Experimental project - work in progress

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An arbitrary precision arithmetic library for computable real numbers.

Highlights

• Lazy evaluation: Dynamically adjusts precision as needed, enabling efficient computations and on-demand accuracy.
• Supported domains:
  • Z: Big integer numbers.
  • R: Computable real numbers, supporting operations with dynamic precision.
• Algorithmic foundation: Based on algorithms by V. Menissier-Morain and Donald Knuth, ensuring mathematical rigor and reliability.
• Modern C++: Written in modern C++ (C++23), leveraging concepts, coroutines, and advanced type traits for performance and clarity.
• Cross-platform: The library can be compiled by clang, g++, and cl (MSVC).

Features

• Efficient, on-demand computation of real numbers with adjustable precision.
• Operator overloading for natural arithmetic expressions.
• Conversion utilities for parsing and formatting numbers.
• Extensible design for custom digit and container types.

CLI

A command-line calculator (cli) is included. It supports three modes:

Immediate mode — inline expression:

cli "1 + 2 * 3"
cli -p 10 "sin(pi/2)"

File mode — evaluate each non-empty line of a file (# and // comments are skipped):

cli script.math

REPL mode — interactive session (no arguments):

cli

Option	Description
-V, --version	Print version and exit
-p N, --precision N	Decimal places for real numbers (default: 50)
--strip-zeros, --no-strip-zeros	Strip / keep trailing zeros
--config-path PATH	Path to config file (default: ~/.epsilon/config)

REPL commands: .precision N, .strip_zeros [on|off], .config, .help, exit, quit.

Config file (~/.epsilon/config): precision = 50, strip_zeros = true.

Supported expression syntax: real literals (3.14), integer literals (z'42), operators (+ - * /), functions (sin, cos, tan, exp, log, ln, sqrt, arcsin, arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, pow), and constants (pi, e).

References

• V. Menissier-Morain, "Arbitrary Precision Real Arithmetic: design and algorithms"
• Donald Knuth, "The Art of Computer Programming"

TODOs

• Math expression - parser ✅
• Math expression - evaluation ✅
• CLI application ✅
• Lexer: underscore support in identifiers
• Parser: unary minus
• Parser: multiple statements
• Parser: assignment (=)
• Evaluator: user-defined functions with closures
• Evaluator: richer error diagnostics