Safer Decimal Number (In)Equality Testing Operators

The %d==%, %d!=% %d<%, %d>%, %d<=%, %d>=% (in)equality operators perform decimal (type "double") number truth testing.
They are virtually equivalent to the regular (in)equality operators,
==, !=, <, >, <=, >=,
except for 2 aspects:

1. The decimal number (in)equality operators assume that if the absolute difference between any 2 numbers x and y is smaller than the Machine tolerance, sqrt(.Machine$double.eps), then x and y should be consider to be equal.
   For example: (0.1 * 7) == 0.7 returns FALSE, even though they are equal, due to the way decimal numbers are stored in programming languages like 'R' and 'Python'.
   But (0.1 * 7) %d==% 0.7 returns TRUE.
   

2. Only numeric input is allowed, so characters are not coerced to numbers.
   I.e. 1 < "a" gives TRUE, whereas 1 %d<% "a" gives an error.
   For character equality testing, see %s==% from the 'stringi' package.
   

Thus these operators provide safer decimal number (in)equality tests.

There are also the x %d{}% bnd and x %d!{}% bnd operators, where bnd is a vector of length 2, or a 2-column matrix (nrow(bnd)==length(x) or nrow(bnd)==1).
The x %d{}% bnd operator checks if x is within the closed interval with bounds defined by bnd.
The x %d!{}% bnd operator checks if x is outside the closed interval with bounds defined by bnd.

Moreover, the function is_wholenumber() is added, to safely test for whole numbers.

Usage

x %d==% y

x %d!=% y

x %d<% y

x %d>% y

x %d<=% y

x %d>=% y

x %d{}% bnd

x %d!{}% bnd

is_wholenumber(x, tol = sqrt(.Machine$double.eps))

Arguments

x, y

numeric vectors, matrices, or arrays.

bnd

either a vector of length 2, or a matrix with 2 columns and 1 row, or else a matrix with 2 columns where nrow(bnd)==length(x) (or can be recycled to be nrow(bnd)==length(x)).
The first element/column of bnd gives the lower bound of the closed interval;
The second element/column of bnd gives the upper bound of the closed interval.

tol

a single, strictly positive number close to zero, giving the tolerance.

Value

For the %d...% operators:

A logical vector with the same dimensions as x, indicating the result of the element by element comparison.

NOTE: Inf by Inf and -Inf by -Inf comparisons with the %d...% operators return NA.

For is_wholenumber():

A logical vector with the same dimensions as x, indicating the result of the element by element comparison.

NOTE: Inf, -Inf, NaN and NA all return NA for is_wholenumber().

See also

tinycodet_safer

Examples

x <- c(0.3, 0.6, 0.7)
y <- c(0.1 * 3, 0.1 * 6, 0.1 * 7)
print(x)
#> [1] 0.3 0.6 0.7
print(y)
#> [1] 0.3 0.6 0.7

x == y # gives FALSE, but should be TRUE
#> [1] FALSE FALSE FALSE
x != y # gives TRUE, should be FALSE
#> [1] TRUE TRUE TRUE
x > y # not wrong
#> [1] FALSE FALSE FALSE
x < y # gives TRUE, should be FALSE
#> [1] TRUE TRUE TRUE

# same as above, but here the results are correct:
x %d==% y # correct
#> [1] TRUE TRUE TRUE
x %d!=% y # correct
#> [1] FALSE FALSE FALSE
x %d<% y # correct
#> [1] FALSE FALSE FALSE
x %d>% y # correct
#> [1] FALSE FALSE FALSE
x %d<=% y # correct
#> [1] TRUE TRUE TRUE
x %d>=% y # correct
#> [1] TRUE TRUE TRUE

# check if numbers are in closed interval:
x <- c(0.3, 0.6, 0.7)
bnd <- cbind(x - 0.1, x + 0.1)
x %d{}% bnd
#> [1] TRUE TRUE TRUE
x %d!{}% bnd
#> [1] FALSE FALSE FALSE

# These operators work for integers also:
x <- 1L:5L
y <- 1L:5L
x %d==% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d!=% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d<% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d>% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d<=% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d>=% y
#> [1] TRUE TRUE TRUE TRUE TRUE

x <- 1L:5L
y <- x + 1L
x %d==% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d!=% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d<% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d>% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d<=% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d>=% y
#> [1] FALSE FALSE FALSE FALSE FALSE

x <- 1L:5L
y <- x - 1L
x %d==% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d!=% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d<% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d>% y
#> [1] TRUE TRUE TRUE TRUE TRUE
x %d<=% y
#> [1] FALSE FALSE FALSE FALSE FALSE
x %d>=% y
#> [1] TRUE TRUE TRUE TRUE TRUE

# is_wholenumber:
is_wholenumber(1:10 + c(0, 0.1))
#>  [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE