Module arith

Arithmetic trait and its implementations.

Traits

An Arithmetic defines fallible arithmetic operations on primitive values of an ExecutableModule, namely, addition, subtraction, multiplication, division, exponentiation (all binary ops), and negation (a unary op). Any module can be run with any Arithmetic on its primitive values, although some modules are reasonably tied to a particular arithmetic or a class of arithmetics (e.g., arithmetics on finite fields).

OrdArithmetic extends Arithmetic with a partial comparison operation (i.e., an analogue to PartialOrd). This is motivated by the fact that comparisons may be switched off during parsing, and some Arithmetics do not have well-defined comparisons.

ArithmeticExt helps converting an Arithmetic into an OrdArithmetic.

Implementations

This module defines the following kinds of arithmetics:

• StdArithmetic takes all implementations from the corresponding ops traits. This means that it’s safe to use provided the ops are infallible. As a counter-example, using StdArithmetic with built-in integer types (such as u64) is usually not a good idea since the corresponding ops have failure modes (e.g., division by zero or integer overflow).
• WrappingArithmetic is defined for integer types; it uses wrapping semantics for all ops.
• CheckedArithmetic is defined for integer types; it uses checked semantics for all ops.
• ModularArithmetic operates on integers modulo the specified number.

All defined Arithmetics strive to be as generic as possible.

Structs

Checked

Marker for CheckedArithmetic signalling that negation should be inherited from the CheckedNeg trait.

CheckedArithmetic

Arithmetic on an integer type (e.g., i32) that checks overflow and other failure conditions for all operations.

FullArithmetic

Wrapper type allowing to extend an Arithmetic to an OrdArithmetic implementation.

ModularArithmetic

Modular arithmetic on integers.

NegateOnlyZero

Marker for CheckedArithmetic signalling that negation is only possible for zero.

StdArithmetic

Arithmetic on a number type that implements all necessary operations natively.

Unchecked

Marker for CheckedArithmetic signalling that negation should be inherited from the Neg trait. This is appropriate if Neg never panics (e.g., for signed big integers).

WrappingArithmetic

Arithmetic on an integer type (e.g., i32), in which all operations have wrapping semantics.

Traits

Arithmetic

Encapsulates arithmetic operations on a certain primitive type (or an enum of primitive types).

ArithmeticExt

Extension trait for Arithmetic allowing to combine the arithmetic with comparisons.

CheckedArithmeticKind

Helper trait for CheckedArithmetic describing how number negation should be implemented.

DoubleWidth

Encapsulates extension of an unsigned integer type into signed and unsigned double-width types. This allows performing certain operations (e.g., multiplication) without a possibility of integer overflow.

OrdArithmetic

Extends an Arithmetic with a comparison operation on values.