Scalable memory-optimized hardware for matrix-solve
View Patent ↗Systems and methods for matrix-solve applications include a memory-optimized hardware acceleration (HWA) solution with scalable architecture (i.e. specialized circuitry) for HWA matrix-solve operations. The matrix-solve solutions described herein may include a scalable hardware architecture with parallel processing (e.g., “within column” processing), which provides the ability to compute several output values in parallel. The HWA matrix-solve solutions described herein may include simultaneous multi-column processing, which provides a lower execution cycle count and a reduced total number of memory accesses. This HWA matrix-solve provides a low latency and energy-efficient matrix-solve solutions, which may be used to reduce energy consumption and improve performance in various matrix-based applications, such as computer vision, SLAM, AR/VR/mixed-reality, machine learning, data analytics, and other matrix-based applications.
1. A hardware accelerated (HWA) matrix-solve system comprising:
a fetch-A block to retrieve and provide a portion of a matrix A; and
a matrix column computation block including:
an X-buffer block to fetch at least one value of a matrix X;
a within-column parallel compute block to generate a plurality of partial dot products based on the portion of the matrix A and on the at least one value of the matrix X; and
a serial compute block to generate a new element of matrix X based on the plurality of partial dot products, the new element of matrix X provided to the X-buffer block for storage in a memory.
2. The HWA matrix-solve system of claim 1 , the matrix column computation block including a fetch-B block to retrieve and provide a matrix B element to the parallel compute block.
3. The HWA matrix-solve system of claim 2 , the parallel compute block including a negation block to generate a negated matrix B element.
4. The HWA matrix-solve system of claim 3 , the serial compute block further to generate a matrix-solve difference value based on a sum of the negated matrix B element and the plurality of partial dot products.
5. The HWA matrix-solve system of claim 4 , wherein the serial compute block including a matrix multiplier block to generate the new element of matrix X by multiplying the matrix-solve difference value by a matrix A inverse, the matrix A inverse received from the parallel compute block at the serial compute block.
6. The HWA matrix-solve system of claim 5 , wherein:
the fetch-A block is further to retrieve and provide the matrix A inverse to the parallel compute block; and
the parallel compute block further to receive the matrix A inverse and provide the matrix A inverse to the serial compute block.
7. The HWA matrix-solve system of claim 2 , wherein the fetch-B block includes:
a fetch-B memory address register to send a memory address request for the matrix B element; and
a fetch-B memory data register FIFO buffer to store and provide the matrix B element.
8. The HWA matrix-solve system of claim 1 , wherein the fetch-A block includes:
a fetch-A memory address register to send a memory address request of the portion of matrix A; and
a fetch-A memory data register first-in-first-out (FIFO) buffer to store and provide the portion of matrix A.
9. The HWA matrix-solve system of claim 1 , wherein the determined value of the matrix X includes at least one of a forward substitution value and a backward substitution value.
10. The HWA matrix-solve system of claim 9 , wherein the forward substitution value is determined according to
X
pq
=
B
pq
-
∑
i
=
0
p
-
1
A
pi
X
iq
A
pp
.
11. The HWA matrix-solve system of claim 9 , wherein the forward substitution value is determined according to
X
pq
=
B
pq
-
∑
i
=
p
+
1
M
-
1
A
pi
X
iq
A
pp
.
12. The HWA matrix-solve system of claim 1 , further comprising a plurality of column compute blocks, each of the plurality of column compute blocks including a matrix column computation block.
13. A hardware accelerated (HWA) matrix-solve method comprising:
providing a portion of a matrix A at a fetch-A block to a matrix column computation block; and
generating a new element of matrix X at the matrix column computation block, including:
fetching at least one value of a matrix X at an X-buffer block within the matrix column computation block;
generating a plurality of partial dot products at a within-column parallel compute block within the matrix column computation block, the plurality of partial dot products determined based on the portion of the matrix A and on the at least one value of the matrix X; and
generating the new element of matrix X at a serial compute block within the matrix column computation block, the new element of matrix X determined based on the plurality of partial dot products.
14. The HWA matrix-solve method of claim 13 , further including:
fetching a matrix B element at a fetch-B block within the matrix column computation block;
sending the matrix B element from the fetch-B block to the parallel compute block;
generating a negated matrix B element at a negation block within the parallel compute block; and
generating a matrix-solve difference value at the serial compute block, the matrix-solve difference value based on a sum of the negated matrix B element and the plurality of partial dot products.
15. The HWA matrix-solve method of claim 14 , further including receiving a matrix A inverse from the parallel compute block at the serial compute block, wherein generating the new element of matrix X includes multiplying the matrix-solve difference value by the matrix A inverse at a matrix multiplier block within the serial compute block.
16. At least one non-transitory machine-readable storage medium, comprising a plurality of instructions that, responsive to being executed with processor circuitry of a computer-controlled device, cause the computer-controlled device to:
provide a portion of a matrix A at a fetch-A block to a matrix column computation block; and
generate a new element of matrix X at the matrix column computation block, including instructions causing the computer controlled device to:
fetch at least one value of a matrix X at an X-buffer block within the matrix column computation block;
generate a plurality of partial dot products at a within-column parallel compute block within the matrix column computation block, the plurality of partial dot products determined based on the portion of the matrix A and on the at least one value of the matrix X; and
generate the new element of matrix X at a serial compute block within the matrix column computation block, the new element of matrix X determined based on the plurality of partial dot products.
17. The machine-readable storage medium of claim 16 , the instructions further causing the computer-controlled device to:
fetch a matrix B element at a fetch-B block within the matrix column computation block;
send the matrix B element from the fetch-B block to the parallel compute block;
generate a negated matrix B element at a negation block within the parallel compute block; and
generate a matrix-solve difference value at the serial compute block, the matrix-solve difference value based on a sum of the negated matrix B element and the plurality of partial dot products.
18. The machine-readable storage medium of claim 17 , the instructions further causing the computer-controlled device to receive a matrix A inverse from the parallel compute block at the serial compute block, wherein the instructions causing the computer-controlled device to generate the new element of matrix X includes instructions further causing the computer-controlled device to multiply the matrix-solve difference value by the matrix A inverse at a matrix multiplier block within the serial compute block.
19. The machine-readable storage medium of claim 18 , wherein the matrix multiplier block includes a multi-cycle-path multiplier block.
20. The machine-readable storage medium of claim 18 , wherein the instructions causing the computer-controlled device to receive a matrix A inverse from the parallel compute block at the serial compute block further include instructions causing the computer-controlled device to:
retrieve the matrix A inverse at the fetch-A block; and
send the matrix A inverse from the fetch-A block through the parallel compute block to the serial compute block.
21. The machine-readable storage medium of claim 17 , the instructions further causing the computer-controlled device to:
send a memory address request for the portion of matrix B from a fetch-B memory address register within the fetch-B block; and
store and provide the portion of matrix B at a fetch-B memory data register FIFO buffer within the fetch-B block.
22. The machine-readable storage medium of claim 16 , the instructions further causing the computer-controlled device to:
send a memory address request for the portion of matrix A from a fetch-A memory address register within the fetch-A block; and
store and provide the portion of matrix A at a fetch-A memory data register FIFO buffer within the fetch-A block.
23. The machine-readable storage medium of claim 16 , wherein the instructions causing the computer-controlled device to determine the value of the matrix X further includes instructions causing the computer-controlled device to determine at least one of a forward substitution value and a backward substitution value.
24. The machine-readable storage medium of claim 23 , wherein the forward substitution value is determined according to
X
pq
=
B
pq
-
∑
i
=
0
p
-
1
A
pi
X
iq
A
pp
.
25. The machine-readable storage medium of claim 23 , wherein the forward substitution value is determined according to
X
pq
=
B
pq
-
∑
i
=
p
+
1
M
-
1
A
pi
X
iq
A
pp
.