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Floating Point Utilities

Source: R/fp_utilities.R
fp_utilities.Rd

Utilities for floating-point number manipulation and analysis, including adjacent representable values, ULP distances, and condition numbers.

Floating-Point Navigation:

  • float_next(x) / float_prior(x) move to the next greater/smaller representable value.

  • float_distance(x, y) returns the representation distance in ULPs.

  • float_advance(x, n) advances by \(n\) ULPs.

  • ulp(x) returns the size of one unit in the last place at x.

Comparisons:

  • relative_difference(x, y) and epsilon_difference(x, y) provide scale-aware measures of deviation.

Condition Numbers: summation_condition_number and evaluation_condition_number help quantify numerical sensitivity to perturbations.

Usage

float_next(x)

float_prior(x)

float_distance(x, y)

float_advance(x, distance)

ulp(x)

relative_difference(x, y)

epsilon_difference(x, y)

Arguments

x

A numeric value.

y

A numeric value.

distance

Integer number of ULPs to advance by.

Value

A numeric value after performing the specified floating point operation.

See also

Boost Documentation for more details on the mathematical background.

Examples

print(float_next(1.0), digits = 20)
#> [1] 1.000000000000000222
print(float_distance(1.0, 2.0), digits = 20)
#> [1] 4503599627370496
print(float_prior(1.0), digits = 20)
#> [1] 0.99999999999999988898
print(float_advance(1.0, 10), digits = 20)
#> [1] 1.0000000000000022204
print(ulp(1.0), digits = 20)
#> [1] 2.2204460492503130808e-16
print(relative_difference(1.1, 1.1000009), digits = 20)
#> [1] 8.1818181805395140825e-07
print(epsilon_difference(1.1, 1.1000009), digits = 20)
#> [1] 3684763330.909090519