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Basic Mathematical Functions

Source: R/basic_functions.R
basic_functions.Rd

High-precision implementations of basic mathematical functions with enhanced numerical stability for special cases.

These functions provide numerically stable alternatives to standard operations, particularly useful when working with values near zero or when high precision is required.

Trigonometric Functions with \(\pi\):

  • sin_pi(x): Computes \(\sin(\pi x)\)

  • cos_pi(x): Computes \(\cos(\pi x)\)

Logarithmic and Exponential Functions:

  • log1p_boost(x): Computes \(\log(1 + x)\) accurately for small \(|x|\)

  • expm1_boost(x): Computes \(\exp(x) - 1\) accurately for small \(|x|\)

Root Functions:

  • cbrt(x): Computes the cube root \(x^{1/3}\)

  • sqrt1pm1(x): Computes \(\sqrt{1 + x} - 1\) accurately for small \(|x|\)

  • rsqrt(x): Computes the reciprocal square root \(\tfrac{1}{\sqrt{x}}\)

Power Functions:

  • powm1(x, y): Computes \(x^y - 1\) accurately

Geometric Functions:

  • hypot(x, y): Computes \(\sqrt{x^2 + y^2}\) without overflow/underflow

Usage

sin_pi(x)

cos_pi(x)

log1p_boost(x)

expm1_boost(x)

cbrt(x)

sqrt1pm1(x)

powm1(x, y)

hypot(x, y)

rsqrt(x)

Arguments

x

Input numeric value

y

Second input numeric value (for power and hypotenuse functions)

Value

A single numeric value with the computed result of the function.

See also

Boost Documentation for more details on the mathematical background.

Examples

# sin(pi/2) = 1 (exact)
sin_pi(0.5)
#> [1] 1
# cos(pi/2) = 0 (exact)
cos_pi(0.5)
#> [1] 0
# log(1 + x) for small x
log1p_boost(0.001)
#> [1] 0.0009995003
# exp(x) - 1 for small x
expm1_boost(0.001)
#> [1] 0.0010005
# Cube root
cbrt(8)  # Returns 2
#> [1] 2
# sqrt(1 + x) - 1 for small x
sqrt1pm1(0.001)
#> [1] 0.0004998751
# x^y - 1 accurately
powm1(2, 3)  # Returns 7 (2^3 - 1)
#> [1] 7
# Euclidean distance
hypot(3, 4)  # Returns 5
#> [1] 5
# Reciprocal square root
rsqrt(4)  # Returns 0.5
#> [1] 0.5