More optimizations

• A lot of misc. optimization work, notably parallelization of Rodinia CPU schedules.
• Support >32 tiles in GPU backend.
• Tweak some transformations.

juno_samples/rodinia/backprop/src/backprop.jn

@@ -6,10 +6,9 @@ fn squash(x: f32) -> f32 {
 fn layer_forward<n, m: usize>(vals: f32[n + 1], weights: f32[n + 1, m + 1]) -> f32[m + 1] {
   @res let result : f32[m + 1];
   result[0] = 1.0;
-
   @outer_loop for j in 1..=m {
-    let sum = 0.0;
-    @inner_loop for k in 0..=n {
+    let sum = weights[0, j] * vals[0];
+    @inner_loop for k in 1..=n {
       sum += weights[k, j] * vals[k];
     }
     result[j] = squash(sum);
@@ -19,13 +18,16 @@ fn layer_forward<n, m: usize>(vals: f32[n + 1], weights: f32[n + 1, m + 1]) -> f
 }
 
 fn output_error<n: usize>(target: f32[n + 1], actual: f32[n + 1]) -> f32, f32[n + 1] {
-  let errsum = 0.0;
-  let delta : f32[n + 1];
-
-  for j in 1..=n {
+  @loop1 @res let delta : f32[n + 1];
+  @loop1 delta[0] = 0.0;
+  @loop1 for j in 1..=n {
     let a = actual[j];
     let t = target[j];
     delta[j] = a * (1.0 - a) * (t - a);
+  }
+
+  let errsum = 0.0;
+  @loop2 for j in 1..=n {
     errsum += abs!(delta[j]);
   }
 
@@ -37,10 +39,9 @@ fn hidden_error<hidden_n, output_n: usize>(
   hidden_weights: f32[hidden_n + 1, output_n + 1],
   hidden_vals: f32[hidden_n + 1],
 ) -> f32, f32[hidden_n + 1] {
-  let errsum = 0.0;
-  let delta : f32[hidden_n + 1];
-
-  for j in 1..=hidden_n {
+  @loop1 @res let delta : f32[hidden_n + 1];
+  @loop1 delta[0] = 0.0;
+  @loop1 for j in 1..=hidden_n {
     let h = hidden_vals[j];
 
     let sum = 0.0;
@@ -49,6 +50,10 @@ fn hidden_error<hidden_n, output_n: usize>(
     }
 
     delta[j] = h * (1.0 - h) * sum;
+  }
+
+  let errsum = 0.0;
+  @loop2 for j in 1..=hidden_n {
     errsum += abs!(delta[j]);
   }
 
@@ -89,8 +94,8 @@ fn backprop<input_n, hidden_n, output_n: usize>(
   let hidden_vals = layer_forward::<input_n, hidden_n>(input_vals, input_weights);
   let output_vals = layer_forward::<hidden_n, output_n>(hidden_vals, hidden_weights);
 
-  let out_err, out_delta = output_error::<output_n>(target, output_vals);
-  let hid_err, hid_delta = hidden_error::<hidden_n, output_n>(out_delta, hidden_weights, hidden_vals);
+  @output_error let out_err, out_delta = output_error::<output_n>(target, output_vals);
+  @hidden_error let hid_err, hid_delta = hidden_error::<hidden_n, output_n>(out_delta, hidden_weights, hidden_vals);
 
   let hidden_weights, hidden_prev_weights
     = adjust_weights::<hidden_n, output_n>(out_delta, hidden_vals, hidden_weights, hidden_prev_weights);