From 27e768639d4c74ac95ab530f63559c8a848e2960 Mon Sep 17 00:00:00 2001
From: Marek Kaluba <kalmar@amu.edu.pl>
Date: Sat, 17 Jul 2021 20:11:32 +0200
Subject: [PATCH] first try at compiled automorphisms

---
 src/autgroups.jl                | 61 +++++++++++++++++++++++++++++++++
 src/groups/symplectic_twists.jl |  8 ++---
 2 files changed, 65 insertions(+), 4 deletions(-)

diff --git a/src/autgroups.jl b/src/autgroups.jl
index 53db353..7c30686 100644
--- a/src/autgroups.jl
+++ b/src/autgroups.jl
@@ -173,3 +173,64 @@ function evaluate!(res::AbstractWord, w::AbstractWord, lm::LettersMap)
     end
     return res
 end
+
+# compile automorphisms
+
+compiled(a) = eval(generated_evaluate(a))
+
+function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
+    lm = Groups.LettersMap(a)
+    d = Groups.domain(a)
+    @assert all(length.(word.(d)) .== 1)
+    A = alphabet(first(d))
+    first_ltrs = first.(word.(d))
+
+    args = [Expr(:call, :*) for _ in first_ltrs]
+
+    for (idx, letter) in enumerate(first_ltrs)
+        for l in lm[letter]
+            k = findfirst(==(l), first_ltrs)
+            if k !== nothing
+                push!(args[idx].args, :(d[$k]))
+                continue
+            end
+            k = findfirst(==(inv(A, l)), first_ltrs)
+            if k !== nothing
+                push!(args[idx].args, :(inv(d[$k])))
+                continue
+            end
+            throw("Letter $l doesn't seem to be mapped anywhere!")
+        end
+    end
+    locals = Dict{Expr, Symbol}()
+    locals_counter = 0
+    for (i,v) in enumerate(args)
+        @assert length(v.args) >= 2
+        if length(v.args) > 2
+            for (j, a) in pairs(v.args)
+                if a isa Expr &&  a.head == :call "$a"
+                    @assert a.args[1] == :inv
+                    if !(a in keys(locals))
+                        locals[a] = Symbol("var_#$locals_counter")
+                        locals_counter += 1
+                    end
+                    v.args[j] = locals[a]
+                end
+            end
+        else
+            args[i] = v.args[2]
+        end
+    end
+
+    q = quote
+        $([:(local $v = $k) for (k,v) in locals]...)
+    end
+
+    # return args, locals
+
+    return :(d -> begin
+        @boundscheck @assert length(d) == $(length(d))
+        $q
+        @inbounds tuple($(args...))
+    end)
+end
diff --git a/src/groups/symplectic_twists.jl b/src/groups/symplectic_twists.jl
index bef6f3e..d9f5929 100644
--- a/src/groups/symplectic_twists.jl
+++ b/src/groups/symplectic_twists.jl
@@ -161,7 +161,8 @@ function SymplecticMappingClass(
     g = genus(Σ)
     perm = [2g:-2:1; (2g-1):-2:1]
 
-    f(t) = evaluate!(t, a)
+    f = compiled(a)
+    # f = t -> evaluate!(t, a)
 
     res = SymplecticMappingClass(id, UInt(i), UInt(j), minus, inverse, a, perm, f)
 
@@ -180,7 +181,8 @@ end
 
 function Base.inv(m::SymplecticMappingClass)
     inv_w = inv(m.autFn_word)
-    f(t) = evaluate!(t, inv_w)
+    # f(t) = evaluate!(t, inv_w)
+    f = compiled(inv_w)
     return SymplecticMappingClass(m.id, m.i, m.j, m.minus, !m.inv, inv_w, m.perm, f)
 end
 
@@ -192,8 +194,6 @@ function evaluate!(
 ) where {N,T}
 
     t = smc.f(t[smc.perm])[invperm(smc.perm)]
-    # t = evaluate!(t[smc.perm], smc.autFn_word, tmp)
-    # t = t[invperm(smc.perm)]
     return t
 end