Rewrite integer lerp using intrinsics (#6426)

* Rewrite integer lerp using intrinsics

* Comment

src/Lerp.cpp

@@ -134,17 +134,11 @@ Expr lower_lerp(Expr zero_val, Expr one_val, const Expr &weight) {
             case 8:
             case 16:
             case 32: {
-                Expr zero_expand = Cast::make(UInt(2 * bits, computation_type.lanes()),
-                                              zero_val);
-                Expr one_expand = Cast::make(UInt(2 * bits, one_val.type().lanes()),
-                                             one_val);
-
-                Expr rounding = Cast::make(UInt(2 * bits), 1) << Cast::make(UInt(2 * bits), (bits - 1));
-                Expr divisor = Cast::make(UInt(2 * bits), 1) << Cast::make(UInt(2 * bits), bits);
-
-                Expr prod_sum = zero_expand * inverse_typed_weight +
-                                one_expand * typed_weight + rounding;
-                Expr divided = ((prod_sum / divisor) + prod_sum) / divisor;
+                Expr shift = Cast::make(UInt(2 * bits), bits);
+                Expr prod_sum = widening_mul(zero_val, inverse_typed_weight) + widening_mul(one_val, typed_weight);
+                // Computes x / (2 ** N - 1) as (x / 2 ** N + x) / 2 ** N.
+                // TODO: on x86 it's actually one instruction cheaper to do the division directly.
+                Expr divided = rounding_shift_right(rounding_shift_right(prod_sum, shift) + prod_sum, shift);
 
                 result = Cast::make(UInt(bits, computation_type.lanes()), divided);
                 break;