Calculating SHA1 hashes with digest() and sha1()

knitr::opts_chunk$set(collapse = TRUE,
                      class.output = NULL,
                      class.message = NULL,
                      class.warning = NULL,
                      class.error = NULL)

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



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digest documentation built on Sept. 23, 2021, 5:10 p.m.