%~==% {cppdoubles}

Relative comparison of double-precision floating point numbers

Description

Fast and efficient methods for comparing floating point numbers using relative differences.

Usage

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))
)

Arguments

x

A double vector.

y

A double vector.

tol

A double vector of tolerances.

Details

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.

Value

A logical vector.

Examples

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))