Crate mpmfnum

Number formats, precisions, and rounding modes.

mpmfnum is a numbers library for emulation various number formats, at multiple precisions with many rounding modes. Hence its name “Multi-Precision, Multi-Format” (MPMF). Unlike other number libraries like BigInt or Rug (MPFR), this library emphasizes a clean abstraction of various computer number systems rather than high-performance computation.

This library embraces design principles found in the FPCore standard. Most importantly, numerical programs need only be specified by (i) real-number mathematical operations and (ii) rounding. Number formats, e.g., double or float, are not first-class, as in most programming languages. Rather, formats are side effects of rounding and should be de-emphasized or eliminated entirely. Furthermore, all values within a numerical program should be viewed as (extended) real numbers.

These design principles are reflected in the two primary traits of this library:

• Real is an extended real value;
• RoundingContext is a rounding operation on Real values.

For implementation purposes, we restrict any Real value to be of the form (-1)^s * c * 2^exp where s is 0 or 1, c is a non-negative integer, and exp is an integer. Implementations of RoundingContext may support any of the numerous operations (as traits) found under crate::ops. Operations provided by this library are correctly rounded.

mpmfnum supports various number systems through implementations of RoundingContext:

• RealContext performs no rounding, that is, the operation is exact,
• RFloatContext rounds a Real value to an arbitrary-precision, floating-point numbers with unbounded exponent,
• FloatContext rounds a Real value to a fixed-precision, floating-point numbers with unbounded exponent,
• IEEE754Context rounds a Real value to a floating-point number as described by the IEEE 754 standard,
• FixedContext rounds a Real value to a fixed-point numbers,
• PositContext rounds a Real value to a posit number as described by the Posit standard.

Re-exports

• pub use crate::rfloat::RFloat;

Modules

• fixed
  Multiple flavors of fixed-point numbers.
• float
  Fixed-precision, floating-pont numbers with unbounded exponent.
• ieee754
  Floating-point numbers as described in the IEEE 754-2019 standard.
• mpfr
  Round-to-odd arithmetic using MPFR.
• ops
  Rounded mathematical operations.
• posit
  “Posit” numbers as described in the 2022 Posit Standard.
• real
  Exact arithmetic.
• rfloat
  Floating-point numbers with unbounded significand and exponent.

Macros

• context_alias
  Similar to the unstable trait_alias feature. Associates a groups a set of traits into a single named trait.

Structs

• Split
  An exact sum of two Real values split at an absolute binary digit.

Enums

• RoundingDirection
  Directed rounding.
• RoundingMode
  Rounding modes for rounding contexts.

Traits

• Real
  Universal trait for extended real numbers.
• RoundingContext
  Universal trait for rounding contexts.