# LibBF Library

## News

• New version with decimal floating point support.
• Try LibBF online.
• A benchmark comparing MPFR/GMP and LibBF.

## Introduction

LibBF is a small library to handle arbitrary precision floating point numbers. Its compiled size is about 90 KB of x86 code and has no dependency on other libraries. It is not the fastest library nor the smallest but it tries to be simple while using asymptotically optimal algorithms. The basic arithmetic operations have a near linear running time.

The TinyPI example computes billions of digits of Pi using the Chudnovsky formula.

Features:
• Arbitrary precision floating point numbers in base 2 using the IEEE 754 semantics (including subnormal numbers, infinities and NaN).
• All operations are exactly rounded using the 5 IEEE 754 rounding modes (round to nearest with ties to even or away from zero, round to zero, -/+ infinity). The additional non-deterministic faithful rounding mode is supported when a lower or deterministic running time is necessary.
• Stateless API (each function takes as input the rounding mode, mantissa and exponent precisions in bits and return the IEEE status flags).
• The basic arithmetic operations (addition, subtraction, multiplication, division, square root) have a near linear running time.
• Multiplication using a SIMD optimized Number Theoretic Transform.
• Exactly rounded floating point input and output in any base between 2 and 36 with near linear runnning time. Floating point output can select the smallest amount of digits to get the required precision.
• Transcendental functions are supported (exp, log, pow, sin, cos, tan, asin, acos, atan, atan2).
• Operations on arbitrarily large integers are supported by using a special "infinite" precision. Integer division with remainder and logical operations (assuming two complement binary representation) are implemented.
• Arbitrary precision floating point numbers in base 10 corresponding to the IEEE 754 2008 semantics with the limitation that the mantissa is always normalized. The basic arithmetic operations, output and input are supported with a quadratic running time.
• Easy to embed: a few C files need to be copied, the memory allocator can be redefined, the memory allocation failures are tested.

## Benchmark

Source code: libbf-2020-01-19.tar.gz.

Windows executables of TinyPI: tinypi-2018-02-03-win.zip.

TinyPI is also included in the RISCVEMU Javascript demo

## Related projects

QuickJS relies on LibBF to handle the BigInt, BigFloat and BigDecimal numbers.

Arbitrary precision floating point libraries:

Other small open source programs to compute large number of digits of PI: Larger and faster programs to compute PI:

## Licensing

It is released under the MIT license.
Fabrice Bellard - http://bellard.org/