Methods and systems to convert a scalar computer program loop having loop-carried dependences into a vector computer program loop are disclosed. One such method includes, replacing the scalar recurrence operation in the scalar computer program loop with a first vector summing operation and a first vector recurrence operation. The first vector summing operation is to generate a first running sum and the first vector recurrence operation is to generate a first vector. In some examples, the first vector recurrence operation is based on the scalar recurrence operation. Disclosed methods also include inserting: 1) a renaming operation to rename the first vector, 2) a second vector summing operation that is to generate a second running sum; and 3) a second vector recurrence operation to generate a second vector based on the renamed first vector.