Improve substitution performance by fixing type instabilities

perf/runbenchmarks.jl

@@ -0,0 +1,15 @@
+using MultivariatePolynomials
+using BenchmarkTools
+
+let
+    @polyvar x y
+    p = x + y + 2x^2 + y^3
+
+    vars = [x, y]
+    vals = [1.0, 2.0]
+
+    println(@benchmark(($p)($vals, $vars)))
+
+    vars_out_of_order = [vars[2], vars[1]]
+    println(@benchmark(($p)($vals, $vars_out_of_order)))
+end

src/subs.jl

@@ -1,14 +1,21 @@
-function evalmap(vars, x::Vector, varorder::Vector{PolyVar})
-    vals = Any[var for var in vars]
-    for (i, var) in enumerate(varorder)
-        j = findfirst(vars, var)
-        # If i == 0, that means that the variable is not present
-        # so it is ignored
-        if j > 0
-            vals[j] = x[i]
+function evalmap{T}(vars, x::Vector{T}, varorder::Vector{PolyVar})
+    if vars == varorder
+        x
+    else
+        vals = Vector{T}(length(vars))
+        for (i, var) in enumerate(varorder)
+            j = findfirst(vars, var)
+            # If i == 0, that means that the variable is not present
+            # so it is ignored
+            if j > 0
+              vals[j] = x[i]
+            end
         end
+        for i in 1:length(vals)
+            @assert isdefined(vals, i) "Variable $(vars[i]) was not assigned a value"
+        end
+        vals
     end
-    vals
 end
 
 function monoeval(z::Vector{Int}, vals::Vector)
@@ -39,11 +46,7 @@ end
 
 function (p::VecPolynomial)(x::Vector, varorder)
     vals = evalmap(vars(p), x, varorder)
-    q = zero(p)
-    for i in 1:length(p)
-        q += p.a[i] * monoeval(p.x.Z[i], vals)
-    end
-    q
+    sum(i -> p.a[i] * monoeval(p.x.Z[i], vals), 1:length(p))
 end
 
 function (p::MatPolynomial)(x::Vector, varorder)

test/REQUIRE

@@ -1 +1,2 @@
 FactCheck
+BenchmarkTools

test/subs.jl

@@ -1,3 +1,5 @@
+import Base.Test: @inferred
+
 facts("Substitution") do
     @polyvar x[1:3]
 
@@ -23,4 +25,7 @@ facts("Substitution") do
     P = [1 2 3; 2 4 5; 3 5 6]
     p = MatPolynomial(P, x)
     @fact p(ones(3), x) --> 31
+
+    p = x[1] + x[2] + 2*x[1]^2 + 3*x[1]*x[2]^2
+    @inferred p([1.0, 2.0], [x[1], x[2]])
 end