This package provides the `@muladd`

macro. It automatically converts expressions
with multiplications and additions or subtractions to calls with `muladd`

which then fuse via
FMA when it would increase the performance of the code. The `@muladd`

macro
can be placed on code blocks and it will automatically find the appropriate
expressions and nest muladd expressions when necessary. In mixed expressions summands without multiplication
will be grouped together and evaluated first but otherwise the order of evaluation of multiplications and additions is not changed.

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

```
julia> using MuladdMacro
julia> @macroexpand(@muladd k3 = f(t + c3 * dt, @. uprev + dt * (a031 * k1 + a032 * k2)))
:(k3 = f((muladd)(c3, dt, t), (muladd).(dt, (muladd).(a032, k2, (*).(a031, k1)), uprev)))
julia> @macroexpand(@muladd integrator.EEst = integrator.opts.internalnorm((update -
dt * (bhat1 * k1 +
bhat4 * k4 +
bhat5 * k5 +
bhat6 * k6 +
bhat7 * k7 +
bhat10 * k10)) ./
@. (integrator.opts.abstol +
max(abs(uprev),
abs(u)) * integrator.opts.reltol)))
:(integrator.EEst = integrator.opts.internalnorm((muladd)(-dt, (muladd)(bhat10, k10, (muladd)(bhat7, k7, (muladd)(bhat6, k6, (muladd)(bhat5, k5, (muladd)(bhat4, k4, bhat1 * k1))))), update) ./ (muladd).(max.(abs.(uprev), abs.(u)), integrator.opts.reltol, integrator.opts.abstol)))
```

A `muladd`

call will be broadcasted if both the `*`

and the `+`

or `-`

are broadcasted.
If either one is not broadcasted, then the expression will be converted to a
non-dotted `muladd`

.

Currently, `@muladd`

handles only explicit calls of `+`

and `*`

. In particular, assignments
using `+=`

or literal power such as `^2`

are not supported. Thus, you need to rewrite them, e.g.

```
julia> using MuladdMacro
julia> a = 1.0;
b = 2.0;
c = 3.0;
julia> @macroexpand @muladd a += b * c # does not work
:(a += b * c)
julia> @macroexpand @muladd a = a + b * c # good alternative
:(a = (muladd)(b, c, a))
julia> @macroexpand @muladd a + b^2 # does not work
:(a + b ^ 2)
julia> @macroexpand @muladd a + b * b # good alternative
:((muladd)(b, b, a))
```

Most of the credit goes to @fcard and @devmotion for building the first version and greatly refining the macro. These contributions are not directly shown as this was developed in Gitter chats and in the DiffEqBase.jl repository, but these two individuals did almost all of the work.