Patent Application
20200342921
The present invention relates to in-memory computing and, more particularly, to a memory cell structure and a memory array configured for in-memory computing.
Current state-of-the-art image and voice processing techniques employ convolutional neural networks (CNNs) for recognition and classification. A CNN is a deep learning algorithm and approximately 90% of the computations performed in the algorithm are multiply and accumulate (MAC) operations. In a CNN for image processing, the various MAC operations are used to compute the products of inputs (also referred to as activations), which are identified intensity values of the pixels in a receptive field, and weights in a convolution filter matrix (also referred to as a kernel) of the same size as the receptive field, and to further compute the sum of the products. Historically, the input and weight values used in CNNs were real numbers and software solutions were employed. Hardware-implemented CNNs were subsequently developed to increase processing speed. Recently, binary neural networks (BNNs) have been developed. A BNN is essentially a CNN where binary input and/or weight values are used. In one exemplary hardware-implemented BNN (referred to as an XNOR-NET BNN), real input and weight values are converted to binary input and weight values and the MAC computations are accomplished through hardware architectures configured to perform XNOR-bitcount-compare functions (also referred to as XNOR-popcount-compare functions). Hardware-implemented XNOR-NET BNNs offer large memory and computation savings without sacrificing much in terms of accuracy. It would, however, be advantageous to provide a modified configuration for a hardware-implemented XNOR-NET BNN designed to further improve performance, scalability, and/or manufacturability.
In view of the foregoing, disclosed herein are embodiments of a three-port static random access memory (3P-SRAM) cell configured to perform XNOR operations. Specifically, the disclosed 3P-SRAM cell includes a write port and two read ports (i.e., a first read port and a second read port). In this 3P-SRAM cell, the read ports share a common read bitline and read operations are enabled using either a first read wordline and the common read bitline or a second read wordline and the common read bitline. Activation of the first and second read wordlines is selectively controlled such that only one of the two read wordlines is activated (i.e., receives a read pulse) at a time. As a result, a read operation performed through either read port effectively accomplishes an XNOR operation. Also disclosed herein are embodiments of a memory array, which incorporates such 3P-SRAM cells and which is specifically configured to perform XNOR-bitcount-compare functions. Since, as discussed above, XNOR-bitcount-compare functions are used in XNOR-NET type binary neural networks (BNNs), the disclosed memory array can be employed for implementing an XNOR-NET BNN designed for improved performance, scalability, and manufacturability. Also disclosed herein are embodiments of an in-memory computing method that employs the above-described memory cells and memory array.
More particularly, disclosed herein are embodiments of 3P-SRAM cell having a write port and a pair of read ports (i.e., a first read port and a second read port). The 3P-SRAM cell can include a true storage node that stores a true bit and a complement storage node that stores a complement bit (i.e., that stores the complement of the true bit). For the first read port, the 3P-SRAM cell can have a first read pass-gate transistor and a first read pull-down transistor connected in series between a common read bitline and a first voltage rail (e.g., a ground or negative voltage rail). The gates of the first read pass-gate transistor and the first read pull-down transistor can be connected to a first read wordline and to the true storage node, respectively. For the second read port, the 3P-SRAM cell can have a second read pass-gate transistor and a second read pull-down transistor connected in series between the common read bitline and the first voltage rail. The gates of the second read pass-gate transistor and the second read pull-down transistor can be connected to a second read wordline and to the complement storage node, respectively.
With the above-described configuration, a read operation initiated through either the first read port or the second read port can be used to effectively accomplish an XNOR operation. Specifically, during a read operation, the common read bitline and a capacitor connected thereto can be pre-charged and a read pulse can be applied selectively and exclusively to only one of the two read wordlines. That is, a read pulse can be applied to either the first read wordline for a read operation through the first read port or to the second read wordline for a read operation through the second read port, but not both. It should be understood that a read pulse refers to a pulse of a sufficiently high positive voltage to represent a high logic state (i.e., a logic value of “1”) on the read wordline during the duration of the pulse. When a read pulse is applied to only one of the two read wordlines, the other of the two read wordlines has a low logic state (i.e., a logic value of “0”). During the read pulse, a first digital input for the XNOR operation will be the logic state of the first read wordline, a second digital input for the XNOR operation will be the logic state of the true bit and the output of the XNOR operation is determinable based on whether the voltage level on the common read bitline discharges through the 3P-SRAM cell or not.
Also disclosed herein are embodiments of a memory array that incorporates such 3P-SRAM cells. Specifically, the embodiments of the memory array can include 3P-SRAM cells arranged in columns and row. For each column, the memory array can include a common read bitline connected to all of the 3P-SRAM cells in the column, a voltage comparator connected to the common read bitline, and a capacitor also connected to the common read bitline. For scalability, each capacitor can be a back end of the line (BEOL) capacitor formed within one or more of the BEOL metal levels and positioned above the memory cells such that incorporation of the capacitors does not increase the chip surface area consumed by the memory array. Additionally, for each row, the memory array can include a pair of read wordlines (i.e., a first read wordline and a second read wordline) connected to all of the memory cells in the row.
As discussed above, each 3P-SRAM cell can be configured so as to have a write port and a pair of read ports (i.e., a first read port and a second read port). Each 3P-SRAM cell can include a true storage node that stores a true bit and a complement storage node that stores a complement bit (i.e., the complement of the true bit). For the first read port, each 3P-SRAM cell can include a first read pass-gate transistor and a first read pull-down transistor connected in series between the common read bitline for the specific column and a first voltage rail (e.g., a ground or negative voltage rail). The gates of the first read pass-gate transistor and the first read pull-down transistor can be connected to a first read wordline for a specific row and to the true storage node, respectively. For the second read port, each 3P-SRAM cell can include a second read pass-gate transistor and a second read pull-down transistor connected in series between the common read bitline for the specific column and the first voltage rail. The gates of the second read pass-gate transistor and the second read pull-down transistor can be connected to a second read wordline for the specific row and to the complement storage node, respectively.
With the above-described configuration, concurrent read operations of the 3P-SRAM cells in any selected column can be used to accomplish an XNOR-bitcount-compare function.
Specifically, the memory array can include bitline drivers and wordline drivers. During concurrent read operations and, thereby during concurrent XNOR operations in all of the 3P-SRAM cells in a selected column, a bitline driver can pre-charge the common read bitline for the selected column and thereby the capacitor connected thereto and the wordline drivers can selectively and exclusively apply read pulses to only one of the first read wordline and the second read wordline in each of the rows. As mentioned above, a read pulse refers to a pulse of a on the read wordline positive voltage to represent a high logic state (i.e., a logic value of “1”) during the duration of the pulse. When a read pulse is applied to only one of the two read wordlines in each of the rows, the other of the two read wordlines will have a low logic state (i.e., a logic value of “0”). At the end of the concurrent XNOR operations and, particularly, following concurrent application of the read pulse to the selected read wordline in each row (i.e., when the selected read wordline in each row is returned to a low voltage state), the voltage comparator of the selected column can perform a compare operation to compare an actual voltage level on the common read bitline for the selected column to a reference voltage level and can output a digital output indicating whether the actual voltage level is below the reference voltage level or not. It should be noted that the actual voltage level (VCRBL) on the common read bitline at the end of the concurrent XNOR operations will be indicative of how many of the 3P-SRAM cells in the selected column enabled discharging of the voltage level on the common read bitline. Thus, the actual voltage will be indicative of a bitcount of the results of the concurrent XNOR operations. Furthermore, the reference voltage level (Vref) can be predetermined so that it corresponds to a bitcount threshold (e.g., so that it is approximately equal to the expected voltage level on the common read bitline if one-half of the memory cells enable discharging of the common read bitline). Thus, the digital output of the voltage comparator for the selected column will indicate whether or not the actual bitcount is below the bitcount threshold. In other words, the digital output from the voltage comparator of a selected column following the concurrent XNOR operations performed therein is effectively a final result of an XNOR-bitcount-compare function.
As discussed further in the detailed description section below, multiple XNOR-bitcount-compare functions may be performed in parallel and, particularly, during the same clock cycle, in the different columns, respectively, when the first inputs, which are to be applied to the first read wordlines of the rows are the same for all the XNOR-bitcount-compare functions and when only the second inputs, which are stored in the 3P-SRAM cells vary from column to column. It should be noted that, since XNOR-bitcount-compare functions are used in XNOR-NET type binary neural networks (BNNs), the disclosed memory array can be employed for implementing an XNOR-NET BNN designed for improved performance, scalability, and manufacturability.
Also disclosed herein are embodiments of an in-memory computing method that employs 3P-SRAM cells in a memory array. Specifically, an embodiment of an in-memory computing method can include providing a memory array, as described above, with 3P-SRAM cells, also as described above. The method can include pre-charging the common read bitline and thereby the capacitor of a selected column and selectively and exclusively applying a read pulse to only one of the first read wordline and the second read wordline in each of the rows (i.e., to either the first read wordline or the second read wordline, but not both so that concurrent XNOR operations are performed by all memory cells in the selected column. It should be understood that a read pulse refers to a pulse of a sufficiently high positive voltage to represent a high logic state (i.e., a logic value of “1”) on the read wordline during the duration of the pulse. When a read pulse is applied to only one of the two read wordlines, the other of the two read wordlines will have a low logic state (i.e., a logic value of “0”).
The method can further include performing a comparison of an actual voltage level (VCRBL) on the common read bitline of the column at the end of the concurrent XNOR operations to a reference voltage level (Vref) and outputting a digital output based on the results of the comparison. As discussed above, the actual voltage level (VCRBL) that is on the common read bitline of the selected column at the end of the concurrent XNOR operations and, particularly, that is on the common read bitline of the selected column following concurrent application of the read pulse to the selected read wordline in each row (i.e., when the selected read wordline in each row is returned to a low voltage state) will be indicative of how many of the 3P-SRAM cells in the selected column enabled discharging of the voltage level on the common read bitline. Thus, the actual voltage level (VCRBL) will be indicative of a bitcount of the results of the concurrent XNOR operations. Furthermore, the reference voltage level (Vref) can be predetermined so that it corresponds to a bitcount threshold (e.g., so that it is approximately equal to the expected voltage level on the common read bitline if one-half of the memory cells enable discharging of the common read bitline). Thus, the digital output will indicate whether or not the actual bitcount is below the bitcount threshold. In other words, the digital output following the concurrent XNOR operations in a selected column is effectively a final result of an XNOR-bitcount-compare function.
As discussed further in the detailed description section below, multiple XNOR-bitcount-compare functions may be performed in parallel and, particularly, during the same clock cycle, in the different columns, respectively, when the first inputs, which are to be applied to the first read wordlines of the rows are the same for all the XNOR-bitcount-compare functions and when only the second inputs, which are stored in the 3P-SRAM cells at the true storage node vary from column to column. Furthermore, since XNOR-bitcount-compare functions are used in XNOR-NET type binary neural networks (BNNs), the disclosed in-memory computing method can be employed for implementing an XNOR-NET BNN designed for improved performance, scalability, and manufacturability.
The present invention will be better understood from the following detailed description with reference to the drawings, which are not necessarily drawn to scale and in which:
As mentioned above, a binary neural network (BNN) is essentially a convolutional neural network (CNN) that uses binary input and/or weight values to accomplish the multiply and accumulate (MAC) operations. In one exemplary hardware-implemented BNN (referred to as an XNOR-NET BNN), real input and weight values are converted to binary input and weight values and the MAC computations are accomplished through hardware architectures configured to perform XNOR-bitcount-compare functions (also referred to as XNOR-popcount-compare functions). Hardware-implemented XNOR-NET BNNs offer large memory and computation savings without sacrificing much in terms of accuracy. It would, however, be advantageous to provide a modified configuration for a hardware-implemented XNOR-NET BNN designed to further improve performance, scalability, and/or manufacturability.
In view of the foregoing, disclosed herein are embodiments of a three-port static random access memory (3P-SRAM) cell configured to perform XNOR operations. Specifically, the disclosed 3P-SRAM cell includes a write port and two read ports (i.e., a first read port and a second read port). In this 3P-SRAM cell, the read ports share a common read bitline and read operations are enabled using either a first read wordline and the common read bitline or a second read wordline and the common read bitline. Activation of the first and second read wordlines is selectively controlled such that only one of the two read wordlines is activated (i.e., receives a read pulse) at a time. As a result, a read operation performed through either read port effectively accomplishes an XNOR operation. Also disclosed herein are embodiments of a memory array, which incorporates such 3P-SRAM cells and which is specifically configured to perform XNOR-bitcount-compare functions. Since, as discussed above, XNOR-bitcount-compare functions are used in XNOR-NET type binary neural networks (BNNs), the disclosed memory array can be employed for implementing an XNOR-NET BNN designed for improved performance, scalability, and manufacturability. Also disclosed herein are embodiments of an in-memory computing method that employs the above-described memory cells and memory array.
More particularly, referring to
Specifically, the 3P-SRAM cell 101 can include a pair of cross-coupled inverters connected between a first voltage rail 198 (e.g., a ground rail or negative voltage rail, Vss) and a second voltage rail 199 (e.g., a positive voltage rail, Vcs or Vdd). The cross-coupled inverters can include a first inverter and a second inverter. The first inverter can include a pull-down transistor 113.1 and a pull-up transistor 112.1 electrically connected in series between the first voltage rail 198 and the second voltage rail 199. The first inverter can further include a true storage node 115.1 (NT) at the junction between the drain of the pull-down transistor 113.1 and the drain of the pull-up transistor 112.1. The second inverter can include a pull-down transistor 113.2 and a pull-up transistor 112.2 electrically connected in series between the first voltage rail 198 and the second voltage rail 199. The second inverter can further include a complement storage node 115.2 (NC) at the junction between the drain of the pull-down transistor 113.2 and the drain of the pull-up transistor 112.2. The gates of the pull-down transistor 113.1 and the pull-up transistor 112.1 of the first inverter can be electrically connected to the complement storage node 115.2 and the gates of the pull-down transistor 113.2 and the pull-up transistor 112.2 of the second inverter can be electrically connected to the true storage node 115.1 such that the first inverter and the second inverter are cross-coupled.
The 3P-SRAM cell 101 can further include a first read pass-gate transistor 134 and a first read pull-down transistor 133 for the first read port, a second read pass-gate transistor 144 and a second read pull-down transistor 143 for the second read port and a pair of additional pass-gate transistors (i.e., a first additional pass-gate transistor 114.1 and a second additional pass-gate transistor 114.2) for the write port. Thus, the 3P-SRAM cell 101 is a ten-transistor (10T) SRAM cell. It should be noted that the write port could alternatively be a read/write port depending upon the peripheral circuitry of a memory array that incorporates the 3P-SRAM cell.
In any case, the first read pass-gate transistor 134 and the first read pull-down transistor 133 can be electrically connected in series between a common read bitline 152 (CRBL) (i.e., a read bitline that is shared by both the first read port and the second read port) and the first voltage rail 198. The gate of the first read pass-gate transistor 134 can be electrically connected to a first read wordline 131 (RWL1) for the first read port and the gate of the first read pull-down transistor 133 can be electrically connected to the true storage node 115.1. The second read pass-gate transistor 144 and the second read pull-down transistor 143 can also be electrically connected in series between the common read bitline 152 and the first voltage rail 198. The gate of the second read pass-gate transistor 144 can be electrically connected to a second read wordline 141 (RWL2) for the second read port and the gate of the second read pull-down transistor 143 can be electrically connected to the complement storage node 115.2.
The first additional pass-gate transistor 114.1 can be electrically connected between the true storage node 115.1 and a true bitline 122.1 (BLT) of a pair of complementary bitlines for the write port. That is, the source of the first additional pass-gate transistor 114.1 can be electrically connected to the true storage node 115.1 and the drain of the first additional pass-gate transistor 114.1 can be electrically connected to the true bitline 122.1. The second additional pass-gate transistor 114.2 can be electrically connected between the complement storage node 115.2 and a complement bitline 122.2 (BLC) of the pair of complementary bitlines for the write port. That is, the source of the second additional pass-gate transistor 114.2 can be electrically connected to the complement storage node 115.2 and the drain of the second additional pass-gate transistor 114.2 can be electrically connected to the complement bitline 122.2. The gates of the first additional pass-gate transistor 114.1 and the second additional pass-gate transistor 114.2 can both be electrically connected to the same write wordline 121 (WWL) for the write port.
Those skilled in the art will recognize that the various pass-gate and pull-down transistors of the 3P-SRAM cell 101 can be n-type field effect transistors (NFETs). Additionally, the various pull-up transistors of the 3P-SRAM cell 101 can p-type field effect transistors (PFETs).
The 3P-SRAM cell 101 can have three different modes of operation: standby, write through the write port or read through a selected one of the two read ports.
In the standby mode, the 3P-SRAM cell 101 is idle.
In the write mode, a true bit is written into the true storage node 115.1 and, as a result, a complement bit with an opposite logic value than the true bit is written into the complement storage node 115.2. That is, if a true bit with a binary data value of “1” (also referred to herein as a high data value, a high logic state, a logic value of “1”, a logic “1”, etc.) is written to the true storage node 115.1, then a complement bit with a binary data value of “0” (also referred to herein as a low data value, a low logic state, a logic value of “0”, a logic “0”, etc.) will be concurrently written to the complement storage node 115.2 and vice versa. In order to write a binary data value of “1” to the true storage node 115.1 and, thereby a binary data value of “0” to the complement storage node 115.2, a high voltage level can be applied to the true bitline 122.1 (e.g., by a bitline driver) and a low voltage level can be applied to the complement bitline 122.2 (e.g., the complement bitline 122.2 can be discharged to ground). The write wordline 121 can then be activated, thereby turning on the first additional pass-gate transistor 114.1 and the second additional pass-gate transistor 114.2 and storing the binary data value of “1” in the true storage node 115.1 and the binary data value of “0” in the complement storage node 115.2. Contrarily, in order to write a binary data value of “0” into the true storage node 115.1 and a binary data value of “1” into the complement storage node 115.2, the low voltage level can be applied to the true bitline 122.1 (e.g., the true bitline 122.1 can be discharged to ground) and the high voltage level can be applied to the complement bitline 122.2 (e.g., by a bitline driver). Then, the write wordline 121 can be activated (e.g., by a wordline driver), thereby turning on both the first additional pass-gate transistor 114.1 and the second additional pass-gate transistor 114.2 and storing the binary data value of “0” in the true storage node 115.1 and the binary data value of “1” in the complement storage node 115.2. In the above-described write operations, the write wordline 121 is activated when a write pulse is applied to the write wordline 121 and, particularly, when the voltage level of a write wordline activation signal on the write wordline 121 is switched from a low voltage level, which represents a low logic state (i.e., a logic “0”), to a higher positive voltage level, which is sufficiently high to represent a high logic state (i.e., a logic “1”) for a period of time (i.e., the pulse width) so that any pass-gate transistor having a gate electrically connected to that write wordline 121 (WWL) will be turned on during that period of time.
In the read mode, a read operation initiated through one read port or the other (but not both) can be used to accomplish an in-memory XNOR operation (also referred to herein as an XNOR function or an exclusive NOR operation) because the 3P-SRAM cell 101 has two different read ports that can be accessed through two different read wordlines 131 and 141 but that share a common read bitline 152 and because of the true bit stored at the true storage node 115.1 and the complement bit stored at the complement storage node 115.2.
Specifically,
For the 3P-SRAM cell 101, essentially the same truth table will hold true if the logic states of the first read wordline 141 and the true bit stored at the true storage node 115.1 are considered the first digital input A and the second digital input B, respectively, following activation of either the first read wordline 131 for a read operation initiated through the first read port or the second read wordline 141 for a read operation initiated through the second read port (but not both).
For example, referring to
When a read pulse is applied through a first read wordline activation signal (RWL_AS1) to the first read wordline 131 in order to initiate a read operation through the first read port, no read pulse will be applied through a second read wordline activation signal (RWL_AS2) to the second read wordline 141. Thus, the logic state of the first read wordline 131 will be a logic “1” and the logic state of the second read wordline 141 will be a logic “0”. Alternatively, when a read pulse is applied through RWL_AS2 to the second read wordline 141 in order to initiate a read operation through the second port, no read pulse will be applied through RWL_AS1 to the first read wordline 131. Thus, the logic state of the first read wordline 131 will be a logic “0” and the logic state of the second read wordline 141 will be a logic “1”. The result of a read operation through either the first read port or the second read port will be either: (a) the voltage level (VCRBL) on the common read bitline 152 is discharged through the 3P-SRAM cell 101 (i.e., VCRBL drops), as indicated by the down arrow; or (b) the voltage level (VCRBL) on the common read bitline 152 is not discharged through the 3P-SRAM cell 101, as indicated by the dash.
It should be noted that the pulse width of the read pulse (i.e., the period of time during which the higher positive voltage level is applied to a read wordline) as well as the pulse amplitude (i.e., the actual voltage level) can be predetermined and finely tuned so that, if/when the voltage level (VCRBL) on the common read bitline 152 is discharged through the 3P-SRAM cell 101 (i.e., VCRBL drops), it can be registered (i.e., sensed by the particular sensing device employed). See also the detailed discussion below with regard to the memory array embodiments, which are configured to allow concurrent read operations (i.e., concurrent XNOR operations) of all 3P-SRAM cells in the same column to be performed and wherein a capacitor, a tunable pulse width and a tunable pulse amplitude are employed to discriminate when the voltage level (VCRBL) on the common read bitline 152 is discharged through some number (e.g., half) of the 3P-SRAM cells in the column.
During a read operation through the first read port, the first read wordline 131 has the higher positive voltage level (i.e., when A is a logic “1”) so that the first read pass-gate transistor 134 is on and the second read wordline 141 has a low voltage level (i.e., a logic state of “0”) so that the second read pass-gate transistor 144 is off. When the true bit stored on the true storage node 115.1 is a logic “0” (i.e., when B is a logic “0”) and, thus, the complement bit stored on the complement storage node 115.2 is a logic “1”, the first read pull-down transistor 133 will be off and the second read pull-down transistor 143 will be on. In this case, even though the first read pass-gate transistor 134 is on, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the first side of the 3P-SRAM cell 101 because the first read pull-down transistor 133 is off. Furthermore, even though the second read pull-down transistor 143 is on, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the second side of the 3P-SRAM cell 101 because the second read pass-gate transistor 144 is off. Thus, when A is a logic “1” and B is a logic “0”, an XNOR operation output of logic “0” is indicated. Alternatively, when the true bit stored on the true storage node 115.1 is a logic “1” (i.e., when B is a logic “1”) and, thus, the complement bit stored on the complement storage node 115.2 is a logic “0”, the first read pull-down transistor 133 will be on and the second read pull-down transistor 143 will be off. In this case, because both the second read pass-gate transistor 144 and the second read pull-down transistor 143 are off, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the second side of the 3P-SRAM cell 101. However, because both the first read pass-gate transistor 134 and the first read pull-down transistor 133 are on, the voltage level (VCRBL) on the common read bitline 152 will discharge through the first side of the 3P-SRAM cell 101. Thus, when A is a logic “1” and B is also a logic “1”, an XNOR operation output of logic “1” is indicated.
During a read operation through the second read port, the first read wordline 131 has a low voltage level (i.e., A is a logic “0”) so that the first read pass-gate transistor 134 is off and the second read wordline 141 has the higher positive voltage level (i.e., a logic state of “1”) so that the second read pass-gate transistor 144 is on. When the true bit stored on the true storage node 115.1 is a logic “0” (i.e., when B is a logic “0”) and, thus, the complement bit stored on the complement storage node 115.2 is a logic “1”, the first read pull-down transistor 133 will be off and the second read pull-down transistor 143 will be on. In this case, because both the first read pass-gate transistor 134 and the first read pull-down transistor 133 are off, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the first side of the 3P-SRAM cell 101. However, because both the second read pass-gate transistor 144 and the second read pull-down transistor 143 are on, the voltage level (VCRBL) on the common read bitline 152 will discharge through the second side of the 3P-SRAM cell 101. Thus, when A is a logic “0” and B is a logic “0”, an XNOR operation output of logic “1” is indicated. Alternatively, when the true bit stored on the true storage node 115.1 is a logic “1” (i.e., when B is a logic “1”) and, thus, the complement bit stored on the complement storage node 115.2 is a logic “0”, the first read pull-down transistor 133 will be on and the second read pull-down transistor 143 will be off. In this case, even though the second read pass-gate transistor 144 is on, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the second side of the 3P-SRAM cell 101 because the second read pull-down transistor 143 is off. Furthermore, even though the first read pull-down transistor 133 is on, the voltage level (VCRBL) on the common read bitline 152 will not discharge through the first side of the 3P-SRAM cell 101 because the first read pass-gate transistor 134 is off. Thus, when A is a logic “0” and B is a logic “1”, an XNOR operation output of logic “0” is indicated.
Multiple 3P-SRAM cells 101, as described above, could be incorporated into a memory array with one-input devices (e.g., inverters, skewed logic gates, etc.) connected to the ends of the common read bitlines for the columns, respectively. Such a single-input device could be used for large signal sensing of the XNOR output from a selected 3P-SRAM cell (i.e., a 3P-SRAM cell in a given column and row).
Alternatively, multiple 3P-SRAM cells 101, as described above, could be incorporated into a memory array with two-input devices (e.g., op-amp voltage comparators etc.) connected to the ends of the common read bitlines for the columns, respectively. Such a two-input device could be used to compare the actual voltage level on a common read bitline of a column to a reference voltage for small signal sensing of the XNOR output from a selected 3P-SRAM cell (i.e., a 3P-SRAM cell in a given column and row).
Alternatively, multiple 3P-SRAM cells 101, as described above, could be incorporated into a memory array specifically configured for in-memory computing of XNOR-bitcount-compare functions, as described below. More specifically, referring to
Each column can include a pair of complementary bitlines (see true and complementary bitlines 122.1A-122.2A, 122.1B-122.2B, . . . 122.1m-122.2m). For a given column, the true bitline can be electrically connected to all the 3P-SRAM cells 101 in that column at the drain of the pass-gate transistor 114.1 on the first side (e.g., the right-hand side) and the complement bitline can be electrically connected to all the 3P-SRAM cell 101 in that column at the drain of the pass-gate transistor 114.2 on the second side (e.g., the left-hand side). Each column can also include a single common read bitline (see common read bitlines 152A, 152B, . . . 152m). For a given column, the common read bitline can be electrically connected to all the 3P-SRAM cells 101 in that column at the drains of both the first read pass-gate transistor 134 on the first side and the second read pass-gate transistor 144 on the second side. Each column can also be electrically connected to both a voltage comparator and a capacitor (see the voltage comparator 401A and capacitors 402A for column A, the voltage comparator 401B and capacitor 402B for column B, . . . and the voltage comparator 401m and the capacitor 402m for column m). Each voltage comparator for each column can be, for example, an op-am voltage comparator formed within the active device layer and configured to compare an actual voltage level (VCRBL) at one end of the common read bitline for the column to a reference voltage (Vref), discussed in greater detail below, and to output a digital output (Q) indicating whether VCRBL is less than Vref or not. Voltage comparators are well known in the art and, thus, the details thereof have been omitted from this specification in order to allow the reader to focus on the salient aspects of the disclosed embodiments. Each capacitor for each column can include a first conductive plate electrically connected to a node on the common read bitline for the column, a second conductive plate electrically connected to the first voltage rail 498 (e.g., a ground or negative voltage rail), and a dielectric layer between and in contact with the first conductive plate and the second conductive plate.
Each row can include a write wordline (WWL) (see WWL 1211 for row 1, WWL 1212 for row 2, WWL 1213 for row 3, . . . and WWL 121n for row n). For each row, the write wordline can be connected to all the 3P-SRAM cells 101 in the row at the gates of the pass-gate transistors 114.1 and 114.2. Each row can further include a first read wordline (RWL1) (see RWL11311 of row 1, RWL11312 of row 2, RWL11313 of row 3, . . . and RWL1131n of row n) and a second read wordline (RWL2) (see RWL2141i of row 1, RWL21412 of row 2, RWL21413 of row 3, . . . and RWL2141n of row n). For each row, the first read wordline (RWL1) can be connected to all the 3P-SRAM cells 101 in the row at the gate of the first read pass-gate transistor 134 and the second read wordline (RWL2) can be connected to all the 3P-SRAM cells 101 in the row at the gate of the second read pass-gate transistor 144.
The above-described wordlines and bitlines can, for example, be formed in the back end of the line (BEOL) metal levels of the IC chip above the active device layer. BEOL and MOL interconnects (e.g., vias, wires, contacts, metal plugs, etc.) can be employed to electrically connect the wordlines and bitlines to the memory cells as described above. Optionally, the capacitor for each column can also be formed in one or more of the BEOL metal levels (e.g., as metal-on-metal (MOM) capacitors) and electrically connected to the corresponding common read bitline by BEOL interconnects (e.g., vias and/or wires). Furthermore, these MOM capacitors can be located in a region of the BEOL metal levels aligned above the memory cells such that incorporating them into the memory array does not result in an increase in chip surface area consumption.
The memory array 400 can further include a memory controller 495 and peripheral circuitry 491-492. In response to control signals (e.g., row address and column address signals for selecting SRAM cells and read, write or standby signals for indicating the operations to be performed with respect to the selected SRAM cells) from the memory controller 495, the peripheral circuitry 491-492 can enable write operations (i.e., selectively writing data values to the true storage node of each of the 3P-SRAM cells 101) and also read operations (as described in greater detail below). Peripheral circuitry 491 connected to the rows (at one end or at a combination of both ends) can include, for example, address decode logic and wordline drivers for selectively activating any of the wordlines during write or read operations. Peripheral circuitry 492 connected to the columns (at one end or at a combination of both ends) can include column address decode logic and bitline drivers for appropriately biasing selected bitlines during write or read operations. Controllers and other circuitry used in memory arrays to write data to and read data from selected memory cells are well known in the art. Thus, the details thereof have been omitted from this specification in order to allow the reader to focus on the salient aspects of the disclosed embodiments.
With the above-described configuration, concurrent read operations of all the 3P-SRAM cells in a selected column can be used to effectively accomplish an XNOR-bitcount-compare function because the digital output (Q) of a voltage comparator at the end of the selected column will indicate the final result from multiple XNOR operations, a bitcount of the outputs of the XNOR operations, and a comparison of the bitcount to a bitcount threshold.
Specifically, to accomplish an XNOR-bitcount-compare function, a bitline driver can pre-charge the common read bitline (e.g., 152A, 152B, . . . or 152m) and the corresponding capacitor (e.g., 402A, 402B, . . . or 402m) of a selected column (e.g., A, B, . . . or m) within the memory array 400. Next, the wordline drivers can selectively and exclusively activate only one of the two read bitlines in each of the rows (but not the other) during the same clock cycle in order to initiate concurrent read operations (i.e., parallel read operations). That is, the wordline drivers can be controlled so as to concurrently apply read pulses to a selected one of either the first read wordline or the second read wordline in each of the rows (i.e., to either 1311 or 1411 of row 1, either 1312 or 1412 of row 3, either 1313 or 1413 of row 3, . . . and either 131n or 141n of row n).
As discussed in detail above and illustrated in the truth table of
The more 3P-SRAM cells 101 that enable discharging of VCRBL, the lower VCRBL will be. Consequently, the actual voltage level (VCRBL) on the common read bitline of a selected column at the end of the concurrent XNOR operations is also indicative of the bitcount of the results of the concurrent XNOR operations in that selected column. It should be understood that the bitcount of the results refers to the total number of logic “1” XNOR outputs by the 3P-SRAM cells 101 in the selected column.
Thus, at the end of the concurrent XNOR operations by the 3P-SRAM cells 101 in a selected column, the voltage comparator (e.g., 402A, 402B, . . . or 402m) for that selected column (e.g., A, B, . . . or m) can perform a compare operation to compare the actual voltage level (VCRBL) on the common read bitline (e.g., 401A, 401B, . . . or 401m) to a reference voltage level (Vref), which is predetermined so that it corresponds to a bitcount threshold, and can output a digital output (e.g., QA, QB, . . . or Qm) indicating whether or not the actual voltage level (VCRBL) is below the reference voltage level (Vref). Thus, the digital output of the voltage comparator of the selected column will indicate whether or not the actual bitcount is below the bitcount threshold. For example, the bitcount threshold could be equal to one-half the total number of 3P-SRAM cells 101 in a column and the reference voltage (Vref) can be set so that it is approximately equal to the expected voltage level on a common read bitline if one-half of the total number of 3P-SRAM cells 101 in a column enabled discharging of VCRBL. In this case, the digital output of a given voltage comparator would be a logic “0”, if less than half of the 3P-SRAM cells 101 enabled discharging of VCRBL; whereas the digital output would be a logic “1”, if at least half of the 3P-SRAM cells 101 enabled discharging of VCRBL.
Those skilled in the art will recognize that the discharge rate (D) of any given common read bitline can be estimated as follows:
D=I/CV, (1)
where C refers to read bitline capacitance, where V refers to the voltage change (i.e., the initial voltage—the final voltage at the end of the concurrent XNOR operations; e.g. if half of the bitcells discharge, V will be equal to the pre-charge voltage (Vpre_charge) minus the reference voltage (Vref)) and where I refers to discharge current. The capacitance (C) of the common read bitline is a function of the size of the capacitor and the size of the capacitor can vary depending upon the technology node and the layout, but will be essentially fixed in the final structure. The discharge current (I) will depend upon the pull down strength of the read stacks of the memory cells. While the pull down strength is a function of the size of the FETs within the memory cells, it is also a function of the voltage level applied to the pass-gate transistor during a read operation. Thus, for concurrent read operations, the amplitude of the read pulse (i.e., the maximum voltage level of the read pulse) applied to the selected read wordline in each of the rows of memory cells can be adjusted to selectively tune the discharge rate. Furthermore, the pulse width can be selectively adjusted based on the expected discharge rate and the reference voltage (Vref). That is, a higher pulse amplitude (i.e., a higher read wordline activation voltage) can employed to speed up the discharge rate and in this case a shorter pulse width can be used to detect if/when more than half of the memory cells have enabled discharging, thereby increasing throughput albeit with a possible tradeoff for accuracy. Alternatively, a lower pulse amplitude (i.e., a lower read wordline activation voltage) can employed to slow down the discharge rate and in this case a longer pulse width can be used to detect if/when more than half of the memory cells have enabled discharging, thereby decreasing throughput but improving accuracy.
Additionally, those skilled in the art will recognize that, due to process variations, the pull down strengths of the memory cells may vary across the memory array. As a result, the voltage levels on different common read bitlines for different columns may vary even when the exact same number of memory cells in each of those columns enabled discharging of the read bitline voltage. Such process variation-induced voltage variation across the common read bitlines could lead to read errors depending upon where the reference voltage is set. In order to minimize this process variation-induced voltage variation across the common read bitlines within the memory array and thereby to reduce read errors, the number of memory cells per read bitline column can be increased.
Thus, it should be understood that the specific characteristics of the memory array components (e.g., the size of the capacitors 402A, 402B, . . . and 402m, the sizes of the transistors within the 3P-SRAM cells 101, etc.) and the configuration of the memory array itself (e.g., the number of memory cells per common read bitline) can be predetermined during the design phase and, depending upon the BNN application, the specifications employed when performing the concurrent XNOR-bitcount-compare operations using the memory array (e.g., the read pulse amplitude, the read pulse width, the reference voltage, etc.) can be selectively adjusted during operation for optimal BNN speed and/or power consumption and accuracy. That is, a combination of design and operational decisions can be made in order to ensure that, after pre-charging, the VCRBL on each common read bitline can be stepped down at a given discharge rate without being fully discharged to ground within a predetermined time period (i.e., by the end of the read pulse) when less than some predetermined number of the 3P-SRAM cells 101 in the column enable discharging of VCRBL. For example, as illustrated in
In any case, the digital output (e.g., QA, QB, . . . or Qm) from one voltage comparator (e.g., 402A, 402B, . . . or 402m) of one selected column (e.g., A, B, . . . or m) following the concurrent XNOR operations performed by the 3P-SRAM cells in that selected column is effectively a final result of an XNOR-bitcount-compare function.
The above-discussion refers to an XNOR-bitcount-compare function being performed using one selected column. However, if multiple XNOR-bitcount-compare functions need to be performed and if those multiple XNOR-bitcount-compare functions have the same first digital inputs (A) and different second digital inputs (B), then the multiple XNOR-bitcount-compare functions can be performed in parallel (i.e., concurrently) in different columns of the memory array 400. Specifically, for parallel XNOR-bitcount-compare functions performed in different columns in the memory array, the logic states on the first read wordlines 1311, 1312, 1313, . . . and 131n will correspond to the same first digital inputs (A) that are applied across all of the columns. For each one of those XNOR-bitcount-compare functions, the true bits stored in the 3P-SRAM cells of a given column will correspond to column-specific second digital inputs (B). As a result, the voltage comparators (e.g., 402A, 402B, . . . and 402m) for the different columns can concurrently output different digital outputs (e.g., QA, QB, . . . and Qm) indicating the results of the XNOR-bitcount-compare functions. Furthermore, since XNOR-bitcount-compare functions using the same first digital inputs are used in XNOR-NET type binary neural networks (BNNs), the disclosed memory array 400 can, for example, be employed for implementing an XNOR-NET BNN and, particularly, for performing in-parallel XNOR-bitcount-compare functions as a part of XNOR-NET BNN processing.
More specifically,
During BNN processing each of many different features can be convolved and pooled using corresponding kernels (see discussion below) and the defined receptive fields 7031-7039 in the multi-layer image 701 in order to generate feature maps that are eventually employed to recognize and characterize the image.
For example, a specific feature A could be a horizontal line, vertical line, etc. A kernel 710A can be developed (i.e., learned) for that specific feature A and can include a 3D matrix of weight values. The kernel 710A (i.e., the 3D matrix of weight values) will be the same size as each 3D receptive field. That is, the kernel 710A will have the same number of layers in the Z direction as each receptive field and the same width and height in the X and Y directions. Thus, for each pixel at each location in a given receptive field, there will be one corresponding weight value at a corresponding location in the kernel 710A for the specific feature A. It should be noted that the layers of the kernel can be identical. Additionally, it should be noted that in XNOR-NET BNN's, the actual weight value is converted to a binary weight value. Techniques for converting actual weight values to binary weight values are known in the art. Thus, the details of the converting process are omitted from the specification in order to allow the reader to focus on the salient aspects of the disclosed embodiments.
XNOR-bitcount-compare functions can then be performed by applying the kernel 710A to each of the receptive fields 7031-7039 in order to generate digital outputs QA1-QA9, respectively, for insertion into a feature map 750A for the specific feature A. Specifically, consider an XNOR-bitcount-compare operation performed with respect to the kernel 710A and the receptive field 7031. First, XNOR operations can be performed with respect to the binary weight value and the binary pixel intensity value acquired from corresponding locations in the kernel 710A and the receptive field 7031. The illustration at the bottom left corner of
The same XNOR-bitcount-compare operation can be performed with respect to the kernel 710A for the specific feature A and each of the other receptive fields 7032-7039 so that digital outputs for the specific feature A are generated for each receptive field. Thus, in
Multiple different feature maps associated with different specific features, respectively, can generated for the same multi-layer image 701 in the same manner as described above using the exact same receptive fields 7031-7039 (i.e., with the same binary pixel intensity values) and but different kernels with different binary weight values. All of the feature's maps for all of the specific features can be employed during subsequent BNN processing used to recognize and characterize the image.
The above-described XNOR-bitcount-compare functions can be performed using the disclosed memory array 400 with the 3P-SRAM cells 101 and, depending upon the set up, multiple ones of these XNOR-bitcount-compare functions can be performed in parallel such that the memory array 400 can be employed to implement an XNOR-NET BNN.
Specifically, as illustrated in
To accomplish this, the number of columns can be equal to some number m of different features and the number of rows can be equal to a total number n of pixels in each 3D receptive field (and in each 3D kernel).
Write operations can be performed to store a true bit in the true storage node 115.1 (NT) of the 3P-SRAM cell and, thus, a complement bit in the complement storage node 115.2 (NC) of each 3P-SRAM cell 101. Those skilled in the art will recognize that the complement bit will always be the complement of the stored true bit. That is, if the stored true bit is a logic “1”, then the complement bit at the complement storage node 115.2 (NC) will be a logic “0” and vice versa. Furthermore, the true bits stored at the true storage node 115.1 (NT) of each 3P-SRAM cell 101 in a given column can correspond to the binary weight values for each pixel location in a specific 3D kernel for a specific feature. Thus, the true bits stored in the 3P-SRAM cells 101 in column A can correspond to the binary weight values in the kernel 710A for the specific feature A, the true bits stored in the 3P-SRAM cells 101 in column B can correspond to the binary weight values in a different kernel for the specific feature B, and so on.
Because, as discussed above, in XNOR-NET BNN processing different features maps are generated using different kernels, but the same receptive fields (i.e., with the same binary pixel intensity values), parallel XNOR-bitcount-compare functions can be performed across all the different columns of the memory array. Specifically, for a first run, the common read bitlines 152A, 152B, . . . and 152m and, thereby the capacitors 402A, 402B, . . . and 402m for all of the columns can be pre-charged (e.g., by the bitline drivers) to select all columns. Then, either the first read wordline or the second read wordline in each row can be selectively and exclusively activated (e.g., by the wordline drivers) through application of read pulses only one of the read wordlines in each row such that the logic states of the first read wordlines 1311, 1312, . . . 131n in the rows correspond to the binary pixel intensity values for each pixel location in a first 3D receptive field. Thus, the digital outputs QA1, QB1, . . . , and Qm1 from the voltage comparators 401A, 401B, . . . and 401m of each column can be inserted into the first locations in the corresponding feature maps 750A, 750B, . . . , and 750m, respectively. For a second run, the common read bitlines 152A, 152B, . . . and 152m and, thereby the capacitors 402A, 402B, . . . and 402m for all of the columns can again be pre-charged (e.g., by the bitline drivers) to select all columns. Then, either the first read wordline or the second read wordline in each row can be selectively and exclusive activated (e.g., by the wordline drivers) through application of read pulses only on of the two read wordlines in each row such that the logic states of the first read wordlines 1311, 1312, . . . 131n in the rows correspond to the binary pixel intensity values for each pixel location in a second 3D receptive field. Thus, the digital outputs QA2, QB2, . . . , and Qm2 from the voltage comparators 401A, 401B, . . . and 401m of each column can be inserted into the second locations in the corresponding feature maps 750A, 750B, . . . , and 750m, respectively. Such runs can be performed until a last run is completed and the digital outputs QAz, QBz, . . . , and Qmz have been inserted into the last locations in the corresponding feature maps 750A, 750B, . . . , and 750m, respectively.
As mentioned above, due to process variations, the pull down strengths of the memory cells may vary across the memory array 400. As a result, the voltage levels on different common read bitlines for different columns may vary even when the exact same number of memory cells in each of those column have enabled read bitline voltage discharging. The process variation-induced voltage variation across the common read bitlines can lead to errors and, particularly, can reduce the accuracy of the compare results depending upon where the reference voltage is set. In order to minimize process variation-induced voltage variation across the common read bitlines and thereby reduce read errors, the number of memory cells per read bitline column can be increased. Thus, the accuracy of the BNN Q values can be improved by increasing the number of the 2D kernels that subsequently increases the size of the 3D filters for the hidden layers of the BNN. Increasing the size of the 3D filters necessitates a corresponding increase in the number of 3P-SRAM cells 101 per column.
It should be understood that
In any case, since, as discussed above, the memory array embodiments can include a single capacitor per common read bitline and since each capacitor can be formed in the BEOL metal levels of the IC chip above the active device layer with the 3P-SRAM cells, the disclosed memory array embodiments can be employed to minimize chip area consumption. Furthermore, since, as discussed above, the specifications for performing concurrent XNOR-bitcount-compare operations using the disclosed memory array (e.g., the read pulse amplitude, the read pulse width, the reference voltage, etc.) can be selectively adjusted for optimal BNN speed and/or power consumption and accuracy, the disclosed memory array embodiments can further be employed for improved manufacturability and performance (i.e., processing speed) and/or power consumption and accuracy.
Referring to the flow diagram of
The method can include providing a memory array 400, as described in detail above and illustrated in
The method can further include selecting at least one column in the memory array 400 and, optionally, all of the columns in the memory array 400 and using bitline driver(s) to pre-charge the common read bitline 152 and thereby the capacitor 402 of each selected column (see process step 1006).
The method can further include using wordline drivers to selectively and exclusively applying read pulses to only one of the first read wordline 131 and the second read wordline 141 in each of the rows (i.e., to either the first read wordline 131 or the second read wordline 141 in each row, but not both) so that concurrent XNOR operations are performed by all of the 3P-SRAM cells 101 in each selected column (see process step 1008). It should be understood that a read pulse refers to a pulse of a sufficiently high positive voltage to represent a high logic state (i.e., a logic value of “1”) on the read wordline during the duration of the pulse. When a read pulse is applied to only one of the two read wordlines, the other of the two read wordlines will have a low logic state (i.e., a logic value of “0”).
As discussed in detail above with regard to the truth table of
The method can further include, at the end of the concurrent XNOR operations in each selected column (i.e., when the selected read wordline in each row is returned to a low voltage state following the read pulse), using the voltage comparator of each selected column (e.g., voltage comparator 401A for column A, 401B for column B, etc.) to perform a comparison of the actual voltage level (VCRBL), which is on the common read bitline of the selected column, to a reference voltage level (Vref) and to output a digital output (Q) for the selected column based on the results of the comparison (see process step 1010). As discussed above, the actual voltage level (VCRBL) on the common read bitline of a selected column at the end of the concurrent XNOR operations performed by the 3P-SRAM cells in the selected column will be indicative of how many of the 3P-SRAM cells in that selected column enabled discharging of the common read bitline. Thus, the actual voltage level (VCRBL) will be indicative of a bitcount of the results of the concurrent XNOR operations in the selected column. Furthermore, the reference voltage level (Vref) can be predetermined so that it corresponds to a bitcount threshold (e.g., so that it is approximately equal to the expected voltage level on the common read bitline if one-half of the memory cells enable discharging of the common read bitline). Thus, the digital output (Q) from the voltage comparator of each selected column will indicate whether or not the actual bitcount for the concurrent XNOR operations performed therein is below the bitcount threshold.
For example, the bitcount threshold could be equal to one-half the total number of 3P-SRAM cells in a column and the reference voltage (Vref) can be set so that it corresponds to what the voltage level (VCRBL) on a common read bitline would be if one-half of the total number of 3P-SRAM cells 101 in the column enabled discharging of VCRBL. In this case, the digital output (Q) of a voltage comparator 401 would be a logic “0”, if less than half of the 3P-SRAM cells 101 enabled discharging of VCRBL, whereas the digital output (Q) of a voltage comparator 401 would be a logic “1”, if at least half of the 3P-SRAM cells 101 enabled discharging of VCRBL. In other words, the digital output (Q) of the voltage comparator 401 of a selected column following the concurrent XNOR operations performed in the selected column is effectively a final result of an XNOR-bitcount-compare function.
As discussed in greater detail above with regard to the memory array 400, multiple XNOR-bitcount-compare functions may be performed in parallel and, particularly, during the same clock cycle, in the different columns, respectively, when the first digital inputs, which are to be applied to the first read wordlines of the rows are the same for all the XNOR-bitcount-compare functions and when only the second digital inputs, which are stored in the true storage nodes of the 3P-SRAM cells, vary from column to column. Furthermore, since XNOR-bitcount-compare functions are used in XNOR-NET type binary neural networks (BNNs), the in-memory computing method can be employed for implementing an XNOR-NET BNN.
It should be understood that the terminology used herein is for the purpose of describing the disclosed structures and methods and is not intended to be limiting. For example, as used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Additionally, as used herein, the terms “comprises” “comprising”, “includes” and/or “including” specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Furthermore, as used herein, terms such as “right”, “left”, “vertical”, “horizontal”, “top”, “bottom”, “upper”, “lower”, “under”, “below”, “underlying”, “over”, “overlying”, “parallel”, “perpendicular”, etc., are intended to describe relative locations as they are oriented and illustrated in the drawings (unless otherwise indicated) and terms such as “touching”, “in direct contact”, “abutting”, “directly adjacent to”, “immediately adjacent to”, etc., are intended to indicate that at least one element physically contacts another element (without other elements separating the described elements). The term “laterally” is used herein to describe the relative locations of elements and, more particularly, to indicate that an element is positioned to the side of another element as opposed to above or below the other element, as those elements are oriented and illustrated in the drawings. For example, an element that is positioned laterally adjacent to another element will be beside the other element, an element that is positioned laterally immediately adjacent to another element will be directly beside the other element, and an element that laterally surrounds another element will be adjacent to and border the outer sidewalls of the other element. The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed.
The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.
