%~==% | R Documentation |
Fast and efficient methods for comparing floating point numbers using relative differences.
x %~==% y
x %~>=% y
x %~>% y
x %~<=% y
x %~<% y
double_equal(
x,
y,
tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))
)
double_gte(
x,
y,
tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))
)
double_gt(
x,
y,
tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))
)
double_lte(
x,
y,
tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))
)
double_lt(
x,
y,
tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))
)
x |
A double vector. |
y |
A double vector. |
tol |
A double vector of tolerances. |
When either x[i]
or y[i]
contain a number very close to zero,
absolute differences are used, otherwise relative differences are used.
The output of double_equal()
is commutative,
which means the order of arguments don't matter
whereas this is not the case for all.equal.numeric()
.
The calculation is done in C++ and is quite efficient. Recycling follows the usual R rules and is done without allocating additional memory.
A logical vector.
library(cppdoubles)
### Basic usage ###
# Standard equality operator
sqrt(2)^2 == 2
# approximate equality operator
sqrt(2)^2 %~==% 2
sqrt(2)^2 %~>=% 2
sqrt(2)^2 %~<=% 2
sqrt(2)^2 %~>% 2
sqrt(2)^2 %~<% 2
# Alternatively
double_equal(2, sqrt(2)^2)
double_gte(2, sqrt(2)^2)
double_lte(2, sqrt(2)^2)
double_gt(2, sqrt(2)^2)
double_lt(2, sqrt(2)^2)
rel_diff(1, 1 + 2e-10)
double_equal(1, 1 + 2e-10, tol = sqrt(.Machine$double.eps))
double_equal(1, 1 + 2e-10, tol = 1e-10)
# Optionally set a threshold for all comparison
options(cppdoubles.tolerance = 1e-10)
double_equal(1, 1 + 2e-10)
# Floating point errors magnified example
x1 <- 1.1 * 100 * 10^200
x2 <- 110 * 10^200
abs_diff(x1, x2) # Large absolute difference
rel_diff(x1, x2) # Very small relative difference as expected
double_equal(x1, x2)
# all.equal is not commutative but double_equal is
all.equal(10^-8, 2 * 10^-8)
all.equal(2 * 10^-8, 10^-8)
double_equal(10^-8, 2 * 10^-8)
double_equal(2 * 10^-8, 10^-8)
# All comparisons are vectorised and recycled
double_equal(sqrt(1:10),
sqrt(1:5),
tol = c(-Inf, 1e-10, Inf))
# One can check for whole numbers like so
whole_number <- function(x, tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))){
double_equal(x, round(x))
}
whole_number(seq(-5, 5, 0.25))
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