Calculating SHA1 hashes with digest() and sha1()

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) a0 - a1 a <- c(a0, a1) # hexadecimal representation sprintf("%a", a)

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") # same hash with sha1 with default digits (14) sapply(a, sha1) # larger digits can lead to different hashes sapply(a, sha1, digits = 15) # 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) sapply(a, sha1, digits = 10) # case where truncating gives different hexadecimal value c(sha1(pi), sha1(pi, digits = 13), sha1(pi, digits = 10))

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.

# taken from the help file of lm.influence lm_SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings) lm_sum <- summary(lm_SR) class(lm_sum) # str() gives the structure of the lm object str(lm_sum) # extract the coefficients and their standard error coef_sum <- coef(lm_sum)[, c("Estimate", "Std. Error")] # extract sigma sigma <- lm_sum$sigma # check the class of each component class(coef_sum) class(sigma) # sha1() has methods for both matrix and numeric # because the values originate from floating point arithmetic it is better to use a low number of digits sha1(coef_sum, digits = 4) sha1(sigma, digits = 4) # we want a single hash # combining the components in a list is a solution that works sha1(list(coef_sum, sigma), digits = 4) # now turn everything into an S3 method # - a function with name "sha1.classname" # - must have the same arguments as sha1() sha1.summary.lm <- function(x, digits = 4, zapsmall = 7){ coef_sum <- coef(x)[, c("Estimate", "Std. Error")] sigma <- x$sigma combined <- list(coef_sum, sigma) sha1(combined, digits = digits, zapsmall = zapsmall) } sha1(lm_sum) # try an altered dataset LCS2 <- LifeCycleSavings[rownames(LifeCycleSavings) != "Zambia", ] lm_SR2 <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LCS2) sha1(summary(lm_SR2))

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) # str() gives the structure of the lm object str(lm_SR) # extract the model and the terms lm_model <- lm_SR$model lm_terms <- lm_SR$terms # check their class class(lm_model) # handled by sha1() class(lm_terms) # not handled by sha1() # define a method for formula sha1.formula <- function(x, digits = 14, zapsmall = 7, ..., algo = "sha1"){ sha1(as.character(x), digits = digits, zapsmall = zapsmall, algo = algo) } sha1(lm_terms) sha1(lm_model) # define a method for lm sha1.lm <- function(x, digits = 14, zapsmall = 7, ..., algo = "sha1"){ lm_model <- x$model lm_terms <- x$terms combined <- list(lm_model, lm_terms) sha1(combined, digits = digits, zapsmall = zapsmall, ..., algo = algo) } sha1(lm_SR) sha1(lm_SR2)

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
    • other metadata
    • resulting model
  • calculate sha1()

    file fingerprint

    ~ `sha1()` on the stable parts
    

    status fingerprint

    ~ `sha1()` on the parts that result for the model
    
  • Prepare analysis objects

  • 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
  • Loop over all rda files
    • Do nothing if the analysis was run
    • Otherwise run the analysis and update the status and status fingerprint