Constant Folding

Background

Constant folding is an optimization technique that eliminates expressions that calculate a value that can already be determined before code execution. These are typically calculations that only reference constant values or expressions that reference variables whose values are constant.

For example, consider the statement:

i <- 320 * 200 * 32

Most compilers would not actually generate two multiply instructions. Instead, they identify constructs such as these and substitute the computed values (in this case, 2048000). This way, the code will be replaced by:

i <- 2048000

Example

A simple example would be to have to convert the unit of many temporary samples from hours to miliseconds miliseconds <- 1000 * 60 * 60 * hours.

code <- paste(
  "hours_vector <- runif(1000, 0, 24)",
  "ms_vector <- numeric(1000)",
  "# of course it would be much efficient to do vectorized operations xP",
  "for (i in seq_along(hours_vector)) {",
  "  ms_vector[i] <- 1000 * 60 * 60 * hours_vector[i]",
  "}",
  sep = "\n"
)
cat(code)

## hours_vector <- runif(1000, 0, 24)
## ms_vector <- numeric(1000)
## # of course it would be much efficient to do vectorized operations xP
## for (i in seq_along(hours_vector)) {
##   ms_vector[i] <- 1000 * 60 * 60 * hours_vector[i]
## }

Then, the automatically optimized code would be:

opt_code <- opt_constant_folding(list(code))
cat(opt_code$codes[[1]])

## hours_vector <- runif(1000, 0, 24)
## ms_vector <- numeric(1000)
## # of course it would be much efficient to do vectorized operations xP
## for (i in seq_along(hours_vector)) {
##   ms_vector[i] <- 3600000 * hours_vector[i]
## }

And if we measure the execution time of each one, and the speed-up:

bmark_res <- microbenchmark({
  eval(parse(text = code))
}, {
  eval(parse(text = opt_code))
})
autoplot(bmark_res)

plot of chunk unnamed-chunk-4

speed_up(bmark_res)

##            Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
## Expr_2 29.43468 29.32992 26.74016 29.57885 30.70978 32.88494

Implementation

Actually, opt_constant_folding will fold expressions that are conformed solely by operators and constants which tokens parsed with utils::getParseData function are:

##  [1] "'+'"  "'-'"  "'*'"  "'/'"  "'^'"  "GT"   "GE"   "LT"   "LE"   "EQ"  
## [11] "NE"   "'!'"  "AND"  "OR"   "AND2" "OR2"

## [1] "NUM_CONST"  "STR_CONST"  "NULL_CONST"

## [1] "'('" "')'" "'{'" "'}'"

Floating-point precision

When folding, we can have floating-point precision issues, for instance, consider the following code:

x <- 1 / (2 + 1)
y <- 1 / (2 + 1)
z <- 1 / (2 + 1)
x + y + z == 1

## [1] TRUE

If we fold it, we would have:

code <- paste(
  "x <- 1/(2+1)",
  "y <- 1/(2+1)",
  "z <- 1/(2+1)",
  "x + y + z == 1",
  sep = "\n"
)
opt_code <- opt_constant_folding(list(code), fold_floats = TRUE)$codes[[1]]
cat(opt_code)

## x <- 0.333333333333333 
## y <- 0.333333333333333 
## z <- 0.333333333333333 
## x + y + z == 1

However, this code is not equivalent due to precision:

eval(parse(text = code))

## [1] TRUE

eval(parse(text = opt_code))

## [1] FALSE

In this case, we can use the parameter fold_floats. If set to FALSE, then the optimizer will fold every expression except those which will lose precision:

opt_code <- opt_constant_folding(list(code), fold_floats = FALSE)$codes[[1]]
cat(opt_code)

## x <- 1/ 3 
## y <- 1/ 3 
## z <- 1/ 3 
## x + y + z == 1

Consider this example where a sub-expression folding causes precision loss, but as it is not important in overall, then it can be folded:

opt_code <- opt_constant_folding(list(paste(
  "x <- 1/(2+1)", # will not fold it because we lose precision
  "y <- 1/(2+1) > 3", # however, folded or not, it is not > 3, so folds it
  sep = "\n"
)), fold_floats = FALSE)$codes[[1]]
cat(opt_code)

## x <- 1/ 3 
## y <- FALSE

To-Do