arpfloat's Introduction

Arbitrary-Precision Floating-Point Library

ARPFloat is an implementation of arbitrary precision floating point data structures and utilities. The library can be used to emulate floating point operation, in software, or create new floating point data types.

Example

  // Create a new type: 15 bits exponent, 112 significand.
  type FP128 = Float<15, 112>;

  // Use Newton-Raphson to find the square root of 5.
  let n = FP128::from_u64(5);

  let two = FP128::from_u64(2);
  let mut x = n;

  for _ in 0..1000 {
      x = (x + (n / x))/two;
  }

  println!("fp128: {}", x);
  println!("fp64:  {}", x.as_f64());

The program above will print this output:

fp128: 2.2360679774997896964091736687312763
fp64:  2.23606797749979

The library also provides API that exposes rounding modes, and low-level operations.

    // Explicit control over rounding modes:
    let val = FP128::mul_with_rm(y, z, RoundingMode::NearestTiesToEven);

    // View the internals of the float:
    let fp = FP16::from_i64(15);
    let m = fp.get_mantissa();

    // Prints FP[+ E=+3 M=11110000000]
    fp.dump();

Control the rounding-mode for type conversion:

   use arpfloat::{FP16, FP32, RoundingMode};
   let x = FP32::from_u64(2649);

   // Convert from FP64 to FP16.
   let b : FP16 = x.cast_with_rm(RoundingMode::Zero);
   println!("{}", b); // Prints 2648!

The examples directory contains a program that computes many digits of pi in float-256.

Resources

There are excellent resources out there, some of which are referenced in the code:

Books:
- Handbook of Floating-Point Arithmetic 2010th by Jean-Michel Muller et al.
- Elementary Functions: Algorithms and Implementation by Jean-Michel Muller.
Papers:
- How to print floating-point numbers accurately
Other excellent software implementations: APFloat by Neil Booth, RYU, newlib, musl, etc.