Extended Precision Numerical Library

A comprehensive MATLAB library for extended precision arithmetic, providing two precision tiers: double-double (~32 digits) and quad-double (~64 digits).

This library was originally inspired by the QD library (http://crd-legacy.lbl.gov/~dhbailey/mpdist/), but has been modernized and expanded into a full polymorphic class hierarchy (BaseExtDouble) with native MATLAB integration, optimized recursive arithmetic, full array support, and complex number capabilities.

The Numerical Hierarchy

The library provides three extended precision classes, each building upon the last to achieve higher precision bounds:

1. DoubleDouble: The foundational class. Represents numbers as an unevaluated sum of two 53-bit double primitives, providing roughly 106 bits (~32 decimal digits) of precision.
2. QuadDouble: The standard quad-double implementation. Provides 212 bits (~64 decimal digits) of precision using explicitly overloaded, optimized numerical kernels.
3. QuadDoubleSlow: A mathematically equivalent pure-MATLAB fallback to QuadDouble. It achieves 212-bit precision by recursively executing Dekker's split/TwoProd algorithms using DoubleDouble objects as its underlying components rather than explicit scalar kernels.

Features

The classes natively support almost all standard MATLAB operations, seamlessly integrating into existing codebases. Because they inherit from BaseExtDouble, operations scale polymorphically across all precision tiers:

• Basic Arithmetic: +, -, .*, ./, .\, .^
• Linear Algebra: lu, qr, chol, ldl, inv, det, eig, mldivide (\), mrdivide (/), dot, norm
• Trigonometry & Exponentials: sin, cos, tan, asin, acos, atan, atan2, sinh, cosh, tanh, exp, log, log2, log10
• Statistics & Arrays: sum, prod, mean, median, std, var, cumsum, diff, reshape, repmat, sort, unique
• Relational Operations: <, >, <=, >=, ==, ~=, any, all, find
• Complex Support: real, imag, conj, angle

Testing & Validation

The library is backed by a rigorous unit testing suite located in the UnitTests/ directory.

To execute the test suite:

cd UnitTests/
res = RunTests()

The suite thoroughly validates standard arithmetic, matrix decompositions, and transcendental approximations. A critical component is the TestCrossValidationVPA test suite, which isolates rounding errors by evaluating exact binary conversions (vpa(sym(Data, 'f'), 135)) against MATLAB's Symbolic Math Toolbox (135-digit ground truth). This enforces strict error bounds to guarantee precision boundaries across the hierarchy:

• DoubleDouble: Enforces strict accuracy to a 1e-30 absolute tolerance.
• QuadDouble & QuadDoubleSlow: Enforces strict accuracy to a 1e-60 absolute tolerance.

Development & Coding Standards

If you are extending or modifying the library, you should strictly adhere to the project conventions outlined in CODING_STANDARDS.md.

These standards enforce:

• Architectural encapsulation (e.g., using .Assign() and .Index() rather than direct native subsetting).
• Strict casing conventions (PascalCase for files, static initializers, and methods).
• Mandatory spacing, bracket padding, and blank-line declarations.

All new logic must successfully clear the RunTests execution with zero regressions before being considered mathematically sound.