## no-std arpfloat

Arbitrary-precision floating point library

### 10 releases

 0.1.9 Jan 28, 2023 Jan 17, 2023 Dec 31, 2022

#224 in Algorithms

Apache-2.0

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# 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 existing floating point types, such as FP16, and create new floating point types. Floating point types can scale to hundreds of digits, and perform very accurate calculations. In ARPFloat the rounding mode is a part of the type-system, and this defines away a number of problem that show up when using fenv.h.

`no_std` environments are supported by disabling the `std` feature.

### Example

``````  use arpfloat::Float;
use arpfloat::FP128;

// Create the number '5' in FP128 format.
let n = Float::from_f64(5.).cast(FP128);

// Use Newton-Raphson to find the square root of 5.
let mut x = n.clone();
for _ in 0..20 {
x += (&n / &x)/2;
}

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.

``````    use arpfloat::FP128;
use arpfloat::RoundingMode::NearestTiesToEven;
use arpfloat::Float;

let x = Float::from_u64(FP128, 1<<53);
let y = Float::from_f64(1000.0).cast(FP128);

let val = Float::mul_with_rm(&x, &y, NearestTiesToEven);
``````

View the internal representation of numbers:

``````   use arpfloat::Float;
use arpfloat::FP16;

let fp = Float::from_i64(FP16, 15);

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

let m = fp.get_mantissa();
m.dump(); // Prints 11110000000
``````

Control the rounding mode for type conversion:

``````    use arpfloat::{FP16, FP32, RoundingMode, Float};

let x = Float::from_u64(FP32, 2649);
let b = x.cast_with_rm(FP16, RoundingMode::Zero);
println!("{}", b); // Prints 2648!
``````

Define new float formats and use high-precision transcendental functions:

``````  use arpfloat::{Float, Semantics};
// Define a new float format with 120 bits of accuracy, and
// dynamic range of 2^10.
let sem = Semantics::new(10, 120);

let pi = Float::pi(sem);
let x = Float::exp(&pi);
println!("e^pi = {}", x); // Prints 23.1406926327792....
``````

Floating point numbers can be converted to Continued Fractions that approximate the value.

`````` use arpfloat::{Float, FP256, RoundingMode};

let ln = Float::ln2(FP256);
println!("ln(2) = {}", ln);
for i in 1..20 {
let (p,q) = ln.as_fraction(i);
println!("{}/{}", p.as_decimal(), q.as_decimal());
}
``````

The program above will print this output:

``````  ln(2) = .6931471805599453094172321214581765680755001343602552.....
0/1
1/1
2/3
7/10
9/13
61/88
192/277
253/365
445/642
1143/1649
1588/2291
2731/3940
....
``````

The examples directory contains a few programs that demonstrate the use of this library.

### 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.
• Modern Computer Arithmetic by Brent and Zimmermann.
• Papers:
• An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard, by Gal and Bachels.
• How to print floating-point numbers accurately by Steele, White.
• What Every Computer Scientist Should Know About Floating-Point Arithmetic by David Goldberg.
• Fast Multiple-Precision Evaluation of Elementary Functions by Richard Brent.
• Fast Trigonometric functions for Arbitrary Precision number by Henrik Vestermark.
• Other excellent software implementations: APFloat, RYU, libBF, newlib, musl, etc.