Using Physical Constants in a Type-Stable Way

This tutorial demonstrates how to work with physical constants defined using Base.@irrational in a type-preserving way, i.e., ensuring that calculations don't accidentally upcast to a different floating-point type due to the constant's default type.

In QEDcore.jl, the following constants are defined:

ALPHA
ALPHA_SQUARE
ELEMENTARY_CHARGE
ELEMENTARY_CHARGE_SQUARE
ELECTRONMASS
ONE_OVER_FOURPI

These constants are defined with the exact values given by [1], and they can be used with any floating-point type (Float64, Float32, Float16) without requiring runtime conversion.

Converting to a Different Floating-Point Type

You can explicitly convert a constant to a target type using a constructor, like:

Float32(ALPHA)

0.0072973524f0

or:

Float16(ELEMENTARY_CHARGE)

Float16(0.3027)

This works with any of the constants. The result is a value of the requested type, and the conversion occurs at compile time:

@code_typed Float32(ALPHA)

CodeInfo(
1 ─     return $(QuoteNode(0.0072973524f0))
) => Float32

This adds no runtime overhead.

Automatic Conversion during Arithmetic Operations

For Base.AbstractIrrational types, arithmetic operations are defined such that the result adopts the type of the other operand. For example:

typeof(1.0 * ALPHA)

Float64

typeof(1.0f0 * ALPHA)

Float32

This page was generated using Literate.jl.