Abstract:
High-precision floating-point function estimates are split in two instructions each: a low precision table lookup instruction and a linear interpolation instruction. Estimates of different functions can be implemented using this scheme: A separate table-lookup instruction is provided for each different function, while only a single interpolation instruction is needed, since the single interpolation instruction can perform the interpolation step for any of the functions to be estimated. Thus, significantly less overhead is incurred than would be incurred with specialized hardware, while still maintaining a uniform FPU latency, which allows for much simpler control logic.

Description:
[0001]    This application is a continuation application of co-pending U.S. Non-Provisional patent application Ser. No. 11/127,848, entitled “Processor Having Efficient Function Estimate Instructions,” filed on May 12, 2005. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Technical Field 
         [0003]    The present invention is related generally to the architecture and instruction sets of processors, such as a microprocessor, microcontroller, or digital signal processor. More specifically, the present invention is directed to a processor having efficient instructions for estimating the values of certain floating-point functions. 
         [0004]    2. Background Art 
         [0005]    Many processor architectures, such as the PowerPC architecture, support estimate instructions for reciprocal and reciprocal square root as an extension of a fused multiply-add floating-point unit (FPU). For such estimate instructions the primary design goals are twofold: The estimate should be of a relatively high precision, so that with one iteration step of a numerical approximation algorithm, such as Newton-Raphson, one can get to full single precision accuracy or at least close to full precision. It should be possible to implement the estimate instructions with little hardware overhead and with little impact on the processor&#39;s cycle time and pipeline structure. In particular, the design should not increase the pipeline depth of the FPU for any non-estimate instruction. 
         [0006]    There are a number of different ways in which such an estimate instruction might be implemented. One way is to simply look up the estimate in a table. The usefulness of this technique, however, is limited, since the level of precision available is limited by the size of the table. To achieve a desirable level of accuracy, a very large table would be needed (which would be expensive in terms of the hardware needed to store the table). 
         [0007]    A conventional implementation for such estimate instructions therefore consists of two steps: First, a table lookup provides a base value and a slope. Then, the base and slope values are used to linearly interpolate an estimate with the desired precision. Since the table lookup is followed by an interpolation step, the results of the table lookup can have a low precision, and therefore the required table is much smaller than would be necessary for a direct table lookup without interpolation. 
         [0008]    In this two-step procedure, the interpolation can either be executed using the general-purpose FPU hardware of the processor or by adding specialized hardware for computing the interpolation. When the general-purpose FPU datapaths are used, the estimate instruction turns out to have a longer latency than a basic fused multiply-add instruction. That adds complexity to the processor&#39;s control logic, since it means that the latency of the FPU will vary according to the instruction type. Some existing implementations avoid this complexity at the expense of performance by assuming a single FPU latency and stalling the execution for the additional cycles while executing an estimate instruction. Furthermore, the longer latency can cause significant hardware overhead in the instruction issue and dependency check hardware. 
         [0009]    As suggested above, the interpolation step does not require a full general-purpose FPU. Instead, it can be executed with a multiplier of reduced size, an adder, and some additional logic. With this specialized hardware, the interpolation step can be processed much more quickly than with a general-purpose FPU, i.e., the latency of the estimate instruction approaches that of a regular multiply-add instruction. The obvious drawback of this solution is the extra hardware required to speed-up the interpolation step. 
         [0010]    What is needed, therefore, is a processor design in which floating-point function estimate instructions can be implemented without incurring significant costs in terms of performance and hardware complexity. The present invention provides a solution to these and other problems, and offers other advantages over previous solutions. 
       SUMMARY OF THE INVENTION 
       [0011]    A preferred embodiment of the present invention provides a method, computer program product, and processor design for supporting high-precision floating-point function estimates that are split in two instructions each: a low precision table lookup instruction and a linear interpolation instruction. Estimates of different functions can be implemented using this scheme: A separate table-lookup instruction is provided for each different function, while only a single interpolation instruction is needed, since the single interpolation instruction can perform the interpolation step for any of the functions to be estimated. 
         [0012]    The base and slope provided by the table lookup instructions are stored together in the fraction part of the floating-point result, so that the result of the table lookup can, by itself, serve as a low precision estimate result. Thus, the present invention allows a programmer the flexibility to choose high precision or speed, according to the application at hand. 
         [0013]    The estimate instructions can be implemented with little hardware overhead. The tables for the table lookup are small since they provide only a low precision base and a slope. Except for requiring some simple packing and unpacking of bits, the interpolation instruction can be executed in a fused multiply-add FPU core with virtually no additional hardware overhead. Thus, a preferred embodiment of the present invention incurs significantly less overhead than would specialized hardware, while still maintaining a uniform FPU latency, which allows for much simpler control logic. Moreover, breaking the estimate operation into two instructions allows one to take advantage of software pipelining to increase overall instruction throughput. 
         [0014]    The foregoing is a summary and thus contains, by necessity, simplifications, generalizations, and omissions of detail; consequently, those skilled in the art will appreciate that the summary is illustrative only and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the present invention, as defined solely by the claims, will become apparent in the non-limiting detailed description set forth below. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0015]    The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings, wherein: 
           [0016]      FIG. 1  is a diagram illustrating the IEEE-754 standard floating-point number representation; 
           [0017]      FIG. 2  is a flowchart representation of a process of estimating a floating-point function in accordance with a preferred embodiment of the present invention; 
           [0018]      FIG. 3  is a diagram illustrating the operation of a table lookup operation in accordance with a preferred embodiment of the present invention; 
           [0019]      FIG. 4  is a diagram illustrating the operation of an interpolate operation in accordance with a preferred embodiment of the present invention; and 
           [0020]      FIG. 5  is a block diagram of an information processing system in which a preferred embodiment of the present invention may be implemented. 
       
    
    
     DETAILED DESCRIPTION  
       [0021]    The following is intended to provide a detailed description of an example of the invention and should not be taken to be limiting of the invention itself. Rather, any number of variations may fall within the scope of the invention, which is defined in the claims following the description. 
         [0022]    A preferred embodiment of the present intention is directed to a processor architecture and instruction set containing efficient instructions for estimating the values of particular floating-point functions. Specifically, a preferred embodiment of the present invention is directed to function estimate instructions for the reciprocal function (1/x) and reciprocal square root function (1/sqrt(x)).  FIG. 1  is a diagram illustrating a floating point number  100 . Floating point number  100  is represented in IEEE-754 floating-point format, a standard promulgated by the Institute of Electrical and Electronics Engineers (IEEE). 
         [0023]    Specifically floating point number  100  is a single-precision floating point number, which according to the standard, comprises 32 bits. These 32 bits are arranged as follows: the most significant bit (MSB) is sign bit  102 , which represents the sign of floating point number  100 , such that if sign bit  102  is equal to one, then floating point number  100  is negative, and if sign bit  102  is equal to zero, floating point number  100  is positive. Bit field  104 , which immediately follows sign bit  102 , represents an 8-bit exponent value, while bit field  106 , which occupies the maintaining 23 bits of floating point number  100 , represents all but the most-significant bit of a 24-bit mantissa. Generally, floating point numbers in IEEE-754 format are expressed in a normalized form, where the most-significant bit is implicitly “1” and is the only bit to the left of the binary point, although this is not strictly necessary. A preferred embodiment of the present invention utilizes normalized numbers, but non-normalized numbers could also be used without departing from the scope and spirit of the present invention. Thus, if bit field  106  contains bits 01010101 . . . , then the 24-bit mantissa represented by bit field  106  is 1.01010101 . . . . Exponent field  104  is biased by adding  127  (to make exponent field  104  an unsigned number), such that the absolute value of floating point number  100  is equal to mantissa  106  times 2 to the power of the difference between exponent field  104  and  127 . In this way, floating point number  100  is capable of representing numbers having a negative exponent (i.e., fractions), as well as numbers having a positive exponent (i.e., real numbers in excess of unity). 
         [0024]    One of ordinary skill in the art will recognize that embodiments of the present invention may be executed using numeric formats other than the IEEE-754 standard shown here, although a preferred embodiment of the present invention utilizes 32-bit single-precision floating-point numbers in IEEE-754 format. For example, the IEEE-754 standard also supports 64-bit (double-precision) and extended floating point representations (such as an 80-bit format), and there are other non-IEEE-754 floating-point representations as well. Moreover, one of ordinary skill in the art will recognize that the teachings of the present invention are not strictly limited in scope to floating-point numbers, but may also be applied, in whole or in part, to other number types and formats, including (but not limited to) integers and other fixed-point numbers. 
         [0025]    Many mathematical functions, including in particular the transcendental functions, are computed in floating-point computer mathematics using numerical approximation techniques, such as the Newton-Raphson method. Many of these approximation techniques, such as the aforementioned Newton-Raphson method, are iterative, meaning that several successive iterations of the approximation method must be completed to achieve an approximation of sufficient accuracy for the application in question. Because of the time-consuming nature of computing these functions iteratively, some processor architectures supporting floating point operations include instructions for obtaining a rapid estimate of the function in question, which can be made more accurate through a small number of iterations of an approximation technique, such as a single iteration of Newton-Raphson. Typically, this is done by combining a table look-up with a linear, polynomial, or other interpolation step. Because of the complex nature of this operation, however, such instructions may require large latency delays, thus hindering their performance and raising the complexity of the underlying hardware. 
         [0026]    A preferred embodiment of the present invention seeks to reduce this complexity by breaking the estimation process into two instructions, rather than a single instruction.  FIG. 2  is a flowchart representation of a process of computing a function estimate in accordance with a preferred embodiment of the present invention. 
         [0027]    As represented by block  200 , the estimation process begins with a single instruction in which the instruction&#39;s input operand is used to obtain, by table lookup, base value and slope parameters for a subsequent linear interpolation. In a preferred embodiment of the present invention, the instruction returns these parameters in the form of a 32-bit word making up a packed-bit representation of the interpolation parameters. As shown in  FIG. 3  and described in the accompanying text, this packed format is arranged such that the 32-bit representation of the interpolation parameters is also a low-precision estimate of the function to be estimated, when interpreted as a single IEEE-754 floating-point number. Thus, an alternative estimation process to that described in  FIG. 2  consists of only block  200  and is characterized by greater speed, but lower precision. 
         [0028]    Next, as shown by block  202 , the processor executes a second instruction on the previously obtained base value and slope, in which the processor uses the base value and slope to perform linear interpolation to obtain an estimate of the desired function evaluated at the value of the original operand. Note that, although a preferred embodiment of the present invention utilizes linear interpolation to complete the estimation process, one of ordinary skill in the art will recognize that other forms of approximation, including other polynomial interpolation schemes, may be used in place of linear interpolation without departing from the scope and spirit of the present invention. 
         [0029]    This two-instruction scheme is advantageous in that it requires less hardware to be cascaded in the processor&#39;s data path in order to perform estimation. In fact, the look up operation and the interpolation operation can be executed in separate functional units in a processor supporting instructions-level parallelism. 
         [0030]      FIGS. 3 and 4  are diagrams providing a more detailed illustration of the two instructions described in  FIG. 2 .  FIG. 3  is a diagram representing a process of executing an initial table look up operation, as represented by block  200  in  FIG. 2 . In this example, we will refer to the instruction as “fes 1 ” (representing a “first function estimate instruction”). The instruction being executed in  FIG. 3  is “fes 1  X, r 1 ,” which means look up base and slope values for operand X and store the base and slope values in register r 1 . Floating point number  300  represents the operand X, as represented in IEEE-754 standard format. In a preferred embodiment in which a reciprocal estimate is calculated, the five most significant bits of the mantissa of floating point number  300  are used as an index to look up table  304 , which contains base and slope values for each of the 32 different combinations of the five most significant bits of an arbitrary mantissa. Other combinations of mantissa and exponent bits may be used as an index without departing from the scope and spirit of the present invention. For example, an index for a reciprocal square-root estimate function would need to include at least one exponent bit (the least significant exponent bit), since the value of the mantissa of a reciprocal square root function is dependent on whether the exponent of the function&#39;s argument is even or odd. What is retrieved from look up table  304  is placed by the processor into the destination register (here “r 1 ”) as a bit-packed representation  306  of base and slope values for performing interpolation to obtain an estimate of a particular function as evaluated at operand X. 
         [0031]    Like floating point number  300 , base/slope representation  306  is a 32-bit number, which facilitates the execution of instruction fes 1  on a 32 bit processor. Base/slope representation  306  includes sign bit  308 , an eight bit exponent value  310 , a 13-bit base mantissa value  312 , and a 10-bit slope value  314 . No exponent value for the slope is needed, since the required degree of precision is achieved (at least for the reciprocal and reciprocal square root functions) by base exponent value  310 . 
         [0032]    The processor retrieves mantissa value  312  and slope value  314  via table lookup, while the processor computes sign bit  308  and exponent value  310  according to whatever rules govern the particular function to be estimated. In the case of a reciprocal, the processor copies sign bit  308  from sign bit  309  of floating-point operand  300 . In the case of a reciprocal square-root, since the reciprocal square-root is only defined for positive X, sign bit  308  will simply be positive. Exponent value  310  is computed by performing simple operations, such as addition and subtraction of offsets and shifts, on exponent value  311  of floating-point operand  300 . The processor retrieves this offset value from the table along with mantissa value  312 , and slope value  314 . 
         [0033]    At this point, it should be noted that the arrangement of bit fields in base/slope representation  306  closely follows the IEEE-754 floating-point number format, as depicted in  FIG. 1 . Because base mantissa value  312  is itself a low-precision estimate of the function being estimated, and because base mantissa value  312  is placed where the most-significant bits of mantissa field  106  in the IEEE-754 representation (as in  FIG. 1 ), base/slope representation  306 , in its entirety, is itself a low-precision estimate of the function in question. In cases where a programmer wishes to sacrifice precision for speed of computation, therefore, base/slope representation  306  may be used, as is, as a low-precision estimate of the function in question. Otherwise, base/slope representation  306  may be presented as input to a subsequent interpolation instruction, as depicted in  FIG. 4 . 
         [0034]    As shown in  FIG. 4 , the interpolation instruction, here “fes 2 ,” takes the original operand (floating point number  300 ) and the base/slope representation  306  as input. In this example, one writes the instruction as “fes 2  X, r 1 , r 2 ,” which means compute an interpolation using X as the operand and the contents of register r 1  as the base/slope representation, then store the results in register r 2 . From base mantissa value  312  (recognizing an implicit “1” to the left of the binary point in the case of a normalized number), a product of two numbers is subtracted. The processor obtains the first of the factors in this product by placing slope bits  314  four places to the right of the binary point (e.g., if the slope bits are 1101110101, then the first factor is 0.0001101110101). The second factor in the product is simply made up of the eighteen least significant bits  400  in the mantissa of X (floating point number  300 ). The result of the subtraction is then multiplied by the sign and exponent of the base/slope representation. The resulting product is then normalized by the processor and placed into the 23 bit mantissa  412 , sign bit  408 , and 8-bit exponent portion  410  of interpolation result  406 . 
         [0035]      FIG. 5  illustrates information handling system  501 , which is a simplified example of a computer system capable of performing the computing operations of the host computer described herein with respect to a preferred embodiment of the present invention. Computer system  501  includes processor  500  which is coupled to host bus  502 . A level two (L2) cache memory  504  is also coupled to host bus  502 . Host-to-PCI bridge  506  is coupled to main memory  508 , includes cache memory and main memory control functions, and provides bus control to handle transfers among PCI bus  510 , processor  500 , L2 cache  504 , main memory  508 , and host bus  502 . Main memory  508  is coupled to Host-to-PCI bridge  506  as well as host bus  502 . Devices used solely by host processor(s)  500 , such as LAN card  530 , are coupled to PCI bus  510 . Service Processor Interface and ISA Access Pass-through  512  provides an interface between PCI bus  510  and PCI bus  514 . In this manner, PCI bus  514  is insulated from PCI bus  510 . Devices, such as flash memory  518 , are coupled to PCI bus  514 . In one implementation, flash memory  518  includes BIOS code that incorporates the necessary processor executable code for a variety of low-level system functions and system boot functions. 
         [0036]    PCI bus  514  provides an interface for a variety of devices that are shared by host processor(s)  500  and Service Processor  516  including, for example, flash memory  518 . PCI-to-ISA bridge  535  provides bus control to handle transfers between PCI bus  514  and ISA bus  540 , universal serial bus (USB) functionality  545 , power management functionality  555 , and can include other functional elements not shown, such as a real-time clock (RTC), DMA control, interrupt support, and system management bus support. Nonvolatile RAM  520  is attached to ISA Bus  540 . Service Processor  516  includes JTAG and I2C buses  522  for communication with processor(s)  500  during initialization steps. JTAG/I2C buses  522  are also coupled to L2 cache  504 , Host-to-PCI bridge  506 , and main memory  508  providing a communications path between the processor, the Service Processor, the L2 cache, the Host-to-PCI bridge, and the main memory. Service Processor  516  also has access to system power resources for powering down information handling device  501 . 
         [0037]    Peripheral devices and input/output (I/O) devices can be attached to various interfaces (e.g., parallel interface  562 , serial interface  564 , keyboard interface  568 , and mouse interface  570  coupled to ISA bus  540 . Alternatively, many I/O devices can be accommodated by a super I/O controller (not shown) attached to ISA bus  540 . 
         [0038]    In order to attach computer system  501  to another computer system to copy files over a network, LAN card  530  is coupled to PCI bus  510 . Similarly, to connect computer system  501  to an ISP to connect to the Internet using a telephone line connection, modem  575  is connected to serial port  564  and PCI-to-ISA Bridge  535 . 
         [0039]    While the computer system described in  FIG. 5  is capable of supporting the instruction set architecture described herein, this computer system is simply one example of a computer system. Those skilled in the art will appreciate that many other computer system designs are capable of performing the processes described herein. 
         [0040]    Particular aspects and possible embodiments of the invention fall within the realm of software. In particular, to utilize the features of a preferred embodiment of the present invention, one must execute software containing estimate instructions in accordance with the teachings of the present invention. An embodiment of the present invention may also include or take the form of microcode, which is software that is internal to the processor and that specifies some of the detailed control steps needed to perform an instruction. 
         [0041]    Software, as the term is used herein, is a set of instructions (program code) or other functional descriptive material in a code module that may, for example, be resident in memory (whether random-access memory or read-only memory) of the computer (either internal to a processor or external to it). Until required by the computer, the set of instructions may be stored in another computer memory, for example, in a hard disk drive, or in a removable memory such as an optical disk (for eventual use in a CD-ROM) or floppy disk (for eventual use in a floppy disk drive), or downloaded via the Internet or other computer network. Thus, the present invention may be implemented as a computer program product for use in a computer. In addition, although the various methods described are conveniently implemented in a general purpose computer selectively activated or reconfigured by software, one of ordinary skill in the art would also recognize that such methods may be carried out in hardware, in firmware, or in more specialized apparatus constructed to perform the required method steps. Functional descriptive material is information that imparts functionality to a machine. Functional descriptive material includes, but is not limited to, computer programs, instructions, rules, facts, definitions of computable functions, objects, and data structures. 
         [0042]    While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that, based upon the teachings herein, changes and modifications may be made without departing from this invention and its broader aspects. Therefore, the appended claims are to encompass within their scope all such changes and modifications as are within the true spirit and scope of this invention. Furthermore, it is to be understood that the invention is solely defined by the appended claims. It will be understood by those with skill in the art that if a specific number of an introduced claim element is intended, such intent will be explicitly recited in the claim, and in the absence of such recitation no such limitation is present. For non-limiting example, as an aid to understanding, the following appended claims contain usage of the introductory phrases “at least one” and “one or more” to introduce claim elements. However, the use of such phrases should not be construed to imply that the introduction of a claim element by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an;” the same holds true for the use in the claims of definite articles.