Optimized matrix and vector operations in instruction limited algorithms that perform EOS calculations

1. A method of optimizing matrix and vector operations in instruction limited algorithms that perform EOS calculations, comprising:

dividing each matrix associated with an EOS stability equation or an EOS phase split equation into a number of tiles, wherein the tile size is heterogeneous or homogenous;

dividing each vector associated with the EOS stability equation or the EOS phase split equation into a number of strips;

storing the tiles and strips in main memory, cache, or registers, wherein the tiles or strips are stored sequentially or interleaved in main memory, cache, or registers; and

performing the matrix and vector operations associated with successive substitutions and Newton iterations in parallel using the tiles and strips.

2. The method recited in claim 1 , wherein the tile size is selected in order to minimize data transfers between different levels of a memory within a single hardware architecture.

3. The method recited in claim 1 , comprising unrolling loops based on tile or strip sizes associated with the EOS calculations.

4. The method recited in claim 1 , comprising dividing each matrix into a number of tiles, wherein the matrix is padded to a size that allows for the use of homogeneous tiles.

5. The method recited in claim 1 , comprising unrolling loops through specialization, wherein a number of different EOS algorithms are generated for mixtures with different numbers of components.

6. The method recited in claim 1 , comprising single precision, double precision, or mixed precision vectorization of EOS calculations or data elements within the tiles and strips associated with EOS calculations using single instruction multiple data or single instruction multiple thread vector instructions.

7. A computer system that is adapted to optimize matrix and vector operations in instruction limited algorithms that perform EOS calculations, the computer system comprising:

a processor; and

a tangible, machine-readable storage medium that stores machine-readable instructions for execution by the processor, the machine-readable instructions comprising:

code that, when executed by the processor, is adapted to cause the processor to divide each matrix associated with an EOS stability equation and an EOS phase split equation into a number of tiles, wherein the tile size is heterogeneous or homogenous;

code that, when executed by the processor, is adapted to cause the processor to divide each vector associated with the EOS stability equation and the EOS phase split equation into a number of strips;

code that, when executed by the processor, is adapted to cause the processor to store the tiles and strips in main memory, cache, or registers, wherein the tiles or strips are stored sequentially or interleaved in the main memory, cache, or registers; and

code that, when executed by the processor, is adapted to cause the processor to perform the matrix and vector operations associated with successive substitutions and Newton iterations in parallel using the tiles and strips.

8. The system recited in claim 7 , wherein the processor forms a scalar hardware architecture or a vector hardware architecture.

9. The system recited in claim 7 , comprising code that, when executed by the processor, is adapted to cause the processor to unroll loops based on tile or strip sizes associated with the EOS calculations.

10. The system recited in claim 7 , comprising code that, when executed by the processor, is adapted to cause the processor to divide each matrix into a number of tiles, wherein the matrix is padded to a size that allows for the use of homogeneous tiles.

11. The system recited in claim 7 , comprising code that, when executed by the processor, is adapted to cause the processor to generate a number of different EOS algorithms for mixtures with different numbers of components.

12. The system recited in claim 7 , comprising code that, when executed by the processor, is adapted to cause the processor to perform vectorization of single precision, double precision, or mixed precision EOS calculations or data elements within the tiles and strips associated with EOS calculations using single instruction multiple data or single instruction multiple thread vector instructions.

13. A non-transitory, computer readable medium comprising code configured to direct a processor to:

divide each matrix associated with an EOS stability equation and an EOS phase split equation into a number of tiles, wherein the tile size is heterogeneous or homogenous;

divide each vector associated with the EOS stability equation and the EOS phase split equation into a number of strips;

store the tiles and strips in main memory, cache, or registers, wherein the tiles or strips are stored sequentially or interleaved in main memory, cache, or registers; and

perform the matrix and vector operations associated with successive substitutions and Newton iterations in parallel using the tiles and strips.

14. The non-transitory, computer readable medium recited in claim 13 , comprising unrolling loops based on tile or strip sizes associated with the EOS calculations.

15. The non-transitory, computer readable medium recited in claim 13 , comprising dividing each matrix into a number of tiles, wherein the matrix is padded to a size that allows for the use of homogeneous tiles.

16. The non-transitory, computer readable medium recited in claim 13 , comprising unrolling loops through specialization, wherein a number of different EOS algorithms are generated for mixtures with different numbers of components.

17. The non-transitory, computer readable medium recited in claim 13 , comprising single precision, double precision, or mixed precision vectorization of EOS calculations or data elements within the tiles and strips associated with EOS calculations using single instruction multiple data or single instruction multiple thread vector instructions.