Primitive promotions for primitive numeric types

According to Rust's reference, primitive numeric types in Rust are such:

Numeric types

Integer types

The unsigned integer types consist of:

The signed two's complement integer types consist of:

Floating-point types

The IEEE 754-2008 "binary32" and "binary64" floating-point types are f32 and f64, respectively.

Machine-dependent integer types

The usize type is an unsigned integer type with the same number of bits as the platform's pointer type. It can represent every memory address in the process.

The isize type is a signed integer type with the same number of bits as the platform's pointer type. The theoretical upper bound on object and array size is the maximum isize value. This ensures that isize can be used to calculate differences between pointers into an object or array and can address every byte within an object along with one byte past the end.

usize and isize are at least 16-bits wide.

Note: Many pieces of Rust code may assume that pointers, usize, and isize are either 32-bit or 64-bit. As a consequence, 16-bit pointer support is limited and may require explicit care and acknowledgment from a library to support.

Why this trait is needed

All primitive numeric types, including machine-dependent types, come with known size that can be obtained via core::mem::size_of<T>(). The greater the size is, the greater the number of possible values that can be represented by the type. Integer intervals as sets are not closed under many operations, notably addition and multiplication. Since u8 represents the integer interval [0..2⁸-1], the same holds for this type. By analogy, the same is true for u16, u32, etc. Similarly, the set of values representable by floating point numbers with algebraic structure avoiding imprecision (i.e. distinct from the algebraic structure on floating point numbers) is not closed under many operations as well.

One way to circumvent the problem is to use type promotion. Type promotion allows to use a type representing a superset of the original type. For every primitive numeric type (except for u128, i128, and f64) there is a canonical type promotion. For u8 the canonical type promotion is u16, for i16 the canonical type promotion is i32, and so on.

Signed integers

Unsigned integers

Floating-point numbers

Theoretically, one could go one step further and define u256, yet it would not be primitive and even simple operations on that type (such as addition) would not have the corresponding CPU instructions.

Note Strictly speaking, u128 and i128 are poorly supported on current architectures and it may or may not be reasonable to use implementation of PrimitivePromotionExt extension trait on u64 and i64. However, if you want to use these implementations, primitive_promotion crate is what you need because u64 and i64 implement the PrimitivePromotionExt trait.

Example

You can notice that PrimitivePromotionExt is quite long to type. To make it shorter, you are advised to rename the imported trait as PP. Because its uses are meant to be accompanied with fully qualified syntax, such shorthand is indispensible.

use primitive_promotion::PrimitivePromotionExt as PP;

fn midpoint(a: &u8, b: &u8) -> u8 {
  // <u8 as TraitName>:: is an example of fully qualified syntax
  let a = *a as <u8 as PP>::PrimitivePromotion;
  let b = *b as <u8 as PP>::PrimitivePromotion;
  ((a+b)/2) as u8
}

fn main() {
  let a: u8 = u8::MAX;
  let b: u8 = u8::MAX;
  assert_eq!(midpoint(&a,&b), u8::MAX);
}

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