feat: adds api.MAC(..)

[gbotrel]

	// MAC sets and return a = a + (b*c)
	// ! may mutate a without allocating a new result
	// ! always use MAC(...) result for correctness
	MAC(a, b, c Variable) Variable

Fixes #416 . Impact in std/math/emulated for rsh is significant (~40% less memallocs).

	for i := 0; i < len(bits); i++ {
		Σbi = api.MAC(Σbi, bits[i], c)
		ΣbiRShift = api.MAC(ΣbiRShift, bits[i], cRShift)

		c.Lsh(c, 1)
		cRShift.Lsh(cRShift, 1)
		api.AssertIsBoolean(bits[i])
	}

Also, this new api would result in less constraint in a PlonKish arithmetization, since it will create one constraint instead of 2.

[ivokub]

Looks good. I think it is a clean and required change.

[ivokub]

I think it can be done. And this is also helpful for the case if we want to have a transpiler from some other circuit description to gnark.

[gbotrel]

Am going to wait on @ThomasPiellard new backend on that one; plonk frontend is in a need of a refactor to convert input to term, and add custom constraints etc... keeping the TODO around for now.

[ivokub]

Suggested edit:

diff --git a/std/math/emulated/wrapped_api.go b/std/math/emulated/wrapped_api.go
index aa433d24..6d40f4ee 100644
--- a/std/math/emulated/wrapped_api.go
+++ b/std/math/emulated/wrapped_api.go
@@ -77,8 +77,10 @@ func (w *FieldAPI[T]) Add(i1 frontend.Variable, i2 frontend.Variable, in ...fron
 }
 
 func (w *FieldAPI[T]) MulAcc(a, b, c frontend.Variable) frontend.Variable {
-	// TODO can we do better here to limit allocations?
-	return w.Add(a, w.Mul(b, c))
+	els := w.varsToElements(a, b, c)
+	mul := w.f.Mul(els[1], els[2])
+	res := w.f.Add(els[0], mul)
+	return res
 }
 
 func (w *FieldAPI[T]) Neg(i1 frontend.Variable) frontend.Variable {

[ivokub]

Suggested edit:

diff --git a/std/math/emulated/wrapped_api.go b/std/math/emulated/wrapped_api.go
index aa433d24..6d40f4ee 100644
--- a/std/math/emulated/wrapped_api.go
+++ b/std/math/emulated/wrapped_api.go
@@ -77,8 +77,10 @@ func (w *FieldAPI[T]) Add(i1 frontend.Variable, i2 frontend.Variable, in ...fron
 }
 
 func (w *FieldAPI[T]) MulAcc(a, b, c frontend.Variable) frontend.Variable {
-	// TODO can we do better here to limit allocations?
-	return w.Add(a, w.Mul(b, c))
+	els := w.varsToElements(a, b, c)
+	mul := w.f.Mul(els[1], els[2])
+	res := w.f.Add(els[0], mul)
+	return res
 }
 
 func (w *FieldAPI[T]) Neg(i1 frontend.Variable) frontend.Variable {

Tried to see if could reduce allocating new Element, but seems to be larger overhaul to have methods on Field type which also take the destination. I think it makes sense to do it separate PR.