Crate twofloat

Source
Expand description

§twofloat

This library provides an implementation of double-double arithmetic for the Rust language. Note that this is not the same as the IEEE quadruple-precision floating-point format. Instead, higher precision is obtained by representing the value as the sum of two non-overlapping f64 values.

§Usage

The basic type is TwoFloat which represents the sum of two non-overlapping f64 values, which may be initialized from a single f64 or by calling a constructor that performs an arithmetic operation on a pair of f64 values.

extern crate twofloat;
use twofloat::TwoFloat;

let a = TwoFloat::from(3.4);
let b = TwoFloat::new_add(1.0, 1.0e-300);
let c = TwoFloat::new_sub(1.0, 1.0e-300);
let d = TwoFloat::new_mul(5.0, 0.7);
let e = TwoFloat::new_div(1.0, 7.0);

Basic arithmetic operators and comparisons are available, together with the utility functions abs(), is_positive_sign() and is_negative_sign(). Mathematical functions are provided if the math_funcs feature is enabled (this is enabled by default), though the implementations should be regarded as preliminary.

Operations on non-finite values are not supported. At the moment this is not automatically checked. The is_valid() method is provided for this purpose.

If the std feature is enabled (as it is by default), the fused multiply-add operation from the standard library is used. This may be more performant if the target architecture has a dedicated instruction for this. See the documentation of f64::mul_add for details. Otherwise the libm implementation is used.

If the serde feature is enabled, serialization and deserialization is possible through the Serde library.

§Known issues

  • The MinGW fma implementation appears to give incorrect results in some cases, so the libm function is always used on this platform.

§References

  • Mioara Joldes, Jean-Michel Muller, Valentina Popescu. Tight and rigourous error bounds for basic building blocks of double-word arithmetic. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2017, 44 (2), pp.1 - 27. 10.1145/3121432. hal-01351529v3

  • Alan H. Karp, Peter Markstein. High Precision Division and Square Root. ACM Transactions on Mathematical Software, Association for Computing Machinery, 1997, 23 (4), pp. 561-589. 10.1145/279232.279237.

  • S. Chevillard, M. Joldeș and C. Lauter. Sollya: an environment for the development of numerical codes. Mathematical Software - ICMS 2010, pp. 28–31.

Modules§

consts
Basic mathematical constants.

Structs§

TwoFloat
Represents a two-word floating point type, represented as the sum of two non-overlapping f64 values.

Enums§

TwoFloatError
The error type for TwoFloat operations.

Functions§

no_overlap
Checks if two f64 values do not overlap, with the first value being the more significant. This matches definition 1.4 in Joldes et al. (2017).