Crate fraction

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Fraction is designed to be a precise lossless drop-in replacement for floating types (f32, f64).

It comes with a number of predefined type aliases covering the most common use cases such as Fraction, Decimal, BigFraction, DynaDecimal and so on (see prelude module for more examples).

The public API provides you with the generic types that you may use straightforwardly to build your own types, suiting your needs best (see prelude module for the examples).

Library features

  • Drop in replacement for floats with the exception for NaN == NaN so that it’s hashable
  • It’s hashable, so may be used as values in Sets and keys in dictionaries and hash maps
  • Display implementation for fractions and decimals
  • Fraction type, representing fractions
  • Decimal type, based on Fraction type represents floats as lossless decimals
  • DynaInt implements dynamically growing integer type that perfarms checked math and avoids stack overflows
  • PostgreSQL binary protocol integration for both fractions and decimals
  • Juniper support for both fractions and decimals
  • Generic integer conversions, such as i8 -> u8, usize -> u8 and so on
  • Lossless division with no allocations and infinite precision

Disclaimer

Even though we do our best to keep it well covered with tests, there may be bugs out there. The library API is still in flux. When it gets stable we will release the version 1.0.0. You may find more info about Semantic Versioning on https://semver.org/. Bug reports and contributions are appreciated.

Crate features

  • with-bigint (default) integration with num::BigInt and num::BigUint data types
  • with-decimal (default) Decimal type implemented upon GenericFraction
  • with-dynaint (default) dynamically growing integer avoiding stack overflows
  • with-juniper-support Juniper integration
  • with-postgres-support PostgreSQL integration; Numeric/Decimal type
  • with-serde-support Serde traits implementation

Implementation

Basic math implemented upon the num crate (in particular the num::rational module). The utilised traits from the num crate are re-exported, so you don’t have to explicitly depend on that crate however, you may import them from either of crates if necessary.

Usage

To start using types see the Prelude module.

Examples

Simple use:

type F = fraction::Fraction; // choose the type accordingly to your needs (see prelude module docs)

let two = F::from(0) + F::from(2);   // 0 + 2 = 2
let two_third = two / F::from(3);    // 2/3 = 0.666666[...]

assert_eq!(F::from(2), two);
assert_eq!(F::new(2u64, 3u64), two_third);

assert_eq!("2/3", format!("{}", two_third));  // print as Fraction (by default)
assert_eq!("0.6666", format!("{:.4}", two_third));  // format as decimal and print up to 4 digits after floating point

Decimal is implemented as a representation layer on top of Fraction. Thus, it is also lossless and may require explicit control over “precision” for comparison and formatting operations.

type D = fraction::Decimal;

let result = D::from(0.5) / D::from(0.3);

assert_eq!(format!("{}", result), "1.6"); // calculation result uses precision of the operands
assert_eq!(format!("{:.4}", result), "1.6666");  // explicitly passing precision to format

assert_eq!("1.6666", format!("{}", result.set_precision(4))); // the other way to set precision explicitly on Decimal

Construct:

Fraction:

use std::str::FromStr;
use fraction::{Fraction, Sign};  // choose the type accordingly with your needs (see prelude module docs)

fn main() {
    // There are several ways to construct a fraction, depending on your use case

    let f = Fraction::new(1u8, 2u8);  // constructs with numerator/denominator and normalizes the fraction (finds least common denominator)
    assert_eq!(f, Fraction::new_generic(Sign::Plus, 1i32, 2u8).unwrap());  // with numerator/denominator of different integer types
    assert_eq!(f, Fraction::from(0.5));  // convert from float (f32, f64)
    assert_eq!(f, Fraction::from_str("0.5").unwrap());  // parse a string

    // Raw construct with no extra calculations.
    // Most performant, but does not look for common denominator and may lead to unexpected results
    // in following calculations. Only use if you are sure numerator/denominator are already normalized.
    assert_eq!(f, Fraction::new_raw(1u64, 2u64));
}

Decimal:

use std::str::FromStr;
use fraction::{Decimal, Fraction};  // choose the type accordingly with your needs (see prelude module docs)

fn main() {
    // There are similar ways to construct Decimal. Underneath it is always represented as Fraction.
    // When constructed, Decimal preserves its precision (number of digits after floating point).
    // When two decimals are calculated, the result takes the biggest precision of both.
    // The precision is used for visual representation (formatting and printing) and for comparison of two decimals.
    // Precision is NOT used in any calculations. All calculations are lossless and implemented through Fraction.
    // To override the precision use Decimal::set_precision.

    let d = Decimal::from(1);  // from integer, precision = 0
    assert_eq!(d, Decimal::from_fraction(Fraction::from(1))); // from fraction, precision is calculated from fraction

    let d = Decimal::from(1.3);  // from float (f32, f64)
    assert_eq!(d, Decimal::from_str("1.3").unwrap());
}

Format (convert to string)

Formatting works similar for both Decimal and Fraction (Decimal uses Fraction internally). The format implementation closely follows the rust Format trait documentation.

type F = fraction::Fraction;

let result = F::from(0.7) / F::from(0.4);
assert_eq!(format!("{}", result), "7/4");  // Printed as fraction by default
assert_eq!(format!("{:.2}", result), "1.75"); // if precision is defined, printed as decimal
assert_eq!(format!("{:#.3}", result), "1.750"); // to print leading zeroes, pass hash to the format

Generic integer conversion

use fraction::{Sign, GenericFraction};

type F = GenericFraction<u32>;

let fra = F::new_generic(Sign::Plus, 1i8, 42usize).unwrap();
assert_eq!(fra, F::new(1u32, 42u32));

Postgres usage

Postgres uses i16 for its binary protocol, so you’ll have to use at least u16 as the base type for fractions/decimals. Otherwise you may workaround with DynaInt<u8, something_more_than_u8>. The safest way to go with would be DynaInt based types such as DynaFraction or DynaDecimal as they would prevent stack overflows for high values.

Beware bad numbers such as 1/3, 1/7. Fraction keeps the highest achievable precision (up to 16383 digits after floating point). Decimal uses its own precision. So, if you may end up with bad numbers, it may be preferable to go with Decimals over Fractions.

Both types (fractions and decimals) should work transparently in accordance with Postgres crate documentation

Re-exports

Modules

Structs

Enums

Traits

  • Bounded
    Numbers which have upper and lower bounds
  • CheckedAdd
    Performs addition that returns None instead of wrapping around on overflow.
  • CheckedDiv
    Performs division that returns None instead of panicking on division by zero and instead of wrapping around on underflow and overflow.
  • CheckedMul
    Performs multiplication that returns None instead of wrapping around on underflow or overflow.
  • CheckedSub
    Performs subtraction that returns None instead of wrapping around on underflow.
  • FromPrimitive
    A generic trait for converting a number to a value.
  • Integer
  • Num
    The base trait for numeric types, covering 0 and 1 values, comparisons, basic numeric operations, and string conversion.
  • One
    Defines a multiplicative identity element for Self.
  • Signed
    Useful functions for signed numbers (i.e. numbers that can be negative).
  • ToPrimitive
    A generic trait for converting a value to a number.
  • Zero
    Defines an additive identity element for Self.