# Patent

## Title
Variable precision floating point multiply-add circuit

## Abstract

Embodiments of the present invention may provide methods and circuits for energy efficient floating point multiply and/or add operations. A variable precision floating point circuit may determine the certainty of the result of a multiply-add floating point calculation in parallel with the floating-point calculation. The variable precision floating point circuit may use the certainty of the inputs in combination with information from the computation, such as, binary digits that cancel, normalization shifts, and rounding, to perform a calculation of the certainty of the result. A floating point multiplication circuit may determine whether a lowest portion of a multiplication result could affect the final result and may induce a replay of the multiplication operation when it is determined that the result could affect the final result.

## Background
This invention was made with U.S. Government support under H98230-11-3-0011 awarded by the Department of Defense. The government has certain rights in this invention.


FIELD OF THE INVENTION
The present disclosure relates to the field of processors and, in particular, to an energy efficient variable precision floating point computation circuit.
DESCRIPTION OF RELATED ART
In computing, each number can be represented as Significand×baseexponent. The significand (also coefficient or mantissa) includes significant digits. The base can be any positive number but is normally 2, 10 or 16. For example, in base 10, the number 1234 may be represented as 1.234×103, in which 1.234 is the significand, 10 is the base and 3 is the exponent. In this representation, floating the radix point (or more specifically, the decimal point in base 10, or binary point in base 2) won't affect the value of the number (e.g., 1.234×103 may be presented as 12.34×102) and can support a wide range of values. For example, a fixed-point representation that has seven decimal digits with two decimal places can represent the numbers 12345.67, 123.45, 1.23 and so on, whereas a floating point representation (such as the IEEE 754 decimal 32 format (IEEE 754-2008 published in August 2008)) with seven decimal digits could in addition represent 1.234567, 123456.7, 0.00001234567, 1234567000000000, and so on.
When working in binary, the significand is characterized by its width in binary digits (bits). Because the most significant bit is always 1 for a normalized number, this bit is not typically stored and is called the “hidden bit”. Depending on the context, the hidden bit may or may not be counted towards the width of the significand. For example, the IEEE 754 double precision format is commonly described as having either a 53-bit significand, including the hidden bit, or a 52-bit significand, not including the hidden bit. The notion of a hidden bit only applies to binary representations. IEEE 754 defines the precision, p, to be the number of digits in the significand, including any implicit leading bit (e.g. precision of double precision format is 53 and single precision format is 24).
High-throughput floating point computations are key building blocks of 3D graphics, signal processing and high-performance computing workload. However, while a high floating point precision offer better accuracy compared to a low floating point precision, the high floating point precision requires more computing resources (e.g., circuitry, computation time) and more energy. Floating point algorithms today are typically designed for either single precision or double precision hardware. This requirement is based on the worst-case data that may be involved in the computations. Errors may be incurred from using lower precision hardware. Thus, achieving both high energy efficiency and accuracy is mutually exclusive in a fixed-precision floating point computation. Further, many lower bits of the mantissa typically do not affect the final result, but add significantly to the power and delay of the circuits. Other algorithms, typically for graphics, sacrifice quality in order to operate with reduced mantissa precisions. Therefore, there is a need in the art for variable precision floating point circuits that can preserve high-precision accuracy and maintain high energy efficiency.



DESCRIPTION OF THE FIGURES
Embodiments are illustrated by way of example and not limitation in the Figures of the accompanying drawings:
FIG. 1A is a block diagram of a system according to one embodiment;
FIG. 1B is a block diagram of a system according to one embodiment;
FIG. 1C is a block diagram of a system according to one embodiment;
FIG. 2 is a block diagram of a processor according to one embodiment;
FIG. 3A illustrates packed data types according to one embodiment;
FIG. 3B illustrates packed data types according one embodiment;
FIG. 3C illustrates packed data types according to one embodiment;
FIG. 3D illustrates an instruction encoding according to one embodiment;
FIG. 3E illustrates an instruction encoding according to one embodiment;
FIG. 3F illustrates an instruction encoding according to one embodiment;
FIG. 4A illustrates elements of a processor micro-architecture according to one embodiment;
FIG. 4B illustrates elements of a processor micro-architecture according to one embodiment;
FIG. 5 is a block diagram of a processor according to one embodiment;
FIG. 6 is a block diagram of a computer system according to one embodiment;
FIG. 7 is a block diagram of a computer system according to one embodiment;
FIG. 8 is a block diagram of a computer system according to one embodiment;
FIG. 9 is a block diagram of a system-on-a-chip according to one embodiment;
FIG. 10 is a block diagram of a processor according to one embodiment;
FIG. 11 is a block diagram of an IP core development system according to one embodiment;
FIG. 12 illustrates an architecture emulation system according to one embodiment.
FIG. 13 illustrates a system to translate instructions according to one embodiment;
FIG. 14A is an illustration of a variable precision floating point circuit according to one embodiment;
FIG. 14B is an illustration of a plurality of operation modes according to one embodiment;
FIG. 15 is an illustration of a variable precision floating point mantissa unit according to one embodiment;
FIG. 16 illustrates a multiplier according to one embodiment;
FIG. 17A illustrates right shifts for different operation modes of a right shifter according to one embodiment;
FIG. 17B illustrates a plurality of shift stages of a right shifter according to one embodiment;
FIG. 17C illustrates circuitry for variable precision shifting of a right shifter according to one embodiment;
FIG. 18 illustrates a sparse carry-tree adder according to one embodiment;
FIG. 19 illustrates a left shift computation unit according to one embodiment;
FIG. 20 illustrates a leading zero anticipation circuit according to one embodiment;
FIG. 21 illustrates a plurality of operation modes of a left shifter according to one embodiment;
FIG. 22 illustrates a variable precision incrementer according to one embodiment;
FIG. 23 illustrates an certainty tracking circuit according to one embodiment;
FIG. 24 is an illustration of gate-clocking of a floating point multiplier according to one embodiment.



DETAILED DESCRIPTION
Embodiments of the present invention may provide methods and circuits for energy efficient floating point multiply and/or add operations. The embodiments may provide energy-efficient variable-precision multiply and/or add operations while keeping track of how many mantissa bits of a floating-point number may be certain and/or provide energy efficient floating point multiplication that includes a replay of the multiplication when a lowest portion of a multiplication result could affect the final result.
The variable precision floating point circuit may use real-time certainty tracking to provide run-time precision selection. The certainty tracking may enable low-precision calculations, whose result may be uncertain, to be redone with higher precision if necessary. Because the certainty may be dependent upon the data, it may be determined along with the numerical computations. To achieve improved power and performance, the circuits keeping track of the certainty may add minimal overhead, while the majority of calculations produce correct results with lower precisions.
The floating point multiplication may be performed by an n-bit by n-bit multiplier circuit including a parallelogram configured to set carries of a predetermined number of least significant bits of a multiplication product to zero for a multiplication operation, and a detection circuit to induce a replay of the multiplication operation by the multiplier to generate a full multiplication result if necessary.
In an embodiment, the variable precision floating point circuit may determine the certainty of the result of a multiply-add floating point calculation in parallel with the floating-point calculation. The variable precision floating point circuit may use the certainty of the inputs in combination with information from the computation, such as, binary digits that cancel, normalization shifts, and rounding, to perform a calculation of the certainty of the result. An exemplary variable precision floating point circuit may comprise a variable precision mantissa unit that can support multiple precisions, multiple exponent datapaths that supports a maximum parallelism at a lowest precision, and certainty calculation units that provide certainty bounds of the outputs. The variable precision mantissa unit may also be referred to as a variable precision mantissa datapath.
The following description describes a variable precision floating point circuit with real-time certainty tracking within or in association with a processor, computer system, or other processing apparatus. In the following description, numerous specific details such as processing logic, processor types, micro-architectural conditions, events, enablement mechanisms, and the like are set forth in order to provide a more thorough understanding of embodiments of the present invention. It will be appreciated, however, by one skilled in the art that the invention may be practiced without such specific details. Additionally, some well known structures, circuits, and the like have not been shown in detail to avoid unnecessarily obscuring embodiments of the present invention.
One embodiment of the present invention may provide a single core or multi-core processor. The processor may comprise a register file and a permutation unit coupled to the register file. The register file may have a plurality of register banks and an input to receive a selection signal. The selection signal may select one or more unit widths of a register bank as a data element boundary for read or write operations.
Although the following embodiments are described with reference to a processor, other embodiments are applicable to other types of integrated circuits and logic devices. Similar techniques and teachings of embodiments of the present invention can be applied to other types of circuits or semiconductor devices that can benefit from higher pipeline throughput and improved performance. The teachings of embodiments of the present invention are applicable to any processor or machine that performs data manipulations. However, the present invention is not limited to processors or machines that perform 1024 bit, 512 bit, 256 bit, 128 bit, 64 bit, 32 bit, or 16 bit data operations and can be applied to any processor and machine in which manipulation or management of data is performed.
Although the below examples describe instruction handling and distribution in the context of execution units and logic circuits, other embodiments of the present invention can be accomplished by way of a data or instructions stored on a machine-readable, tangible medium, which when performed by a machine cause the machine to perform functions consistent with at least one embodiment of the invention. In one embodiment, functions associated with embodiments of the present invention are embodied in machine-executable instructions. The instructions can be used to cause a general-purpose or special-purpose processor that is programmed with the instructions to perform the steps of the present invention. Embodiments of the present invention may be provided as a computer program product or software which may include a machine or computer-readable medium having stored thereon instructions which may be used to program a computer (or other electronic devices) to perform one or more operations according to embodiments of the present invention. Alternatively, steps of embodiments of the present invention might be performed by specific hardware components that contain fixed-function logic for performing the steps, or by any combination of programmed computer components and fixed-function hardware components.
Instructions used to program logic to perform embodiments of the invention can be stored within a memory in the system, such as DRAM, cache, flash memory, or other storage. Furthermore, the instructions can be distributed via a network or by way of other computer readable media. Thus a machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer), but is not limited to, floppy diskettes, optical disks, Compact Disc, Read-Only Memory (CD-ROMs), and magneto-optical disks, Read-Only Memory (ROMs), Random Access Memory (RAM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), magnetic or optical cards, flash memory, or a tangible, machine-readable storage used in the transmission of information over the Internet via electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.). Accordingly, the computer-readable medium includes any type of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer).
A design may go through various stages, from creation to simulation to fabrication. Data representing a design may represent the design in a number of manners. First, as is useful in simulations, the hardware may be represented using a hardware description language or another functional description language. Additionally, a circuit level model with logic and/or transistor gates may be produced at some stages of the design process. Furthermore, most designs, at some stage, reach a level of data representing the physical placement of various devices in the hardware model. In the case where conventional semiconductor fabrication techniques are used, the data representing the hardware model may be the data specifying the presence or absence of various features on different mask layers for masks used to produce the integrated circuit. In any representation of the design, the data may be stored in any form of a machine readable medium. A memory or a magnetic or optical storage such as a disc may be the machine readable medium to store information transmitted via optical or electrical wave modulated or otherwise generated to transmit such information. When an electrical carrier wave indicating or carrying the code or design is transmitted, to the extent that copying, buffering, or re-transmission of the electrical signal is performed, a new copy is made. Thus, a communication provider or a network provider may store on a tangible, machine-readable medium, at least temporarily, an article, such as information encoded into a carrier wave, embodying techniques of embodiments of the present invention.
In modern processors, a number of different execution units are used to process and execute a variety of code and instructions. Not all instructions are created equal as some are quicker to complete while others can take a number of clock cycles to complete. The faster the throughput of instructions, the better the overall performance of the processor. Thus it would be advantageous to have as many instructions execute as fast as possible. However, there are certain instructions that have greater complexity and require more in terms of execution time and processor resources. For example, there are floating point instructions, load/store operations, data moves, etc.
As more computer systems are used in internet, text, and multimedia applications, additional processor support has been introduced over time. In one embodiment, an instruction set may be associated with one or more computer architectures, including data types, instructions, register architecture, addressing modes, memory architecture, interrupt and exception handling, and external input and output (I/O).
In one embodiment, the instruction set architecture (ISA) may be implemented by one or more micro-architectures, which includes processor logic and circuits used to implement one or more instruction sets. Accordingly, processors with different micro-architectures can share at least a portion of a common instruction set. For example, Intel® Pentium 4 processors, Intel® CoreTM processors, and processors from Advanced Micro Devices, Inc. of Sunnyvale Calif. implement nearly identical versions of the x86 instruction set (with some extensions that have been added with newer versions), but have different internal designs. Similarly, processors designed by other processor development companies, such as ARM Holdings, Ltd., MIPS, or their licensees or adopters, may share at least a portion a common instruction set, but may include different processor designs. For example, the same register architecture of the ISA may be implemented in different ways in different micro-architectures using new or well-known techniques, including dedicated physical registers, one or more dynamically allocated physical registers using a register renaming mechanism (e.g., the use of a Register Alias Table (RAT), a Reorder Buffer (ROB) and a retirement register file). In one embodiment, registers may include one or more registers, register architectures, register files, or other register sets that may or may not be addressable by a software programmer.
In one embodiment, an instruction may include one or more instruction formats. In one embodiment, an instruction format may indicate various fields (number of bits, location of bits, etc.) to specify, among other things, the operation to be performed and the operand(s) on which that operation is to be performed. Some instruction formats may be further broken defined by instruction templates (or sub formats). For example, the instruction templates of a given instruction format may be defined to have different subsets of the instruction format's fields and/or defined to have a given field interpreted differently. In one embodiment, an instruction is expressed using an instruction format (and, if defined, in a given one of the instruction templates of that instruction format) and specifies or indicates the operation and the operands upon which the operation will operate.
Scientific, financial, auto-vectorized general purpose, RMS (recognition, mining, and synthesis), and visual and multimedia applications (e.g., 2D/3D graphics, image processing, video compression/decompression, voice recognition algorithms and audio manipulation) may require the same operation to be performed on a large number of data items. In one embodiment, Single Instruction Multiple Data (SIMD) refers to a type of instruction that causes a processor to perform an operation on multiple data elements. SIMD technology may be used in processors that can logically divide the bits in a register into a number of fixed-sized or variable-sized data elements, each of which represents a separate value. For example, in one embodiment, the bits in a 64-bit register may be organized as a source operand containing four separate 16-bit data elements, each of which represents a separate 16-bit value. This type of data may be referred to as ‘packed’ data type or ‘vector’ data type, and operands of this data type are referred to as packed data operands or vector operands. In one embodiment, a packed data item or vector may be a sequence of packed data elements stored within a single register, and a packed data operand or a vector operand may a source or destination operand of a SIMD instruction (or ‘packed data instruction’ or a ‘vector instruction’). In one embodiment, a SIMD instruction specifies a single vector operation to be performed on two or more source vector operands to generate a destination vector operand (also referred to as a result vector operand) of the same or different size, with the same or different number of data elements, and in the same or different data element order.
SIMD technology, such as that employed by the Intel® CoreTM processors having an instruction set including x86, MMXTM, Streaming SIMD Extensions (SSE), SSE2, SSE3, SSE4.1, and SSE4.2 instructions, ARM processors, such as the ARM Cortex® family of processors having an instruction set including the Vector Floating Point (VFP) and/or NEON instructions, and MIPS processors, such as the Loongson family of processors developed by the Institute of Computing Technology (ICT) of the Chinese Academy of Sciences, has enabled a significant improvement in application performance (CoreTM and MMXTM are registered trademarks or trademarks of Intel Corporation of Santa Clara, Calif.).
In one embodiment, destination and source registers/data are generic terms to represent the source and destination of the corresponding data or operation. In some embodiments, they may be implemented by registers, memory, or other storage areas having other names or functions than those depicted. For example, in one embodiment, “DEST1” may be a temporary storage register or other storage area, whereas “SRC1” and “SRC2” may be a first and second source storage register or other storage area, and so forth. In other embodiments, two or more of the SRC and DEST storage areas may correspond to different data storage elements within the same storage area (e.g., a SIMD register). In one embodiment, one of the source registers may also act as a destination register by, for example, writing back the result of an operation performed on the first and second source data to one of the two source registers serving as a destination registers.
FIG. 1A is a block diagram of an exemplary computer system formed with a processor that includes execution units to execute an instruction in accordance with one embodiment of the present invention. System 100 includes a component, such as a processor 102 to employ execution units including logic to perform algorithms for process data, in accordance with the present invention, such as in the embodiment described herein. System 100 is representative of processing systems based on the PENTIUM® III, PENTIUM® 4, XeonTM, Itanium®, XScaleTM and/or StrongARMTM microprocessors available from Intel Corporation of Santa Clara, Calif., although other systems (including PCs having other microprocessors, engineering workstations, set-top boxes and the like) may also be used. In one embodiment, sample system 100 may execute a version of the WINDOWSTM operating system available from Microsoft Corporation of Redmond, Wash., although other operating systems (UNIX and Linux for example), embedded software, and/or graphical user interfaces, may also be used. Thus, embodiments of the present invention are not limited to any specific combination of hardware circuitry and software.
Embodiments are not limited to computer systems. Alternative embodiments of the present invention can be used in other devices such as handheld devices and embedded applications. Some examples of handheld devices include cellular phones, Internet Protocol devices, digital cameras, personal digital assistants (PDAs), and handheld PCs. Embedded applications can include a micro controller, a digital signal processor (DSP), system on a chip, network computers (NetPC), set-top boxes, network hubs, wide area network (WAN) switches, or any other system that can perform one or more instructions in accordance with at least one embodiment.
FIG. 1A is a block diagram of a computer system 100 formed with a processor 102 that includes one or more execution units 108 to perform an algorithm to perform at least one instruction in accordance with one embodiment of the present invention. One embodiment may be described in the context of a single processor desktop or server system, but alternative embodiments can be included in a multiprocessor system. System 100 is an example of a ‘hub’ system architecture. The computer system 100 includes a processor 102 to process data signals. The processor 102 can be a complex instruction set computer (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a processor implementing a combination of instruction sets, or any other processor device, such as a digital signal processor, for example. The processor 102 is coupled to a processor bus 110 that can transmit data signals between the processor 102 and other components in the system 100. The elements of system 100 perform their conventional functions that are well known to those familiar with the art.
In one embodiment, the processor 102 includes a Level 1 (L1) internal cache memory 104. Depending on the architecture, the processor 102 can have a single internal cache or multiple levels of internal cache. Alternatively, in another embodiment, the cache memory can reside external to the processor 102. Other embodiments can also include a combination of both internal and external caches depending on the particular implementation and needs. Register file 106 can store different types of data in various registers including integer registers, floating point registers, status registers, and instruction pointer register.
Execution unit 108, including logic to perform integer and floating point operations, also resides in the processor 102. The processor 102 also includes a microcode (ucode) ROM that stores microcode for certain macroinstructions. For one embodiment, execution unit 108 includes logic to handle a packed instruction set 109. By including the packed instruction set 109 in the instruction set of a general-purpose processor 102, along with associated circuitry to execute the instructions, the operations used by many multimedia applications may be performed using packed data in a general-purpose processor 102. Thus, many multimedia applications can be accelerated and executed more efficiently by using the full width of a processor's data bus for performing operations on packed data. This can eliminate the need to transfer smaller units of data across the processor's data bus to perform one or more operations one data element at a time.
Alternate embodiments of an execution unit 108 can also be used in micro controllers, embedded processors, graphics devices, DSPs, and other types of logic circuits. System 100 includes a memory 120. Memory 120 can be a dynamic random access memory (DRAM) device, a static random access memory (SRAM) device, flash memory device, or other memory device. Memory 120 can store instructions and/or data represented by data signals that can be executed by the processor 102.
A system logic chip 116 is coupled to the processor bus 110 and memory 120. The system logic chip 116 in the illustrated embodiment is a memory controller hub (MCH). The processor 102 can communicate to the MCH 116 via a processor bus 110. The MCH 116 provides a high bandwidth memory path 118 to memory 120 for instruction and data storage and for storage of graphics commands, data and textures. The MCH 116 is to direct data signals between the processor 102, memory 120, and other components in the system 100 and to bridge the data signals between processor bus 110, memory 120, and system I/O 122. In some embodiments, the system logic chip 116 can provide a graphics port for coupling to a graphics controller 112. The MCH 116 is coupled to memory 120 through a memory interface 118. The graphics card 112 is coupled to the MCH 116 through an Accelerated Graphics Port (AGP) interconnect 114.
System 100 uses a proprietary hub interface bus 122 to couple the MCH 116 to the I/O controller hub (ICH) 130. The ICH 130 provides direct connections to some I/O devices via a local I/O bus. The local I/O bus is a high-speed I/O bus for connecting peripherals to the memory 120, chipset, and processor 102. Some examples are the audio controller, firmware hub (flash BIOS) 128, wireless transceiver 126, data storage 124, legacy I/O controller containing user input and keyboard interfaces, a serial expansion port such as Universal Serial Bus (USB), and a network controller 134. The data storage device 124 can comprise a hard disk drive, a floppy disk drive, a CD-ROM device, a flash memory device, or other mass storage device.
For another embodiment of a system, an instruction in accordance with one embodiment can be used with a system on a chip. One embodiment of a system on a chip comprises of a processor and a memory. The memory for one such system is a flash memory. The flash memory can be located on the same die as the processor and other system components. Additionally, other logic blocks such as a memory controller or graphics controller can also be located on a system on a chip.
FIG. 1B illustrates a data processing system 140 which implements the principles of one embodiment of the present invention. It will be readily appreciated by one of skill in the art that the embodiments described herein can be used with alternative processing systems without departure from the scope of embodiments of the invention.
Computer system 140 comprises a processing core 159 capable of performing at least one instruction in accordance with one embodiment. For one embodiment, processing core 159 represents a processing unit of any type of architecture, including but not limited to a CISC, a RISC or a VLIW type architecture. Processing core 159 may also be suitable for manufacture in one or more process technologies and by being represented on a machine readable media in sufficient detail, may be suitable to facilitate said manufacture.
Processing core 159 comprises an execution unit 142, a set of register file(s) 145, and a decoder 144. Processing core 159 also includes additional circuitry (not shown) which is not necessary to the understanding of embodiments of the present invention. Execution unit 142 is used for executing instructions received by processing core 159. In addition to performing typical processor instructions, execution unit 142 can perform instructions in packed instruction set 143 for performing operations on packed data formats. Packed instruction set 143 includes instructions for performing embodiments of the invention and other packed instructions. Execution unit 142 is coupled to register file 145 by an internal bus. Register file 145 represents a storage area on processing core 159 for storing information, including data. As previously mentioned, it is understood that the storage area used for storing the packed data is not critical. Execution unit 142 is coupled to decoder 144. Decoder 144 is used for decoding instructions received by processing core 159 into control signals and/or microcode entry points. In response to these control signals and/or microcode entry points, execution unit 142 performs the appropriate operations. In one embodiment, the decoder is used to interpret the opcode of the instruction, which will indicate what operation should be performed on the corresponding data indicated within the instruction.
Processing core 159 is coupled with bus 141 for communicating with various other system devices, which may include but are not limited to, for example, synchronous dynamic random access memory (SDRAM) control 146, static random access memory (SRAM) control 147, burst flash memory interface 148, personal computer memory card international association (PCMCIA)/compact flash (CF) card control 149, liquid crystal display (LCD) control 150, direct memory access (DMA) controller 151, and alternative bus master interface 152. In one embodiment, data processing system 140 may also comprise an I/O bridge 154 for communicating with various I/O devices via an I/O bus 153. Such I/O devices may include but are not limited to, for example, universal asynchronous receiver/transmitter (UART) 155, universal serial bus (USB) 156, Bluetooth wireless UART 157 and I/O expansion interface 158.
One embodiment of data processing system 140 provides for mobile, network and/or wireless communications and a processing core 159 capable of performing SIMD operations including a text string comparison operation. Processing core 159 may be programmed with various audio, video, imaging and communications algorithms including discrete transformations such as a Walsh-Hadamard transform, a fast Fourier transform (FFT), a discrete cosine transform (DCT), and their respective inverse transforms; compression/decompression techniques such as color space transformation, video encode motion estimation or video decode motion compensation; and modulation/demodulation (MODEM) functions such as pulse coded modulation (PCM).
FIG. 1C illustrates yet alternative embodiments of a data processing system that may include execution units to execute an instruction in accordance with an embodiment of the present invention. In accordance with one alternative embodiment, data processing system 160 may include a main processor 166, a SIMD coprocessor 161, a cache memory 167, and an input/output system 168. The input/output system 168 may optionally be coupled to a wireless interface 169. SIMD coprocessor 161 is capable of performing operations including instructions in accordance with one embodiment. Processing core 170 may be suitable for manufacture in one or more process technologies and by being represented on a machine readable media in sufficient detail, may be suitable to facilitate the manufacture of all or part of data processing system 160 including processing core 170.
For one embodiment, SIMD coprocessor 161 comprises an execution unit 162 and a set of register file(s) 164. One embodiment of main processor 165 comprises a decoder 165 to recognize instructions of instruction set 163 including instructions in accordance with one embodiment for execution by execution unit 162. For alternative embodiments, SIMD coprocessor 161 also comprises at least part of decoder 165B to decode instructions of instruction set 163. Processing core 170 also includes additional circuitry (not shown) which is not necessary to the understanding of embodiments of the present invention.
In operation, the main processor 166 executes a stream of data processing instructions that control data processing operations of a general type including interactions with the cache memory 167, and the input/output system 168. Embedded within the stream of data processing instructions are SIMD coprocessor instructions. The decoder 165 of main processor 166 recognizes these SIMD coprocessor instructions as being of a type that should be executed by an attached SIMD coprocessor 161. Accordingly, the main processor 166 issues these SIMD coprocessor instructions (or control signals representing SIMD coprocessor instructions) on the coprocessor bus 171 where from they are received by any attached SIMD coprocessors. In this case, the SIMD coprocessor 161 will accept and execute any received SIMD coprocessor instructions intended for it.
Data may be received via wireless interface 169 for processing by the SIMD coprocessor instructions. For one example, voice communication may be received in the form of a digital signal, which may be processed by the SIMD coprocessor instructions to regenerate digital audio samples representative of the voice communications. For another example, compressed audio and/or video may be received in the form of a digital bit stream, which may be processed by the SIMD coprocessor instructions to regenerate digital audio samples and/or motion video frames. For one embodiment of processing core 170, main processor 166, and a SIMD coprocessor 161 are integrated into a single processing core 170 comprising an execution unit 162, a set of register file(s) 164, and a decoder 165 to recognize instructions of instruction set 163 including instructions in accordance with one embodiment.
FIG. 2 is a block diagram of the micro-architecture for a processor 200 that includes logic circuits to perform instructions in accordance with one embodiment of the present invention. In some embodiments, an instruction in accordance with one embodiment can be implemented to operate on data elements having sizes of byte, word, doubleword, quadword, etc., as well as datatypes, such as single and double precision integer and floating point datatypes. In one embodiment the in-order front end 201 is the part of the processor 200 that fetches instructions to be executed and prepares them to be used later in the processor pipeline. The front end 201 may include several units. In one embodiment, the instruction prefetcher 226 fetches instructions from memory and feeds them to an instruction decoder 228 which in turn decodes or interprets them. For example, in one embodiment, the decoder decodes a received instruction into one or more operations called “micro-instructions” or “micro-operations” (also called micro op or uops) that the machine can execute. In other embodiments, the decoder parses the instruction into an opcode and corresponding data and control fields that are used by the micro-architecture to perform operations in accordance with one embodiment. In one embodiment, the trace cache 230 takes decoded uops and assembles them into program ordered sequences or traces in the uop queue 234 for execution. When the trace cache 230 encounters a complex instruction, the microcode ROM 232 provides the uops needed to complete the operation.
Some instructions are converted into a single micro-op, whereas others need several micro-ops to complete the full operation. In one embodiment, if more than four micro-ops are needed to complete an instruction, the decoder 228 accesses the microcode ROM 232 to do the instruction. For one embodiment, an instruction can be decoded into a small number of micro ops for processing at the instruction decoder 228. In another embodiment, an instruction can be stored within the microcode ROM 232 should a number of micro-ops be needed to accomplish the operation. The trace cache 230 refers to an entry point programmable logic array (PLA) to determine a correct micro-instruction pointer for reading the micro-code sequences to complete one or more instructions in accordance with one embodiment from the micro-code ROM 232. After the microcode ROM 232 finishes sequencing micro-ops for an instruction, the front end 201 of the machine resumes fetching micro-ops from the trace cache 230.
The out-of-order execution engine 203 is where the instructions are prepared for execution. The out-of-order execution logic has a number of buffers to smooth out and re-order the flow of instructions to optimize performance as they go down the pipeline and get scheduled for execution. The allocator logic allocates the machine buffers and resources that each uop needs in order to execute. The register renaming logic renames logic registers onto entries in a register file. The allocator also allocates an entry for each uop in one of the two uop queues, one for memory operations and one for non-memory operations, in front of the instruction schedulers: memory scheduler, fast scheduler 202, slow/general floating point scheduler 204, and simple floating point scheduler 206. The uop schedulers 202, 204, 206, determine when a uop is ready to execute based on the readiness of their dependent input register operand sources and the availability of the execution resources the uops need to complete their operation. The fast scheduler 202 of one embodiment can schedule on each half of the main clock cycle while the other schedulers can only schedule once per main processor clock cycle. The schedulers arbitrate for the dispatch ports to schedule uops for execution.
Register files 208, 210, sit between the schedulers 202, 204, 206, and the execution units 212, 214, 216, 218, 220, 222, 224 in the execution block 211. There is a separate register file 208, 210, for integer and floating point operations, respectively. Each register file 208, 210, of one embodiment also includes a bypass network that can bypass or forward just completed results that have not yet been written into the register file to new dependent uops. The integer register file 208 and the floating point register file 210 are also capable of communicating data with the other. For one embodiment, the integer register file 208 is split into two separate register files, one register file for the low order 32 bits of data and a second register file for the high order 32 bits of data. The floating point register file 210 of one embodiment has 128 bit wide entries because floating point instructions typically have operands from 64 to 128 bits in width.
The execution block 211 contains the execution units 212, 214, 216, 218, 220, 222, 224, where the instructions are actually executed. This section includes the register files 208, 210, that store the integer and floating point data operand values that the micro-instructions need to execute. The processor 200 of one embodiment is comprised of a number of execution units: address generation unit (AGU) 212, AGU 214, fast ALU 216, fast ALU 218, slow ALU 220, floating point ALU 222, floating point move unit 224. For one embodiment, the floating point execution blocks 222, 224, execute floating point, MMX, SIMD, and SSE, or other operations. The floating point ALU 222 of one embodiment includes a 64 bit by 64 bit floating point divider to execute divide, square root, and remainder micro-ops. For embodiments of the present invention, instructions involving a floating point value may be handled with the floating point hardware. In one embodiment, the ALU operations go to the high-speed ALU execution units 216, 218. The fast ALUs 216, 218, of one embodiment can execute fast operations with an effective latency of half a clock cycle. For one embodiment, most complex integer operations go to the slow ALU 220 as the slow ALU 220 includes integer execution hardware for long latency type of operations, such as a multiplier, shifts, flag logic, and branch processing. Memory load/store operations are executed by the AGUs 212, 214. For one embodiment, the integer ALUs 216, 218, 220, are described in the context of performing integer operations on 64 bit data operands. In alternative embodiments, the ALUs 216, 218, 220, can be implemented to support a variety of data bits including 16, 32, 128, 256, etc. Similarly, the floating point units 222, 224, can be implemented to support a range of operands having bits of various widths. For one embodiment, the floating point units 222, 224, can operate on 128 bits wide packed data operands in conjunction with SIMD and multimedia instructions.
In one embodiment, the uops schedulers 202, 204, 206, dispatch dependent operations before the parent load has finished executing. As uops are speculatively scheduled and executed in processor 200, the processor 200 also includes logic to handle memory misses. If a data load misses in the data cache, there can be dependent operations in flight in the pipeline that have left the scheduler with temporarily incorrect data. A replay mechanism tracks and re-executes instructions that use incorrect data. Only the dependent operations need to be replayed and the independent ones are allowed to complete. The schedulers and replay mechanism of one embodiment of a processor are also designed to catch instruction sequences for text string comparison operations.
The term “registers” may refer to the on-board processor storage locations that are used as part of instructions to identify operands. In other words, registers may be those that are usable from the outside of the processor (from a programmer's perspective). However, the registers of an embodiment should not be limited in meaning to a particular type of circuit. Rather, a register of an embodiment is capable of storing and providing data, and performing the functions described herein. The registers described herein can be implemented by circuitry within a processor using any number of different techniques, such as dedicated physical registers, dynamically allocated physical registers using register renaming, combinations of dedicated and dynamically allocated physical registers, etc. In one embodiment, integer registers store thirty-two bit integer data. A register file of one embodiment also contains eight multimedia SIMD registers for packed data. For the discussions below, the registers are understood to be data registers designed to hold packed data, such as 64 bits wide MMXTM registers (also referred to as ‘mm’ registers in some instances) in microprocessors enabled with MMX technology from Intel Corporation of Santa Clara, Calif. These MMX registers, available in both integer and floating point forms, can operate with packed data elements that accompany SIMD and SSE instructions. Similarly, 128 bits wide XMM registers relating to SSE2, SSE3, SSE4, or beyond (referred to generically as “SSEx”) technology and 256 bits wide YMM registers relating to AVX, VAX2 or AVX3 can also be used to hold such packed data operands. In one embodiment, in storing packed data and integer data, the registers do not need to differentiate between the two data types. In one embodiment, integer and floating point are either contained in the same register file or different register files. Furthermore, in one embodiment, floating point and integer data may be stored in different registers or the same registers.
In the examples of the following figures, a number of data operands are described. FIG. 3A illustrates various packed data type representations in multimedia registers according to one embodiment of the present invention. FIG. 3A illustrates data types for a packed byte 310, a packed word 320, and a packed doubleword (dword) 330 for 128 bits wide operands. The packed byte format 310 of this example is 128 bits long and contains sixteen packed byte data elements. A byte is defined here as 8 bits of data. Information for each byte data element is stored in bit 7 through bit 0 for byte 0, bit 15 through bit 8 for byte 1, bit 23 through bit 16 for byte 2, and finally bit 120 through bit 127 for byte 15. Thus, all available bits are used in the register. This storage arrangement increases the storage efficiency of the processor. As well, with sixteen data elements accessed, one operation can now be performed on sixteen data elements in parallel.
Generally, a data element is an individual piece of data that is stored in a single register or memory location with other data elements of the same length. In packed data sequences relating to SSEx technology, the number of data elements stored in a XMM register is 128 bits divided by the length in bits of an individual data element. Similarly, in packed data sequences relating to MMX and SSE technology, the number of data elements stored in an MMX register is 64 bits divided by the length in bits of an individual data element. Although the data types illustrated in FIG. 3A are 128 bit long, embodiments of the present invention can also operate with 64 bit wide or other sized operands. The packed word format 320 of this example is 128 bits long and contains eight packed word data elements. Each packed word contains sixteen bits of information. The packed doubleword format 330 of FIG. 3A is 128 bits long and contains four packed doubleword data elements. Each packed doubleword data element contains thirty two bits of information. A packed quadword is 128 bits long and contains two packed quad-word data elements.
FIG. 3B illustrates alternative in-register data storage formats. Each packed data can include more than one independent data element. Three packed data formats are illustrated; packed half 341, packed single 342, and packed double 343. One embodiment of packed half 341, packed single 342, and packed double 343 contain fixed-point data elements. For an alternative embodiment one or more of packed half 341, packed single 342, and packed double 343 may contain floating point data elements. One alternative embodiment of packed half 341 is one hundred twenty-eight bits long containing eight 16-bit data elements. One embodiment of packed single 342 is one hundred twenty-eight bits long and contains four 32-bit data elements. One embodiment of packed double 343 is one hundred twenty-eight bits long and contains two 64-bit data elements. It will be appreciated that such packed data formats may be further extended to other register lengths, for example, to 96-bits, 160-bits, 192-bits, 224-bits, 256-bits or more.
FIG. 3C illustrates various signed and unsigned packed data type representations in multimedia registers according to one embodiment of the present invention. Unsigned packed byte representation 344 illustrates the storage of an unsigned packed byte in a SIMD register. Information for each byte data element is stored in bit seven through bit zero for byte zero, bit fifteen through bit eight for byte one, bit twenty-three through bit sixteen for byte two, and finally bit one hundred twenty through bit one hundred twenty-seven for byte fifteen. Thus, all available bits are used in the register. This storage arrangement can increase the storage efficiency of the processor. As well, with sixteen data elements accessed, one operation can now be performed on sixteen data elements in a parallel fashion. Signed packed byte representation 345 illustrates the storage of a signed packed byte. Note that the eighth bit of every byte data element is the sign indicator. Unsigned packed word representation 346 illustrates how word seven through word zero are stored in a SIMD register. Signed packed word representation 347 is similar to the unsigned packed word in-register representation 346. Note that the sixteenth bit of each word data element is the sign indicator. Unsigned packed doubleword representation 348 shows how doubleword data elements are stored. Signed packed doubleword representation 349 is similar to unsigned packed doubleword in-register representation 348. Note that the necessary sign bit is the thirty-second bit of each doubleword data element.
FIG. 3D is a depiction of one embodiment of an operation encoding (opcode) format 360, having thirty-two or more bits, and register/memory operand addressing modes corresponding with a type of opcode format described in the “IA-32 Intel Architecture Software Developer's Manual Volume 2: Instruction Set Reference,” which is which is available from Intel Corporation, Santa Clara, Calif. on the world-wide-web (www) at intel.com/design/litcentr. In one embodiment, and instruction may be encoded by one or more of fields 361 and 362. Up to two operand locations per instruction may be identified, including up to two source operand identifiers 364 and 365. For one embodiment, destination operand identifier 366 is the same as source operand identifier 364, whereas in other embodiments they are different. For an alternative embodiment, destination operand identifier 366 is the same as source operand identifier 365, whereas in other embodiments they are different. In one embodiment, one of the source operands identified by source operand identifiers 364 and 365 is overwritten by the results of the text string comparison operations, whereas in other embodiments identifier 364 corresponds to a source register element and identifier 365 corresponds to a destination register element. For one embodiment, operand identifiers 364 and 365 may be used to identify 32-bit or 64-bit source and destination operands.
FIG. 3E is a depiction of another alternative operation encoding (opcode) format 370, having forty or more bits. Opcode format 370 corresponds with opcode format 360 and comprises an optional prefix byte 378. An instruction according to one embodiment may be encoded by one or more of fields 378, 371, and 372. Up to two operand locations per instruction may be identified by source operand identifiers 374 and 375 and by prefix byte 378. For one embodiment, prefix byte 378 may be used to identify 32-bit or 64-bit source and destination operands. For one embodiment, destination operand identifier 376 is the same as source operand identifier 374, whereas in other embodiments they are different. For an alternative embodiment, destination operand identifier 376 is the same as source operand identifier 375, whereas in other embodiments they are different. In one embodiment, an instruction operates on one or more of the operands identified by operand identifiers 374 and 375 and one or more operands identified by the operand identifiers 374 and 375 is overwritten by the results of the instruction, whereas in other embodiments, operands identified by identifiers 374 and 375 are written to another data element in another register. Opcode formats 360 and 370 allow register to register, memory to register, register by memory, register by register, register by immediate, register to memory addressing specified in part by MOD fields 363 and 373 and by optional scale-index-base and displacement bytes.
Turning next to FIG. 3F, in some alternative embodiments, 64 bit single instruction multiple data (SIMD) arithmetic operations may be performed through a coprocessor data processing (CDP) instruction. Operation encoding (opcode) format 380 depicts one such CDP instruction having CDP opcode fields 382 and 389. The type of CDP instruction, for alternative embodiments, operations may be encoded by one or more of fields 383, 384, 387, and 388. Up to three operand locations per instruction may be identified, including up to two source operand identifiers 385 and 390 and one destination operand identifier 386. One embodiment of the coprocessor can operate on 8, 16, 32, and 64 bit values. For one embodiment, an instruction is performed on integer data elements. In some embodiments, an instruction may be executed conditionally, using condition field 381. For some embodiments, source data sizes may be encoded by field 383. In some embodiments, Zero (Z), negative (N), carry (C), and overflow (V) detection can be done on SIMD fields. For some instructions, the type of saturation may be encoded by field 384.
FIG. 4A is a block diagram illustrating an in-order pipeline and a register renaming stage, out-of-order issue/execution pipeline according to at least one embodiment of the invention. FIG. 4B is a block diagram illustrating an in-order architecture core and a register renaming logic, out-of-order issue/execution logic to be included in a processor according to at least one embodiment of the invention. The solid lined boxes in FIG. 4A illustrate the in-order pipeline, while the dashed lined boxes illustrate the register renaming, out-of-order issue/execution pipeline. Similarly, the solid lined boxes in FIG. 4B illustrate the in-order architecture logic, while the dashed lined boxes illustrate the register renaming logic and out-of-order issue/execution logic.
In FIG. 4A, a processor pipeline 400 includes a fetch stage 402, a length decode stage 404, a decode stage 406, an allocation stage 408, a renaming stage 410, a scheduling (also known as a dispatch or issue) stage 412, a register read/memory read stage 414, an execute stage 416, a write back/memory write stage 418, an exception handling stage 422, and a commit stage 424.
In FIG. 4B, arrows denote a coupling between two or more units and the direction of the arrow indicates a direction of data flow between those units. FIG. 4B shows processor core 490 including a front end unit 430 coupled to an execution engine unit 450, and both are coupled to a memory unit 470.
The core 490 may be a reduced instruction set computing (RISC) core, a complex instruction set computing (CISC) core, a very long instruction word (VLIW) core, or a hybrid or alternative core type. As yet another option, the core 490 may be a special-purpose core, such as, for example, a network or communication core, compression engine, graphics core, or the like.
The front end unit 430 includes a branch prediction unit 432 coupled to an instruction cache unit 434, which is coupled to an instruction translation look-aside buffer (TLB) 436, which is coupled to an instruction fetch unit 438, which is coupled to a decode unit 440. The decode unit or decoder may decode instructions, and generate as an output one or more micro-operations, micro-code entry points, microinstructions, other instructions, or other control signals, which are decoded from, or which otherwise reflect, or are derived from, the original instructions. The decoder may be implemented using various different mechanisms. Examples of suitable mechanisms include, but are not limited to, look-up tables, hardware implementations, programmable logic arrays (PLAs), microcode read only memories (ROMs), etc. The instruction cache unit 434 is further coupled to a level 2 (L2) cache unit 476 in the memory unit 470. The decode unit 440 is coupled to a rename/allocator unit 452 in the execution engine unit 450.
The execution engine unit 450 includes the rename/allocator unit 452 coupled to a retirement unit 454 and a set of one or more scheduler unit(s) 456. The scheduler unit(s) 456 represents any number of different schedulers, including reservations stations, central instruction window, etc. The scheduler unit(s) 456 is coupled to the physical register file(s) unit(s) 458. Each of the physical register file(s) units 458 represents one or more physical register files, different ones of which store one or more different data types, such as scalar integer, scalar floating point, packed integer, packed floating point, vector integer, vector floating point, etc., status (e.g., an instruction pointer that is the address of the next instruction to be executed), etc. The physical register file(s) unit(s) 458 is overlapped by the retirement unit 154 to illustrate various ways in which register renaming and out-of-order execution may be implemented (e.g., using a reorder buffer(s) and a retirement register file(s), using a future file(s), a history buffer(s), and a retirement register file(s); using a register maps and a pool of registers; etc.). Generally, the architectural registers are visible from the outside of the processor or from a programmer's perspective. The registers are not limited to any known particular type of circuit. Various different types of registers are suitable as long as they are capable of storing and providing data as described herein. Examples of suitable registers include, but are not limited to, dedicated physical registers, dynamically allocated physical registers using register renaming, combinations of dedicated and dynamically allocated physical registers, etc. The retirement unit 454 and the physical register file(s) unit(s) 458 are coupled to the execution cluster(s) 460. The execution cluster(s) 460 includes a set of one or more execution units 162 and a set of one or more memory access units 464. The execution units 462 may perform various operations (e.g., shifts, addition, subtraction, multiplication) and on various types of data (e.g., scalar floating point, packed integer, packed floating point, vector integer, vector floating point). While some embodiments may include a number of execution units dedicated to specific functions or sets of functions, other embodiments may include only one execution unit or multiple execution units that all perform all functions. The scheduler unit(s) 456, physical register file(s) unit(s) 458, and execution cluster(s) 460 are shown as being possibly plural because certain embodiments create separate pipelines for certain types of data/operations (e.g., a scalar integer pipeline, a scalar floating point/packed integer/packed floating point/vector integer/vector floating point pipeline, and/or a memory access pipeline that each have their own scheduler unit, physical register file(s) unit, and/or execution cluster—and in the case of a separate memory access pipeline, certain embodiments are implemented in which only the execution cluster of this pipeline has the memory access unit(s) 464). It should also be understood that where separate pipelines are used, one or more of these pipelines may be out-of-order issue/execution and the rest in-order.
The set of memory access units 464 is coupled to the memory unit 470, which includes a data TLB unit 472 coupled to a data cache unit 474 coupled to a level 2 (L2) cache unit 476. In one exemplary embodiment, the memory access units 464 may include a load unit, a store address unit, and a store data unit, each of which is coupled to the data TLB unit 472 in the memory unit 470. The L2 cache unit 476 is coupled to one or more other levels of cache and eventually to a main memory.
By way of example, the exemplary register renaming, out-of-order issue/execution core architecture may implement the pipeline 400 as follows: 1) the instruction fetch 438 performs the fetch and length decoding stages 402 and 404; 2) the decode unit 440 performs the decode stage 406; 3) the rename/allocator unit 452 performs the allocation stage 408 and renaming stage 410; 4) the scheduler unit(s) 456 performs the schedule stage 412; 5) the physical register file(s) unit(s) 458 and the memory unit 470 perform the register read/memory read stage 414; the execution cluster 460 perform the execute stage 416; 6) the memory unit 470 and the physical register file(s) unit(s) 458 perform the write back/memory write stage 418; 7) various units may be involved in the exception handling stage 422; and 8) the retirement unit 454 and the physical register file(s) unit(s) 458 perform the commit stage 424.
The core 490 may support one or more instructions sets (e.g., the x86 instruction set (with some extensions that have been added with newer versions); the MIPS instruction set of MIPS Technologies of Sunnyvale, Calif.; the ARM instruction set (with optional additional extensions such as NEON) of ARM Holdings of Sunnyvale, Calif.).
It should be understood that the core may support multithreading (executing two or more parallel sets of operations or threads), and may do so in a variety of ways including time sliced multithreading, simultaneous multithreading (where a single physical core provides a logical core for each of the threads that physical core is simultaneously multithreading), or a combination thereof (e.g., time sliced fetching and decoding and simultaneous multithreading thereafter such as in the Intel® Hyperthreading technology).
While register renaming is described in the context of out-of-order execution, it should be understood that register renaming may be used in an in-order architecture. While the illustrated embodiment of the processor also includes a separate instruction and data cache units 434/474 and a shared L2 cache unit 476, alternative embodiments may have a single internal cache for both instructions and data, such as, for example, a Level 1 (L1) internal cache, or multiple levels of internal cache. In some embodiments, the system may include a combination of an internal cache and an external cache that is external to the core and/or the processor. Alternatively, all of the cache may be external to the core and/or the processor.
FIG. 5 is a block diagram of a single core processor and a multicore processor 500 with integrated memory controller and graphics according to embodiments of the invention. The solid lined boxes in FIG. 5 illustrate a processor 500 with a single core 502A, a system agent 510, a set of one or more bus controller units 516, while the optional addition of the dashed lined boxes illustrates an alternative processor 500 with multiple cores 502A-N, a set of one or more integrated memory controller unit(s) 514 in the system agent unit 510, and an integrated graphics logic 508.
The memory hierarchy includes one or more levels of cache within the cores, a set or one or more shared cache units 506, and external memory (not shown) coupled to the set of integrated memory controller units 514. The set of shared cache units 506 may include one or more mid-level caches, such as level 2 (L2), level 3 (L3), level 4 (L4), or other levels of cache, a last level cache (LLC), and/or combinations thereof. While in one embodiment a ring based interconnect unit 512 interconnects the integrated graphics logic 508, the set of shared cache units 506, and the system agent unit 510, alternative embodiments may use any number of well-known techniques for interconnecting such units.
In some embodiments, one or more of the cores 502A-N are capable of multi-threading. The system agent 510 includes those components coordinating and operating cores 502A-N. The system agent unit 510 may include for example a power control unit (PCU) and a display unit. The PCU may be or include logic and components needed for regulating the power state of the cores 502A-N and the integrated graphics logic 508. The display unit is for driving one or more externally connected displays.
The cores 502A-N may be homogenous or heterogeneous in terms of architecture and/or instruction set. For example, some of the cores 502A-N may be in order while others are out-of-order. As another example, two or more of the cores 502A-N may be capable of execution the same instruction set, while others may be capable of executing only a subset of that instruction set or a different instruction set.
The processor may be a general-purpose processor, such as a CoreTM i3, i5, i7, 2 Duo and Quad, XeonTM, ItaniumTM, XScaleTM or StrongARMTM processor, which are available from Intel Corporation, of Santa Clara, Calif. Alternatively, the processor may be from another company, such as ARM Holdings, Ltd, MIPS, etc. The processor may be a special-purpose processor, such as, for example, a network or communication processor, compression engine, graphics processor, co-processor, embedded processor, or the like. The processor may be implemented on one or more chips. The processor 500 may be a part of and/or may be implemented on one or more substrates using any of a number of process technologies, such as, for example, BiCMOS, CMOS, or NMOS.
FIGS. 6-8 are exemplary systems suitable for including the processor 500, while FIG. 9 is an exemplary system on a chip (SoC) that may include one or more of the cores 502. Other system designs and configurations known in the arts for laptops, desktops, handheld PCs, personal digital assistants, engineering workstations, servers, supercomputers, network devices, network hubs, switches, embedded processors, digital signal processors (DSPs), graphics devices, video game devices, set-top boxes, micro controllers, cell phones, portable media players, hand held devices, and various other electronic devices, are also suitable. In general, a huge variety of systems or electronic devices capable of incorporating a processor and/or other execution logic as disclosed herein are generally suitable.
Referring now to FIG. 6, shown is a block diagram of a system 600 in accordance with one embodiment of the present invention. The system 600 may include one or more processors 610, 615, which are coupled to graphics memory controller hub (GMCH) 620. The optional nature of additional processors 615 is denoted in FIG. 6 with broken lines.
Each processor 610,615 may be some version of the processor 500. However, it should be noted that it is unlikely that integrated graphics logic and integrated memory control units would exist in the processors 610,615. FIG. 6 illustrates that the GMCH 620 may be coupled to a memory 640 that may be, for example, a dynamic random access memory (DRAM). The DRAM may, for at least one embodiment, be associated with a non-volatile cache.
The GMCH 620 may be a chipset, or a portion of a chipset. The GMCH 620 may communicate with the processor(s) 610, 615 and control interaction between the processor(s) 610, 615 and memory 640. The GMCH 620 may also act as an accelerated bus interface between the processor(s) 610, 615 and other elements of the system 600. For at least one embodiment, the GMCH 620 communicates with the processor(s) 610, 615 via a multi-drop bus, such as a frontside bus (FSB) 695.
Furthermore, GMCH 620 is coupled to a display 645 (such as a flat panel display). GMCH 620 may include an integrated graphics accelerator. GMCH 620 is further coupled to an input/output (I/O) controller hub (ICH) 650, which may be used to couple various peripheral devices to system 600. Shown for example in the embodiment of FIG. 6 is an external graphics device 660, which may be a discrete graphics device coupled to ICH 650, along with another peripheral device 670.
Alternatively, additional or different processors may also be present in the system 600. For example, additional processor(s) 615 may include additional processors(s) that are the same as processor 610, additional processor(s) that are heterogeneous or asymmetric to processor 610, accelerators (such as, e.g., graphics accelerators or digital signal processing (DSP) units), field programmable gate arrays, or any other processor. There can be a variety of differences between the physical resources 610, 615 in terms of a spectrum of metrics of merit including architectural, micro-architectural, thermal, power consumption characteristics, and the like. These differences may effectively manifest themselves as asymmetry and heterogeneity amongst the processors 610, 615. For at least one embodiment, the various processors 610, 615 may reside in the same die package.
Referring now to FIG. 7, shown is a block diagram of a second system 700 in accordance with an embodiment of the present invention. As shown in FIG. 7, multiprocessor system 700 is a point-to-point interconnect system, and includes a first processor 770 and a second processor 780 coupled via a point-to-point interconnect 750. Each of processors 770 and 780 may be some version of the processor 500 as one or more of the processors 610,615.
While shown with only two processors 770, 780, it is to be understood that the scope of the present invention is not so limited. In other embodiments, one or more additional processors may be present in a given processor.
Processors 770 and 780 are shown including integrated memory controller units 772 and 782, respectively. Processor 770 also includes as part of its bus controller units point-to-point (P-P) interfaces 776 and 778; similarly, second processor 780 includes P-P interfaces 786 and 788. Processors 770, 780 may exchange information via a point-to-point (P-P) interface 750 using P-P interface circuits 778, 788. As shown in FIG. 7, IMCs 772 and 782 couple the processors to respective memories, namely a memory 732 and a memory 734, which may be portions of main memory locally attached to the respective processors.
Processors 770, 780 may each exchange information with a chipset 790 via individual P-P interfaces 752, 754 using point to point interface circuits 776, 794, 786, 798. Chipset 790 may also exchange information with a high-performance graphics circuit 738 via a high-performance graphics interface 739.
A shared cache (not shown) may be included in either processor or outside of both processors, yet connected with the processors via P-P interconnect, such that either or both processors' local cache information may be stored in the shared cache if a processor is placed into a low power mode.
Chipset 790 may be coupled to a first bus 716 via an interface 796. In one embodiment, first bus 716 may be a Peripheral Component Interconnect (PCI) bus, or a bus such as a PCI Express bus or another third generation I/O interconnect bus, although the scope of the present invention is not so limited.
As shown in FIG. 7, various I/O devices 714 may be coupled to first bus 716, along with a bus bridge 718 which couples first bus 716 to a second bus 720. In one embodiment, second bus 720 may be a low pin count (LPC) bus. Various devices may be coupled to second bus 720 including, for example, a keyboard and/or mouse 722, communication devices 727 and a storage unit 728 such as a disk drive or other mass storage device which may include instructions/code and data 730, in one embodiment. Further, an audio I/O 724 may be coupled to second bus 720. Note that other architectures are possible. For example, instead of the point-to-point architecture of FIG. 7, a system may implement a multi-drop bus or other such architecture.
Referring now to FIG. 8, shown is a block diagram of a third system 800 in accordance with an embodiment of the present invention. Like elements in FIGS. 7 and 8 bear like reference numerals, and certain aspects of FIG. 7 have been omitted from FIG. 8 in order to avoid obscuring other aspects of FIG. 8.
FIG. 8 illustrates that the processors 870, 880 may include integrated memory and I/O control logic (“CL”) 872 and 882, respectively. For at least one embodiment, the CL 872, 882 may include integrated memory controller units such as that described above in connection with FIGS. 5 and 7. In addition, CL 872, 882 may also include I/O control logic. FIG. 8 illustrates that not only are the memories 832, 834 coupled to the CL 872, 882, but also that I/O devices 814 are also coupled to the control logic 872, 882. Legacy I/O devices 815 are coupled to the chipset 890.
Referring now to FIG. 9, shown is a block diagram of a SoC 900 in accordance with an embodiment of the present invention. Similar elements in FIG. 5 bear like reference numerals. Also, dashed lined boxes are optional features on more advanced SoCs. In FIG. 9, an interconnect unit(s) 902 is coupled to: an application processor 910 which includes a set of one or more cores 902A-N and shared cache unit(s) 906; a system agent unit 910; a bus controller unit(s) 916; an integrated memory controller unit(s) 914; a set or one or more media processors 920 which may include integrated graphics logic 908, an image processor 924 for providing still and/or video camera functionality, an audio processor 926 for providing hardware audio acceleration, and a video processor 928 for providing video encode/decode acceleration; an static random access memory (SRAM) unit 930; a direct memory access (DMA) unit 932; and a display unit 940 for coupling to one or more external displays.
FIG. 10 illustrates a processor containing a central processing unit (CPU) and a graphics processing unit (GPU), which may perform at least one instruction according to one embodiment. In one embodiment, an instruction to perform operations according to at least one embodiment could be performed by the CPU. In another embodiment, the instruction could be performed by the GPU. In still another embodiment, the instruction may be performed through a combination of operations performed by the GPU and the CPU. For example, in one embodiment, an instruction in accordance with one embodiment may be received and decoded for execution on the GPU. However, one or more operations within the decoded instruction may be performed by a CPU and the result returned to the GPU for final retirement of the instruction. Conversely, in some embodiments, the CPU may act as the primary processor and the GPU as the co-processor.
In some embodiments, instructions that benefit from highly parallel, throughput processors may be performed by the GPU, while instructions that benefit from the performance of processors that benefit from deeply pipelined architectures may be performed by the CPU. For example, graphics, scientific applications, financial applications and other parallel workloads may benefit from the performance of the GPU and be executed accordingly, whereas more sequential applications, such as operating system kernel or application code may be better suited for the CPU.
In FIG. 10, processor 1000 includes a CPU 1005, GPU 1010, image processor 1015, video processor 1020, USB controller 1025, UART controller 1030, SPI/SDIO controller 1035, display device 1040, memory interface controller 1045, MIPI controller 1050, flash memory controller 1055, dual data rate (DDR) controller 1060, security engine 1065, and I2S/I2C controller 1070. Other logic and circuits may be included in the processor of FIG. 10, including more CPUs or GPUs and other peripheral interface controllers.
One or more aspects of at least one embodiment may be implemented by representative data stored on a machine-readable medium which represents various logic within the processor, which when read by a machine causes the machine to fabricate logic to perform the techniques described herein. Such representations, known as “IP cores” may be stored on a tangible, machine readable medium (“tape”) and supplied to various customers or manufacturing facilities to load into the fabrication machines that actually make the logic or processor. For example, IP cores, such as the CortexTM family of processors developed by ARM Holdings, Ltd. and Loongson IP cores developed the Institute of Computing Technology (ICT) of the Chinese Academy of Sciences may be licensed or sold to various customers or licensees, such as Texas Instruments, Qualcomm, Apple, or Samsung and implemented in processors produced by these customers or licensees.
FIG. 11 shows a block diagram illustrating the development of IP cores according to one embodiment. Storage 1130 includes simulation software 1120 and/or hardware or software model 1110. In one embodiment, the data representing the IP core design can be provided to the storage 1130 via memory 1140 (e.g., hard disk), wired connection (e.g., internet) 1150 or wireless connection 1160. The IP core information generated by the simulation tool and model can then be transmitted to a fabrication facility where it can be fabricated by a 3rd party to perform at least one instruction in accordance with at least one embodiment.
In some embodiments, one or more instructions may correspond to a first type or architecture (e.g., x86) and be translated or emulated on a processor of a different type or architecture (e.g., ARM). An instruction, according to one embodiment, may therefore be performed on any processor or processor type, including ARM, x86, MIPS, a GPU, or other processor type or architecture.
FIG. 12 illustrates how an instruction of a first type is emulated by a processor of a different type, according to one embodiment. In FIG. 12, program 1205 contains some instructions that may perform the same or substantially the same function as an instruction according to one embodiment. However the instructions of program 1205 may be of a type and/or format that is different or incompatible with processor 1215, meaning the instructions of the type in program 1205 may not be able to be executed natively by the processor 1215. However, with the help of emulation logic, 1210, the instructions of program 1205 are translated into instructions that are natively capable of being executed by the processor 1215. In one embodiment, the emulation logic is embodied in hardware. In another embodiment, the emulation logic is embodied in a tangible, machine-readable medium containing software to translate instructions of the type in the program 1205 into the type natively executable by the processor 1215. In other embodiments, emulation logic is a combination of fixed-function or programmable hardware and a program stored on a tangible, machine-readable medium. In one embodiment, the processor contains the emulation logic, whereas in other embodiments, the emulation logic exists outside of the processor and is provided by a third party. In one embodiment, the processor is capable of loading the emulation logic embodied in a tangible, machine-readable medium containing software by executing microcode or firmware contained in or associated with the processor.
FIG. 13 is a block diagram contrasting the use of a software instruction converter to convert binary instructions in a source instruction set to binary instructions in a target instruction set according to embodiments of the invention. In the illustrated embodiment, the instruction converter is a software instruction converter, although alternatively the instruction converter may be implemented in software, firmware, hardware, or various combinations thereof. FIG. 13 shows a program in a high level language 1302 may be compiled using an x86 compiler 1304 to generate x86 binary code 1306 that may be natively executed by a processor with at least one x86 instruction set core 1316. The processor with at least one x86 instruction set core 1316 represents any processor that can perform substantially the same functions as a Intel processor with at least one x86 instruction set core by compatibly executing or otherwise processing (1) a substantial portion of the instruction set of the Intel x86 instruction set core or (2) object code versions of applications or other software targeted to run on an Intel processor with at least one x86 instruction set core, in order to achieve substantially the same result as an Intel processor with at least one x86 instruction set core. The x86 compiler 1304 represents a compiler that is operable to generate x86 binary code 1306 (e.g., object code) that can, with or without additional linkage processing, be executed on the processor with at least one x86 instruction set core 1316. Similarly, FIG. 13 shows the program in the high level language 1302 may be compiled using an alternative instruction set compiler 1308 to generate alternative instruction set binary code 1310 that may be natively executed by a processor without at least one x86 instruction set core 1314 (e.g., a processor with cores that execute the MIPS instruction set of MIPS Technologies of Sunnyvale, Calif. and/or that execute the ARM instruction set of ARM Holdings of Sunnyvale, Calif.). The instruction converter 1312 is used to convert the x86 binary code 1306 into code that may be natively executed by the processor without an x86 instruction set core 1314. This converted code is not likely to be the same as the alternative instruction set binary code 1310 because an instruction converter capable of this is difficult to make; however, the converted code will accomplish the general operation and be made up of instructions from the alternative instruction set. Thus, the instruction converter 1312 represents software, firmware, hardware, or a combination thereof that, through emulation, simulation or any other process, allows a processor or other electronic device that does not have an x86 instruction set processor or core to execute the x86 binary code 1306.
FIG. 14A is an illustration of a variable precision floating point circuit 1400 according to one embodiment. The variable precision floating point circuit 1400 may include a variable precision mantissa unit 1402 and a plurality of exponent units 1404.1 ̃1404.4. Each exponent unit 1404.1 ̃1404.4 may include an exponent portion and a certainty calculation unit, respectively. The variable precision floating point circuit 1400 may support a plurality of precision modes with a single mantissa unit. For example, FIG. 14B illustrates a plurality of operation modes according to one embodiment. The variable precision mantissa unit 1402 may include circuitry to be selectively used as one high precision unit, two parallel middle precision units or four parallel low precision units. When the variable precision mantissa unit 1402 is operating in the high precision mode, only one exponent unit (e.g., one of the exponent unit 1404.1 ̃1404.4) may be used. When the variable precision mantissa unit 1402 is operating in the middle precision mode, two of the four exponent units 1404.1 ̃1404.4 may be selected for use. When the variable precision mantissa unit 1402 is operating in the low precision mode, all four exponent units 1404.1 ̃1404.4 may be used that each corresponds to a respective one of the four parallel low precision units.
As shown in FIG. 14B, as an example, the high precision may be single precision (e.g., 24 bits) with 5b certainty, the middle precision may be 12 bits precision with 4b certainty, and the low precision may be 6 bits precision with 3b certainty. In addition to the certainty bits, there are a sign bit and 8 bits of exponent for each precision mode. As shown in FIG. 14B, the greyed out areas of the sign, exponent and mantissa values in the high precision mode are typically stored in a conventional single-precision machine.
In one embodiment, the variable precision floating point circuit 1400 may be a floating point multiply-add (FMA) circuit. That is, the variable precision floating point circuit 1400 may multiply two inputs A and B, and add the result of the multiplication to a third input C. If either the third input C or the multiplication result is negated, then the multiply-add may in fact be a multiply-subtract, and whether the final result is greater than zero may indicate a comparison result between A×B and C. Thus, the multiply-add circuit may be used for comparing a multiplication result of two inputs to another number.
The certainty calculation unit for each exponent units 1404.1 ̃1404.4 may enable the variable precision floating point circuit 1400 to compute certainty of computation results based on certainties of the inputs simultaneously when computing the computation results. This certainty tracking capability may enable operating in the lowest precision mode with highest parallelism for most computations and increasing computation precision only when detected errors are large enough to affect the output of the program. Therefore, embodiments of the present invention may achieve higher efficiency by operating at low-precision most of the time, detecting in parallel if the output certainty affects the result and may reconfigure to a higher precision mode when needed to maintain accuracy. Thus, power and performance of floating point calculations may be improved without sacrificing quality.
The right shift (RS) signals from the exponent units 1404.1 ̃1404.4 to the variable precision mantissa unit 1402 may be used for shifting portions of the third input to be aligned with the multiplier output in the variable precision mantissa unit 1402. In lower precision modes, each of the inputs A and B may include multiple low precision numbers. For example, in the lowest precision mode, each of the inputs A and B may include four 6 bits numbers arranged as shown in FIG. 14B for the 6b mantissa portion. The third input C may be right shifted and aligned with the multiplication result to be added with the multiplication result. Thus, four separate right shift signals may be computed by the four exponent units in 6b mode. The left shift signals (LS) from the variable precision mantissa unit 1402 to the exponent units 1404.1 ̃1404.4 may be used for output exponent computation for normalized multiply-add results. The details of the right shift and left shift will be described in detail below.
FIG. 15 is an illustration of a variable precision floating point mantissa unit 1500 according to one embodiment. The variable precision floating point mantissa unit 1500 may comprise a multiplier 1502, a right shifter 1504, a carry-save add 1506, an adder 1508, a multiplexer 1510, a normalization left shifter 1512, a round-up incrementer 1514, a left shift (LS) compute unit 1516 and an incrementer 1518. As an example, the variable precision floating point mantissa unit 1500 uses 24 bits precision as the maximum precision, other embodiments of the variable precision floating point mantissa unit may have different bit width.
The multiplier 1502 may be a 24 bits times 24 bits (24b×24b) multiplier that receives two inputs A and B each with 24 bits. The output of the multiplier 1502 may be left in carry-save format to defer carry-propagation till after the carry-save summation with the addend (e.g., the third input C). Mantissa alignment for the addend may be removed from the datapath of the carry-save multiplication result by making the alignment operation parallel to the multiplier. The preshifted addend from the third input C may go through the alignment right shifter 1504, with the right shift amount computed by the exponent unit based on the exponents of the inputs A, B and C. In an embodiment, the right shift operation for the addend may be performed by the alignment right shifter 1504 in parallel to the multiplication operation performed by the multiplier 1502.
The aligned addend from the third input C may be summed with the 48b multiplier output at the carry-save adder 1506. In an embodiment, the carry-save adder 1506 may be a 3:2 compressor that takes three inputs (e.g., carry-save multiplication result from the multiplier 1502, and the aligned addend from the third input C) and generates two outputs (e.g., a sum and a carry).
The two outputs of the carry-save adder 1506 may be input to the adder 1508. In an embodiment, the adder 1508 may be a sparse carry-tree 48b adder that may convert the lower 48b of the sum from carry-save to a positive 2's complement format. Significant bits to the left of the multiplier may be affected only by the adder carry-out and computed by the incrementer 1518. In an embodiment, the incrementer 1518 may be a 24b incrementer. The output from the incrementer 1518 and the summation result from the adder 1508 may be combined to form a multiplication add result at the output of the adder/incrementer stage.
In the example shown in FIG. 15, this multiplication add result may contain 72 bits (72b). The multiplication add result may be input to the normalization shifter 1512 via the multiplexer 1510. However, not all 72b are required for a normalization stage. Thus, in an embodiment, based on the operation precision and whether the upper 1⁄3rd bits of the mantissa are zero, the appropriate set of 48 bits may be selected for the normalization left shift at the normalization left shifter 1512.
The left shift amounts for the normalization left shifter 1512 may be encoded and computed in parallel to the add operation by the LS Compute unit 1516. The left shift amounts may also be sent to the exponent units for output exponent computation. The final round-up incrementer 1514 may round up the truncated normalized mantissa based on the rounding mode and any resulting overflow bit may be sent to the exponent unit for updating the output exponent computation.
Embodiments of the variable precision floating point mantissa unit 1500 provide a number of features to improve energy efficiency over fixed-precision operations. In an embodiment, only the addend may need to be aligned with respect to the multiplier, thus removing the alignment shifter from the mantissa critical path. Also, the addend may be preshifted to the left so that the alignment shifter needs to perform only right shift operations. Parallelization of alignment and multiplication operations may reduce the area of a single-precision mantissa unit.
Further, in an embodiment, if the output of the 48b adder during a subtract operation has to be negated, after inversion the addition of “1” required to maintain 2's complement format may be delayed till after the normalization stage and performed by the round-up incrementer. Removal of an incrementer from the critical path may further reduce the area of a single-precision mantissa unit.
Moreover, in an embodiment, for subtract operations, only the lower 48b of the aligned addend may need to be negated. This may dramatically reduce the number of negation XORs. For example, in an embodiment, the number of negation XORs may be reduced by 67%.
Overall, compared to a single-precision mantissa datapath, the variable precision floating point mantissa unit 1500 may treat each input operand either as a single precision mantissa (24b), two independent 12b mantissas or four independent 6b mantissas with minimal performance, power and area overhead.
FIG. 16 illustrates a multiplier 1600 according to one embodiment. The multiplier 1600 may be an embodiment for the multiplier 1502 of FIG. 15. The multiplier 1600 may be divided into a plurality of zones 1602.1 ̃1602.4, 1604 and 1606. In an embodiment, the multiplier 1600 may be an unsigned multiplier that uses a unified compressor tree across all modes. The compressor tree may be designed to produce a 48b carry-save output for 24b multiplies. For 24b multiplication, all zones of the multiplier 1600 may be used. In lower precision modes, partial products that do not lie along the diagonal may be set to zero to enable the compressor tree to produce the result of parallel smaller multipliers. For example, for 12b multiplication, the zone 1604 may be set to zero; for 6b multiplication, the zones 1604 and 1606 may be set to zero. Also, in 6b multiplication, the zone 1602.1 may contain the partial products of a[5:0]×b[5:0], the zone 1602.2 may contain the partial products of a[11:6]×b[11:6], the zone 1602.3 may contain the partial products of a[17:12]×b[17:12] and the zone 1602.4 may contain the partial products of a[23:18]×b[23:18].
In an embodiment, one of the inputs (e.g., input b) may be radix-4 Booth-encoded. The Booth select signals for the partial product rows may be locally gated at the granularity of every 6 multiplexors to force those partial product segments to a zero output based on the precision mode. Selective gating of unused partial products in lower precision modes may reduce consumed multiplier power (e.g., 56% (36%) in 6b (12) mode).
FIG. 17A illustrates right shifts for different operation modes of a right shifter according to one embodiment. The right shifter may be the variable precision right shifter 1504 of FIG. 15. The variable precision shifter may combine the functionality of a single 72b shifter, two parallel 36b shifters and four parallel 18b shifters to support 24b, 12b and 6b precision modes, respectively. In the lower precision modes, the shifter aligns and packs the lower 6b (12b) of each of the shifted addends with the respective multiplier outputs as shown in FIG. 17A. Four separate rights shift signals (RS0-RS3) may be used in different sections of the shifter. Since four parallel operations are handled in 6b mode, all shift amounts can be different and may be computed by four independent exponent units. In 12b mode, the right shift amount from 2 separate exponent units may be broadcast over pairs of right shift signals internally, while in 24b mode the right shift amount from one of the exponent units may be broadcast over all right shift signals of the shifter.
FIG. 17B illustrates a plurality of shift stages of a right shifter according to one embodiment. In this embodiment, seven shift stages may be required to enable up to 72b right shift in the single-precision mode. The location of modified circuits along with circuits that are added to the single-precision (SP) shifter to enable the variable precision functionality are shown in FIG. 17B. Addition of variable precision functionality may be enabled without increasing the number of shift stages in the critical path. Circuit optimizations resulting in minimal performance impact for precision boundary crossings are shown in FIG. 17C for one of the shift stages. Any bit may cross such a boundary only once during the entire shift operation. Note that in a conventional shifter targeted for fixed precision operation, each stage could use identical circuits such as 2:1 multiplexers with the connections at each stage different to enable different shift amounts at each stage of the shifter. In this embodiment the shifter is modified to enable the overall shift functionality illustrated in FIG. 17A that takes into account boundaries that separate different numbers at lower precisions (such may be referred to as precision boundaries). FIG. 17C is an example of a circuit to enable this for a shift operation for one bit in the 2nd stage (which performs a shift by 2).
FIG. 18 illustrates a sparse carry-tree adder 1800 according to one embodiment. The adder 1800 may be used as the carry-save adder 1506. As shown in FIG. 18, the sparse carry-tree adder 1800 may comprise a propagate-generate (PG) stage 1802, a sparse carry-merge tree 1804 and 4b conditional sum generators 1806. The carry-merge tree 1804 may comprise a plurality of carry-merge stages CM0, CM1, CM2, CM3, CM4, CM5. In an embodiment, the carry-merge tree 1804 may compute every 4th carry bit (e.g., C3, C7, . . . , C43 as shown in FIG. 18)) for sending to the sum generators 1806, thus reducing wiring (e.g., by 75% compared to a Kogge-Stone adder).
In operation modes other than the highest precision, the PG stage 1802 may contain multiple operands that each occupies several consecutive bits. The PG stage 1802 may generate carry-kill signals at appropriate operand boundaries within the PG block of the adder 1800 to prevent carry propagation from one operand to a next operand. The carry-kill signals may also enable the adder 1800 to act as either two 24b adders or four 12b adders. An example circuit to generate the carry-kill signal is shown in block 1808.
FIG. 19 illustrates a left shift computation unit 1900 according to one embodiment. The left shift computation unit 1900 may be used as the LS Compute unit 1516 of FIG. 15. The left shift amount computation for the normalization stage in single-precision mode depends on whether the upper or lower 48b of the 72b sum are selected. For the case where upper 48b are selected, the left shift amount may be the same as the alignment right shift amount (e.g., RS0, RS1, RS2, RS3) decremented by 1 for addition operations. When the lower 48b are selected, the left shift amount may be computed by a 48b leading zero anticipation (LZA) circuit 1902 that uses the same inputs as the 48b adder (e.g., the 48b adder 1508). Since the upper or lower 48b amount selection is done only after summation at the 48b adder, both left shift amounts may be computed in parallel to remove them from the critical datapath and the correct amount may be selected for normalization. As shown in FIG. 19, for different modes of operations, the left shift computation unit 1900 may comprise four decrementers for the four right shift amounts (e.g., RS0, RS1, RS2, RS3). Further, the LZA unit 1902 may produce one, two or four left shift amounts (e.g., LSL0, LSL1, LSL2, LSL3) by treating its inputs as a pair of 48b operands, two 24b operand pairs or four 12b operand pairs.
FIG. 20 illustrates a leading zero anticipation circuit 2000 according to one embodiment. The LZA circuit 2000 may be a reconfigurable LZA circuit and may be used as the LZA unit 1902 of FIG. 19. The LZA circuit 2000 may comprise a LZA string generation stage 2002 and a leading “1” detection stage 2004. The LZA string generation stage 2002 may generate a logical string from the inputs to the 48b adder in FIG. 15 (e.g., the propagate-generate signals (p,g) from the PG block of the adder stage), with 1's in this string indicating possible positions of leading zeros or ones. In this embodiment, a “1” indicates that the final sum could contain a leading 1 or 0 starting from the MSB as a transition from 1-to-0 or 0-to-1 in the add result. The string generation logic may be modified to recognize 12b operand boundaries based on the precision modes.
The LZA string generation stage 2002 may comprise a plurality of circuit gray blocks and white blocks. One exemplary gray block 2006 and one exemplary white block 2008 are shown in detail. The white block 2008 may be a conventional LZA string bit generation circuit and the gray block 2006 may show modifications to the conventional single-precision (SP) LZA string bit generation circuit. In this embodiment, each white box generates a “1” based on a 3-bit moving window (the window comprises the previous, current and next bits). LSB and boundaries require adjustments for subtract operations (indicated by the signal “sub”) while the “kill” signal breaks the moving window.
The leading “1” detection stage 2004 may be a hierarchical priority encoding circuit (e.g., a hierarchical tree). The hierarchical priority encoding of the logical string may be used to generate the encoded left shift amount for the left-most “1” in this string. Encoding of the position of the left-most “1” in this string is accordingly modified by the hierarchical tree that not only accounts for precision-based operand boundaries in the string but also generates multiple separate shift encodings without increasing the depth of the tree. Circuit blocks, such as, the block 2010, may be added to a conventional SP LZA tree structure. Further, and circuit blocks, such as, the block 2012, may be modified from a conventional SP LZA tree structure. These circuit modifications to a conventional single-precision (SP) LZA tree structure may enable a minimum overhead reconfigurable LZA with multiple parallel shift amounts. Left shift counts are computed hierarchically for larger groups at each stage by the circuits shown in block 2010. This may be done by detecting whether the sub-group toward the MSB contains a “1” (denoted by the signal “detonein1”), using the appropriate sub-group's left shift count “posin” and adding a bit to the left of the sub-group's left-shift count to produce the left shift count for the larger group (“posout”). The circuit shown in block 2012 is a modified form of the circuit of block 2010 so that using the “kill” signal enables an encoding that ignores sub-groups to the right of a boundary between 2 numbers at lower precisions.
FIG. 21 illustrates a plurality of operation modes of a left shifter according to one embodiment. An exemplary left shifter (e.g., left shifter 1512) may use the left shift amounts to normalize the mantissa(s) after the summation stage. The exemplary shifter may support a plurality of precision modes. For example, the left shifter may combine the functionality of a single 48b shifter, two parallel 24b shifters and four parallel 12b shifters to support 24b, 12b and 6b precision modes, respectively. In the single-precision mode, the upper 24b of the normalized mantissa may be aligned and sent to a round-up incrementer (e.g., the round-up incrementer 1514). In the lower precision modes, the inputs to the left shifter may have the upper 6b (12b) of each of the unnormalized mantissas packed into the upper 24b. The left shifter may maintain these precision-based boundary conditions so that the upper 6/12b outputs may be aligned with the round-up incrementer.
Four separate left shift signals (LS0-LS3) may be used in different sections of the left shifter. Since four parallel operations may be handled in 6b mode, all shift amounts for the four parallel operations can be different. In 12b mode the correct left shift amounts may be broadcast over pairs of left shift signals of the left shifter internally. In 24b mode the correct left shift amount may be broadcast over all left shift signals of the left shifter internally. In one embodiment, the left shifter may need 6 shift stages to accommodate up to 48b left shift, followed by a final stage for a possible left shift by 1. Similar to the alignment shifter (e.g., the right shifter 1504), the variable precision functionality does not change the number of shift stages in the normalization shifter critical path.
FIG. 22 illustrates a variable precision incrementer 2200 according to one embodiment. The variable precision incrementer 2200 may be used in the upper 24b of the summation stage and also for the increment operation in the rounding stage of the mantissa unit. In an embodiment, the variable precision incrementer 2200 may have a plurality of operation modes to support different precisions. For example, for a 24 incrementer, the variable precision incrementer 2200 may operate as either a single 24b incrementer, two parallel 12b incrementers or four parallel 6b incrementers, with the inputs a and outputs out packed into 24b in all modes.
As shown in FIG. 22, 24 input signals a23-0 may be XORed with four sub signals to generate signals ma0-23. In particular, each of a5-0 may be XORed with the sub signal sub0 to generate signals ma5-0, each of a11-6 may be XORed with the sub signal sub1 to generate signals ma11-6, each of a17-12 may be XORed with the sub signal sub2 to generate signals ma17-12, and each of a23-18 may be XORed with the sub signal sub3 to generate signals ma23-18. The four sub signals may indicate whether the circuit is in increment or decrement mode. In an embodiment, the four sub signals (sub0, sub1, sub2 and sub3) may be independent in 6b precision mode and correlated in 24b and 12b modes (e.g., in 24b precision: sub0=sub1=sub2=sub3, and in 12b precision: sub0=sub1, sub2=sub3).
The incrementer 2200 may use the increment signals (Cin) as the latest arriving inputs. All four Cin signals may be used in 6b mode, while only the relevant ones are used in 12b and 24b modes. Up to four carry-out signals (Cout) may be generated by the circuit in 6b mode. The incrementer 2200 may comprise a single mux (e.g., 2202, 2204 and 2206) in the critical path from each Cin to outputs. “6b Incr” circuits at the bottom of FIG. 22 may be optimized to use these late arriving 6b increment signals for increment computations at the 6b level as described above.
FIG. 23 illustrates a certainty tracking circuit 2300 according to one embodiment. In contrast to prior work on tracking accuracy (e.g., interval arithmetic), an embodiment of the present invention may use exponent-only certainty calculation. In the exponent-only certainty calculation, a certainty field (Err) may be added for tracking the number of certain bits within the mantissa. For example, for two positive floating point input numbers a and b, the addition result may be calculated as r=a+b and the result's error may be obtained as rerr=max (aerr, berr)+1. Thus, the upper and lower bounds of r may be obtained as rmax=r+2rerr and rmin=r−2rerr. Compared to the interval arithmetic, which typically obtains rmax as amax+bmax and rmin=amin bmin, this approach may underestimate the certainty to prevent an incorrect result but simplify the circuit requirements to limit extra circuits in the exponent datapath.
The certainty field may be given as input to the multiply-add operation with each input operand and the resulting certainty may be calculated and output with the result. The Err field may represent how many bits of the mantissa are certain, such that the error in the result is within the bounds of ±2E-Err. During calculation of the Err field for the result, the final Err may be rounded up to the next power of 2, so that no uncertain mantissa bit is considered certain. Because the Err field is relative to the exponent, it may only need enough bits to represent all positions within the mantissa (3b Err for 6b mantissa, 4b Err for 12b mantissa, 5b Err for 24b mantissa, 6b Err for 53b mantissa). Further, operations to compute Err may involve inexpensive narrow bit-width integer addition, subtraction or comparison.
In an embodiment, three inputs A, B and C may be given for a floating point multiply-add calculation. Certainty for the three inputs may be represented by ErrA, ErrB, and ErrC, respectively. Certainty ErrO associated with the result O may be calculated pessimistically taking into account the contribution from the certainty of all three inputs and the final rounding. This certainty calculation also takes into account the operand numbers, themselves, and the operations being performed (add/subtract). With EA/EB/EC/EO as exponents of A/B/C/O, ErrA/ErrB/ErrC/ErrO as certainty of A/B/C/O, ΔA/ΔB/ΔC/ΔO as error bounds of A/B/C/O, ΔR=Rounding Error, and N=Precision, these calculations may be shown below in table 1.








TABLE 1











(1)             (2)         (3)


 


{M0, M1, M2} = Sort[(EA + EB + 1 − ERRA), (EA + EB + 1 − ERRB), (EC − ERRC), (EO − N)]
(4)


ErrO = EO − M0 − 1 − ((M1= =M0) or (M2= =M1= =(M0 − 1)))
(5)









In an embodiment, A and B values in the B*ΔA and A*ΔB error terms in equation (2) may be maximized by setting their mantissas to 2, resulting in a maximum value of 2EA+1 and 2EB+1. An additional error term 2EA+EB−ERRA−ERRB, which is due to the product ΔA*ΔB, may be accounted for by adding a “1” to the multiplication in an appropriate compressor column (e.g., the carry-save adder 1506). This operation may have the effect of recentering the product about the center O enabling a smaller value for ΔO.
Referring to FIG. 23, the certainty tracking circuit 2300 may comprise exponent datapath circuits from input exponents EA, EB and EC to result exponent EO, in which EP is an exponent product result and EN is an exponent normalized result. The certainty tracking circuit 2300 may further comprise certainty calculation circuits from input certainties ErrA, ErrB and ErrC to result certainty ErrO, in which ErrP is the minimum relative certainty of ErrA and ErrB and ErrN is the result certainty relative to the normalized result before rounding or accounting for the smaller certainty terms. The certainty logic may sort the input and rounding error components, shown in equation (3), to find the largest one. As shown in FIG. 23, the certainty tracking circuit 2300 may comprise a circuit block 2302 to find the minimum relative certainty ErrP of ErrA and ErrB, which may be achieved by finding a maximum of 2Eb+1+Ea−ErrA and 2Ea+1+Eb−ErrB or by comparing (EA+EB+1−ERRA) to (EA+EB+1−ERRB). That is, max(2Eb+1+Ea−ErrA,2Ea+1+Eb−ErrB)→min(ErrA,ErrB). The certainty tracking circuit 2300 may also comprise a circuit block 2304 to find the minimum absolute certainty of ErrP and ErrC. The circuit block 2304 may generate a comparison signal of “ΔC>ΔP,” which may be true if (EC−ERRC)>max[(EA+EB+1−ERRA), (EA+EB+1−ERRB)]. The certainty tracking circuit 2300 may further comprise a circuit block 2306 to adjust certainty for new exponent. In an embodiment, an extra circuit block (not shown) may be used to generate a comparison signal that is true if

(EO−N)>max[(EA+EB+1−ERRA),(EA+EB+1ERRB),(EC−ERRC)].

Minimum relative certainty is actually a simpler form of finding larger absolute uncertainty from the multiplier absolute certainty terms. The certainty tracking circuit 2300 finds the relative certainty term associated with maximum absolute certainty term and then adjusts it to make it relative to the result exponent (prior to normalization and rounding) using existing computations within the exponent circuit. Any computational adjustments for normalization, rounding certainty, rounding overflow and smaller certainty terms are then performed on this relative certainty term directly. Accordingly, the comparison signal for EO−N>max[ . . . ] (above) is taken care of by the computation min(ErrN, Precision) shown in FIG. 23. In an embodiment, 1 or 2 is subtracted from (not added to) the output certainty to account for the smaller terms.
The certainty calculation circuit may reuse intermediate computations from the exponent unit and reduce hardware cost. The output certainty may be computed relative to the output exponent by subtracting the computed error from the output exponent. Since the normalization left shift amounts and mantissa rounding overflow signals affect the output exponent, these signals are also used within the certainty logic to compute ErrO. The table in the lower right of FIG. 23 represents functionality of the circuit that performs the detection for the extra 1 subtraction based on equation (5) in Table 1 above.
Unlike integer multiplication, the result of floating point multiplication is only an approximation to the real theoretical result. Further, for inputs and an output in normal form (e.g., implied leading one in mantissa), the multiplication of the mantissas of the two n-bit inputs A (A=1.a0a1 . . . an-1) and B (B=1.b0b1 . . . bn-1) may amount to 1≦A*B<4 (because 1≦A,B<2). However, the result, C=A*B, will also be converted to normal form, meaning that the 2n bits that result from multiplying A and B will be truncated and C will ultimately consist of the first n bits after the leading 1 of the multiplication. Therefore, an exemplary multiplier may achieve a power savings by clock gating some lower portions of the multiplier result, taking advantage of the fact that rarely does it impact the final result. FIG. 24 is an illustration of gate-clocking of a floating point multiplier 2400 according to one embodiment. In an embodiment, the floating point multiplier 2400 may be a booth encoded multiplier but also may be other multipliers.
The floating point multiplier 2400 may comprise a plurality of points forming a parallelogram 2402 and a detection circuit 2404. Each point in the parallelogram may represent a 3-2 full carry save adder (CSA), with carries pushed to the left. The three inputs may be a) the AND of a pair of the input bits, b) the ‘save’ portion of the Carry-Save Adder above it and c) the ‘carry’ from the CSA above and to the right of it. The parallelogram 2402 may be delineated into a result region, a carry region and a gated region. The result region may be determined by the precision of the multiplication operation. For example, for a 24b×24b multiplier, the result region may be 24 bits wide and for a 32b×32b multiplier, the result region may be 32 bits wide. The width of the gated region may be set depending on energy saving needs (e.g., 42nd bits from the most significant bit (MSB) in a 32b×32b multiplier). The detection circuit 2404 may detect whether the lowest portion of the result could have affected the result and induce a replay of the full multiplication if necessary (e.g., the full result may be needed due to carries that ripple across many bit positions).
In a multiplication operation, the gated region may be data-gated that all of the carries in this region may be replaced with hard-wired zeroes. In addition, the previous cycle's inputs to all of the inputs to the logic in the gated region may be latched to keep the internal nodes from toggling. Moreover, any pipestage latches in the gated region may use the same conditionally gated clock in order to eliminate unnecessary data movement, therefore further reducing energy.
In an embodiment, there may be a maximum possible carry that may move from the gated region into the carry region. If that maximum carry propagation path into the result region exists, the correct multiplication result may not be guaranteed. The maximum carry is less than 2k (where k is the width of the gated region in bits), so if the value of the carry region is greater than 2n-k−2k (where n is the width of the carry region in bits), then a carry from the gated region may escape into the result region. In one embodiment, the detection circuit 2404 may be a rather simple and inexpensive circuit that detects all 1's in the upper n−k−log (2k) (log base 2) bits of the carry region. This may provide a slightly higher false-positive rate than necessary (ie. replay the multiplication more than really need to). In another embodiment, the detection circuit 2404 may detect all 1's in the upper n−k−log (2 k) (log base 2) bits and further include an adder (with one fixed input (shown in dashed arrow in FIG. 24)) on the lower log (2k) (log base 2) bits of the carry region.
In some situations, the result of the multiply may be greater than 2, meaning that the carry region may be actually one bit larger (because the leading one has shifted to the left because the product of the two operands are greater than 2)—this happens with probability 2∫12x−1dx−1=2(1−ln (2))≅0.61 (assuming that the bits of input operands are equally likely to be ones as zeroes). When this happens, it is approximately half as likely to have a false-positive. In an embodiment, to take advantage of this, the carry region may make a check state in the carry region when the leading bit is shifted to the left and the detection circuit 2404 may detect that check state as an input.
Embodiments of the variable precision floating point circuit may be implemented in hardware, software, firmware, or a combination of such implementation approaches. Embodiments of the invention may be implemented as computer programs or program code executing on programmable systems comprising at least one processor, a storage system (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device.
Program code may be applied to input instructions to perform the functions described herein and generate output information. The output information may be applied to one or more output devices, in known fashion. For purposes of this application, a processing system includes any system that has a processor, such as, for example; a digital signal processor (DSP), a microcontroller, an application specific integrated circuit (ASIC), or a microprocessor.
The program code may be implemented in a high level procedural or object oriented programming language to communicate with a processing system. The program code may also be implemented in assembly or machine language, if desired. In fact, the mechanisms described herein are not limited in scope to any particular programming language. In any case, the language may be a compiled or interpreted language.
One or more aspects of at least one embodiment may be implemented by representative instructions stored on a machine-readable medium which represents various logic within the processor, which when read by a machine causes the machine to fabricate logic to perform the techniques described herein. Such representations, known as “IP cores” may be stored on a tangible, machine readable medium and supplied to various customers or manufacturing facilities to load into the fabrication machines that actually make the logic or processor.
Such machine-readable storage media may include, without limitation, non-transitory, tangible arrangements of articles manufactured or formed by a machine or device, including storage media such as hard disks, any other type of disk including floppy disks, optical disks, compact disk read-only memories (CD-ROMs), compact disk rewritable's (CD-RWs), and magneto-optical disks, semiconductor devices such as read-only memories (ROMs), random access memories (RAMs) such as dynamic random access memories (DRAMs), static random access memories (SRAMs), erasable programmable read-only memories (EPROMs), flash memories, electrically erasable programmable read-only memories (EEPROMs), magnetic or optical cards, or any other type of media suitable for storing electronic instructions.
Accordingly, embodiments of the invention also include non-transitory, tangible machine-readable media containing instructions or containing design data, such as Hardware Description Language (HDL), which defines structures, circuits, apparatuses, processors and/or system features described herein. Such embodiments may also be referred to as program products.
In some cases, an instruction converter may be used to convert an instruction from a source instruction set to a target instruction set. For example, the instruction converter may translate (e.g., using static binary translation, dynamic binary translation including dynamic compilation), morph, emulate, or otherwise convert an instruction to one or more other instructions to be processed by the core. The instruction converter may be implemented in software, hardware, firmware, or a combination thereof. The instruction converter may be on processor, off processor, or part on and part off processor.
Thus, techniques for implementing a SIMD reconfigurable vector register file and permutation circuit according to at least one embodiment are disclosed. While certain exemplary embodiments have been described and shown in the accompanying drawings, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention, and that this invention not be limited to the specific constructions and arrangements shown and described, since various other modifications may occur to those ordinarily skilled in the art upon studying this disclosure. In an area of technology such as this, where growth is fast and further advancements are not easily foreseen, the disclosed embodiments may be readily modifiable in arrangement and detail as facilitated by enabling technological advancements without departing from the principles of the present disclosure or the scope of the accompanying claims.

## Claims

1. A variable precision floating point circuit comprising:
a variable precision mantissa unit to selectively operate in any one of a plurality of precision modes wherein in each precision mode a level of parallelism in the variable precision floating point circuit is inversely proportional to a level of precision,
multiple exponent units to selectively operate in one of a plurality of parallelism modes corresponding to a selected precision mode,
and certainty calculation units to calculate certainty bounds of one or more outputs of the variable precision unit.

2. The circuit of claim 1, wherein the variable precision mantissa unit includes a multiplier that multiplies first and second inputs to generate a multiplication result in a carry-save format, the multiplier is configured to operate in the plurality of precision modes that includes at least one of a high precision mode, a middle precision mode and a low precision mode.

3. The circuit of claim 2, wherein in the middle precision and low precision modes, the multiplier is delineated into a plurality of zones and partial products that do not lie along a predetermined diagonal are set to zero or not used.

4. The circuit of claim 2, wherein the variable precision mantissa unit further includes an alignment shifter that aligns a third input with the multiplication result.

5. The circuit of claim 2, wherein the variable precision mantissa unit further includes an alignment shifter that right shifts a third input to be aligned with the multiplication result according to the selected precision mode, the right shift amount(s) are determined by the exponent units based on exponents of the first, second and third inputs.

6. The circuit of claim 5, wherein the variable precision mantissa unit further includes a reconfigurable adder to convert carry-save outputs to 2's complement format.

7. The circuit of claim 6, wherein the reconfigurable adder is a reconfigurable sparse carry-tree adder.

8. The circuit of claim 6, wherein the variable precision mantissa unit further includes a shifter to perform normalization shift, the shift amount(s) are determined by a variable precision leading zero anticipation unit.

9. The circuit of claim 8, wherein the shifter is a left shifter to perform normalization left shift.

10. The circuit of claim 8 further comprising:
a round-up incrementer coupled to an output of the shifter, said round-up incrementer which is also used to increment an output of the shifter for a subtraction operation to maintain said output in 2's complement format.

11. The circuit of claim 10 further comprising:
a plurality of XOR negation circuits to negate only a plurality of lower significant bits of a shifted addend supplied to said adder for the subtraction operation.

12. The circuit of claim 1, wherein the certainty calculation units operate in parallel with the exponent units to calculate output certainty based on input certainties, input numbers, the selected precision mode, and whether multiply-add or multiply-subtract operations are to be performed.

13. The circuit of claim 1 further comprising:
a certainty tracking circuit to calculate a certainty value as a power of 2 representing how may bits of the mantissa in the mantissa unit are certain relative to the exponent in the exponent units.

14. The circuit of claim 13 wherein said certainty tracking circuit is to calculate an error term due to a product of error bounds for operands to the floating point circuit and compensate for said error term by adding a “1” to a compressor column in the multiplier to reduce error bounds of a result for the floating point circuit.

15. A system comprising:
a multiply-add circuit comprising:
a variable precision mantissa unit to selectively operate in anyone of a plurality of precision modes,
multiple exponent units to selectively operate in one of a plurality of parallelism corresponding to a selected precision mode,
and certainty calculation units to calculate certainty bounds of output(s) of the variable precision unit.

16. The system of claim 15, wherein the variable precision mantissa unit includes a multiplier that multiplies a first and second inputs to generate a multiplication result in a carry-save format, the multiplier is configured to operate in the plurality of precision modes that includes at least one of a high precision mode, a middle precision mode and a low precision mode.

17. The system of claim 16, wherein in the middle precision and low precision modes, the multiplier is delineated into a plurality of zones and partial products that do not lie along a predetermined diagonal are set to zero or not used.

18. The system of claim 17, wherein the variable precision mantissa unit further includes an alignment shifter that right shifts a third input to be aligned with the multiplication result according to the selected precision mode, the right shift amount(s) are determined by the exponent units based on exponents of the first, second and third inputs.

19. The system of claim 18, wherein the variable precision mantissa unit further includes a reconfigurable sparse carry-tree adder to convert carry-save outputs to 2's complement format.

20. The system of claim 19, wherein the variable precision mantissa unit further includes a shifter to perform normalization shift, the shift amount(s) are determined by a variable precision leading zero anticipation unit.

21. The system of claim 15, wherein the certainty calculation units operate in parallel with the exponent units to calculate output certainty based on input certainties, input numbers, the selected precision mode, and whether multiply-add or multiply-subtract operations are to be performed.

22. A n-bit by n-bit multiplier circuit comprising:
a parallelogram configured to set carries of a predetermined number (k) of least significant bits (LSBs) of a multiplication product to zero for a multiplication operation, and
a detection circuit configured to induce a replay of the multiplication operation by the multiplier to generate a full multiplication result, wherein inducing a replay of the multiplication operation is dependent on the multiplication product for the multiplication operation.

23. The n-bit by n-bit multiplier circuit of claim 22, wherein the parallelogram comprises a plurality of points that each represents a 3-2 full carry save adder (CSA) with carries pushed to the left.

24. The n-bit by n-bit multiplier circuit of claim 22, wherein if the detection circuit determines that the carries of k LSBs within a carry region could propagate a carry into a results region, the detection circuit induces the replay utilizing a full-multiplier array.

25. The n-bit by n-bit multiplier circuit of claim 22, wherein the detection circuit detects whether all upper n−k−log, (2k) bits of a carry region are ones (1s), the carry region is determined by a bit-width of the multiplication result and k LSBs.

26. The n-bit by n-bit multiplier circuit of claim 25, wherein the detection circuit further includes an adder to add lower log2 (2k) bits of the carry region.

27. The n-bit by n-bit multiplier circuit of claim 22, wherein inputs to be multiplied are booth encoded.