# Calculating SHA1 hashes with digest() and sha1()

Written Jan 2016, updated Jan 2018 and Oct 2020

NB: This vignette is (still) work-in-progress and not yet complete.

TBD

## Difference between digest() and sha1()

R FAQ 7.31 illustrates potential problems with floating point arithmetic. Mathematically the equality $x = \sqrt{x}^2$ should hold. But the precision of floating points numbers is finite. Hence some rounding is done, leading to numbers which are no longer identical.

An illustration:

> a0 <- 2
> b <- sqrt(a0)
> a1 <- b^2
> identical(a0, a1)
[1] FALSE
> a0 - a1
[1] -4.440892e-16
> a <- c(a0, a1)
> sprintf("%a", a)
[1] "0x1p+1"               "0x1.0000000000001p+1"

Although the difference is small, any difference will result in different hash when using the digest() function. However, the sha1() function tackles this problem by using the hexadecimal representation of the numbers and truncates that representation to a certain number of digits prior to calculating the hash function.

> library(digest)
> sapply(a, digest, algo = "sha1")
[1] "315a5aa84aa6cfa4f3fb4b652a596770be0365e8"
[2] "5e3999bf79c230f7430e97d7f30070a7eff5ec92"
> sapply(a, sha1)
[1] "8a938d8f5fb9b8ccb6893aa1068babcc517f32d4"
[2] "8a938d8f5fb9b8ccb6893aa1068babcc517f32d4"
> sapply(a, sha1, digits = 15)
[2] "5a173e2445df1134908037f69ac005fbd8afee74"
> sapply(a, sha1, digits = 13)
[1] "43b3b465c975af322c85473190a9214b79b79bf6"
[2] "43b3b465c975af322c85473190a9214b79b79bf6"
> sapply(a, sha1, digits = 10)
[1] "6b537a9693c750ed535ca90527152f06e358aa3a"
[2] "6b537a9693c750ed535ca90527152f06e358aa3a"
> c(sha1(pi), sha1(pi, digits = 13), sha1(pi, digits = 10))
[1] "169388cf1ce60dc4e9904a22bc934c5db33d975b"
[2] "20dc38536b6689d5f2d053f30efb09c44af78378"
[3] "3a727417bd1807af2f0148cf3de69abff32c23ec"

The result of floating point arithematic on 32-bit and 64-bit can be slightly different. E.g. print(pi ^ 11, 22) returns 294204.01797389047 on 32-bit and 294204.01797389053 on 64-bit. Note that only the last 2 digits are different.

command 32-bit 64-bit
print(pi ^ 11, 22) 294204.01797389047 294204.01797389053
sprintf("%a", pi ^ 11) "0x1.1f4f01267bf5fp+18" "0x1.1f4f01267bf6p+18"
digest(pi ^ 11, algo = "sha1") "c5efc7f167df1bb402b27cf9b405d7cebfba339a" "b61f6fea5e2a7952692cefe8bba86a00af3de713"
sha1(pi ^ 11, digits = 14) "5c7740500b8f78ec2354ea6af58ea69634d9b7b1" "4f3e296b9922a7ddece2183b1478d0685609a359"
sha1(pi ^ 11, digits = 13) "372289f87396b0877ccb4790cf40bcb5e658cad7" "372289f87396b0877ccb4790cf40bcb5e658cad7"
sha1(pi ^ 11, digits = 10) "c05965af43f9566bfb5622f335817f674abfc9e4" "c05965af43f9566bfb5622f335817f674abfc9e4"

TBD

## Creating a sha1 method for other classes

### How to

1. Identify the relevant components for the hash.
2. Determine the class of each relevant component and check if they are handled by sha1().
• Write a method for each component class not yet handled by sha1.
3. Extract the relevant components.
4. Combine the relevant components into a list. Not required in case of a single component.
5. Apply sha1() on the (list of) relevant component(s).
6. Turn this into a function with name sha1._classname_.
7. sha1._classname_ needs exactly the same arguments as sha1()
8. Choose sensible defaults for the arguments
• zapsmall = 7 is recommended.
• digits = 14 is recommended in case all numerics are data.
• digits = 4 is recommended in case some numerics stem from floating point arithmetic.

### summary.lm

Let’s illustrate this using the summary of a simple linear regression. Suppose that we want a hash that takes into account the coefficients, their standard error and sigma.

> lm_SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
> lm_sum <- summary(lm_SR)
> class(lm_sum)
[1] "summary.lm"
> str(lm_sum)
List of 11
$call : language lm(formula = sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)$ terms        :Classes 'terms', 'formula'  language sr ~ pop15 + pop75 + dpi + ddpi
.. ..- attr(*, "variables")= language list(sr, pop15, pop75, dpi, ddpi)
.. ..- attr(*, "factors")= int [1:5, 1:4] 0 1 0 0 0 0 0 1 0 0 ...
.. .. ..- attr(*, "dimnames")=List of 2
.. .. .. ..$: chr [1:5] "sr" "pop15" "pop75" "dpi" ... .. .. .. ..$ : chr [1:4] "pop15" "pop75" "dpi" "ddpi"
.. ..- attr(*, "term.labels")= chr [1:4] "pop15" "pop75" "dpi" "ddpi"
.. ..- attr(*, "order")= int [1:4] 1 1 1 1
.. ..- attr(*, "intercept")= int 1
.. ..- attr(*, "response")= int 1
.. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
.. ..- attr(*, "predvars")= language list(sr, pop15, pop75, dpi, ddpi)
.. ..- attr(*, "dataClasses")= Named chr [1:5] "numeric" "numeric" "numeric" "numeric" ...
.. .. ..- attr(*, "names")= chr [1:5] "sr" "pop15" "pop75" "dpi" ...
$residuals : Named num [1:50] 0.864 0.616 2.219 -0.698 3.553 ... ..- attr(*, "names")= chr [1:50] "Australia" "Austria" "Belgium" "Bolivia" ...$ coefficients : num [1:5, 1:4] 28.566087 -0.461193 -1.691498 -0.000337 0.409695 ...
..- attr(*, "dimnames")=List of 2
.. ..$: chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ... .. ..$ : chr [1:4] "Estimate" "Std. Error" "t value" "Pr(>|t|)"
$aliased : Named logi [1:5] FALSE FALSE FALSE FALSE FALSE ..- attr(*, "names")= chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ...$ sigma        : num 3.8
$df : int [1:3] 5 45 5$ r.squared    : num 0.338
$adj.r.squared: num 0.28$ fstatistic   : Named num [1:3] 5.76 4 45
..- attr(*, "names")= chr [1:3] "value" "numdf" "dendf"
$cov.unscaled : num [1:5, 1:5] 3.74 -7.24e-02 -4.46e-01 -7.86e-05 -1.88e-02 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ...
.. ..$: chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ... - attr(*, "class")= chr "summary.lm" > coef_sum <- coef(lm_sum)[, c("Estimate", "Std. Error")] > sigma <- lm_sum$sigma
> class(coef_sum)
[1] "matrix" "array"
> class(sigma)
[1] "numeric"
> sha1(coef_sum, digits = 4)
[1] "3f0b0c552f94d753fcc8deb4d3e9fc11a83197af"
> sha1(sigma, digits = 4)
> sha1(list(coef_sum, sigma), digits = 4)
[1] "476d27265365cd41662eedf059b335d38a221cc2"
> sha1.summary.lm <- function(x, digits = 4, zapsmall = 7) {
+     coef_sum <- coef(x)[, c("Estimate", "Std. Error")]
+     sigma <- x$sigma + com .... [TRUNCATED] > sha1(lm_sum) [1] "476d27265365cd41662eedf059b335d38a221cc2" > LCS2 <- LifeCycleSavings[rownames(LifeCycleSavings) != + "Zambia", ] > lm_SR2 <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LCS2) > sha1(summary(lm_SR2)) [1] "90beb028833bf0542997fde7c3f19e5b9fdfeef4" ### lm Let’s illustrate this using the summary of a simple linear regression. Suppose that we want a hash that takes into account the coefficients, their standard error and sigma. > class(lm_SR) [1] "lm" > str(lm_SR) List of 12$ coefficients : Named num [1:5] 28.566087 -0.461193 -1.691498 -0.000337 0.409695
..- attr(*, "names")= chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ...
$residuals : Named num [1:50] 0.864 0.616 2.219 -0.698 3.553 ... ..- attr(*, "names")= chr [1:50] "Australia" "Austria" "Belgium" "Bolivia" ...$ effects      : Named num [1:50] -68.38 -14.29 7.3 -3.52 -7.94 ...
..- attr(*, "names")= chr [1:50] "(Intercept)" "pop15" "pop75" "dpi" ...
$rank : int 5$ fitted.values: Named num [1:50] 10.57 11.45 10.95 6.45 9.33 ...
..- attr(*, "names")= chr [1:50] "Australia" "Austria" "Belgium" "Bolivia" ...
$assign : int [1:5] 0 1 2 3 4$ qr           :List of 5
..$qr : num [1:50, 1:5] -7.071 0.141 0.141 0.141 0.141 ... .. ..- attr(*, "dimnames")=List of 2 .. .. ..$ : chr [1:50] "Australia" "Austria" "Belgium" "Bolivia" ...
.. .. ..$: chr [1:5] "(Intercept)" "pop15" "pop75" "dpi" ... .. ..- attr(*, "assign")= int [1:5] 0 1 2 3 4 ..$ qraux: num [1:5] 1.14 1.17 1.16 1.15 1.05
..$pivot: int [1:5] 1 2 3 4 5 ..$ tol  : num 1e-07
..$rank : int 5 ..- attr(*, "class")= chr "qr"$ df.residual  : int 45
$xlevels : Named list()$ call         : language lm(formula = sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
$terms :Classes 'terms', 'formula' language sr ~ pop15 + pop75 + dpi + ddpi .. ..- attr(*, "variables")= language list(sr, pop15, pop75, dpi, ddpi) .. ..- attr(*, "factors")= int [1:5, 1:4] 0 1 0 0 0 0 0 1 0 0 ... .. .. ..- attr(*, "dimnames")=List of 2 .. .. .. ..$ : chr [1:5] "sr" "pop15" "pop75" "dpi" ...
.. .. .. ..$: chr [1:4] "pop15" "pop75" "dpi" "ddpi" .. ..- attr(*, "term.labels")= chr [1:4] "pop15" "pop75" "dpi" "ddpi" .. ..- attr(*, "order")= int [1:4] 1 1 1 1 .. ..- attr(*, "intercept")= int 1 .. ..- attr(*, "response")= int 1 .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> .. ..- attr(*, "predvars")= language list(sr, pop15, pop75, dpi, ddpi) .. ..- attr(*, "dataClasses")= Named chr [1:5] "numeric" "numeric" "numeric" "numeric" ... .. .. ..- attr(*, "names")= chr [1:5] "sr" "pop15" "pop75" "dpi" ...$ model        :'data.frame':  50 obs. of  5 variables:
..$sr : num [1:50] 11.43 12.07 13.17 5.75 12.88 ... ..$ pop15: num [1:50] 29.4 23.3 23.8 41.9 42.2 ...
..$pop75: num [1:50] 2.87 4.41 4.43 1.67 0.83 2.85 1.34 0.67 1.06 1.14 ... ..$ dpi  : num [1:50] 2330 1508 2108 189 728 ...
..$ddpi : num [1:50] 2.87 3.93 3.82 0.22 4.56 2.43 2.67 6.51 3.08 2.8 ... ..- attr(*, "terms")=Classes 'terms', 'formula' language sr ~ pop15 + pop75 + dpi + ddpi .. .. ..- attr(*, "variables")= language list(sr, pop15, pop75, dpi, ddpi) .. .. ..- attr(*, "factors")= int [1:5, 1:4] 0 1 0 0 0 0 0 1 0 0 ... .. .. .. ..- attr(*, "dimnames")=List of 2 .. .. .. .. ..$ : chr [1:5] "sr" "pop15" "pop75" "dpi" ...
.. .. .. .. ..$: chr [1:4] "pop15" "pop75" "dpi" "ddpi" .. .. ..- attr(*, "term.labels")= chr [1:4] "pop15" "pop75" "dpi" "ddpi" .. .. ..- attr(*, "order")= int [1:4] 1 1 1 1 .. .. ..- attr(*, "intercept")= int 1 .. .. ..- attr(*, "response")= int 1 .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> .. .. ..- attr(*, "predvars")= language list(sr, pop15, pop75, dpi, ddpi) .. .. ..- attr(*, "dataClasses")= Named chr [1:5] "numeric" "numeric" "numeric" "numeric" ... .. .. .. ..- attr(*, "names")= chr [1:5] "sr" "pop15" "pop75" "dpi" ... - attr(*, "class")= chr "lm" > lm_model <- lm_SR$model
> lm_terms <- lm_SR$terms > class(lm_model) [1] "data.frame" > class(lm_terms) [1] "terms" "formula" > sha1.formula <- function(x, digits = 14, zapsmall = 7, + ..., algo = "sha1") { + sha1(as.character(x), digits = digits, zapsmall = zapsmall .... [TRUNCATED] > sha1(lm_terms) [1] "2737d209720aa7d1c0555050ad06ebe89f3850cd" > sha1(lm_model) [1] "27b7dd9e3e09b9577da6947b8473b63a1d0b6eb4" > sha1.lm <- function(x, digits = 14, zapsmall = 7, + ..., algo = "sha1") { + lm_model <- x$model
+     lm_terms <- x\$terms
+     combined <- .... [TRUNCATED]
> sha1(lm_SR)
[1] "7eda2a9d58e458c8e782e40ce140d62b836b2a2f"
> sha1(lm_SR2)
[1] "4d3abdb1f17bd12fdf9d9b91a2ad04c07824fe4a"

## Using hashes to track changes in analysis

Use case

• automated analysis

• update frequency of the data might be lower than the frequency of automated analysis

• similar analyses on many datasets (e.g. many species in ecology)

• analyses that require a lot of computing time

• not rerunning an analysis because nothing has changed saves enough resources to compensate the overhead of tracking changes
• Bundle all relevant information on an analysis in a class

• data
• method
• formula
• resulting model
• calculate sha1()

file fingerprint ~ sha1() on the stable parts

status fingerprint ~ sha1() on the parts that result for the model

1. Prepare analysis objects
2. Store each analysis object in a rda file which uses the file fingerprint as filename
• File will already exist when no change in analysis
• Don’t overwrite existing files
3. Loop over all rda files
• Do nothing if the analysis was run
• Otherwise run the analysis and update the status and status fingerprint