Abstract:
The invention comprises methods and apparatuses for interleaving a number of memory cards of different sizes. A restricted range modulo-N adder for identifying and selecting the correct interleave card is provided. Another aspect of the invention provides a computer system with flexible memory interleaving capability.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to the field of memory addressing. More particularly, the invention relates to a method and apparatus for carrying out block memory addressing in an interleaved fashion, with a variety of block sizes. 
     BACKGROUND OF THE INVENTION 
     Computers and computer systems typically have two busses, an address bus and a data bus. The address bus, used for addressing and control, is usually of a fixed width, and carries the necessary signals to initiate transactions between the computer&#39;s internal memory and peripheral devices. Data is typically transferred over the data bus. In some cases the address bus and data bus are multiplexed for transferring addresses and data. 
     It is often desirable to organize the computer&#39;s storage area into interleaved blocks or cards of memory. Interleaved memory can allow two or more memory blocks to be accessed at a fraction of a cycle apart, thereby significantly reducing cycle time and improving memory speed. The simplest interleave procedure assigns sequential line addresses within a group or list of addresses to sequentially numbered memory blocks. However, this typically requires a large &#34;modulo arithmetic&#34; operation to determine the block number for a given address. 
     Modulo arithmetic is most easily understood as a remainder function. For instance, 21 divided by 4 equals 5 plus a remainder of 1. Therefore, 21 modulo-5 equals 1. Since, as is well known, division is expensive to implement, modulo arithmetic can be carried out by a repetitive subtraction method whereby the modulus (5 in the preceding example) is repetitively subtracted from the original number (21 in the preceding example) until the result is less than the modulus. For example, 21 modulo-5 is computed as follows: ##EQU1## 
     A system having memory organized as 3 blocks of 256 Kbytes each would need a calculation of 256K modulo-3 addresses, which would be difficult in hardware designed for an arbitrary number of N blocks. The easiest simplification is to allow only values of N (the modulus) which are powers of 2, so that the modulo-N operation simply involves extracting a bit field. This method, however, is too inflexible, particularly when adding incremental memory. 
     An alternative to the above &#34;bit shift&#34; interleave method, for interleaving a power of 2 memory cards, employs an address bit to activate the cards. For example, consider a typical, non-interleaved, byte-addressed system. Assume each memory card supplies 32 bits (4 bytes) per access. Assume further that the address space is 20 bits, and that memory cards are each 64 Kbytes. The address space may then be arranged as follows: ##STR1## 
     To modify this arrangement to allow interleaving of 2 memory cards, the offset bits are shifted one bit to the left and the LSB (bit 17) of the original offset bits is used as a fourth card select bit, or an interleave bit. ##STR2## This method and variations of it are in common use. It can be extended easily for systems with memory blocks in powers of 2. However, this method, like the above bit shift method, is too inflexible when adding incremental memory. 
     The foregoing discussion reflects the fact that, to reduce the complexity of the interleaving circuitry, known interleaving systems require memory blocks to be present in powers of two, e.g., 2, 4, 8, etc. In such systems, six banks of memory, for example, would have to be organized as a bank of two and a bank of four, or three banks of two interleaved memory systems. Due to the heretofore relative complexity of the circuitry for carrying out the interleaving, an arbitrary number of banks has not been practical in the prior art. Nonetheless, there are advantages in being able to interleave an arbitrary, non-power of 2, number of memory banks, e.g., when adding memory to the system. 
     Accordingly, an object of the present invention is to provide a practical system for carrying out memory interleaving with an arbitrary number of memory blocks. A further object of the present invention is to provide a method and corresponding apparatus whereby the memory blocks can be connected to the address bus and a block identification number provided which the respective blocks can use to select themselves. The present invention achieves these goals. 
     SUMMARY OF THE INVENTION 
     One embodiment of the invention provides a method of interleaving a plurality of N memory blocks, each of the N blocks being of a size S (bytes). According to the invention, M-bit data addresses are translated into corresponding addresses of interleaved memory blocks, each block having S bytes grouped into lines of size L (bytes). 
     The method comprises the steps of, first, identifying a first group of bits (B --  bits) of an address being translated, and then identifying a second group of bits (I --  bits) defining an interleave index corresponding to the address being translated. In a preferred embodiment, B --  bits and I --  bits are determined by computing the values: A=log 2  (S), B=M--A, and I=truncate(log 2  (N)). B --  bits is then defined as the B MSBs of the address being translated. The A LSBs (&#34;A --  bits&#34;) of the address being translated are then identified. I --  bits is then defined as the I LSBs of A --  bits after first stripping away the log 2  (L) LSBs of A --  bits. Accordingly A --  bits defines an offset within the block defined by B --  bits. 
     Next, an &#34;unadjusted sum&#34; (&#34;SUM&#34;) and an adjusted sum (&#34;ADJ --  SUM&#34;) are computed in accordance with the following definitions: SUM=B --  bits+I --  bits, and ADJ --  SUM=B --  bits+I --  bits-N. 
     Finally, a block number corresponding to the address being translated is defined, the block number being a function of at least one of the values of SUM or ADJ --  SUM. In a preferred embodiment, the block number selected is the value of SUM when ADJ --  SUM is less than zero, and the value of ADJ --  SUM when ADJ --  SUM is greater than or equal to zero. 
     Another embodiment of the invention provides a restricted range modulo-N adder for summing first and second input values and computing a result within a range of 0 to N-1, the actual sum of the input values being within the range of 0 to 2N-1. The restricted range modulo-N adder according to the invention comprises means for computing a first sum of the first and second input values, means for computing a second sum of the first and second input values and subtracting a third input value corresponding to N, and means for testing whether the second sum is negative and for selecting the result from one of the first and second sums, the selection being of the first sum when the second sum is less than zero, and the selection being of the second sum when the second sum is greater than or equal to zero. 
     Another embodiment of the invention provides a digital system comprising a computer, N memory blocks coupled to the computer, and addressing means for reading/writing data values from/to the memory in an interleaved fashion. The addressing means comprises means for carrying out the method described above, including the restricted range modulo-N adder. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a simplified flowchart of a method of translating memory addresses into corresponding interleaved block addresses, in accordance with the present invention. 
     FIG. 2 is a block diagram of a restricted range modulo-N adder in accordance with the present invention. 
     FIG. 3 is a block diagram of a computer system incorporating interleaved block memory, in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The preferred embodiments of the invention include a method and corresponding apparatus for translating the respective addresses of memory locations into corresponding interleaved block addresses and offsets within each block, and a computer system comprising interleaved memory blocks. These embodiments are described below with reference to the drawings, wherein like reference characters designate like elements or steps. 
     To provide an overview, it is noted that the preferred method employs a restricted range modulo-N adder (described below) to add the upper address bits that are unused by the memory blocks, referred to herein as the &#34;B --  bits,&#34; to the I least significant line address bits, referred to herein as the &#34;I --  bits.&#34; In this discussion, I and B represent integers, and &#34;B --  bits&#34; and &#34;I --  bits&#34; represent a particular grouping or subset of neighboring address bits. In addition, a &#34;line&#34; refers to the group of bytes (typically 16 or 32 in a cache-based system) transferred with each memory access. A &#34;line address&#34; is the address of the first byte in a particular line. According to the invention, the sum of B --  bits and I --  bits (referred to as the &#34;unadjusted sum&#34;) is computed in parallel with the sum of B --  bits and I --  bits-N, N being the number of blocks being interleaved. To allow for several groups of interleaved blocks, the beginning address of the group (denominated &#34;GS&#34; herein, for Group Start) is also subtracted from B --  bits. If the blocks are not organized into groups, GS would be set to zero. Thus, the &#34;adjusted sum&#34; of B --  bits and I --  bits-(GS+N) is computed. These sums may be computed by three-term adders, one term of which is a predefined constant determined during system configuration (the predefined constant is -GS and -(GS+N) for the respective adders). Design and implementation of the three term adders is well known in the art. 
     According to the invention, either the adjusted sum or unadjusted sum is used to define a block number identifying a particular memory block corresponding to the address being translated. The determination of whether the adjusted sum or unadjusted sum is used is based upon whether the adjusted sum is negative, zero or positive. These sums, as well as the selection of which of them is used to select the corresponding memory blocks, are carried out by a restricted range modulo-N adder in accordance with the present invention. 
     The method is described next, with reference to FIG. 1. The restricted range modulo-N adder is then described with reference to FIG. 2. Finally, a computer system incorporating the invention is described with reference to FIG. 3. 
     Referring now to FIG. 1, the first operation, step 10, is to define the parameters &#34;S,&#34; &#34;L,&#34; &#34;N&#34; and &#34;GS&#34;. S represents the size, in bytes, of a memory block in a particular group. (Within a group all blocks are required to be of the same size.) L represents the size, in bytes, of a line in a block. As mentioned above, N and GS represent the number of blocks in a particular group and the particular group&#39;s starting address number, respectively. 
     The next step is to compute the values of the variables &#34;A&#34;, &#34;B&#34; and &#34;I&#34;, step 12. These variables are defined as follows: 
     
         A=log.sub.2 (S), 
    
     
         B=M-A, and 
    
     
         I=truncate (log.sub.2 (N)), 
    
     where &#34;M&#34; is equal to the width (i.e., number of bits) of the address bus of the system, which is a predefined constant. 
     Steps 14, 16 and 18 involve the identification of &#34;B --  bits,&#34; &#34;A --  bits&#34; and I --  bits,&#34; respectively. B --  bits is defined by the B most significant bits (MSBs) of the address being translated; A --  bits is defined by the A remaining least significant bits (LSBs) of the address; and I --  bits is defined by the I LSBs of the line address, the line address being defined by the remaining bits of A --  bits after stripping away the bits necessary to identify a particular byte within a line. Thus, for a line size of L, I --  bits is defined by the I LSBs remaining of A --  bits after stripping away the log 2  (L) LSBs of A --  bits. 
     For example, consider 5 blocks (N=5) of 1024 byte memory (S=1024), with a line size of 16 bytes (L=16) and a 16-bit address bus (M=16). Assume further that the group start address (GS) is zero. The number of bits A required to address all locations within a memory block is A=log 2  (1024)=10. B is therefore 16-10=6, and I is truncate(log 2  (5))=2. The interleave bits (I --  bits) are bits 10 and 11, with bit zero being the left most bit of the address. The address, then, is broken up as follows: ##STR3## Note that the subscripts (e.g., k0, k1, k2, etc.) are used to indicate a particular address and bit number; e.g., bit 0 of the kth address in a list of addresses would be represented as b k0 . Thus, in this example, I --  bits, A --  bits and B --  bits corresponding to a particular address are defined as follows (dropping the subscript k): 
     
         I.sub.-- bits=(b.sub.10, b.sub.11), 
    
     
         A.sub.-- bits=(b.sub.6, b.sub.7, . . . b.sub.15), and 
    
     
         B.sub.-- bits=(b.sub.0, b.sub.1, . . . b.sub.5). 
    
     Note that the above steps 10-18 need only be performed once, during system configuration (startup). The following steps 20-24 are performed with each memory access. 
     Turning again to FIG. 1, the unadjusted sum (&#34;SUM&#34;) and adjusted sum (&#34;ADJ --  SUM&#34;) are computed next (with each access), preferably at the same time, step 20. These sums are computed as follows: 
     
         SUM=B.sub.-- bits+I.sub.-- bits-GS 
    
     
         ADJ.sub.-- SUM=B.sub.-- bits+I.sub.-- bits-(GS+N). 
    
     Next, step 22, the adjusted sum (ADJ --  SUM) is selected as the correct result (RESULT) if it is greater than or equal to zero. If not, the unadjusted sum (SUM) is selected as the correct result. 
     The last step, step 24, is to define the block number and offset corresponding to the address being translated. The block number is simply set equal to RESULT, and the offset address is defined by A --  bits. 
     As a further example of the above-described method, the following table shows a list of internal addresses and corresponding translated external bus addresses, the bus addresses comprising a block number (&#34;blk&#34; in the table) and offset address (&#34;offset&#34; in the table). Int he example, S=32, N=7, I=2, M=7, A=4, B=3 and GS=0. 
     
         ______________________________________Address                      Bus AddressB.sub.-- bits xx     I.sub.-- bits                ADJ - SUM SUM   blk   offset______________________________________000   00     00      -7        0     000   0000000   00     01      -6        1     001   0001000   00     10      -5        2     010   0010000   00     11      -4        3     011   0011000   01     00      -7        0     000   0100000   01     01      -6        1     001   0101000   01     10      -5        2     010   0110000   01     11      -4        3     011   0111000   10     00      -7        0     000   1000000   10     01      -6        1     001   1001000   10     10      -5        2     010   1010000   10     11      -4        3     011   1011000   11     00      -7        0     000   1100000   11     01      -6        1     001   1101000   11     10      -5        2     010   1110000   11     11      -4        3     011   1111001   00     00      -6        1     001   0000001   00     01      -5        2     010   0001001   00     10      -4        3     011   0010001   00     11      -3        4     100   0011001   01     00      -6        1     001   0100001   01     01      -5        2     010   0101001   01     10      -4        3     011   0110001   01     11      -3        4     100   0111001   10     00      -6        1     001   1000001   10     01      -5        2     010   1001001   10     10      -4        3     011   1010001   10     11      -3        4     100   1011001   11     00      -6        1     001   1100001   11     01      -5        2     010   1101001   11     10      -4        3     011   1110001   11     11      -3        4     100   1111010   00     00      -5        2     010   0000010   00     01      -4        3     011   0001010   00     10      -3        4     100   0010010   00     11      -2        5     101   0011010   01     00      -5        2     010   0100010   01     01      -4        3     011   0101010   01     10      -3        4     100   0110010   01     11      -2        5     101   0111010   10     00      -5        2     010   1000010   10     01      -4        3     011   1001010   10     10      -3        4     100   1010010   10     11      -2        5     101   1011010   11     00      -5        2     010   1100010   11     01      -4        3     011   1101010   11     10      -3        4     100   1110010   11     11      -2        5     101   1111011   00     00      -4        3     011   0000011   00     01      -3        4     100   0001011   00     10      -2        5     101   0010011   00     11      -1        6     110   0011011   01     00      -4        3     011   0100011   01     01      -3        4     100   0101011   01     10      -2        5     101   0110011   01     11      -1        6     110   0111011   10     00      -4        3     011   1000011   10     01      -3        4     100   1001011   10     10      -2        5     101   1010011   10     11      -1        6     110   1011011   11     00      -4        3     011   1100011   11     01      -3        4     100   1101011   11     10      -2        5     101   1110011   11     11      -1        6     110   1111100   00     00      -3        4     100   0000100   00     01      -2        5     101   0001100   00     10      -1        6     110   0010100   00     11       0        7     000   0011100   01     00      -3        4     100   0100100   01     01      -2        5     101   0101100   01     10      -1        6     110   0110100   01     11       0        7     000   0111100   10     00      -3        4     100   1000100   10     01      -2        5     101   1001100   10     10      -1        6     110   1010100   10     11       0        7     000   1011100   11     00      -3        4     100   1100100   11     01      -2        5     101   1101100   11     10      -1        6     110   1110100   11     11       0        7     000   1111101   00     00      -2        5     101   0000101   00     01      -1        6     110   0001101   00     10       0        7     000   0010101   00     11       1        8     001   0011101   01     00      -2        5     101   0100101   01     01      -1        6     110   0101101   01     10       0        7     000   0110101   01     11       1        8     001   0111101   10     00      -2        5     101   1000101   10     01      -1        6     110   1001101   10     10       0        7     000   1010101   10     11       1        8     001   1011101   11     00      -2        5     101   1100101   11     01      -1        6     110   1101101   11     10       0        7     000   1110101   11     11       1        8     001   1111110   00     00      -1        6     110   0000110   00     01       0        7     000   0001110   00     10       1        8     001   0010110   00     11       2        9     010   0011110   01     00      -1        6     110   0100110   01     01       0        7     000   0101110   01     10       1        8     001   0110110   01     11       2        9     010   0111110   10     00      -1        6     110   1000110   10     01       0        7     000   1001110   10     10       1        8     001   1010110   10     11       2        9     010   1011110   11     00      -1        6     110   1100110   11     01       0        7     000   1101110   11     10       1        8     001   1110110   11     11       2        9     010   1111______________________________________ 
    
     As noted above, differently-sized blocks can be used if each &#34;interleave group&#34; comprises blocks of the same size, and if a group start number (GS), indicating the starting B --  bits value for the group, is subtracted from B --  bits. The resulting block number sent over the bus may need to have GS added back in. Note that there is no requirement that block numbers be consecutive, so that some of the bits of B --  bits can be used to identify the interleave group. 
     For instance, assume that a system supports 4 sizes of DRAM cards. Assume further that hardware allows up to 16-way interleaving (requiring I=4) and up to 16 memory cards in the system. Any combination of the differently-sized memory cards can be supported at once, by assigning all cards of size A with a hexadecimal block number of 0×0?, where &#34;?&#34; may range from 0 to f, assigning cards of size B with a block number of 0×1?, assigning size C cards with block number 0×2?, and assigning size D cards with a block number of 0×3?. Configuration software determines the value for ? based on how many cards of that size are in the system, numbering them sequentially from 0  to the number of cards in that group. The address range for the largest size cards is then determined. Next, its GS number is set to 0. Then, for the next largest group, the same is done, beginning at the end of the previous group, and so on. 
     Referring now to FIG. 2, a restricted range modulo-N adder (there is preferably one for each group of cards) in accordance with the invention comprises a pair of three term adders 20a&#39;, 20b&#39; and means for selecting the 0 correct result, i.e., SUM or ADJ --  SUM, that is between 0 and N-1. The means for selecting the correct result comprises a logic circuit 48 that provides select signals &#34;SEL 1&#34;, &#34;SEL 2&#34; to the respective adders 20a&#39;, 20b&#39;. As shown in the drawing, the computations of SUM and ADJ --  SUM are performed in parallel. The sign bit, denominated &#34;NEG&#34; in the drawing, is employed by select circuit 48 to select SUM when ADJ --  SUM is less than zero, and ADJ --  SUM when ADJ --  SUM is zero or greater than zero. To determine the group-delineating bits (e.g., the upper two bits of B --  bits), a pair of range comparators 40, 42 may be employed for each group. The outputs of comparators 40, 42 are employed by match circuit 44 which provides an enable signal (&#34;ENABLE&#34;) to the select circuit 48. A predefined group number register 46 may also be provided to provide a group number input to select circuit 48. For many of the groups, the low range comparator 42 may be shared by the preceding group as the preceding group&#39;s high range comparator, and the high range comparator 40 may be shared by a succeeding group as the succeeding group&#39;s low range comparator. 
     The values -GS and -(GS+N), which are predefined constants for a given group (determined at startup), are the third inputs to the respective adders 20a&#39;, 20b&#39;. Note also that the list 8 of addresses A 1 , A 2  . . . A k , . . . is translated into a corresponding list of block numbers (&#34;Block --  No&#34;) and offset addresses within a block (&#34;OFFSET&#34;). 
     Referring now to FIG. 3, therein a computer system according to the present invention comprises block memory 34A, 34B, . . . 34N and addressing means 32 for interleaving the block memory. In a preferred embodiment, a computer 30 having an internal list 8 of addresses A 1 , A 2 , A 3  . . . , is coupled to memory blocks or cards 34A-34N via addressing means 32. The addressing means 32 and/or the cards 34A-34N need not be separate devices, but can be integrated into the computer 30. The addressing means 32 comprises the code and circuitry described above for addressing the respective blocks in an interleaved fashion. 
     Finally, it is noted that the preferred embodiments described herein can be modified in many ways that will be apparent to those skilled in the art. For instance, the order for carrying out the steps shown in FIG. 1 can be varied, and indeed the means, (hardware or software) for carrying out the method may be embodied in a variety of devices still within the scope of the invention. In addition, the formulae employed in the preferred embodiment to compute A and I need not use the log 2  function. Instead, the particular bits used for B --  bits, I --  bits and A --  bits may be masked with appropriate bit selection logic. Thus, e.g., blocks 14, 16 and 18 of FIG. 2, for routing I --  bits, B --  bits, etc., to the three-term adders, could be embodied in multiplex-type logic circuitry. In addition, if a system only supports one size of memory, these paths could be hardwired. Accordingly, the scope of the invention is not to be limited by the specific embodiments described above.