81.66969147005445,
72.6,72.59528130671505,
92.9,93.01270417422867,
79.4,79.4010889292196,
94.6,96.64246823956442,
80.2,79.4010889292196,
116.2,113.43012704174228,
95.4,95.73502722323049,
99.5,99.8185117967332
)
data <-
data %>%
mutate(across(where(is.numeric), ~ num(., digits = 3)))
data
#> # A tibble: 9 × 2
#> weight weight_selfreport
#> <num:.3!> <num:.3!>
#> 1 81.500 81.670
#> 2 72.600 72.595
#> 3 92.900 93.013
#> 4 79.400 79.401
#> 5 94.600 96.642
#> 6 80.200 79.401
#> 7 116.200 113.430
#> 8 95.400 95.735
#> 9 99.500 99.819
Thus you can even decide to have different rounding options depending on what your needs are. I find it very helpful and a rather quick solution to printing dfs.
There is an option in R to get control over digit display. For example:
options(digits=10)
is supposed to give the calculation results in 10 digits till the end of R session. In the help file of R, the definition for digits parameter is as follows:
digits: controls the number of digits
to print when printing numeric values.
It is a suggestion only. Valid values
are 1...22 with default 7
So, it says this is a suggestion only. What if I like to always display 10 digits, not more or less?
My second question is, what if I like to display more than 22 digits, i.e. for more precise calculations like 100 digits? Is it possible with base R, or do I need an additional package/function for that?
Edit: Thanks to jmoy's suggestion, I tried sprintf("%.100f",pi) and it gave
[1] "3.1415926535897931159979634685441851615905761718750000000000000000000000000000000000000000000000000000"
which has 48 decimals. Is this the maximum limit R can handle?
The reason it is only a suggestion is that you could quite easily write a print function that ignored the options value. The built-in printing and formatting functions do use the options value as a default.
As to the second question, since R uses finite precision arithmetic, your answers aren't accurate beyond 15 or 16 decimal places, so in general, more aren't required. The gmp and rcdd packages deal with multiple precision arithmetic (via an interace to the gmp library), but this is mostly related to big integers rather than more decimal places for your doubles.
Mathematica or Maple will allow you to give as many decimal places as your heart desires.
EDIT:
It might be useful to think about the difference between decimal places and significant figures. If you are doing statistical tests that rely on differences beyond the 15th significant figure, then your analysis is almost certainly junk.
On the other hand, if you are just dealing with very small numbers, that is less of a problem, since R can handle number as small as .Machine$double.xmin (usually 2e-308).
Compare these two analyses.
x1 <- rnorm(50, 1, 1e-15)
y1 <- rnorm(50, 1 + 1e-15, 1e-15)
t.test(x1, y1) #Should throw an error
x2 <- rnorm(50, 0, 1e-15)
y2 <- rnorm(50, 1e-15, 1e-15)
t.test(x2, y2) #ok
In the first case, differences between numbers only occur after many significant figures, so the data are "nearly constant". In the second case, Although the size of the differences between numbers are the same, compared to the magnitude of the numbers themselves they are large.
As mentioned by e3bo, you can use multiple-precision floating point numbers using the Rmpfr package.
mpfr("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825")
These are slower and more memory intensive to use than regular (double precision) numeric vectors, but can be useful if you have a poorly conditioned problem or unstable algorithm.
If you are producing the entire output yourself, you can use sprintf(), e.g.
> sprintf("%.10f",0.25)
[1] "0.2500000000"
specifies that you want to format a floating point number with ten decimal points (in %.10f the f is for float and the .10 specifies ten decimal points).
I don't know of any way of forcing R's higher level functions to print an exact number of digits.
Displaying 100 digits does not make sense if you are printing R's usual numbers, since the best accuracy you can get using 64-bit doubles is around 16 decimal digits (look at .Machine$double.eps on your system). The remaining digits will just be junk.
One more solution able to control the how many decimal digits to print out based on needs (if you don't want to print redundant zero(s))
For example, if you have a vector as elements and would like to get sum of it
elements <- c(-1e-05, -2e-04, -3e-03, -4e-02, -5e-01, -6e+00, -7e+01, -8e+02)
sum(elements)
## -876.5432
Apparently, the last digital as 1 been truncated, the ideal result should be -876.54321, but if set as fixed printing decimal option, e.g sprintf("%.10f", sum(elements)), redundant zero(s) generate as -876.5432100000
Following the tutorial here: printing decimal numbers, if able to identify how many decimal digits in the certain numeric number, like here in -876.54321, there are 5 decimal digits need to print, then we can set up a parameter for format function as below:
decimal_length <- 5
formatC(sum(elements), format = "f", digits = decimal_length)
## -876.54321
We can change the decimal_length based on each time query, so it can satisfy different decimal printing requirement.
If you work primarily with tibbles, there is a function that enforces digits: num().
Here is an example:
library(tidyverse)
data <- tribble(
~ weight, ~ weight_selfreport,
81.5,81.66969147005445,
72.6,72.59528130671505,
92.9,93.01270417422867,
79.4,79.4010889292196,
94.6,96.64246823956442,
80.2,79.4010889292196,
116.2,113.43012704174228,
95.4,95.73502722323049,
99.5,99.8185117967332
)
data <-
data %>%
mutate(across(where(is.numeric), ~ num(., digits = 3)))
data
#> # A tibble: 9 × 2
#> weight weight_selfreport
#> <num:.3!> <num:.3!>
#> 1 81.500 81.670
#> 2 72.600 72.595
#> 3 92.900 93.013
#> 4 79.400 79.401
#> 5 94.600 96.642
#> 6 80.200 79.401
#> 7 116.200 113.430
#> 8 95.400 95.735
#> 9 99.500 99.819
Thus you can even decide to have different rounding options depending on what your needs are. I find it very helpful and a rather quick solution to printing dfs.
There is an option in R to get control over digit display. For example:
options(digits=10)
is supposed to give the calculation results in 10 digits till the end of R session. In the help file of R, the definition for digits parameter is as follows:
digits: controls the number of digits
to print when printing numeric values.
It is a suggestion only. Valid values
are 1...22 with default 7
So, it says this is a suggestion only. What if I like to always display 10 digits, not more or less?
My second question is, what if I like to display more than 22 digits, i.e. for more precise calculations like 100 digits? Is it possible with base R, or do I need an additional package/function for that?
Edit: Thanks to jmoy's suggestion, I tried sprintf("%.100f",pi) and it gave
[1] "3.1415926535897931159979634685441851615905761718750000000000000000000000000000000000000000000000000000"
which has 48 decimals. Is this the maximum limit R can handle?
The reason it is only a suggestion is that you could quite easily write a print function that ignored the options value. The built-in printing and formatting functions do use the options value as a default.
As to the second question, since R uses finite precision arithmetic, your answers aren't accurate beyond 15 or 16 decimal places, so in general, more aren't required. The gmp and rcdd packages deal with multiple precision arithmetic (via an interace to the gmp library), but this is mostly related to big integers rather than more decimal places for your doubles.
Mathematica or Maple will allow you to give as many decimal places as your heart desires.
EDIT:
It might be useful to think about the difference between decimal places and significant figures. If you are doing statistical tests that rely on differences beyond the 15th significant figure, then your analysis is almost certainly junk.
On the other hand, if you are just dealing with very small numbers, that is less of a problem, since R can handle number as small as .Machine$double.xmin (usually 2e-308).
Compare these two analyses.
x1 <- rnorm(50, 1, 1e-15)
y1 <- rnorm(50, 1 + 1e-15, 1e-15)
t.test(x1, y1) #Should throw an error
x2 <- rnorm(50, 0, 1e-15)
y2 <- rnorm(50, 1e-15, 1e-15)
t.test(x2, y2) #ok
In the first case, differences between numbers only occur after many significant figures, so the data are "nearly constant". In the second case, Although the size of the differences between numbers are the same, compared to the magnitude of the numbers themselves they are large.
As mentioned by e3bo, you can use multiple-precision floating point numbers using the Rmpfr package.
mpfr("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825")
These are slower and more memory intensive to use than regular (double precision) numeric vectors, but can be useful if you have a poorly conditioned problem or unstable algorithm.
If you are producing the entire output yourself, you can use sprintf(), e.g.
> sprintf("%.10f",0.25)
[1] "0.2500000000"
specifies that you want to format a floating point number with ten decimal points (in %.10f the f is for float and the .10 specifies ten decimal points).
I don't know of any way of forcing R's higher level functions to print an exact number of digits.
Displaying 100 digits does not make sense if you are printing R's usual numbers, since the best accuracy you can get using 64-bit doubles is around 16 decimal digits (look at .Machine$double.eps on your system). The remaining digits will just be junk.
One more solution able to control the how many decimal digits to print out based on needs (if you don't want to print redundant zero(s))
For example, if you have a vector as elements and would like to get sum of it
elements <- c(-1e-05, -2e-04, -3e-03, -4e-02, -5e-01, -6e+00, -7e+01, -8e+02)
sum(elements)
## -876.5432
Apparently, the last digital as 1 been truncated, the ideal result should be -876.54321, but if set as fixed printing decimal option, e.g sprintf("%.10f", sum(elements)), redundant zero(s) generate as -876.5432100000
Following the tutorial here: printing decimal numbers, if able to identify how many decimal digits in the certain numeric number, like here in -876.54321, there are 5 decimal digits need to print, then we can set up a parameter for format function as below:
decimal_length <- 5
formatC(sum(elements), format = "f", digits = decimal_length)
## -876.54321
We can change the decimal_length based on each time query, so it can satisfy different decimal printing requirement.
If you work primarily with tibbles, there is a function that enforces digits: num().
Here is an example:
library(tidyverse)
data <- tribble(
~ weight, ~ weight_selfreport,
81.5,81.66969147005445,
72.6,72.59528130671505,
92.9,93.01270417422867,
79.4,79.4010889292196,
94.6,96.64246823956442,
80.2,79.4010889292196,
116.2,113.43012704174228,
95.4,95.73502722323049,
99.5,99.8185117967332
)
data <-
data %>%
mutate(across(where(is.numeric), ~ num(., digits = 3)))
data
#> # A tibble: 9 × 2
#> weight weight_selfreport
#> <num:.3!> <num:.3!>
#> 1 81.500 81.670
#> 2 72.600 72.595
#> 3 92.900 93.013
#> 4 79.400 79.401
#> 5 94.600 96.642
#> 6 80.200 79.401
#> 7 116.200 113.430
#> 8 95.400 95.735
#> 9 99.500 99.819
Thus you can even decide to have different rounding options depending on what your needs are. I find it very helpful and a rather quick solution to printing dfs.
I previously used the prod() function in R that can give me the product, and it works fine for big numbers. The numbers I have are too small like 1.294528e-07 and once I take the product it gives me a 0. How can I get the accurate product with exact decimal numbers?
This sounds like a job for Rmpfr:
x <- 1.294528e-07;
x^100;
## [1] 0
library('Rmpfr');
mpfr200 <- function(...) mpfr(...,precBits=200);
x <- mpfr200(1.294528e-07);
x^100;
## 1 'mpfr' number of precision 200 bits
## [1] 1.6260909947893069252110098843324246495136887016336218206204661e-689
Or you could try using big rationals from gmp, although that can get unwieldy fast:
library('gmp');
x <- as.bigq(1.294528e-07);
x^100;
## Big Rational ('bigq') :
## [1] 863201774730415899361077141424209396921125795515936990572548766128423810485376236957138978501283812494839104247698243918794530436552717763753923415271480284747830193402522833445368586578235815336302329397252055448087703163456038666698935354732741208048881276922439385153961853551463063865863458552423073323374618023089542368149617965922293453325011050815707644365808660423522776994133587512616070446174486428153909409377712433145387919387175172482342168167092570331925560436171324785600650158865676862026009729048525389272889703709380624434349438465164559591242984791355618727989751127260257309242805499481511142165616784856784942417419338154196561431152388897904866047119736434465720555151366859879507712533271194851766672024261634534292974370183919317337519761869292257947511511111895425764926171263133863980854536246390233199502174749146911367500644673909293464659053254182209374190247093969004854275674922622004129684228283369400286413197699863545912211106461047595912964876198783114172495242447965086668614473659343976994896679029656266765528726921384485164153780083326552118475505412074971594197272427677831237385443579950907872485700396062323506489811292749356021319775368577664875790645937426179486396681942844892307294288187671687510056569029216067321069225537944854772595983467728588640812585079820715315382504185719050646602130250650306723313760231069912835376365077115331890400516502810239814459239282321065702537572103441710647744406489548580900916084596895906189449738524638127337711843685456775272799845630310027842996833372802952394634016929280394482001/53084469288402965415857953902888840109250315594591772197851276288408082158869345776872184284291470495326835835491268017776297213098616208286592801322449982740570898437845767564651639451594841758957168240360072929342348878909784083488070009533176658698675760470010215436132534526706916446032842195249059760060209393388578176281027744679436285035293376786965957429093838689438026612141820062960073237944227430409290082873605748455349816343081466372681612738552636294666573661997989000563367893746123926316870120929629731301360766711677076606816082939449299471019533119911247114865751561110071173719092050562287666719013887097553109594042589835370732409680749273477741701995190365166750190649349508586781414000112900259875654673888811075100415790235930270448790550846107436360615795146817327563001398966815753145995110673462134196824939359497706430237425390060733252224220979131253874493851823165781457427314551881655553433521397260371393668335053627112038905459972042994824319713601980913921755210218082851146588240382210406887660412630451416112206306502796230074832738884324233514086958873577398927563897852887699678587467916741882087729456997268017154775450070371874680332524775280043635270781581135769020865808796073362505082201497885288236887117727248916243704472117062440908853938749830047482062530807255930310025959255017626077608884577821899189515192765061903944746945679900747890669013446056647522960607623949336195016784356934505954115977283306997415274187752372480232652878520163417566097389917356958213807994947634794209832173114356392822435844256992216702376456519427913660058510779720382422426729352627871147386069533497741201545766859622239986052843328404669795291152396764393702113455439610494964706121896827191760262984304690887475635610694078746800875955908479469409563047706020039725815572087005410536948676710051947334063697608908539017716795313119629533327813992071776512146390147185444968042597376280912548998385218672413833388480083312283356458666501168482077474943858309275329657545594008977132937574085616539588927255406484838471048801662983695044651588178399267847057683205128610922849562650411762874243138435345707386259866513245949164125352989897783775852403441398200260025840304184956928642989258546038224598392605412214974894309376
(Notice the slash at character 1570 into that digit sequence.)