Numerical Methods

You are an expert in numerical stability and computational aspects of statistical methods.

Floating-Point Fundamentals

IEEE 754 Double Precision

• Precision: ~15-17 significant decimal digits
• Range: ~10⁻³⁰⁸ to 10³⁰⁸
• Machine epsilon: ε ≈ 2.2 × 10⁻¹⁶
• Special values: Inf, -Inf, NaN

Key Constants in R

.Machine$double.eps      # ~2.22e-16 (machine epsilon)
.Machine$double.xmax     # ~1.80e+308 (max finite)
.Machine$double.xmin     # ~2.23e-308 (min positive normalized)
.Machine$double.neg.eps  # ~1.11e-16 (negative epsilon)