Calculating SHA1 hashes with digest() and sha1()

Thierry Onkelinx and Dirk Eddelbuettel

2018-10-10

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

Short intro on hashes

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:

# FAQ 7.31
a0 <- 2
b <- sqrt(a0)
a1 <- b ^ 2
identical(a0, a1)
## [1] FALSE
a0 - a1
## [1] -4.440892e-16
a <- c(a0, a1)
# hexadecimal representation
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)
# different hashes with digest
sapply(a, digest, algo = "sha1")
## [1] "315a5aa84aa6cfa4f3fb4b652a596770be0365e8"
## [2] "5e3999bf79c230f7430e97d7f30070a7eff5ec92"
# same hash with sha1 with default digits (14)
sapply(a, sha1)
## [1] "8a938d8f5fb9b8ccb6893aa1068babcc517f32d4"
## [2] "8a938d8f5fb9b8ccb6893aa1068babcc517f32d4"
# larger digits can lead to different hashes
sapply(a, sha1, digits = 15)
## [1] "98eb1dc9fada00b945d3ef01c77049ee5a4b7b9c"
## [2] "5a173e2445df1134908037f69ac005fbd8afee74"
# decreasing the number of digits gives a stronger truncation
# the hash will change when then truncation gives a different result
# case where truncating gives same hexadecimal value
sapply(a, sha1, digits = 13)
## [1] "43b3b465c975af322c85473190a9214b79b79bf6"
## [2] "43b3b465c975af322c85473190a9214b79b79bf6"
sapply(a, sha1, digits = 10)
## [1] "6b537a9693c750ed535ca90527152f06e358aa3a"
## [2] "6b537a9693c750ed535ca90527152f06e358aa3a"
# case where truncating gives different hexadecimal value
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"

Choosing digest() or sha1()

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.

## [1] "summary.lm"
## 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"
## [1] "matrix"
## [1] "numeric"
## [1] "19de60f22fbb5f31e2f39d043d78126b692f3838"
## [1] "cbc83d1791ef1eeadd824ea9a038891b5889056b"
## [1] "fd6b6805780dcf88e11fe05ba4693170e2dfb170"
## [1] "fd6b6805780dcf88e11fe05ba4693170e2dfb170"
## [1] "0643afd880f6f9c4b2aa935bec91724ba103198e"

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.

## [1] "lm"
## 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"
## [1] "data.frame"
## [1] "terms"   "formula"
## [1] "2737d209720aa7d1c0555050ad06ebe89f3850cd"
## [1] "b1b32bb6d983e1c515706c33ffef6120d811fe52"
## [1] "2b03ad0002dc6c3676555b60f3f59781e1f42eb0"
## [1] "d2bbcc2bfc737e51666d4bf86841f6b25149e224"

Using hashes to track changes in analysis

Use case

  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