Inverse Hyperbolic Functions

Functions to compute the inverse hyperbolic functions with high precision and proper handling of edge cases.

• acosh_boost(x): Inverse hyperbolic cosine, \(\text{cosh}^{-1}(\text{cosh} (x)) = x\)

• asinh_boost(x): Inverse hyperbolic sine, \(\text{sinh}^{-1}(\text{sinh} (x)) = x\)

• atanh_boost(x): Inverse hyperbolic tangent, \(\text{tanh}^{-1}(\text{tanh} (x)) = x\)

Usage

acosh_boost(x)

asinh_boost(x)

atanh_boost(x)

Arguments

x

Input numeric value (domain depends on the function)

Value

A single numeric value with the computed inverse hyperbolic function.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Inverse Hyperbolic Cosine (x >= 1)
acosh_boost(2)  # Returns approximately 1.317
#> [1] 1.316958
# Inverse Hyperbolic Sine (all real x)
asinh_boost(1)  # Returns approximately 0.881
#> [1] 0.8813736
# Inverse Hyperbolic Tangent (|x| < 1)
atanh_boost(0.5)  # Returns approximately 0.549
#> [1] 0.5493061