A computing device to optimize a source program, the computing device comprising: source code having a code segment including a loop, the loop having a first number of iterations and including an exponential function call having an argument including a loop-invariant complex number multiplied by a loop index; and a compiler having i) a loop detect module to detect the code segment, ii) a loop optimize module to optimize the code segment in response to detection of the code segment, and iii) a code generator module to generate output code as a function of the optimized code segment, wherein the loop optimize module is to: tile the loop to generate an outer loop having a second number of iterations and a nested inner loop having a third number of iterations; generate code to calculate a first coefficient array having a number of elements equal to the third number of iterations, wherein each element of the first coefficient array equals an exponential function of the loop-invariant complex number multiplied by a first coefficient array index; generate code to calculate a second coefficient array having a number of elements equal to the second number of iterations, wherein each element of the second coefficient array equals an exponential function of the loop-invariant complex number multiplied by the third number of iterations and a second coefficient array index; and replace the exponential function call with a multiplicative expression of an element of the first coefficient array at an inner loop index multiplied by an element of the second coefficient array at an outer loop index. source code having a code segment including a loop, the loop having a first number of iterations and including an exponential function call having an argument including a loop-invariant complex number multiplied by a loop index; and a compiler having i) a loop detect module to detect the code segment, ii) a loop optimize module to optimize the code segment in response to detection of the code segment, and iii) a code generator module to generate output code as a function of the optimized code segment, wherein the loop optimize module is to: tile the loop to generate an outer loop having a second number of iterations and a nested inner loop having a third number of iterations; generate code to calculate a first coefficient array having a number of elements equal to the third number of iterations, wherein each element of the first coefficient array equals an exponential function of the loop-invariant complex number multiplied by a first coefficient array index; generate code to calculate a second coefficient array having a number of elements equal to the second number of iterations, wherein each element of the second coefficient array equals an exponential function of the loop-invariant complex number multiplied by the third number of iterations and a second coefficient array index; and replace the exponential function call with a multiplicative expression of an element of the first coefficient array at an inner loop index multiplied by an element of the second coefficient array at an outer loop index. tile the loop to generate an outer loop having a second number of iterations and a nested inner loop having a third number of iterations; generate code to calculate a first coefficient array having a number of elements equal to the third number of iterations, wherein each element of the first coefficient array equals an exponential function of the loop-invariant complex number multiplied by a first coefficient array index; generate code to calculate a second coefficient array having a number of elements equal to the second number of iterations, wherein each element of the second coefficient array equals an exponential function of the loop-invariant complex number multiplied by the third number of iterations and a second coefficient array index; and replace the exponential function call with a multiplicative expression of an element of the first coefficient array at an inner loop index multiplied by an element of the second coefficient array at an outer loop index.