PRIORITY APPLICATION

[0001] This application claims the benefit of priority to U.S. Application Serial Number 17/360,407, filed June 28, 2021, which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

[0002] Embodiments of the disclosure relate generally to operations by processing elements to multiply complex numbers and accumulate the results and more specifically to systems and methods for efficiently performing complex multiply and accumulate operations.

BACKGROUND

[0003] Various computer architectures, such as the Von Neumann architecture, conventionally use a shared memory for data, a bus for accessing the shared memory, an arithmetic unit, and a program control unit. However, moving data between processors and memory can require significant time and energy, which in turn can constrain performance and capacity of computer systems. In view of these limitations, new computing architectures and devices are desired to advance computing performance beyond the practice of transistor scaling (i.e., Moore’s Law).

[0004] To accumulate the results of a series of complex multiply operations, the multiply operations are performed serially, with the result of each successive operation added to a previous running total to determine the accumulated value. [0005] A complex number includes a real component and an imaginary component and may be written as (R, I), where R represents the real component and I represents the imaginary component. The product of two complex numbers is another complex number, as shown by the equation below.

[0006] Thus, a complex multiply involves four multiplication operations, a subtraction operation, and an addition operation. In a traditional implementation, the values for each multiply operation are accessed and provided to an arithmetic logic unit (ALU) in four successive operations. The sum of two complex numbers is also a complex number, as shown by the equation below.

( Rsum.’ Isum ) ^— (^l ^~ b ^2> b ^2)

[0007] As shown in the equation above, a complex add operation involves two addition operations. Thus, after a complex result is generated, two more ALU addition operations are used to accumulate the result.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0008] The disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various embodiments of the disclosure. The drawings, however, should not be taken to limit the disclosure to the specific embodiments, but are for explanation and understanding only.

[0009] To easily identify the discussion of any particular element or act, the most significant digit or digits in a reference number refer to the figure number in which that element is first introduced.

[0010] FIG. 1 illustrates generally a first example of a first memory-compute device in the context of a memory-compute system, according to an embodiment. [0011] FIG. 2 illustrates generally an example of a memory subsystem of a memory-compute device, according to an embodiment.

[0012] FIG. 3 illustrates generally an example of a programmable atomic unit for a memory controller, according to an embodiment.

[0013] FIG. 4 illustrates an example of a hybrid threading processor (HTP) accelerator of a memory-compute device, according to an embodiment.

[0014] FIG. 5 illustrates an example of a representation of a hybrid threading fabric (HTF) of a memory-compute device, according to an embodiment.

[0015] FIG. 6A illustrates generally an example of a chiplet system, according to an embodiment.

[0016] FIG. 6B illustrates generally a block diagram showing various components in the chiplet system from the example of FIG. 6A.

[0017] FIG. 7 illustrates generally an example of a chiplet-based implementation for a memory-compute device, according to an embodiment.

[0018] FIG. 8 illustrates an example tiling of memory-compute device chiplets, according to an embodiment.

[0019] FIG. 9 illustrates data provided for complex multiply and accumulate single-input/multiple-data (SIMD) operations, according to some example embodiments.

[0020] FIG. 10 is a flow chart showing operations of a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure.

[0021] FIG. 11 is a flow chart showing operations of a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure.

[0022] FIG. 12 is a flow chart showing operations of a method performed by a circuit in performing a complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. [0023] FIG. 13 is a flow chart showing operations of a method performed by a circuit in performing complex multiply and accumulate operations within a process to control an autonomous vehicle, in accordance with some embodiments of the present disclosure.

[0024] FIG. 14 illustrates initial, final, and intermediate values of SIMD lanes when implementing a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure.

[0025] FIG. 15 illustrates initial, final, and intermediate values of SIMD lanes when implementing a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure.

[0026] FIG. 16 illustrates a block diagram of an example machine with which, in which, or by which any one or more of the techniques (e.g., methodologies) discussed herein can be implemented.

DETAILED DESCRIPTION

[0027] Recent advances in materials, devices, and integration technology can be leveraged to provide memory-centric compute topologies. Such topologies can realize advances in compute efficiency and workload throughput, for example, for applications constrained by size, weight, or power requirements. The topologies can be used to facilitate low-latency compute near, or inside of, memory or other data storage elements. The approaches can be particularly well-suited for various compute-intensive operations with sparse lookups, such as in transform computations (e.g., fast Fourier transform computations (FFT)), or in applications such as neural networks or artificial intelligence (AI), financial analytics, or simulations or modeling such as for computational fluid dynamics (CFD), Enhanced Acoustic Simulator for Engineers (EASE), Simulation Program with Integrated Circuit Emphasis (SPICE), and others. [0028] Systems, devices, and methods discussed herein can include or use memory-compute systems with processors, or processing capabilities, that are provided in, near, or integrated with memory or data storage components. Such systems are referred to generally herein as CNM systems. A CNM system can be a node-based system with individual nodes in the systems coupled using a system scale fabric. Each node can include or use specialized or general- purpose processors and user-accessible accelerators with a custom compute fabric to facilitate intensive operations, particularly in environments where high cache miss rates are expected.

[0029] In an example, each node in a CNM system can have a host processor or processors. Within each node, a dedicated hybrid threading processor can occupy a discrete endpoint of an on-chip network. The hybrid threading processor can have access to some or all of the memory in a particular node of the system, or a hybrid threading processor can have access to memories across a network of multiple nodes via the system scale fabric. The custom compute fabric, or hybrid threading fabric, at each node can have its own processor(s) or accelerator(s) and can operate at higher bandwidth than the hybrid threading processor. Different nodes in a CNM system can be differently configured, such as having different compute capabilities, different types of memories, different interfaces, or other differences. However, the nodes can be commonly coupled to share data and compute resources within a defined address space.

[0030] In an example, a CNM system, or a node within the system, can be user-configured for custom operations. A user can provide instructions using a high-level programming language, such as C/C++, that can be compiled and mapped directly into a dataflow architecture of the system or of one or more nodes in the CNM system. That is, the nodes in the system can include hardware blocks (e.g., memory controllers, atomic units, other customer accelerators, etc.) that can be configured to directly implement or support user instructions to thereby enhance system performance and reduce latency. [0031] In an example, a CNM system can be particularly suited for implementing a hierarchy of instructions and nested loops (e.g., two, three, or more loops deep, or multiple-dimensional loops). A compiler can be used to accept high-level language instructions and, in turn, compile directly into the dataflow architecture of one or more of the nodes. For example, a node in the system can include a hybrid threading fabric accelerator. The hybrid threading fabric accelerator can execute in a user space of the CNM system and can initiate its own threads or sub-threads, which can operate in parallel. Each thread can map to a different loop iteration to thereby support multi dimensional loops. With the capability to initiate such nested loops, among other capabilities, the CNM system can realize significant time savings and latency improvements for compute-intensive operations.

[0032] A CNM system, or nodes or components of a CNM system, can include or use various memory devices, controllers, and interconnects, among other things. In an example, the system can comprise various interconnected nodes and the nodes, or groups of nodes, can be implemented using chiplets. Chiplets are an emerging technique for integrating various processing functionality. Generally, a chiplet system is made up of discrete chips (e.g., integrated circuits (ICs) on different substrate or die) that are integrated on an interposer and packaged together. This arrangement is distinct from single chips (e.g., ICs) that contain distinct device blocks (e.g., intellectual property (IP) blocks) on one substrate (e.g., single die), such as a system-on-a-chip (SoC), or discretely packaged devices integrated on a board. In general, chiplets provide more production benefits than single die chips, including higher yields or reduced development costs. FIG. 6A and FIG. 6B, discussed below, illustrate generally an example of a chiplet system such as can comprise a CNM system.

[0033] Complex multiply with accumulate is commonly used in digital signal processing (DSP) applications. A pair of complex numbers are multiplied together and the result stored. Another pair of complex numbers are multiplied together and the result is added to the stored value. Further pairs of complex numbers are multiplied and the results are accumulated until all pairs of complex numbers in a set of pairs of complex numbers have been multiplied together. The final accumulated value is used for further DSP calculations.

[0034] Two commands are described herein, each of which performs a partial complex multiply and accumulate. By using these two commands together, a full complex multiply and accumulate operation is performed. As compared to the traditional implementation of sequentially determining the complex multiplication result and then performing complex addition, this reduces the number of commands used from eight (four multiplies, one subtraction and three adds) to two. In some example embodiments, a SIMD architecture is used to enable each command to perform multiple partial complex multiply and accumulate operations simultaneously, further increasing efficiency.

[0035] Each command receives as input the two complex numbers to be multiplied and the current accumulated value. Each command provides as output a partially updated accumulated value, such that after both commands have been executed, the accumulated value is fully updated with the result of the complex multiplication.

[0036] A first command ignores the input imaginary component of the first complex number, replacing it internally with a second copy of the real component of the first complex number. Then, a partial product of the two complex numbers is generated and added to the accumulated value.

[0037] A second command ignores the input real component of the first complex number, replacing it internally with a second copy of the imaginary component of the first complex number. Then, a partial product of the two complex numbers is generated and added to the accumulated value.

(ft n

[0038] As can be seen by inspection, after both commands have been executed, the final accumulator value is the same as when the traditional complex multiply and accumulate operations are performed. However, the operations are performed in only two commands instead of eight.

[0039] One application of DSP computations involving complex multiply and accumulate is in generating images from pulse data of a radar or lidar. For example, an image may be generated from a synthetic aperture radar (SAR) on an autonomous vehicle (e.g., a drone). The image may be provided to a trained machine learning model or other control algorithm that generates an output. Based on the output of the machine learning model, inputs to control circuits of the autonomous vehicle are generated.

[0040] Reducing the number of commands used to perform complex multiply and accumulate operations reduces the amount of data sent to and from processing elements, reduces the amount of time taken to generate the results, and reduces the amount of power consumed in performing the operations. Accordingly, devices making use of the partial complex multiply and accumulate operations discussed herein generate results more quickly, have increased battery life, and, in the case of autonomous vehicles, longer range.

[0041] FIG. 1 illustrates generally a first example of a CNM system 102. The example of the CNM system 102 includes multiple different memory-compute nodes, such as each can include various CNM devices. Each node in the system 102 can operate in its own operating system (OS) domain (e.g., Linux, among others). In an example, the nodes can exist collectively in a common OS domain of the CNM system 102.

[0042] The example of FIG. 1 includes an example of a first memory-compute node 104 of the CNM system 102. The CNM system 102 can have multiple nodes, such as including different instances of the first memory-compute node 104, that are coupled using a scale fabric 106. In an example, the architecture of the CNM system 102 can support scaling with up to n different memory- compute nodes (e.g., n=4096) using the scale fabric 106. As further discussed below, each node in the CNM system 102 can be an assembly of multiple devices.

[0043] The CNM system 102 can include a global controller for the various nodes in the system, or a particular memory-compute node in the system can optionally serve as a host or controller to one or multiple other memory- compute nodes in the same system. The various nodes in the CNM system 102 can thus be similarly or differently configured.

[0044] In an example, each node in the CNM system 102 can comprise a host system that uses a specified OS. The OS can be common or different among the various nodes in the CNM system 102. In the example of FIG. 1, the first memory-compute node 104 comprises a host system 108, a first switch 110, and a first memory-compute device 112. The host system 108 can comprise a processor, such as can include an X86, ARM, RISC-V, or other type of processor. The first switch 110 can be configured to facilitate communication between or among devices of the first memory-compute node 104 or of the CNM system 102, such as using a specialized or other communication protocol, generally referred to herein as a chip-to-chip protocol interface (CTCPI). That is, the CTCPI can include a specialized interface that is unique to the CNM system 102, or can include or use other interfaces such as the compute express link (CXL) interface, the peripheral component interconnect express (PCIe) interface, or the chiplet protocol interface (CPI), among others. The first switch 110 can include a switch configured to use the CTCPI. For example, the first switch 110 can include a CXL switch, a PCIe switch, a CPI switch, or other type of switch. In an example, the first switch 110 can be configured to couple differently configured endpoints. For example, the first switch 110 can be configured to convert packet formats, such as between PCIe and CPI formats, among others.

[0045] The CNM system 102 is described herein in various example configurations, such as comprising a system of nodes, and each node can comprise various chips (e.g., a processor, a switch, a memory device, etc.). In an example, the first memory-compute node 104 in the CNM system 102 can include various chips implemented using chiplets. In the below-discussed chiplet-based configuration of the CNM system 102, inter-chiplet communications, as well as additional communications within the system, can use a CPI network. The CPI network described herein is an example of the CTCPI, that is, as a chiplet-specific implementation of the CTCPI. As a result, the below-described structure, operations, and functionality of CPI can apply equally to structures, operations, and functions as may be otherwise implemented using non-chiplet-based CTCPI implementations. Unless expressly indicated otherwise, any discussion herein of CPI applies equally to CTCPI.

[0046] A CPI interface includes a packet-based network that supports virtual channels to enable a flexible and high-speed interaction between chiplets, such as can comprise portions of the first memory-compute node 104 or the CNM system 102. The CPI can enable bridging from intra-chiplet networks to a broader chiplet network. For example, the Advanced extensible Interface (AXI) is a specification for intra-chip communications. AXI specifications, however, cover a variety of physical design options, such as the number of physical channels, signal timing, power, and so forth. Within a single chip, these options are generally selected to meet design goals, such as power consumption, speed, and so forth. However, to achieve the flexibility of a chiplet-based memory- compute system, an adapter, such as using CPI, can interface between the various AXI design options that can be implemented in the various chiplets. By enabling a physical-channel-to-virtual-channel mapping and encapsulating time- based signaling with a packetized protocol, CPI can be used to bridge intra- chiplet networks, such as within a particular memory-compute node, across a broader chiplet network, such as across the first memory-compute node 104, or across the CNM system 102.

[0047] The CNM system 102 is scalable to include multiple-node configurations. That is, multiple different instances of the first memory- compute node 104, or of other differently configured memory-compute nodes, can be coupled using the scale fabric 106 to provide a scaled system. Each of the memory-compute nodes can run its own OS and can be configured to jointly coordinate system-wide resource usage.

[0048] In the example of FIG. 1, the first switch 110 of the first memory- compute node 104 is coupled to the scale fabric 106. The scale fabric 106 can provide a switch (e.g., a CTCPI switch, a PCIe switch, a CPI switch, or other switch) that can facilitate communication among and between different memory-compute nodes. In an example, the scale fabric 106 can help various nodes communicate in a partitioned global address space (PGAS).

[0049] In an example, the first switch 110 from the first memory-compute node 104 is coupled to one or multiple different memory-compute devices, such as including the first memory-compute device 112. The first memory-compute device 112 can comprise a chiplet-based architecture referred to herein as a CNM chiplet. A packaged version of the first memory-compute device 112 can include, for example, one or multiple CNM chiplets. The chiplets can be communicatively coupled using CTCPI for high bandwidth and low latency.

[0050] In the example of FIG. 1, the first memory-compute device 112 can include a network on chip (NOC) or first NOC 118. Generally, a NOC is an interconnection network within a device, connecting a particular set of endpoints. In FIG. 1, the first NOC 118 can provide communications and connectivity between the various memory, compute resources, and ports of the first memory-compute device 112.

[0051] In an example, the first NOC 118 can comprise a folded Clos topology, such as within each instance of a memory-compute device or as a mesh that couples multiple memory-compute devices in a node. The Clos topology, such as can use multiple, smaller radix crossbars to provide functionality associated with a higher radix crossbar topology, offers various benefits. For example, the Clos topology can exhibit consistent latency and bisection bandwidth across the NOC.

[0052] The first NOC 118 can include various distinct switch types including hub switches, edge switches, and endpoint switches. Each of the switches can be constructed as crossbars that provide substantially uniform latency and bandwidth between input and output nodes. In an example, the endpoint switches and the edge switches can include two separate crossbars, one for traffic headed to the hub switches, and the other for traffic headed away from the hub switches. The hub switches can be constructed as a single crossbar that switches all inputs to all outputs.

[0053] In an example, the hub switches can have multiple ports each (e.g., four or six ports each), such as depending on whether the particular hub switch participates in inter-chip communications. A number of hub switches that participate in inter-chip communications can be set by an inter-chip bandwidth requirement.

[0054] The first NOC 118 can support various payloads (e.g., from 8 to 64- byte payloads; other payload sizes can similarly be used) between compute elements and memory. In an example, the first NOC 118 can be optimized for relatively smaller payloads (e.g., 8-16 bytes) to efficiently handle access to sparse data structures.

[0055] In an example, the first NOC 118 can be coupled to an external host via a first physical-layer interface 114, a PCIe subordinate module 116 or endpoint, and a PCIe principal module 126 or root port. That is, the first physical-layer interface 114 can include an interface to allow an external host processor to be coupled to the first memory-compute device 112. An external host processor can optionally be coupled to one or multiple different memory-compute devices, such as using a PCIe switch or other, native protocol switch. Communication with the external host processor through a PCIe-based switch can limit device- to-device communication to that supported by the switch. Communication through a memory-compute device-native protocol switch such as using CTCPI, in contrast, can allow for more full communication between or among different memory-compute devices, including support for a partitioned global address space, such as for creating threads of work and sending events.

[0056] In an example, the CTCPI protocol can be used by the first NOC 118 in the first memory-compute device 112, and the first switch 110 can include a CTCPI switch. The CTCPI switch can allow CTCPI packets to be transferred from a source memory-compute device, such as the first memory-compute device 112, to a different, destination memory-compute device (e.g., on the same or other node), such as without being converted to another packet format.

[0057] In an example, the first memory-compute device 112 can include an internal host processor 122. The internal host processor 122 can be configured to communicate with the first NOC 118 or other components or modules of the first memory-compute device 112, for example, using the internal PCIe principal module 126, which can help eliminate a physical layer that would consume time and energy. In an example, the internal host processor 122 can be based on a RISC-V ISA processor, and can use the first physical-layer interface 114 to communicate outside of the first memory-compute device 112, such as to other storage, networking, or other peripherals to the first memory-compute device 112. The internal host processor 122 can control the first memory- compute device 112 and can act as a proxy for operating system-related functionality. The internal host processor 122 can include a relatively small number of processing cores (e.g., 2-4 cores) and a host memory device 124 (e.g., comprising a dynamic random access memory (DRAM) module).

[0058] In an example, the internal host processor 122 can include PCI root ports. When the internal host processor 122 is in use, then one of its root ports can be connected to the PCIe subordinate module 116. Another of the root ports of the internal host processor 122 can be connected to the first physical-layer interface 114, such as to provide communication with external PCI peripherals. When the internal host processor 122 is disabled, then the PCIe subordinate module 116 can be coupled to the first physical-layer interface 114 to allow an external host processor to communicate with the first NOC 118. In an example of a system with multiple memory-compute devices, the first memory-compute device 112 can be configured to act as a system host or controller. In this example, the internal host processor 122 can be in use, and other instances of internal host processors in the respective other memory-compute devices can be disabled.

[0059] The internal host processor 122 can be configured at power-up of the first memory-compute device 112, such as to allow the host to initialize. In an example, the internal host processor 122 and its associated data paths (e.g., including the first physical-layer interface 114, the PCIe subordinate module 116, etc.) can be configured from input pins to the first memory-compute device 112. One or more of the pins can be used to enable or disable the internal host processor 122 and configure the PCI (or other) data paths accordingly.

[0060] In an example, the first NOC 118 can be coupled to the scale fabric 106 via a scale fabric interface module 136 and a second physical-layer interface 138. The scale fabric interface module 136, or SIF, can facilitate communication between the first memory-compute device 112 and a device space, such as a PGAS. The PGAS can be configured such that a particular memory-compute device, such as the first memory-compute device 112, can access memory or other resources on a different memory-compute device (e.g., on the same or different node), such as using a load/store paradigm. Various scalable fabric technologies can be used, including CTCPI, CPI, Gen-Z, PCI, or Ethernet bridged over CXL. The scale fabric 106 can be configured to support various packet formats. In an example, the scale fabric 106 supports orderless packet communications or supports ordered packets such as can use a path identifier to spread bandwidth across multiple equivalent paths. The scale fabric 106 can generally support remote operations such as remote memory read, write, and other built-in atomics, remote memory atomics, remote memory- compute device send events, and remote memory-compute device call and return operations.

[0061] In an example, the first NOC 118 can be coupled to one or multiple different memory modules, such as including a first memory device 128. The first memory device 128 can include various kinds of memory devices (for example, low-power double data rate 5 (LPDDR5) synchronous DRAM (SDRAM) or graphics double data rate 6 (GDDR6) DRAM, among others). In the example of FIG. 1, the first NOC 118 can coordinate communications with the first memory device 128 via a memory controller 130 that can be dedicated to the particular memory module. In an example, the memory controller 130 can include a memory module cache and an atomic operations module. The atomic operations module can be configured to provide relatively high-throughput atomic operators, such as including integer and floating-point operators. The atomic operations module can be configured to apply its operators to data within the memory module cache (e.g., comprising SRAM memory side cache), thereby allowing back-to-back atomic operations using the same memory location, with minimal throughput degradation.

[0062] The memory module cache can provide storage for frequently accessed memory locations, such as without having to re-access the first memory device 128. In an example, the memory module cache can be configured to cache data only for a particular instance of the memory controller 130. In an example, the memory controller 130 includes a DRAM controller configured to interface with the first memory device 128, such as including DRAM devices. The memory controller 130 can provide access scheduling and bit error management, among other functions.

[0063] In an example, the first NOC 118 can be coupled to a hybrid threading processor (HTP 140), a hybrid threading fabric (HTF 142), and a host interface and dispatch module (HIF 120). The HIF 120 can be configured to facilitate access to host-based command request queues and response queues. In an example, the HIF 120 can dispatch new threads of execution on processor or compute elements of the HTP 140 or the HTF 142. In an example, the HIF 120 can be configured to maintain workload balance across the HTP 140 module and the HTF 142 module.

[0064] The hybrid threading processor, or HTP 140, can include an accelerator, such as can be based on a RISC-V instruction set. The HTP 140 can include a highly threaded, event-driven processor in which threads can be executed in single instruction rotation, such as to maintain high instruction throughput. The HTP 140 comprises relatively few custom instructions to support low-overhead threading capabilities, event send/receive, and shared memory atomic operators.

[0065] The hybrid threading fabric, or HTF 142, can include an accelerator, such as can include a non-von Neumann, coarse-grained, reconfigurable processor. The HTF 142 can be optimized for high-level language operations and data types (e.g., integer or floating point). In an example, the HTF 142 can support data flow computing. The HTF 142 can be configured to use substantially all of the memory bandwidth available on the first memory- compute device 112, such as when executing memory-bound compute kernels.

[0066] The HTP and HTF accelerators of the CNM system 102 can be programmed using various high-level, structured programming languages. For example, the HTP and HTF accelerators can be programmed using C/C++, such as using the LLVM compiler framework. The HTP accelerator can leverage an open source compiler environment, such as with various added custom instruction sets configured to improve memory access efficiency, provide a message passing mechanism, and manage events, among other things. In an example, the HTF accelerator can be designed to enable programming of the

HTF 142 using a high-level programming language, and the compiler can generate a simulator configuration file or a binary file that runs on the HTF 142 hardware. The HTF 142 can provide a mid-level language for expressing algorithms precisely and concisely, while hiding configuration details of the HTF accelerator itself. In an example, the HTF accelerator tool chain can use an LLVM front-end compiler and the LLVM intermediate representation (IR) to interface with an HTF accelerator back end.

[0067] FIG. 2 illustrates generally an example of a memory subsystem 200 of a memory-compute device, according to an embodiment. The example of the memory subsystem 200 includes a controller 202, a programmable atomic unit 208, and a second NOC 206. The controller 202 can include or use the programmable atomic unit 208 to carry out operations using information in a memory device 204. In an example, the memory subsystem 200 comprises a portion of the first memory-compute device 112 from the example of FIG. 1, such as including portions of the first NOC 118 or of the memory controller 130.

[0068] In the example of FIG. 2, the second NOC 206 is coupled to the controller 202, and the controller 202 can include a memory control module 210, a local cache module 212, and a built-in atomics module 214. In an example, the built-in atomics module 214 can be configured to handle relatively simple, single-cycle, integer atomics. The built-in atomics module 214 can perform atomics at the same throughput as, for example, normal memory read or write operations. In an example, an atomic memory operation can include a combination of storing data to the memory, performing an atomic memory operation, and then responding with load data from the memory.

[0069] The local cache module 212, such as can include an SRAM cache, can be provided to help reduce latency for repetitively-accessed memory locations. In an example, the local cache module 212 can provide a read buffer for sub memory line accesses. The local cache module 212 can be particularly beneficial for compute elements that have relatively small or no data caches. In some example embodiments, the local cache module 212 is a 2 kilobyte read only cache. [0070] The memory control module 210, such as can include a DRAM controller, can provide low-level request buffering and scheduling, such as to provide efficient access to the memory device 204, such as can include a DRAM device. In an example, the memory device 204 can include or use a GDDR6 DRAM device, such as having 16 Gb density and 64 Gb/sec peak bandwidth. Other devices can similarly be used.

[0071] In an example, the programmable atomic unit 208 can comprise single cycle or multiple-cycle operators such as can be configured to perform integer addition or more complicated multiple-instruction operations such as bloom filter insert. In an example, the programmable atomic unit 208 can be configured to perform load and store-to-memory operations. The programmable atomic unit 208 can be configured to leverage the RISC-V ISA with a set of specialized instructions to facilitate interactions with the controller 202 to atomically perform user-defined operations.

[0072] Programmable atomic requests, such as received from an on-node or off-node host, can be routed to the programmable atomic unit 208 via the second NOC 206 and the controller 202. In an example, custom atomic operations (e.g., carried out by the programmable atomic unit 208) can be identical to built-in atomic operations (e.g., carried out by the built-in atomics module 214) except that a programmable atomic operation can be defined or programmed by the user rather than the system architect. In an example, programmable atomic request packets can be sent through the second NOC 206 to the controller 202, and the controller 202 can identify the request as a custom atomic operation. The controller 202 can then forward the identified request to the programmable atomic unit 208.

[0073] FIG. 3 illustrates generally an example of a programmable atomic unit

302 for use with a memory controller, according to an embodiment. In an example, the programmable atomic unit 302 can comprise or correspond to the programmable atomic unit 208 from the example of FIG. 2. That is, FIG. 3 illustrates components in an example of a programmable atomic unit 302 (PAU), such as those noted above with respect to FIG. 2 (e.g., in the programmable atomic unit 208), or to FIG. 1 (e.g., in an atomic operations module of the memory controller 130). As illustrated in FIG. 3, the programmable atomic unit 302 includes a PAU processor or PAU core 306, a PAU thread control 304, an instruction SRAM 308, a data cache 310, and a memory interface 312 to interface with a memory controller 314. In an example, the memory controller 314 comprises an example of the controller 202 from the example of FIG. 2.

[0074] In an example, the PAU core 306 is a pipelined processor such that multiple stages of different instructions are executed together per clock cycle. The PAU core 306 can include a barrel-multithreaded processor, with thread control 304 circuitry to switch between different register files (e.g., sets of registers containing current processing state) upon each clock cycle. This enables efficient context switching between currently executing threads. In an example, the PAU core 306 supports eight threads, resulting in eight register files. In an example, some or all of the register files are not integrated into the PAU core 306, but rather reside in a local data cache 310 or the instruction SRAM 308. This reduces circuit complexity in the PAU core 306 by eliminating the traditional flip-flops used for registers in such memories.

[0075] The local PAU memory can include instruction SRAM 308, such as can include instructions for various atomics. The instructions comprise sets of instructions to support various application-loaded atomic operators. When an atomic operator is requested, such as by an application chiplet, a set of instructions corresponding to the atomic operator are executed by the PAU core 306. In an example, the instruction SRAM 308 can be partitioned to establish the sets of instructions. In this example, the specific programmable atomic operator being requested by a requesting process can identify the programmable atomic operator by the partition number. The partition number can be established when the programmable atomic operator is registered with (e.g., loaded onto) the programmable atomic unit 302. Other metadata for the programmable instructions can be stored in memory (e.g., in partition tables) local to the programmable atomic unit 302.

[0076] In an example, atomic operators manipulate the data cache 310, which is generally synchronized (e.g., flushed) when a thread for an atomic operator completes. Thus, aside from initial loading from the external memory, such as from the memory controller 314, latency can be reduced for most memory operations during execution of a programmable atomic operator thread.

[0077] A pipelined processor, such as the PAU core 306, can experience an issue when an executing thread attempts to issue a memory request if an underlying hazard condition would prevent such a request. Here, the memory request is to retrieve data from the memory controller 314, whether it be from a cache on the memory controller 314 or off-die memory. To resolve this issue, the PAU core 306 is configured to deny the memory request for a thread. Generally, the PAU core 306 or the thread control 304 can include circuitry to enable one or more thread rescheduling points in the pipeline. Here, the denial occurs at a point in the pipeline that is beyond (e.g., after) these thread rescheduling points. In an example, the hazard occurred beyond the rescheduling point. Here, a preceding instruction in the thread created the hazard after the memory request instruction passed the last thread rescheduling point prior to the pipeline stage in which the memory request could be made.

[0078] In an example, to deny the memory request, the PAU core 306 is configured to determine (e.g., detect) that there is a hazard on memory indicated in the memory request. Here, hazard denotes any condition such that allowing (e.g., performing) the memory request will result in an inconsistent state for the thread. In an example, the hazard is an in-flight memory request. Here, whether or not the data cache 310 includes data for the requested memory address, the presence of the in-flight memory request makes it uncertain what the data in the data cache 310 at that address should be. Thus, the thread must wait for the in flight memory request to be completed to operate on current data. The hazard is cleared when the memory request completes. [0079] In an example, the hazard is a dirty cache line in the data cache 310 for the requested memory address. Although the dirty cache line generally indicates that the data in the cache is current and the memory controller version of this data is not, an issue can arise on thread instructions that do not operate from the cache. An example of such an instruction uses a built-in atomic operator, or other separate hardware block, of the memory controller 314. In the context of a memory controller, the built-in atomic operators can be separate from the programmable atomic unit 302 and do not have access to the data cache 310 or instruction SRAM 308 inside the PAU 302. If the cache line is dirty, then the built-in atomic operator will not be operating on the most current data until the data cache 310 is flushed to synchronize the cache and the other off-die memories. This same situation could occur with other hardware blocks of the memory controller 314, such as cryptography block, encoder, and so forth.

[0080] FIG. 4 illustrates an example of an HTP accelerator 400. The HTP accelerator 400 can comprise a portion of a memory-compute device, according to an embodiment. In an example, the HTP accelerator 400 can include or comprise the HTP 140 from the example of FIG. 1. The HTP accelerator 400 includes, for example, a HTP core 402, an instruction cache 404, a data cache 406, a translation block 408, a memory interface 410, and a thread controller 412. The HTP accelerator 400 can further include a dispatch interface 414 and a NOC interface 416, such as for interfacing with a NOC such as the first NOC 118 from the example of FIG. 1, the second NOC 206 from the example of FIG. 2, or any other NOC.

[0081] In an example, the HTP accelerator 400 includes a module that is based on a RISC-V instruction set, and can include a relatively small number of other or additional custom instructions to support a low-overhead, threading-capable Hybrid Threading (HT) language. The HTP accelerator 400 can include a highly-threaded processor core, the HTP core 402, in which, or with which, threads can be executed in a single instruction rotation, such as to maintain high instruction throughput. In an example, a thread can be paused when it waits for other pending events to complete. This can allow the compute resources to be efficiently used on relevant work instead of polling. In an example, multiple- thread barrier synchronization can use efficient HTP-to-HTP and HTP-to/from- Host messaging, such as can allow thousands of threads to initialize or wake in, for example, tens of clock cycles.

[0082] In an example, the dispatch interface 414 can comprise a functional block of the HTP accelerator 400 for handling hardware-based thread management. That is, the dispatch interface 414 can manage dispatch of work to the HTP core 402 or other accelerators. Non-HTP accelerators, however, are generally not able to dispatch work. In an example, work dispatched from a host can use dispatch queues that reside in, e.g., host main memory (e.g., DRAM- based memory). Work dispatched from the HTP accelerator 400, on the other hand, can use dispatch queues that reside in SRAM, such as within the dispatches for the target HTP accelerator 400 within a particular node.

[0083] In an example, the HTP core 402 can comprise one or more cores that execute instructions on behalf of threads. That is, the HTP core 402 can include an instruction processing block. The HTP core 402 can further include, or can be coupled to, the thread controller 412. The thread controller 412 can provide thread control and state for each active thread within the HTP core 402. The data cache 406 can include cache for a host processor (e.g., for local and remote memory-compute devices, including for the HTP core 402), and the instruction cache 404 can include cache for use by the HTP core 402. In an example, the data cache 406 can be configured for read and write operations, and the instruction cache 404 can be configured for read only operations.

[0084] In an example, the data cache 406 is a small cache provided per hardware thread. The data cache 406 can temporarily store data for use by the owning thread. The data cache 406 can be managed by hardware or software in the HTP accelerator 400. For example, hardware can be configured to automatically allocate or evict lines as needed, as load and store operations are executed by the HTP core 402. Software, such as using RISC-V instructions, can determine which memory accesses should be cached and when lines should be invalidated or written back to other memory locations.

[0085] Data caching on the HTP accelerator 400 has various benefits, including making larger accesses more efficient for the memory controller, thereby allowing an executing thread to avoid stalling. However, there are situations when using the cache causes inefficiencies. An example includes accesses where data is accessed only once and causes thrashing of the cache lines. To help address this problem, the HTP accelerator 400 can use a set of custom load instructions to force a load instruction to check for a cache hit and, on a cache miss, to issue a memory request for the requested operand and not put the obtained data in the data cache 406. The HTP accelerator 400 thus includes various different types of load instructions, including non-cached and cache line loads. The non-cached load instructions use the cached data if dirty data is present in the cache. The non-cached load instructions ignore clean data in the cache and do not write accessed data to the data cache. For cache line load instructions, the complete data cache line (e.g., comprising 64 bytes) can be loaded from memory into the data cache 406 and can load the addressed memory into a specified register. These loads can use the cached data if clean or dirty data is in the data cache 406. If the referenced memory location is not in the data cache 406, then the entire cache line can be accessed from memory.

Use of the cache line load instructions can reduce cache misses when sequential memory locations are being referenced (such as memory copy operations) but can also waste memory and bandwidth at the NOC interface 416 if the referenced memory data is not used.

[0086] In an example, the HTP accelerator 400 includes a custom store instruction that is non-cached. The non-cached store instruction can help avoid thrashing the data cache 406 with write data that is not sequentially written to memory.

[0087] In an example, the HTP accelerator 400 further includes a translation block 408. The translation block 408 can include a virtual-to-physical translation block for local memory of a memory-compute device. For example, a host processor, such as in the HTP core 402, can execute a load or store instruction, and the instruction can generate a virtual address. The virtual address can be translated to a physical address of the host processor, such as using a translation table from the translation block 408. The memory interface 410, for example, can include an interface between the HTP core 402 and the NOC interface 416.

[0088] FIG. 5 illustrates an example of a representation of an HTF 500 of a memory-compute device, according to an embodiment. In an example, the HTF 500 can include or comprise the HTF 142 from the example of FIG. 1. The HTF 500 is a coarse-grained, reconfigurable compute fabric that can be optimized for high-level language operand types and operators (e.g., using C/C++ or other high-level language). In an example, the HTF 500 can include configurable, n- bit wide (e.g., 512-bit wide) data paths that interconnect hardened single instruction multiple-data (SIMD) arithmetic units.

[0089] In an example, the HTF 500 comprises an HTF cluster 502 that includes multiple HTF tiles, including an example tile 504, or Tile N. Each HTF tile can include one or more compute elements with local memory and arithmetic functions. For example, each tile can include a compute pipeline with support for integer and floating-point operations. In an example, the data path, compute elements, and other infrastructure can be implemented as hardened IP to provide maximum performance while minimizing power consumption and reconfiguration time.

[0090] In the example of FIG. 5, the tiles comprising the HTF cluster 502 are linearly arranged, and each tile in the cluster can be coupled to one or multiple other tiles in the HTF cluster 502. In the example of FIG. 5, the example tile

504, or Tile N, is coupled to four other tiles, including to a base tile 510 (e.g.,

Tile N-2) via the port labeled IN N-2, to an adjacent tile 512 (e.g., Tile N-l) via the port labeled IN N-l, and to a Tile N+l via the port labeled IN N+l and to a

Tile N+2 via the port labeled IN N+2. The example tile 504 can be coupled to the same or other tiles via respective output ports, such as those labeled OUT N- 1, OUT N-2, OUT N+l, and OUT N+2. In this example, the ordered list of names for the various tiles are notional indications of the positions of the tiles.

In other examples, the tiles comprising the HTF cluster 502 can be arranged in a grid or other configuration, with each tile similarly coupled to one or several of its nearest neighbors in the grid. Tiles that are provided at an edge of a cluster can optionally have fewer connections to neighboring tiles. For example, Tile N-2, or the base tile 510 in the example of FIG. 5, can be coupled only to the adjacent tile 512 (Tile N-l) and to the example tile 504 (Tile N). Fewer or additional inter-tile connections can similarly be used.

[0091] The HTF cluster 502 can further include memory interface modules, including a first memory interface module 506. The memory interface modules can couple the HTF cluster 502 to a NOC, such as the first NOC 118 of FIG. 1. In an example, the memory interface modules can allow tiles within a cluster to make requests to other locations in a memory-compute system, such as in the same or different node in the system. That is, the representation of the HTF 500 can comprise a portion of a larger fabric that can be distributed across multiple nodes, such as with one or more HTF tiles or HTF clusters at each of the nodes. Requests can be made between tiles or nodes within the context of the larger fabric.

[0092] In the example of FIG. 5, the tiles in the HTF cluster 502 are coupled using a synchronous fabric (SF). The synchronous fabric can provide communication between a particular tile and its neighboring tiles in the HTF cluster 502, as described above. Each HTF cluster 502 can further include an asynchronous fabric (AF) that can provide communication among, e.g., the tiles in the cluster, the memory interfaces in the cluster, and a dispatch interface 508 in the cluster.

[0093] In an example, the synchronous fabric can exchange messages that include data and control information. The control information can include, among other things, instruction RAM address information or a thread identifier. The control information can be used to set up a data path, and a data message field can be selected as a source for the path. Generally, the control fields can be provided or received earlier, such that they can be used to configure the data path. For example, to help minimize any delay through the synchronous domain pipeline in a tile, the control information can arrive at a tile a few clock cycles before the data field. Various registers can be provided to help coordinate dataflow timing in the pipeline.

[0094] In an example, each tile in the HTF cluster 502 can include multiple memories. Each memory can have the same width as the data path (e.g., 512 bits) and can have a specified depth, such as in a range of 512 to 1024 elements. The tile memories can be used to store data that supports data path operations. The stored data can include constants loaded as part of a kernel's cluster configuration, for example, or can include variables calculated as part of the data flow. In an example, the tile memories can be written from the asynchronous fabric as a data transfer from another synchronous domain or can include a result of a load operation such as initiated by another synchronous domain. The tile memory can be read via synchronous data path instruction execution in the synchronous domain.

[0095] In an example, each tile in an HTF cluster 502 can have a dedicated instruction RAM (INST RAM). In an example of an HTF cluster 502 with sixteen tiles, and instruction RAM instances with sixty-four entries, the cluster can allow algorithms to be mapped with up to 1024 multiply-shift and/or arithmetic-logic unit (ALU) operations. The various tiles can optionally be pipelined together, such as using the synchronous fabric, to allow data flow compute with minimal memory access, thus minimizing latency and reducing power consumption. In an example, the asynchronous fabric can allow memory references to proceed in parallel with computation, thereby providing more efficient streaming kernels. In an example, the various tiles can include built-in support for loop-based constructs and can support nested looping kernels. [0096] The synchronous fabric can allow multiple tiles to be pipelined, such as without a need for data queuing. Tiles that participate in a synchronous domain can, for example, act as a single pipelined data path. A first or base tile (e.g., Tile N-2, in the example of FIG. 5) of a synchronous domain can initiate a thread of work through the pipelined tiles. The base tile can be responsible for starting work on a predefined cadence referred to herein as a Spoke Count. For example, if the Spoke Count is 3, then the base tile can initiate work every third clock cycle.

[0097] In an example, the synchronous domain comprises a set of connected tiles in the HTF cluster 502. Execution of a thread can begin at the domain's base tile and can progress from the base tile, via the synchronous fabric, to other tiles in the same domain. The base tile can provide the instruction to be executed for the first tile. The first tile can, by default, provide the same instruction for the other connected tiles to execute. However, in some examples, the base tile, or a subsequent tile, can conditionally specify or use an alternative instruction. The alternative instruction can be chosen by having the tile’s data path produce a Boolean conditional value and then can use the Boolean value to choose between an instruction set of the current tile and the alternate instruction.

[0098] The asynchronous fabric can be used to perform operations that occur asynchronously relative to a synchronous domain. Each tile in the HTF cluster 502 can include an interface to the asynchronous fabric. The inbound interface can include, for example, a first-in first-out (FIFO) buffer or queue (e.g., AF IN QUEUE) to provide storage for messages that cannot be immediately processed. Similarly, the outbound interface of the asynchronous fabric can include a FIFO buffer or queue (e.g., AF OUT QUEUE) to provide storage for messages that cannot be immediately sent out.

[0099] In an example, messages in the AF can be classified as data messages or control messages. Data messages can include a SIMD width data value that is written to either tile memory 0 (MEM_0) or memory 1 (MEM_1). Control messages can be configured to control thread creation, free resources, or issue external memory references.

[0100] A tile in the HTF cluster 502 can perform various compute operations for the HTF. The compute operations can be performed by configuring the data path within the tile. In an example, a tile includes two functional blocks that perform the compute operations for the tile: a Multiply and Shift Operation block (MS OP) and an Arithmetic, Logical, and Bit Operation block (ALB OP). The two blocks can be configured to perform pipelined operations such as a Multiply and Add, or a Shift and Add, among others.

[0101] In an example, each instance of a memory-compute device in a system can have a complete supported instruction set for its operator blocks (e.g., MS OP and ALB OP). In this case, binary compatibility can be realized across all devices in the system. However, in some examples, it can be helpful to maintain a base set of functionality and optional instruction set classes, such as to meet various design tradeoffs, such as die size. The approach can be similar to how the RISC-V instruction set has a base set and multiple optional instruction subsets.

[0102] In an example, the example tile 504 can include a Spoke RAM. The

Spoke RAM can be used to specify which input (e.g., from among the four SF tile inputs and the base tile input) is the primary input for each clock cycle. The

Spoke RAM read address input can originate at a counter that counts from zero to Spoke Count minus one. In an example, different spoke counts can be used on different tiles, such as within the same HTF cluster 502, to allow a number of slices, or unique tile instances, used by an inner loop to determine the performance of a particular application or instruction set. In an example, the

Spoke RAM can specify when a synchronous input is to be written to a tile memory, for instance when multiple inputs for a particular tile instruction are used and one of the inputs arrives before the others. The early-arriving input can be written to the tile memory and can be later read when all of the inputs are available. In this example, the tile memory can be accessed as a FIFO memory, and FIFO read and write pointers can be stored in a register-based memory region or structure in the tile memory.

[0103] FIG. 6A and FIG. 6B illustrate generally an example of a chiplet system that can be used to implement one or more aspects of the CNM system 102. As similarly mentioned above, a node in the CNM system 102, or a device within a node in the CNM system 102, can include a chiplet-based architecture or CNM chiplet. A packaged memory-compute device can include, for example, one, two, or four CNM chiplets. The chiplets can be interconnected using high- bandwidth, low-latency interconnects such as using a CPI interface. Generally, a chiplet system is made up of discrete modules (each a “chiplet”) that are integrated on an interposer and, in many examples, are interconnected as desired through one or more established networks to provide a system with the desired functionality. The interposer and included chiplets can be packaged together to facilitate interconnection with other components of a larger system. Each chiplet can include one or more individual ICs, or “chips,” potentially in combination with discrete circuit components, and can be coupled to a respective substrate to facilitate attachment to the interposer. Most or all chiplets in a system can be individually configured for communication through established networks.

[0104] The configuration of chiplets as individual modules of a system is distinct from such a system being implemented on single chips that contain distinct device blocks (e.g., IP blocks) on one substrate (e.g., single die), such as a SoC, or multiple discrete packaged devices integrated on a printed circuit board (PCB). In general, chiplets provide better performance (e.g., lower power consumption, reduced latency, etc.) than discrete packaged devices, and chiplets provide greater production benefits than single die chips. These production benefits can include higher yields or reduced development costs and time.

[0105] Chiplet systems can include, for example, one or more application (or processor) chiplets and one or more support chiplets. Here, the distinction between application and support chiplets is simply a reference to the likely design scenarios for the chiplet system. Thus, for example, a synthetic vision chiplet system can include, by way of example only, an application chiplet to produce the synthetic vision output along with support chiplets, such as a memory controller chiplet, a sensor interface chiplet, or a communication chiplet. In a typical use case, the synthetic vision designer can design the application chiplet and source the support chiplets from other parties. Thus, the design expenditure (e.g., in terms of time or complexity) is reduced by avoiding the design and production of functionality embodied in the support chiplets.

[0106] Chiplets also support the tight integration of IP blocks that can otherwise be difficult, such as those manufactured using different processing technologies or using different feature sizes (or utilizing different contact technologies or spacings). Thus, multiple ICs or IC assemblies, with different physical, electrical, or communication characteristics, can be assembled in a modular manner to provide an assembly with various desired functionalities. Chiplet systems can also facilitate adaptation to suit the needs of different larger systems into which the chiplet system will be incorporated. In an example, ICs or other assemblies can be optimized for the power, speed, or heat generation for a specific function — as can happen with sensors — and can be integrated with other devices more easily than attempting to do so on a single die. Additionally, by reducing the overall size of the die, the yield for chiplets tends to be higher than that of more complex, single die devices.

[0107] FIG. 6A and FIG. 6B illustrate generally an example of a chiplet system, according to an embodiment. FIG. 6A is a representation of the chiplet system 602 mounted on a peripheral board 604, that can be connected to a broader computer system by a (PCIe, for example). The chiplet system 602 includes a package substrate 606, an interposer 608, and four chiplets: an application chiplet 610, a host interface chiplet 612, a memory controller chiplet 614, and a memory device chiplet 616. Other systems can include many additional chiplets to provide additional functionalities as will be apparent from the following discussion. The package of the chiplet system 602 is illustrated with a lid or cover 618, though other packaging techniques and structures for the chiplet system can be used. FIG. 6B is a block diagram labeling the components in the chiplet system for clarity.

[0108] The application chiplet 610 is illustrated as including a chiplet system NOC 620 to support a chiplet network 622 for inter-chiplet communications. In example embodiments, the chiplet system NOC 620 can be included on the application chiplet 610. In an example, the first NOC 118 from the example of FIG. 1 can be defined in response to selected support chiplets (e.g., host interface chiplet 612, memory controller chiplet 614, and memory device chiplet 616), thus enabling a designer to select an appropriate number of chiplet network connections or switches for the chiplet system NOC 620. In an example, the chiplet system NOC 620 can be located on a separate chiplet, or within the interposer 608. In examples as discussed herein, the chiplet system NOC 620 implements a CPI network.

[0109] In an example, the chiplet system 602 can include or comprise a portion of the first memory-compute node 104 or the first memory-compute device 112. That is, the various blocks or components of the first memory-compute device 112 can include chiplets that can be mounted on the peripheral board 604, the package substrate 606, and the interposer 608. The interface components of the first memory-compute device 112 can comprise, generally, the host interface chiplet 612. The memory and memory control-related components of the first memory-compute device 112 can comprise, generally, the memory controller chiplet 614. The various accelerator and processor components of the first memory-compute device 112 can comprise, generally, the application chiplet 610 or instances thereof, and so on.

[0110] The CPI interface, such as can be used for communication between or among chiplets in a system, is a packet-based network that supports virtual channels to enable a flexible and high-speed interaction between chiplets. CPI enables bridging from intra-chiplet networks to the chiplet network 622. For example, AXI is a widely used specification to design intra-chip communications. AXI specifications, however, cover a great variety of physical design options, such as the number of physical channels, signal timing, power, and so forth. Within a single chip, these options are generally selected to meet design goals, such as power consumption, speed, and so forth. However, to achieve the flexibility of the chiplet system, an adapter, such as CPI, is used to interface between the various AXI design options that can be implemented in the various chiplets. By enabling a physical-channel-to-virtual-channel mapping and encapsulating time-based signaling with a packetized protocol, CPI bridges intra-chiplet networks across the chiplet network 622.

[0111] CPI can use a variety of different physical layers to transmit packets. The physical layer can include simple conductive connections, drivers to increase the voltage, or otherwise facilitate transmitting the signals over longer distances. An example of one such a physical layer can include the Advanced Interface Bus (AIB), which, in various examples, can be implemented in the interposer 608. An AIB transmits and receives data using source synchronous data transfers with a forwarded clock. Packets are transferred across the AIB at single data rate (SDR) or dual data rate (DDR) with respect to the transmitted clock. Various channel widths are supported by AIB. The channel can be configured to have a symmetrical number of transmit (TX) and receive (RX) input/outputs (I/Os) or have a non-symmetrical number of transmitters and receivers (e.g., either all transmitters or all receivers). The channel can act as an AIB principal or subordinate depending on which chiplet provides the principal clock. AIB I/O cells support three clocking modes: asynchronous (i.e., non- clocked), SDR, and DDR. In various examples, the non-clocked mode is used for clocks and some control signals. The SDR mode can use dedicated SDR only I/O cells or dual use SDR/DDR I/O cells.

[0112] In an example, CPI packet protocols (e.g., point-to-point or routable) can use symmetrical receive and transmit I/O cells within an AIB channel. The CPI streaming protocol allows more flexible use of the AIB I/O cells. In an example, an AIB channel for streaming mode can configure the I/O cells as all TX, all RX, or half TX and half RX. CPI packet protocols can use an AIB channel in either SDR or DDR operation mode. In an example, the AIB channel is configured in increments of 80 I/O cells (i.e., 40 TX and 40 RX) for SDR mode and 40 I/O cells for DDR mode. The CPI streaming protocol can use an AIB channel in either SDR or DDR operation modes. Here, in an example, the AIB channel is in increments of 40 I/O cells for both SDR and DDR modes. In an example, each AIB channel is assigned a unique interface identifier. The identifier is used during CPI reset and initialization to determine paired AIB channels across adjacent chiplets. In an example, the interface identifier is a 20- bit value comprising a seven-bit chiplet identifier, a seven-bit column identifier, and a six-bit link identifier. The AIB physical layer transmits the interface identifier using an AIB out-of-band shift register. The 20-bit interface identifier is transferred in both directions across an AIB interface using bits 32-51 of the shift registers.

[0113] AIB defines a stacked set of AIB channels as an AIB channel column. An AIB channel column has some number of AIB channels plus an auxiliary channel. The auxiliary channel contains signals used for AIB initialization. All AIB channels (other than the auxiliary channel) within a column are of the same configuration (e.g., all TX, all RX, or half TX and half RX), as well as having the same number of data I/O signals. In an example, AIB channels are numbered in continuous increasing order starting with the AIB channel adjacent to the AUX channel. The AIB channel adjacent to the AUX is defined to be AIB channel zero.

[0114] Generally, CPI interfaces on individual chiplets can include serialization-deserialization (SERDES) hardware. SERDES interconnects work well for scenarios in which high-speed signaling with low signal count is desirable. SERDES, however, can result in additional power consumption and longer latencies for multiplexing and demultiplexing, error detection or correction (e.g., using block level cyclic redundancy checking (CRC)), link- level retry, or forward error correction. However, when low latency or energy consumption is a primary concern for ultra-short reach, chiplet-to-chiplet interconnects, a parallel interface with clock rates that allow data transfer with minimal latency can be utilized. CPI includes elements to minimize both latency and energy consumption in these ultra-short reach chiplet interconnects.

[0115] For flow control, CPI employs a credit-based technique. A recipient, such as the application chiplet 610, provides a sender, such as the memory controller chiplet 614, with credits that represent available buffers. In an example, a CPI recipient includes a buffer for each virtual channel for a given time-unit of transmission. Thus, if the CPI recipient supports five messages in time and a single virtual channel, the recipient has five buffers arranged in five rows (e.g., one row for each unit time). If four virtual channels are supported, then the recipient has twenty buffers arranged in five rows. Each buffer holds the payload of one CPI packet.

[0116] When the sender transmits to the recipient, the sender decrements the available credits based on the transmission. Once all credits for the recipient are consumed, the sender stops sending packets to the recipient. This ensures that the recipient always has an available buffer to store the transmission.

[0117] As the recipient processes received packets and frees buffers, the recipient communicates the available buffer space back to the sender. This credit return can then be used by the sender to allow transmitting of additional information.

[0118] The example of FIG. 6A includes a chiplet mesh network 624 that uses a direct, chiplet-to-chiplet technique without a need for the chiplet system NOC 620. The chiplet mesh network 624 can be implemented in CPI or another chiplet-to-chiplet protocol. The chiplet mesh network 624 generally enables a pipeline of chiplets where one chiplet serves as the interface to the pipeline while other chiplets in the pipeline interface only with themselves.

[0119] Additionally, dedicated device interfaces, such as one or more industry standard memory interfaces (such as, for example, synchronous memory interfaces, such as DDR5, DDR6), can be used to connect a device to a chiplet. Connection of a chiplet system or individual chiplets to external devices (such as a larger system) can be through a desired interface (for example, a PCIe interface). Such an external interface can be implemented, in an example, through the host interface chiplet 612, which, in the depicted example, provides a PCIe interface external to the chiplet system. Such dedicated chiplet interfaces 626 are generally employed when a convention or standard in the industry has converged on such an interface. The illustrated example of a DDR interface connecting the memory controller chiplet 614 to a DRAM memory device chiplet 616 is just such an industry convention.

[0120] Of the variety of possible support chiplets, the memory controller chiplet 614 is likely present in the chiplet system due to the near omnipresent use of storage for computer processing as well as sophisticated state-of-the-art for memory devices. Thus, using memory device chiplets 616 and memory controller chiplets 614 produced by others gives chiplet system designers access to robust products by sophisticated producers. Generally, the memory controller chiplet 614 provides a memory device-specific interface to read, write, or erase data. Often, the memory controller chiplet 614 can provide additional features, such as error detection, error correction, maintenance operations, or atomic operator execution. For some types of memory, maintenance operations tend to be specific to the memory device chiplet 616, such as garbage collection in NAND flash or storage class memories and temperature adjustments (e.g., cross temperature management) in NAND flash memories. In an example, the maintenance operations can include logical-to-physical (L2P) mapping or management to provide a level of indirection between the physical and logical representation of data. In other types of memory, for example DRAM, some memory operations, such as refresh, can be controlled by a host processor or a memory controller at some times, and at other times, controlled by the DRAM memory device, or by logic associated with one or more DRAM devices, such as an interface chip (in an example, a buffer). [0121] Atomic operators are a data manipulation that, for example, can be performed by the memory controller chiplet 614. In other chiplet systems, the atomic operators can be performed by other chiplets. For example, an atomic operator of “increment” can be specified in a command by the application chiplet 610, the command including a memory address and possibly an increment value. Upon receiving the command, the memory controller chiplet 614 retrieves a number from the specified memory address, increments the number by the amount specified in the command, and stores the result. Upon a successful completion, the memory controller chiplet 614 provides an indication of the command success to the application chiplet 610. Atomic operators avoid transmitting the data across the chiplet mesh network 624, resulting in lower latency execution of such commands.

[0122] Atomic operators can be classified as built-in atomics or programmable (e.g., custom) atomics. Built-in atomics are a finite set of operations that are immutably implemented in hardware. Programmable atomics are small programs that can execute on a PAU (e.g., a custom atomic unit (CAU)) of the memory controller chiplet 614.

[0123] The memory device chiplet 616 can be, or include any combination of, volatile memory devices or non-volatile memories. Examples of volatile memory devices include, but are not limited to, RAM, such as DRAM, synchronous DRAM (SDRAM), and GDDR6 SDRAM, among others. Examples of non-volatile memory devices include, but are not limited to, NAND-type flash memory and storage class memory (e.g., phase-change memory or memristor based technologies, ferroelectric RAM (FeRAM), among others).

The illustrated example includes the memory device chiplet 616 as a chiplet; however, the device can reside elsewhere, such as in a different package on the peripheral board 604. For many applications, multiple memory device chiplets can be provided. In an example, these memory device chiplets can each implement one or multiple storage technologies and may include integrated compute hosts. In an example, a memory chiplet can include multiple stacked memory die of different technologies (for example, one or more SRAM devices stacked or otherwise in communication with one or more DRAM devices). In an example, the memory controller chiplet 614 can serve to coordinate operations between multiple memory chiplets in the chiplet system 602 (for example, to use one or more memory chiplets in one or more levels of cache storage and to use one or more additional memory chiplets as main memory). The chiplet system 602 can include multiple memory controller chiplet 614 instances, as can be used to provide memory control functionality for separate hosts, processors, sensors, networks, and so forth. A chiplet architecture, such as in the illustrated system, offers advantages in allowing adaptation to different memory storage technologies and different memory interfaces, through updated chiplet configurations, such as without requiring redesign of the remainder of the system structure.

[0124] FIG. 7 illustrates generally an example of a chiplet-based implementation for a memory-compute device, according to an embodiment.

The example includes an implementation with four CNM chiplets, and each of the CNM chiplets can include or comprise portions of the first memory-compute device 112 or the first memory-compute node 104 from the example of FIG. 1. The various portions can themselves include or comprise respective chiplets.

The chiplet-based implementation can include or use CPI-based intra-system communications, as similarly discussed above in the example chiplet system 602 from FIG. 6A and FIG. 6B.

[0125] The example of FIG. 7 includes a first CNM package 700 comprising multiple chiplets. The first CNM package 700 includes a first chiplet 702, a second chiplet 704, a third chiplet 706, and a fourth chiplet 708, all coupled to a CNM NOC hub 710. Each of the first through fourth chiplets can comprise instances of the same, or substantially the same, components or modules. For example, the chiplets can each include respective instances of an HTP accelerator, an HTF accelerator, and memory controllers for accessing internal or external memories. [0126] In the example of FIG. 7, the first chiplet 702 includes a first NOC hub edge 714 coupled to the CNM NOC hub 710. The other chiplets in the first CNM package 700 similarly include NOC hub edges or endpoints. The switches in the NOC hub edges facilitate intra-chiplet, or intra-chiplet-system, communications via the CNM NOC hub 710.

[0127] The first chiplet 702 can further include one or multiple memory controllers 716. The memory controllers 716 can correspond to respective different NOC endpoint switches interfaced with the first NOC hub edge 714. In an example, the memory controller 716 comprises the memory controller chiplet 614, the memory controller 130, the memory subsystem 200, or other memory- compute implementation. The memory controllers 716 can be coupled to respective different memory devices, for example, including a first external memory module 712a or a second external memory module 712b. The external memory modules can include, e.g., GDDR6 memories that can be selectively accessed by the respective different chiplets in the system.

[0128] The first chiplet 702 can further include a first HTP chiplet 718 and second HTP chiplet 720, such as coupled to the first NOC hub edge 714 via respective different NOC endpoint switches. The HTP chiplets can correspond to HTP accelerators, such as the HTP 140 from the example of FIG. 1, or the HTP accelerator 400 from the example of FIG. 4. The HTP chiplets can communicate with a HTF chiplet 722. The HTF chiplet 722 can correspond to an HTF accelerator, such as the HTF 142 from the example of FIG. 1, or the HTF 500 from the example of FIG. 5.

[0129] The CNM NOC hub 710 can be coupled to NOC hub instances in other chiplets or other CNM packages by way of various interfaces and switches. For example, the CNM NOC hub 710 can be coupled to a CPI interface by way of multiple different NOC endpoints on the first CNM package 700. Each of the multiple different NOC endpoints can be coupled, for example, to a different node outside of the first CNM package 700. In an example, the CNM NOC hub

710 can be coupled to other peripherals, nodes, or devices using CTCPI or other, non-CPI protocols. For example, the first CNM package 700 can include a PCIe scale fabric interface (PCIE/SFI) or a CXL interface configured to interface the first CNM package 700 with other devices. In an example, devices to which the first CNM package 700 is coupled using the various CPI, PCIe, CXL, or other fabric, can make up a common global address space.

[0130] In the example of FIG. 7, the first CNM package 700 includes a host interface 724 (HIF) and a host processor (R5). The host interface 724 can correspond to, for example, the HIF 120 from the example of FIG. 1. The host processor, or R5, can correspond to the internal host processor 122 from the example of FIG. 1. The host interface 724 can include a PCI interface for coupling the first CNM package 700 to other external devices or systems. In an example, work can be initiated on the first CNM package 700, or a tile cluster within the first CNM package 700, by the host interface 724. For example, the host interface 724 can be configured to command individual HTF tile clusters, such as among the various chiplets in the first CNM package 700, into and out of power/clock gate modes.

[0131] FIG. 8 illustrates an example tiling of memory-compute devices, according to an embodiment. In FIG. 8, a tiled chiplet example 800 includes four instances of different CNM clusters of chiplets, where the clusters are coupled together. Each instance of a CNM chiplet can itself include one or more constituent chiplets (e.g., host processor chiplets, memory device chiplets, interface chiplets, and so on).

[0132] The tiled chiplet example 800 includes, as one or multiple of its CNM clusters, instances of the first CNM package 700 from the example of FIG. 7.

For example, the tiled chiplet example 800 can include a first CNM cluster 802 that includes a first chiplet 810 (e.g., corresponding to the first chiplet 702), a second chiplet 812 (e.g., corresponding to the second chiplet 704), a third chiplet 814 (e.g., corresponding to the third chiplet 706), and a fourth chiplet

816 (e.g., corresponding to the fourth chiplet 708). The chiplets in the first

CNM cluster 802 can be coupled to a common NOC hub, which in turn can be coupled to a NOC hub in an adjacent cluster or clusters (e.g., in a second CNM cluster 804 or a fourth CNM cluster 808).

[0133] In the example of FIG. 8, the tiled chiplet example 800 includes the first CNM cluster 802, the second CNM cluster 804, the third CNM cluster 806, and the fourth CNM cluster 808. The various different CNM chiplets can be configured in a common address space such that the chiplets can allocate and share resources across the different tiles. In an example, the chiplets in the cluster can communicate with each other. For example, the first CNM cluster 802 can be communicatively coupled to the second CNM cluster 804 via an inter-chiplet CPI interface 818, and the first CNM cluster 802 can be communicatively coupled to the fourth CNM cluster 808 via another or the same CPI interface. The second CNM cluster 804 can be communicatively coupled to the third CNM cluster 806 via the same or other CPI interface, and so on.

[0134] In an example, one of the CNM chiplets in the tiled chiplet example 800 can include a host interface (e.g., corresponding to the host interface 724 from the example of FIG. 7) that is responsible for workload balancing across the tiled chiplet example 800. The host interface can facilitate access to host- based command request queues and response queues, such as from outside of the tiled chiplet example 800. The host interface can dispatch new threads of execution using hybrid threading processors and the hybrid threading fabric in one or more of the CNM chiplets in the tiled chiplet example 800.

[0135] FIG. 9 illustrates data provided for complex multiply and accumulate single-input/multiple-data (SIMD) operations, according to some example embodiments. Six SIMD operations are shown, divided into two steps of three operations each. Each SIMD operation receives as input a single instruction and multiple data values, one for each lane. Each SIMD operation generates multiple data values as output, one for each lane. In the example of FIG. 9, four lanes are used, but any even number of lanes may be used. [0136] For the first pair of lanes, the two complex numbers being multiplied are denoted as (Ria, Iia) and (R2a, l2a) ; the initial accumulate value is denoted as (A _RS , Aia). For the second pair of lanes, the two complex numbers being multiplied are denoted as (Rib, lib) and (R2b, l2b); the initial accumulate value is denoted as (ARb, Aib).

[0137] The first SIMD command comprises SIMD data 905, comprising the first complex number in each pair of lanes and SIMD instruction 910, DupReal. The DupReal instruction duplicates the values on the even lanes to the next- higher lane, generating output 915. Thus, when the input comprises a real component on each even lane and an imaginary component on each odd lane, the DupReal instruction has the effect of duplicating the real values and overwriting the imaginary values.

[0138] SIMD data 920 comprises the second complex number in each pair of lanes and is provided along with SIMD instruction 925, MulF32. The MulF32 instruction multiplies the previous output value on each lane with the input value on each lane. MulF32 operates on 32-bit values in 32-bit lanes, but lanes of other sizes (e.g., 64-bits or 128-bits) may be used in other example embodiments. The SIMD output 930 contains the partial product of the multiplication of the two complex numbers, with the real and imaginary components of the second complex number having been multiplied by the real component of the first complex number.

[0139] In the third SIMD operation, the real and imaginary components of the accumulator value are provided in SIMD data 935. The SIMD instruction 940 is AddF32. The AddF32 instruction adds, in each lane, the previous output value on the lane with the input value on the lane. Thus, the SIMD output 945 contains, on each pair of lanes, the sum of the complex accumulator with the partial product, completing the first step.

[0140] Due to pipelining, the three SIMD operations of step one may complete on successive clock cycles. Though three SIMD operations are invoked, step one may be initiated by a single instruction in the instruction RAM of the tile 504.

[0141] In step two, the first complex number is provided again as SIMD input 950, along with the SIMD instruction 955, Duplmag. The Duplmag instruction duplicates the values on the odd lanes to the next-lower lane, generating SIMD output 960. Thus, when the input comprises a real component on each even lane and an imaginary component on each odd lane, the Duplmag instruction has the effect of duplicating the imaginary values and overwriting the real values.

[0142] The second SIMD operation of step two comprises the SIMD input 965, containing the second complex number with the real and imaginary components swapped, and the SIMD instruction 970, MulF32. The SIMD output 975 is generated as a result of the MulF32 instruction, containing the product of the imaginary component of the first complex number with the swapped components of the second complex number. Since the product of two imaginary numbers is a real number and the product of an imaginary number with a real number is a complex number, the partial products have a real component in the even lane and an imaginary component in the odd lane.

[0143] Step two completes with a SIMD operation comprising the SIMD input 980, containing the partially updated accumulator value of the SIMD output 945, and the SIMD instruction 985, AddCF32. The AddCF32 instruction performs a different operation for odd- and even-numbered lanes. For odd- numbered lanes, the AddCF32 instruction adds the last output value for the lane to the input value for the lane. For even-numbered lanes, the AddCF32 instruction subtracts the last output value for the lane from the input value for the lane. This has the effect of negating the value of the products of the two imaginary numbers in the even lanes. The SIMD output 990 contains the updated accumulator values. The two steps may be performed by a single tile 502, 512 of FIG. 5 or each step may be performed by a different tile 502, 512. [0144] Due to pipelining, the three SIMD operations of step two may complete on successive clock cycles. Though three SIMD operations are invoked, step two may be initiated by a single instruction in the instruction RAM of the tile 504.

[0145] FIG. 10 is a flow chart showing operations of a method 1000 performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. The method 1000 includes operations 1010, 1020, 1030, 1040, and 1050. By way of example and not limitation, the method 1000 is described as being performed by the HTF 142 of FIG. 1. In other example embodiments, the method 1000 may be performed by the PAU 208 of FIG. 2, the PAU 302 of FIG. 3, the application chiplet 610 of FIGS. 6A-6B, the HTP chiplet 718 of FIG. 7, the HTF chiplet 722 of FIG. 7, the tile 504 of FIG. 5, or any suitable combination thereof.

[0146] In operation 1010, the HTF 142 receives a command comprising a first complex number, a second complex number, and an accumulated value. Each complex number comprises a real value and an imaginary value. As shown in SIMD data 910 of FIG. 9, the single instruction may comprise multiple sets of input data for executing the method 1000. In such example embodiments, operations 1020-1050 may be performed simultaneously for each first complex number, second complex number, and corresponding accumulated value. In some example embodiments, the command is received via the NOC 118. Any one or more of the first complex number, the second complex number, and the accumulated value may be received from by a tile of the HTF 142 from another tile of the HTF 142 via a synchronous or asynchronous fabric.

[0147] The HTF 142, in operation 1020, modifies the first complex number by overwriting the first imaginary value with the first real value. An example of this modification is shown in the SIMD input data 905, the SIMD instruction 910, and the SIMD output data 915 of FIG. 9. [0148] In operation 1030, the HTF 142 multiplies the modified first complex number with the second complex number to generate a multiplication result.

For example, successive values in lane zero may be multiplied together to generate a real value and successive values in lane one may be multiplied together to generate an imaginary value. An example of this operation is shown in the output SIMD data 915, the input SIMD data 920, the SIMD instruction 925, and the output SIMD data 930 of FIG. 9. Taken together, the real value and the imaginary value are a complex multiplication result.

[0149] The accumulated value is modified by the HTF 142 by adding the multiplication result to the accumulated value (operation 1040). For example, the values generated in operation 1030 may be added to successive values on lanes zero and one, as shown by the output SIMD data 930, the input SIMD data 935, the SIMD instruction 940, and the output SIMD data 945 of FIG. 9.

[0150] In operation 1050, the HTF 142 provides, in response to the command, signaling representing the modified accumulated value. For example, after updating the values in the output SIMD data 945, a signal may be raised to indicate that the output data is ready. In response, the NOC 118 may transfer the output values to the processing element that send the command received in operation 1010. In some example embodiments, the providing of the modified accumulated value is via a network on chip (NOC) hub edge 714 to a hybrid threading processor 140. In other example embodiments, the providing of the modified accumulated value is via the hub edge 714 to the host processor 122, to another tile of the HTF via a synchronous or asynchronous fabric, or any suitable combination thereof.

[0151] Thus, the method 1000 ignores the input imaginary component of the first complex number, replacing it internally with a second copy of the real component of the first complex number. Then, a partial product of the two complex numbers is generated and added to the accumulated value. This is shown in equation form below.

[0152] FIG. 11 is a flow chart showing operations of a method 1100 performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. The method 1100 includes operations 1110, 1120, 1130, 1140, and 1150. By way of example and not limitation, the method 1100 is described as being performed by the HTF 142 of FIG. 1. In other example embodiments, the method 1100 may be performed by the PAU 208 of FIG. 2, the PAU 302 of FIG. 3, the application chiplet 610 of FIGS. 6A-6B, the HTP chiplet 718 of FIG. 7, the HTF chiplet 722 of FIG. 7, the tile 504 of FIG. 5, or any suitable combination thereof. Any one or more of the first complex number, the second complex number, and the accumulated value may be received from by a tile of the HTF 142 from another tile of the HTF 142 via a synchronous or asynchronous fabric.

[0153] In operation 1110, the HTF 142 receives a command comprising a first complex number, a second complex number, and an accumulated value. Each complex number comprises a real value and an imaginary value. As shown in FIG. 9, the single instruction may comprise multiple sets of input data for executing the method 1100. In such example embodiments, operations 1120- 1150 may be performed simultaneously for each first complex number, second complex number, and corresponding accumulated value. In some example embodiments, the command is received via the NOC 118.

[0154] The HTF 142, in operation 1120, modifies the first complex number by overwriting the first real value with the first imaginary value. An example of this modification is shown in the input SIMD data 950, the SIMD instruction 955, and the output SIMD data 960 of FIG. 9.

[0155] In operation 1130, the HTF 142 multiplies the modified first complex number with the second complex number to generate a multiplication result.

For example, successive values in the first lane may be multiplied together to generate a real value and successive values in the second lane may be multiplied together to generate an imaginary value. Taken together, the real value and the imaginary value are a complex multiplication result. An example of this multiplication is shown in the output SIMD data 960, the input SIMD data 965, the SIMD instruction 970, and the output SIMD data 975 of FIG. 9.

[0156] The accumulated value is modified by the HTF 142 by subtracting the real result value and adding the imaginary result value to the accumulated value (operation 1140). For example, the resulting product in lane zero may be subtracted from the real component of an accumulator value to generate an updated real component of the accumulator value and the resulting product in lane one may be added to the imaginary component of the accumulator value to generate an updated imaginary component of the accumulator value. An example of these operations is shown in the output SIMD data 975, the input SIMD data 980, the SIMD instruction 985, and the output SIMD data 990 of FIG. 9.

[0157] In operation 1150, the HTF 142 provides, in response to the command, signaling representing the modified accumulated value. For example, after generating the output SIMD data 990, a signal may be raised to indicate that the output data is ready. In response, the NOC 118 may transfer the output values to the processing element that send the command received in operation 1110. In some example embodiments, the providing of the modified accumulated value is via a network on chip (NOC) hub edge 714 to a hybrid threading processor 140. In other example embodiments, the providing of the modified accumulated value is via the hub edge 714 to the host processor 122, to another tile of the HTF via a synchronous or asynchronous fabric, or any suitable combination thereof.

[0158] Thus, the method 1100 ignores the input real component of the first complex number, replacing it internally with a second copy of the imaginary component of the first complex number. Then, a partial product of the two complex numbers is generated and added to the accumulated value.

[0159] After both the method 1000 and the method 1100 have been performed, the final accumulated value will be

[0160] Thus, the final accumulated value is the same as when the traditional complex multiply and accumulate operations are performed. However, the operations are performed in only two commands instead of eight. [0161] FIG. 12 is a flow chart showing operations of a method 1200 performed by a circuit in performing a complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. The method 1200 includes operations 1210, 1220, 1230, and 1240. By way of example and not limitation, the method 1200 is described as being performed by the HTF 142 of FIG. 1. In other example embodiments, the method 1200 may be performed by the HTP 140 of FIG. 1, the application chiplet 610 of FIGS. 6A-6B, the HTP chiplet 718 of FIG. 7, the HTP chiplet 720 of FIG. 7, the tile 504 of FIG. 5, or any suitable combination thereof.

[0162] In operation 1210, the HTF 142 invokes a first command with parameters comprising a first complex value, a second complex value, and an accumulate value. The first command may be stored in the instruction RAM of the tile 504 of FIG. 5. The parameters may be received as synchronous inputs from an adjacent tile (e.g., on the IN lines of FIG. 5), accessed from on-tile memory (e.g., MEM_0 or MEM_1 of FIG. 5), output from a previous operation on the tile (e.g., using the loopback connection after the ALB OP block in FIG. 5), or any suitable combination thereof. In response to the command, the tile 504 may perform multiple SIMD operations, such as the operations of Step 1 of FIG. 9). In that case, operations 1220-1240 also operate on all sets of SIMD data in parallel. The first command may be a command that invokes performance of the method 1000 or the method 1100 by the HTF 142 of FIG. 1. In some example embodiments, multiple data sets are processed by multiple HTFs 142 operating in parallel. For example, generating an image from SAR pulse reflection data may involve processing reflections for hundreds or thousands of pulses for each pixel in the image. These operations are highly parallelizable.

[0163] In response to the first command, the HTF 142 receives a partially updated accumulate value (operation 1220). For example, the partially updated accumulate values may be stored in tile memory (e.g., MEM_0 or MEM_1 of FIG. 5), provided as synchronous outputs (e.g., on the OUT lanes of FIG. 5), provided as asynchronous outputs (e.g., in the AF OUT QUEUE of FIG. 5), or any suitable combination thereof..

[0164] The HTF 142, in operation 1230, invokes a second command with parameters comprising the first complex value, the second complex value, and the partially updated accumulate value. For example, the method 1000 or the method 1100 may be invoked using the same first and second complex values as in operation 1210, but using the modified accumulate value received in operation 1220.

[0165] In operation 1240, the HTF 142 receives a fully updated accumulate value comprising the accumulate value added to the product of the first complex value with the second complex value (e.g., via signaling of the SIMD data in operation 1050 or operation 1150). Thus, by completion of both the method 1000 and 1100, invoked using two commands, the HTF 142 updates the accumulate value with the product of the first and second complex numbers. By comparison with implementations that perform each multiply and addition using a separate command, fewer commands are used, power consumption is reduced, and time is saved. [0166] FIG. 13 is a flow chart showing operations of a method 1300 performed by a circuit in performing complex multiply and accumulate operations within a process to control an autonomous vehicle, in accordance with some embodiments of the present disclosure. The method 1300 includes operations 1310, 1320, 1330, and 1340. By way of example and not limitation, the method 1300 is described as being performed by a control processor. The control processor may be the host processor 122 of FIG. 1, the HTP 140 of FIG. 1, the HTF 142 of FIG. 1, the HTF chiplet 722 of FIG. 7, the HTP chiplet 720 of FIG. 7, or any suitable combination thereof.

[0167] In operation 1310, the control processor initializes an accumulate value. For example, the accumulate value may be initialized to a result from a previous iteration of the method 1300, to zero, or to any other value.

[0168] For each pair of complex numbers in a list of complex number pairs, the control processor multiplies the pair of complex numbers together and adds the result to the accumulated value (operation 1320). For example, the method 1200 may be used on each pair of complex numbers to update the accumulated value.

[0169] In operation 1330, the control processor uses the final accumulate value as an input to a SAR backprojection algorithm that generates an image. For example, complex pulse reflection data may be gathered in response to SAR pulses emitted by a SAR antenna of an autonomous vehicle. By processing the complex pulse reflection data, a two-dimensional or three-dimensional image of an area or volume surrounding the autonomous vehicle may be generated.

[0170] The control processor, in operation 1340, provides the image to a trained machine learning model to control an autonomous vehicle. For example, a trained machine learning model may recognize obstacles or targets in the image and control the autonomous vehicle to seek or avoid one or more of the recognized objects. Controlling the autonomous vehicle may include adjusting pitch, roll, yaw, velocity, altitude, rudder, steering, acceleration, braking, power consumption level, sensor range, sensor sensitivity, or any suitable combination thereof.

[0171] By use of the method 1200 to perform operation 1320, processing cycles and power consumption are reduced, increasing the efficiency of controlling the autonomous vehicle. As a result, the autonomous vehicle enjoys increased range and increased battery life. Alternatively or additionally, a battery of the autonomous vehicle may be reduced in size, reducing the weight and cost of the autonomous vehicle.

[0172] FIG. 14 illustrates initial, final, and intermediate values of SIMD lanes 1400 when implementing a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. SIMD lanes 1400 are shown with initial first complex values 1410, initial second complex values 1430, and initial accumulate values 1450. Also shown are intermediate first complex values 1420, partial product values 1440, and final accumulate values 1460. In the example of FIG. 14, two sets of data are provided for simultaneous processing.

[0173] The initial first complex values 1410 comprise real and imaginary values for the first complex number of two SIMD parameter sets. A processing element (e.g., the tile 504 of FIG. 5) executes a DupReal (duplicate real) command that duplicates the real value for each of the first complex numbers, overwriting the imaginary values. The intermediate first complex values 1420 result.

[0174] The initial second complex values 1430 comprise real and imaginary values for the second complex number of the two SIMD parameter sets. The processing element executes a MulF32 (multiply 32-bit float) command that multiplies each value in the intermediate first complex values 1420 with the corresponding value in the initial second complex values 1430. The partial product values 1440 result. [0175] The initial accumulate values 1450 comprise real and imaginary values for the accumulate numbers of the two SIMD parameter sets. The processing element executes an AddF32 (add 32-bit float) command that adds each value in the partial product values 1440 with the corresponding value in the initial accumulate values 1450. The final accumulate values 1460 result. The DupReal, MulF32, and AddF32 commands may be implemented within the processing element. In various example embodiments, values of different sizes are used (e.g., 16-bit values, 48-bit values, 64-bit values, or 128-bit values).

[0176] FIG. 15 illustrates initial, final, and intermediate values of SIMD lanes 1500 when implementing a method performed by a circuit in performing a partial complex multiply and accumulate operation, in accordance with some embodiments of the present disclosure. SIMD lanes 1500 are shown with initial first complex values 1510, initial second complex values 1530, and initial accumulate values 1560. Also shown are intermediate first complex values 1520, intermediate second complex values 1540, partial product values 1450, and final accumulate values 1570. In the example of FIG. 15, two sets of data are provided for simultaneous processing. Notation used in FIG. 15 corresponds to the notation used in FIG. 14.

[0177] The initial first complex values 1510 comprise real and imaginary values for the first complex number of two SIMD parameter sets. A processing element (e.g., the tile 504 of FIG. 4) executes a Duplmag (duplicate imaginary) command that duplicates the imaginary value for each of the first complex numbers, overwriting the real values. The intermediate first complex values 1520 result.

[0178] The initial second complex values 1530 comprise real and imaginary values for the second complex number of the two SIMD parameter sets. The processing element executes a SwapReallmag (swap real and imaginary values) command that swaps the real and imaginary values of each second complex number. The intermediate second complex values 1550 result. [0179] The processing element executes a MulF32 (multiply 32-bit float) command that multiplies each value in the intermediate first complex values 1520 with the corresponding value in the intermediate second complex values 1540. The partial product values 1550 result.

[0180] The initial accumulate values 1560 comprise real and imaginary values for the accumulate numbers of the two SIMD parameter sets. The processing element executes an AddCF32 (add complex 32-bit float) command that subtracts each value in even lanes of the partial product values 1550 from the corresponding value in the partial accumulate values 1560 and adds each value in odd lanes of the partial product values 1550 with the corresponding value in the initial accumulate values 1560. The final accumulate values 1570 result.

To accomplish a subtraction on the even lanes and an addition on the odd lanes, circuitry of the even SIMD lanes differs from circuitry of the odd SIMD lanes, in some example embodiments.

[0181] The DupReal, SwapReallmag, MulF32, and AddCF32 commands may be implemented within the processing element. In various example embodiments, values of different sizes are used (e.g., 16-bit values, 48-bit values, 64-bit values, or 128-bit values).

[0182] Thus, if the final accumulate values 1460 are provided as the partial accumulate values 1560 when the same first complex values 1410, 1510 and second complex values 1430, 1530 are provided to both the SIMD command of FIG. 14 and the SIMD command of FIG. 15, the final accumulate values 1570 store the real and imaginary values of a fully-updated accumulation of the complex multiplication of the first and second complex values.

[0183] FIG. 16 illustrates a block diagram of an example machine 1600 with which, in which, or by which any one or more of the techniques (e.g., methodologies) discussed herein can be implemented. Examples, as described herein, can include, or can operate by, logic or a number of components, or mechanisms in the machine 1600. Circuitry (e.g., processing circuitry) is a collection of circuits implemented in tangible entities of the machine 1600 that include hardware (e.g., simple circuits, gates, logic, etc.)· Circuitry membership can be flexible over time. Circuitries include members that can, alone or in combination, perform specified operations when operating. In an example, hardware of the circuitry can be immutably designed to carry out a specific operation (e.g., hardwired). In an example, the hardware of the circuitry can include variably connected physical components (e.g., execution units, transistors, simple circuits, etc.) including a machine-readable medium physically modified (e.g., magnetically, electrically, moveable placement of invariant massed particles, etc.) to encode instructions of the specific operation. In connecting the physical components, the underlying electrical properties of a hardware constituent are changed, for example, from an insulator to a conductor or vice versa. The instructions enable embedded hardware (e.g., the execution units or a loading mechanism) to create members of the circuitry in hardware via the variable connections to carry out portions of the specific operation when in operation. Accordingly, in an example, the machine-readable medium elements are part of the circuitry or are communicatively coupled to the other components of the circuitry when the device is operating. In an example, any of the physical components can be used in more than one member of more than one circuitry. For example, under operation, execution units can be used in a first circuit of a first circuitry at one point in time and reused by a second circuit in the first circuitry, or by a third circuit in a second circuitry at a different time. Additional examples of these components with respect to the machine 1600.

[0184] In alternative embodiments, the machine 1600 can operate as a standalone device or can be connected (e.g., networked) to other machines. In a networked deployment, the machine 1600 can operate in the capacity of a server machine, a client machine, or both in server-client network environments. In an example, the machine 1600 can act as a peer machine in peer-to-peer (P2P) (or other distributed) network environment. The machine 1600 can be a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a mobile telephone, a web appliance, a network router, switch or bridge, or any machine capable of executing instructions (sequential or otherwise) that specify actions to be taken by that machine. Further, while only a single machine is illustrated, the term “machine” shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein, such as cloud computing, software as a service (SaaS), other computer cluster configurations.

[0185] The machine 1600 (e.g., computer system) can include a hardware processor 1602 (e.g., a central processing unit (CPU), a graphics processing unit (GPU), a hardware processor core, or any combination thereof), a main memory 1604, a static memory 1606 (e.g., memory or storage for firmware, microcode, a basic-input-output (BIOS), unified extensible firmware interface (UEFI), etc.), and mass storage device 1608 (e.g., hard drives, tape drives, flash storage, or other block devices) some or all of which can communicate with each other via an interlink 1630 (e.g., bus). The machine 1600 can further include a display device 1610, an alphanumeric input device 1612 (e.g., a keyboard), and a user interface (UI) navigation device 1614 (e.g., a mouse). In an example, the display device 1610, the input device 1612, and the UI navigation device 1614 can be a touch screen display. The machine 1600 can additionally include a signal generation device 1618 (e.g., a speaker), a network interface device 1620, and one or more sensor(s) 1616, such as a global positioning system (GPS) sensor, compass, accelerometer, or other sensor. The machine 1600 can include an output controller 1628, such as a serial (e.g., universal serial bus (USB), parallel, or other wired or wireless (e.g., infrared (IR), near field communication (NFC), etc.) connection to communicate or control one or more peripheral devices (e.g., a printer, card reader, etc.).

[0186] Registers of the hardware processor 1602, the main memory 1604, the static memory 1606, or the mass storage device 1608 can be, or include, a machine-readable media 1622 on which is stored one or more sets of data structures or instructions 1624 (e.g., software) embodying or used by any one or more of the techniques or functions described herein. The instructions 1624 can also reside, completely or at least partially, within any of registers of the hardware processor 1602, the main memory 1604, the static memory 1606, or the mass storage device 1608 during execution thereof by the machine 1600. In an example, one or any combination of the hardware processor 1602, the main memory 1604, the static memory 1606, or the mass storage device 1608 can constitute the machine-readable media 1622. While the machine-readable media 1622 is illustrated as a single medium, the term “machine-readable medium” can include a single medium or multiple media (e.g., a centralized or distributed database, or associated caches and servers) configured to store the one or more instructions 1624.

[0187] The term “machine readable medium” can include any medium that is capable of storing, encoding, or carrying instructions for execution by the machine 1600 and that cause the machine 1600 to perform any one or more of the techniques of the present disclosure, or that is capable of storing, encoding, or carrying data structures used by or associated with such instructions. Non limiting machine-readable medium examples can include solid-state memories, optical media, magnetic media, and signals (e.g., radio frequency signals, other photon-based signals, sound signals, etc.). In an example, a non-transitory machine-readable medium comprises a machine-readable medium with a plurality of particles having invariant (e.g., rest) mass, and thus are compositions of matter. Accordingly, non-transitory machine-readable media are machine readable media that do not include transitory propagating signals. Specific examples of non-transitory machine readable media can include: non volatile memory, such as semiconductor memory devices (e.g., electrically programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM)) and flash memory devices; magnetic disks, such as internal hard disks and removable disks; magneto optical disks; and CD-ROM and DVD-ROM disks. [0188] In an example, information stored or otherwise provided on the machine-readable media 1622 can be representative of the instructions 1624, such as instructions 1624 themselves or a format from which the instructions 1624 can be derived. This format from which the instructions 1624 can be derived can include source code, encoded instructions (e.g., in compressed or encrypted form), packaged instructions (e.g., split into multiple packages), or the like. The information representative of the instructions 1624 in the machine- readable media 1622 can be processed by processing circuitry into the instructions to implement any of the operations discussed herein. For example, deriving the instructions 1624 from the information (e.g., processing by the processing circuitry) can include: compiling (e.g., from source code, object code, etc.), interpreting, loading, organizing (e.g., dynamically or statically linking), encoding, decoding, encrypting, unencrypting, packaging, unpackaging, or otherwise manipulating the information into the instructions 1624.

[0189] In an example, the derivation of the instructions 1624 can include assembly, compilation, or interpretation of the information (e.g., by the processing circuitry) to create the instructions 1624 from some intermediate or preprocessed format provided by the machine-readable media 1622. The information, when provided in multiple parts, can be combined, unpacked, and modified to create the instructions 1624. For example, the information can be in multiple compressed source code packages (or object code, or binary executable code, etc.) on one or several remote servers. The source code packages can be encrypted when in transit over a network and decrypted, uncompressed, assembled (e.g., linked) if necessary, compiled or interpreted (e.g., into a library, stand-alone executable etc.) at a local machine, and executed by the local machine.

[0190] The instructions 1624 can be further transmitted or received over a communications network 1626 using a transmission medium via the network interface device 1620 utilizing any one of a number of transfer protocols (e.g., frame relay, internet protocol, transmission control protocol (TCP), user datagram protocol (UDP), hypertext transfer protocol (HTTP), etc.)· Example communication networks can include a local area network (LAN), a wide area network (WAN), a packet data network (e.g., the Internet), mobile telephone networks (e.g., cellular networks), plain old telephone (POTS) networks, and wireless data networks (e.g., Institute of Electrical and Electronics Engineers (IEEE) 802.11 family of standards known as Wi-Fi®, IEEE 802.16 family of standards known as WiMax®), IEEE 802.15.4 family of standards, peer-to-peer (P2P) networks, among others. In an example, the network interface device 1620 can include one or more physical jacks (e.g., Ethernet, coaxial, or phone jacks) or one or more antennas to connect to the network 1626. In an example, the network interface device 1620 can include a plurality of antennas to wirelessly communicate using at least one of single-input multiple-output (SIMO), multiple-input multiple-output (MIMO), or multiple-input single output (MISO) techniques. The term “transmission medium” shall be taken to include any intangible medium that is capable of storing, encoding or carrying instructions for execution by the machine 1600, and includes digital or analog communications signals or other intangible medium to facilitate communication of such software. A transmission medium is a machine readable medium.

[0191] To better illustrate the methods and apparatuses described herein, a non-limiting set of Example embodiments are set forth below as numerically identified Examples.

[0192] Example 1 is a system comprising: a memory; and one or more tiles of a hybrid threading fabric coupled to the memory and configured to perform operations comprising: receiving a command comprising a first complex number, a second complex number, and an accumulated value, the first complex number comprising a first real value and a first imaginary value, the second complex number comprising a second real value and a second imaginary value; modifying the first complex number by overwriting the first imaginary value with the first real value; multiplying the modified first complex number with the second complex number to generate a multiplication result; modifying the accumulated value by adding the multiplication result to the accumulated value; and in response to the command, providing signaling representing the modified accumulated value to another tile of the hybrid threading fabric.

[0193] In Example 2, the subject matter of Example 1 includes, wherein the operations further comprise: receiving a second command comprising a third complex number, a fourth complex number, and a second accumulated value, the third complex number comprising a third real value and a third imaginary value, the fourth complex number comprising a fourth real value and a fourth imaginary value, the third complex number being equal to the first complex number, the fourth complex number being equal to the second complex number; modifying the third complex number by overwriting the third real value with the third imaginary value; multiplying the modified third complex number with the fourth complex number to generate a second multiplication result comprising a real result value and an imaginary result value; modifying the second accumulated value by subtracting the real result value and adding the imaginary result value; and in response to the second command, providing the modified second accumulated value.

[0194] In Example 3, the subject matter of Examples 1-2 includes, wherein: the command is a single-input multiple-data (SIMD) command; the first real value and the second real value are received on a first SIMD lane; the first imaginary value and the second imaginary value are received on a second SIMD lane; and circuitry of the second SIMD lane differs from circuitry of the first SIMD lane to cause the modification of the second accumulated value by subtracting the real result value and adding the imaginary result value.

[0195] In Example 4, the subject matter of Examples 1-3 includes, a control processor configured to perform operations comprising: causing an image to be generated from synthetic aperture radar (SAR) pulse data by performing complex multiply and accumulate operations including the command. [0196] In Example 5, the subject matter of Example 4 includes, wherein the operations of the control processor further comprise: providing the image to a trained machine learning model; and using a result from the trained machine learning model to generate inputs to a circuit to control a vehicle.

[0197] In Example 6, the subject matter of Examples 4-5 includes, one or more second tiles of the hybrid threading fabric configured to perform complex multiply operations in parallel with the one or more tiles.

[0198] In Example 7, the subject matter of Examples 1-6 includes, wherein the receiving of the command is via a connection to a tile of the hybrid threading fabric.

[0199] Example 8 is a non-transitory machine-readable medium that stores instructions that, when executed by one or more tiles of a hybrid threading fabric, cause the hybrid threading fabric to perform operations comprising: receiving a command comprising a first complex number, a second complex number, and an accumulated value, the first complex number comprising a first real value and a first imaginary value, the second complex number comprising a second real value and a second imaginary value; modifying the first complex number by overwriting the first imaginary value with the first real value; multiplying the modified first complex number with the second complex number to generate a multiplication result; modifying the accumulated value by adding the multiplication result to the accumulated value; and in response to the command, providing signals representing the modified accumulated value to another tile of the hybrid threading fabric.

[0200] In Example 9, the subject matter of Example 8 includes, wherein the operations further comprise: receiving a second command comprising a third complex number, a fourth complex number, and a second accumulated value, the third complex number comprising a third real value and a third imaginary value, the fourth complex number comprising a fourth real value and a fourth imaginary value, the third complex number being equal to the first complex number, the fourth complex number being equal to the second complex number; modifying the third complex number by overwriting the third real value with the third imaginary value; multiplying the modified third complex number with the fourth complex number to generate a second multiplication result comprising a real result value and an imaginary result value; modifying the second accumulated value by subtracting the real result value and adding the imaginary result value; and in response to the second command, providing the modified second accumulated value.

[0201] In Example 10, the subject matter of Examples 8-9 includes, wherein: the command is a single-input multiple-data (SIMD) command; the first real value and the second real value are received on a first SIMD lane; the first imaginary value and the second imaginary value are received on a second SIMD lane; and circuitry of the second SIMD lane differs from circuitry of the first SIMD lane to cause the modification of the second accumulated value by subtracting the real result value and adding the imaginary result value.

[0202] In Example 11, the subject matter of Examples 8-10 includes, wherein the operations further comprise: causing an image to be generated from synthetic aperture radar (SAR) pulse data by performing complex multiply and accumulate operations including the command.

[0203] In Example 12, the subject matter of Example 11 includes, wherein the operations further comprise: providing the image to a trained machine learning model; and using a result from the trained machine learning model to generate inputs to a circuit to control a vehicle.

[0204] In Example 13, the subject matter of Examples 8-12 includes, wherein the receiving of the command is via a connection to another tile of the hybrid threading fabric.

[0205] Example 14 is a method comprising: receiving, by a hybrid threading fabric, a command comprising a first complex number, a second complex number, and an accumulated value, the first complex number comprising a first real value and a first imaginary value, the second complex number comprising a second real value and a second imaginary value; modifying, by the hybrid threading fabric, the first complex number by overwriting the first imaginary value with the first real value; multiplying, by the hybrid threading fabric, the modified first complex number with the second complex number to generate a multiplication result; modifying, by the hybrid threading fabric, the accumulated value by adding the multiplication result to the accumulated value; and in response to the command, providing signals representing the modified accumulated value to a tile of the hybrid threading fabric.

[0206] In Example 15, the subject matter of Example 14 includes, receiving a second command comprising a third complex number, a fourth complex number, and a second accumulated value, the third complex number comprising a third real value and a third imaginary value, the fourth complex number comprising a fourth real value and a fourth imaginary value, the third complex number being equal to the first complex number, the fourth complex number being equal to the second complex number; modifying the third complex number by overwriting the third real value with the third imaginary value; multiplying the modified third complex number with the fourth complex number to generate a second multiplication result comprising a real result value and an imaginary result value; modifying the second accumulated value by subtracting the real result value and adding the imaginary result value; and in response to the second command, providing the modified second accumulated value.

[0207] In Example 16, the subject matter of Examples 14-15 includes, wherein: the command is a single-input multiple-data (SIMD) command; the first real value and the second real value are received on a first SIMD lane; the first imaginary value and the second imaginary value are received on a second SIMD lane; and circuitry of the second SIMD lane differs from circuitry of the first SIMD lane to cause the modification of the second accumulated value by subtracting the real result value and adding the imaginary result value. [0208] In Example 17, the subject matter of Examples 14-16 includes, causing, by a control processor, an image to be generated from synthetic aperture radar (SAR) pulse data by performing complex multiply and accumulate operations including the command.

[0209] In Example 18, the subject matter of Example 17 includes, wherein the operations of the control processor further comprise: providing the image to a trained machine learning model; and using a result from the trained machine learning model to generate inputs to a circuit to control a vehicle.

[0210] In Example 19, the subject matter of Example 18 includes, a second hybrid threading fabric configured to perform complex multiply operations in parallel with the hybrid threading fabric.

[0211] In Example 20, the subject matter of Examples 14-19 includes, wherein the receiving of the command is via a network on chip (NOC).

[0212] Example 21 is at least one machine-readable medium including instructions that, when executed by processing circuitry, cause the processing circuitry to perform operations to implement any of Examples 1-20.

[0213] Example 22 is an apparatus comprising means to implement any of Examples 1-20.

[0214] Example 23 is a system to implement any of Examples 1-20.

[0215] Example 24 is a method to implement any of Examples 1-20.

[0216] The above detailed description includes references to the accompanying drawings, which form a part of the detailed description. The drawings show, by way of illustration, specific embodiments in which the invention can be practiced. These embodiments are also referred to herein as “examples.” Such examples can include elements in addition to those shown or described. However, the present inventors also contemplate examples in which only those elements shown or described are provided. Moreover, the present inventors also contemplate examples using any combination or permutation of those elements shown or described (or one or more aspects thereof), either with respect to a particular example (or one or more aspects thereof), or with respect to other examples (or one or more aspects thereof) shown or described herein.

[0217] In this document, the terms “a” or “an” are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of “at least one” or “one or more.” In this document, the term “or” is used to refer to a nonexclusive or, such that “A or B” can include “A but not B,” “B but not A,” and “A and B,” unless otherwise indicated. In the appended claims, the terms “including” and “in which” are used as the plain- English equivalents of the respective terms “comprising” and “wherein.” Also, in the following claims, the terms “including” and “comprising” are open- ended, that is, a system, device, article, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. Moreover, in the following claims, the terms “first,” “second,” and “third,” and the like are used merely as labels, and are not intended to impose numerical requirements on their objects.

[0218] The above description is intended to be illustrative, and not restrictive. For example, the above-described examples (or one or more aspects thereof) can be used in combination with each other. Other embodiments can be used, such as by one of ordinary skill in the art upon reviewing the above description. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. Also, in the above Detailed Description, various features can be grouped together to streamline the disclosure. This should not be interpreted as intending that an unclaimed disclosed feature is essential to any claim. Rather, inventive subject matter can lie in less than all features of a particular disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment, and it is contemplated that such embodiments can be combined with each other in various combinations or permutations. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.