Block operations for an image processor having a two-dimensional execution lane array and a two-dimensional shift register
A method is described that includes, on an image processor having a two dimensional execution lane array and a two dimensional shift register array, repeatedly shifting first content of multiple rows or columns of the two dimensional shift register array and repeatedly executing at least one instruction between shifts that operates on the shifted first content and/or second content that is resident in respective locations of the two dimensional shift register array that the shifted first content has been shifted into.
1. A processor comprising:
a two-dimensional array of processing elements; and
multiple shift-register planes, each shift-register plane comprising a separate two-dimensional shift-register array, wherein each shift register of each shift-register array is dedicated to one of the processing elements,
wherein the processor is configured to execute instructions to perform a matrix multiplication operation on a first matrix stored in a first shift-register plane and a second matrix stored in a second shift-register plane to generate a result of the matrix multiplication operation stored in a third shift-register plane, wherein the first matrix comprises N columns, and wherein the instructions cause each processing element to perform, for N iterations, operations on shift registers dedicated to the processing element, the operations comprising:
performing a multiplication operation between a first value stored in a first shift register of the first shift-register plane and a second value stored in a second shift register of the second shift-register plane,
performing an addition operation between a result of the multiplication operation and a summation value stored in a third shift register of the third shift-register plane,
updating the summation value stored in the third shift register of the third shift-register plane using a result of the addition operation, and
based on determining that a current iteration is not a last iteration:
shifting data in the first shift-register plane one unit in a first dimension corresponding to rows of the first matrix, and
shifting data in the second shift-register plane one unit in a second dimension corresponding to columns of the second matrix.
2. The processor of claim 1 , wherein the first matrix comprises R rows and the second matrix comprises S columns, and wherein the operations further comprise:
performing a row-wise rotational shearing transformation on the first matrix including shifting each row i, from row 0 to row R−1, by i units; and
performing a column-wise rotational shearing transformation on the second matrix including shifting each column j, from column 0 to column S−1, by j units.
3. The processor of claim 1 , wherein the operations further comprise:
loading an initial condition for the matrix multiplication by loading initial values into shift registers of the third shift-register plane.
4. The processor of claim 1 , wherein the operations further comprise computing a two-dimensional discrete Fourier transform (2D DFT) using a first matrix of real values, a first matrix of imaginary values, a second matrix of real values, and a second matrix of imaginary values including:
computing a real portion of the 2D DFT including:
performing a first matrix multiplication operation between the first matrix of real values and the second matrix of real values,
performing a second matrix multiplication operation between the first matrix of imaginary values and the second matrix of imaginary values, and
subtracting a result of the second matrix multiplication operation from the first matrix multiplication operation; and
computing an imaginary portion of the 2D DFT including:
performing a third matrix multiplication operation between the first matrix of real values and the second matrix of imaginary values,
performing a fourth matrix multiplication operation between the second matrix of real values and the first matrix of imaginary values, and
adding a result of the third matrix multiplication operation and a result of the fourth matrix multiplication operation.
5. The processor of claim 4 , wherein the operations further comprise:
moving the computed real portion of the 2D DFT to another shift-register plane or to memory;
reloading the first matrix of real values and the first matrix of imaginary values back into respective shift-register planes; and
performing a row-wise rotational shearing transformation on the first matrix of real values and the first matrix of imaginary values.
6. A computer program product, encoded on one or more non-transitory computer storage media, comprising instructions that when executed by a processor comprising:
a two-dimensional array of processing elements, and
multiple shift-register planes, each shift-register plane comprising a separate two-dimensional shift-register array, wherein each shift register of each shift-register array is dedicated to one of the processing elements,
cause the processor to perform a matrix multiplication operation on a first matrix stored in a first shift-register plane and a second matrix stored in a second shift-register plane to generate a result of the matrix multiplication operation stored in a third shift-register plane, wherein the first matrix comprises N columns, and wherein the instructions cause each processing element to perform, for N iterations, operations on shift registers dedicated to the processing element, the operations comprising:
performing a multiplication operation between a first value stored in a first shift register of the first shift-register plane and a second value stored in a second shift register of the second shift-register plane,
performing an addition operation between a result of the multiplication operation and a summation value stored in a third shift register of the third shift-register plane,
updating the summation value stored in the third shift register of the third shift-register plane using a result of the addition operation, and
based on determining that a current iteration is not a last iteration:
shifting data in the first shift-register plane one unit in a first dimension corresponding to rows of the first matrix, and
shifting data in the second shift-register plane one unit in a second dimension corresponding to columns of the second matrix.
7. The computer program product of claim 6 , wherein the first matrix comprises R rows and the second matrix comprises S columns, and wherein the operations further comprise:
performing a row-wise rotational shearing transformation on the first matrix including shifting each row i, from row 0 to row R−1, by i units; and
performing a column-wise rotational shearing transformation on the second matrix including shifting each column j, from column 0 to column S−1, by j units.
8. The computer program product of claim 6 , wherein the operations further comprise:
loading an initial condition for the matrix multiplication by loading initial values into shift registers of the third shift-register plane.
9. The computer program product of claim 6 , wherein the operations further comprise computing a two-dimensional discrete Fourier transform (2D DFT) using a first matrix of real values, a first matrix of imaginary values, a second matrix of real values, and a second matrix of imaginary values including:
computing a real portion of the 2D DFT including:
performing a first matrix multiplication operation between the first matrix of real values and the second matrix of real values,
performing a second matrix multiplication operation between the first matrix of imaginary values and the second matrix of imaginary values, and
subtracting a result of the second matrix multiplication operation from the first matrix multiplication operation; and
computing an imaginary portion of the 2D DFT including:
performing a third matrix multiplication operation between the first matrix of real values and the second matrix of imaginary values,
performing a fourth matrix multiplication operation between the second matrix of real values and the first matrix of imaginary values, and
adding a result of the third matrix multiplication operation and a result of the fourth matrix multiplication operation.
10. The computer program product of claim 9 , wherein the operations further comprise:
moving the computed real portion of the 2D DFT to another shift-register plane or to memory;
reloading the first matrix of real values and the first matrix of imaginary values back into respective shift-register planes; and
performing a row-wise rotational shearing transformation on the first matrix of real values and the first matrix of imaginary values.
11. A method performed by a processor having a two-dimensional array of processing elements and multiple shift-register planes,
wherein the method causes the processor to perform a matrix multiplication operation on a first matrix stored in a first shift-register plane and a second matrix stored in a second shift-register plane to generate a result of the matrix multiplication operation stored in a third shift-register plane, wherein the shift-register planes each comprise a separate two-dimensional shift register array, wherein each shift register of each shift register array is dedicated to one processing element in the two-dimensional array of processing elements, and wherein the first matrix comprises N columns, the method comprising:
performing, by each processing element, for N iterations, operations on shift registers dedicated to the processing element, the operations comprising:
performing a multiplication operation between a first value stored in a first shift register of the first shift-register plane and a second value stored in a second shift register of the second shift-register plane,
performing an addition operation between a result of the multiplication operation and a summation value stored in a third shift register of the third shift-register plane,
updating the summation value stored in the third shift register of the third shift-register plane using a result of the addition operation, and
based on determining that a current iteration is not a last iteration:
shifting data in the first shift-register plane one unit in a first dimension corresponding to rows of the first matrix, and
shifting data in the second shift-register plane one unit in a second dimension corresponding to columns of the second matrix.
12. The method of claim 11 , wherein the first matrix comprises R rows and the second matrix comprises S columns, and wherein the method further comprises:
performing a row-wise rotational shearing transformation on the first matrix including shifting each row i, from row 0 to row R−1, by i units; and
performing a column-wise rotational shearing transformation on the second matrix including shifting each column j, from column 0 to column S−1, by j units.
13. The method of claim 11 , further comprising:
loading an initial condition for the matrix multiplication by loading initial values into shift registers of the third shift-register plane.
14. The method of claim 11 , further comprising computing a two-dimensional discrete Fourier transform (2D DFT) using a first matrix of real values, a first matrix of imaginary values, a second matrix of real values, and a second matrix of imaginary values including:
computing a real portion of the 2D DFT including:
performing a first matrix multiplication operation between the first matrix of real values and the second matrix of real values,
performing a second matrix multiplication operation between the first matrix of imaginary values and the second matrix of imaginary values, and
subtracting a result of the second matrix multiplication operation from the first matrix multiplication operation; and
computing an imaginary portion of the 2D DFT including:
performing a third matrix multiplication operation between the first matrix of real values and the second matrix of imaginary values,
performing a fourth matrix multiplication operation between the second matrix of real values and the first matrix of imaginary values, and
adding a result of the third matrix multiplication operation and a result of the fourth matrix multiplication operation.
15. The method of claim 14 , further comprising:
moving the computed real portion of the 2D DFT to another shift-register plane or to memory;
reloading the first matrix of real values and the first matrix of imaginary values back into respective shift-register planes; and
performing a row-wise rotational shearing transformation on the first matrix of real values and the first matrix of imaginary values.