Abstract:
A Sweeney, Robertson, Tocher (SRT) divider for use in a computer system has recoding circuitry to recode the three most significant bits of the dividend into one-hot form as the dividend is loaded into a quotient/partial remainder register. With each clock, a partial remainder is generated also having its most significant three bits in one-hot form and the remaining bits in binary encoded form. 
     The divider has several stages permitting it to generate several bits of quotient in each clock cycle. Each stage has circuitry for estimating a quotient digit, and for computing a partial remainder by subtracting the product of the quotient digit times the divisor from either the dividend or a previous partial remainder. This subtraction is performed upon a one-hot code in the most significant bits and in binary code on the least significant bits. The divider also has circuitry for assembling a plurality of quotient digits into a quotient.

Description:
FIELD OF THE INVENTION 
     This invention relates to the field of high-speed division hardware for general purpose computer systems. In particular, it relates to the class of S.R.T. dividers capable of producing multiple bits of quotient per clock cycle through cascaded divider stages. 
     BACKGROUND OF THE INVENTION 
     Classical binary (radix-2) restoring, nonperforming, and nonrestoring dividers typically require one iteration or cycle, or one full divider stage, per bit of quotient generated. With these dividers, 32 cycles are required for division of a 64-bit dividend by a 32-bit divisor to produce a 32-bit quotient. 
     Dividers that operate in a radix greater than two, such as in radix 4 or radix 8 offer the possibility of performing division in fewer cycles or stages than radix 2 dividers. Radix 4 dividers can divide a 64-bit dividend by a 32 bit divisor to produce a 32 bit quotient in 16 cycles or stages, plus overhead, by producing two bits of quotient in each cycle. A radix 8 divider can perform this division in 11 cycles or stages, plus overhead, by producing three bits of quotient per cycle or divider stage. 
     Dividers that implement two or more cascaded divider stages can produce more than one quotient bit per cycle. These dividers can be challenging to build because of the amount of logic required. 
     SRT division has been in the news because a look-up-table having an incorrect entry in early Pentium processors. This division method, named after D. Sweeney, J. Robertson, and K. Tocher, is a nonrestoring division algorithm using a signed quotient digit set. 
     Prabhu, et al., describe an effectively radix 8 SRT divider in U.S. Pat. No. 5,870,323. Radix 8 SRT dividers like that of Prabhu, et al., may be used in high speed processors to produce more than one quotient bit per clock cycle. 
     SRT division is performed by iterating a sequence of 
     a. estimating one or more digits of quotient, based on the most significant bits, including sign, of the dividend or partial remainder and the divisor. The quotient digit may represent one or more bit positions in the eventual quotient. 
     b. subtracting a product of the quotient digit times the divisor from the dividend or partial remainder to form a new partial remainder. This subtraction is often performed in carry-save form in the least significant bits, but carry must be propagated in the most significant bits during either the subtraction or during the estimation of the next one or more digits of quotient. 
     c. shifting the quotient digit into a quotient register. 
     d. shifting the new partial remainder by at least one bit position(s) and iterating steps a, b, and c until sufficient digits of quotient have been obtained. 
     The divider of Prabhu, et al., has several, preferably three, overlapped stages of radix-2 SRT division to provide the effect of a high radix, preferably radix-8, divider. Three bits of quotient are generated in each clock cycle, one bit from each of the overlapped stages. 
     In each stage, a quotient selection logic look-up table, which may be implemented as logic gates, ROM or PLA, generates each estimate of quotient bits. Multiple quotient bit estimation logic circuits operating in sequence are provided to produce several quotient digits in each clock cycle. In parallel with the estimation of a first, a second, and a third digit, the divisor is multiplied by all possible values of the digit estimates, and these values are subtracted from the dividend or partial remainder to form a set of differences in carry-save form. A multiplexor, controlled by the estimates, then selects a new partial remainder from the set of differences. This computation of several possible differences, followed by selection of the difference corresponding to the digit generated, is speculative execution. In Prabhu&#39;s divider, the partial remainder is recycled in carry-save form, and speculative execution is used to achieve high-speed execution at the cost of many more carry-save adders than would be required without speculative execution. 
     It is known that SRT division can be performed with less speculative execution than in the divider of Prabhu, et. al. In this technique, quotient digit estimates are computed as described. The digit estimate is used to control a multiplexor that selects the divisor multiple corresponding to the digit, the selected divisor multiple is then subtracted from the dividend or partial remainder to form a new partial remainder. 
     One-hot encoding is known to be an alternative method of representing numbers or parts of numbers. One-hot encoding requires a number of lines equal to two raised to the power of the number of equivalent binary bits of the number or part of a number to be represented; hence one-hot encoding three binary bits requires eight lines, one-hot encoding four bits requires sixteen lines, etc. One-hot encoding is therefore rarely used to represent large numbers. 
     It is known that adding to one-hot encoded numbers is equivalent to shifting the one-hot encoded number by a number of bit positions equal to the number added to the one-hot encoded number. For example, two in eight-line one-hot encoded form is 0000 0100. Adding three to this is equivalent to left shifting by three places, to produce 0010 0000, or five in one-hot form. 
     SUMMARY OF THE INVENTION 
     It has been found that, if the most significant bits of partial remainder are generated initially in one-hot encoded form, it is possible to reduce the number of logic levels, and hence the time required for generation of each successive partial remainder. The one-hot encoded form of the most significant bits of the partial remainder is then recoded into a binary form when carry is propagated to produce a final remainder. 
     The reduction of logic levels occurs in part because one-hot encoded addition or subtraction is equivalent to a shift operation, with no need to separately propagate a carry signal, and in part because with a one-hot encoded partial remainder, few levels of logic are necessary to estimate each quotient digit. 
     It has also been found that with the most significant bits of the partial remainder in one-hot encoded form, the quotient digit estimate can be computed quickly enough that it is possible, in some dividers, to avoid using speculative execution logic during computation of the binary encoded less bits of each partial remainder. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a generalized computer system; 
     FIG. 2 a block diagram of the processor of the generalized computer system; 
     FIG. 3 an illustration of the bit fields of a floating point number as often used in typical computer systems; 
     FIG. 4 a block diagram of a portion of a floating point pipeline, showing an SRT divider generating one quotient bit per cycle; 
     FIG. 5 a block diagram of the core of an SRT divider embodying the present invention and generating two quotient bits per cycle with speculative execution; 
     FIG. 6 a block diagram of the core of a high-speed SRT divider embodying the present invention, generating two quotient bits per cycle, and having a merged datapath section with speculative execution; 
     FIG. 7 a block diagram of an integer divider embodying an SRT divider having one-hot encoded most significant bits of each partial remainder; and 
     FIG. 8 a block diagram of a high speed SRT divider embodying the present invention, generating two quotient bits per cycle, but without speculative execution. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Many computer systems used today, such as those portrayed in FIG. 1, have a processing element  100 . One or more additional processing elements  101  may also be present, as is supported by symmetric multiprocessing operating systems including Solaris, Linux, and Windows NT. Each processing element usually has a processor  102 , a Cache memory  103 , and a memory manager  104  that determines which memory addresses are cacheable and translates memory addresses from a virtual address space to a physical address space. 
     Each processing element  100  communicates over one or more data busses  105  to a main memory  106 , which may include additional memory management and caching functions, and, often through a bus bridge  107  and an additional bus  108 , to I/O devices  109 , including disk memory devices  110 . There are many ways of implementing such computer systems, for example some of the I/O functions  109 , including the Disk Memory  110 , may communicate directly with the main memory. 
     In the processor  102  of each processing element, as shown in FIG. 2, there is usually a unit for fetching instructions and tracking instruction addresses  200 , an instruction decoder and dispatcher  201 , and a data fetch and store unit  202  that conducts data transfers between a multiport register file  203  and the various memory and I/O devices of the system, including the cache memory  103 , main memory  106 , disk memory  110  and I/O devices  109 . There are also usually a floating point execution pipeline  204  and an integer execution pipeline  205  that receive data from the multiport register file  203 , operate upon it, and write results back to the multiport register file  203 . The floating point execution pipeline  204  and integer execution pipeline  205  may alternatively be combined into one unit; or a single divider may be shared by both units to perform integer division and division of floating point mantissas. 
     Floating point numbers, as shown in FIG. 3, are usually comprised of three separate fields. A sign bit  300  represents whether the number is positive or negative. The magnitude of the floating point number is that of the mantissa field value  301  multiplied by a base value raised to the power indicated by an exponent field  302 . The base value is fixed for each floating point format, two being a common base value. The IEEE 754 specification provides detailed descriptions of a single precision floating point format, where all three fields fit in a 32-bit word and having 24 bits (including one hidden bit) of mantissa, and a double precision floating point format where all three fields fit in a 64-bit word and having 52 bits allocated to the mantissa. One extra, or hidden, mantissa bit is available because of the way in which normalization is performed, so the mantissa is effectively a 53 bit number. The mantissa portion of the number is always positive, negative numbers are represented through the sign bit; hence the product of a pair of mantissas is always positive. 
     The bits of the operand are numbered for purposes of this discussion such that bit  0  is the least significant bit of the mantissa. For a single precision operand, bit  31  is the sign bit, and bit  22  the most significant bit of the mantissa (there is one additional “hidden” bit). Similarly, for double precision operands, bit  63  is the sign bit, the hidden bit is the most significant bit of the mantissa, and bit  51  the second most significant bit of the mantissa with bit  0  the least significant bit of mantissa. 
     FIG. 4 illustrates the functions performed by a floating point pipeline, embodying the present invention, during execution of a floating point division. Pipeline registers are not shown. This figure illustrates a single-stage divider. 
     A floating point divisor  400  is split into an exponent, a sign, and a mantissa field by exponent/mantissa splitter  401 . Similarly, a floating point dividend  402  is split into its exponent, sign, and mantissa fields by exponent mantissa splitter  403 . The sign path is not shown. An exponent subtractor  404  subtracts the divisor exponent from the dividend exponent to produce a raw quotient exponent  405 . 
     The dividend mantissa is fed through an MSB recoder  410  to a Dividend/recycled remainder register  411 . MSB recoder  410  operates on the most significant three bits of the dividend, recoding these bits in one-hot form, while passing less significant bits unaltered. 
     The most significant bits of the dividend mantissa from the dividend/recycled remainder register  411  and the most significant bits of the divisor mantissa  412  (for radixes greater than two) from the divisor exponent/mantissa splitter are fed to a quotient digit predictor  413 . Simultaneously, the divisor mantissa  412  is fed to a carry-save-adder (CSA) based, multiplier &amp; subtractor array  414 . For speed, the multiplier and subtractor array  414  has two sections, a first section generates products of all possible values of quotient digit  413  times the divisor  412 , and a second section subtracts these products from the dividend/recycled remainder register  411 , generating a set of outputs of all possible differences of the dividend/recycled remainder register and products of the divisor times a quotient digit. Multiplexor array  415  selects the member of the set of all possible differences corresponding to the predicted quotient digit  416  from quotient digit predictor  413 . The selected difference from multiplexor array  415  is shifted left by shifter  417 , recoded as necessary such that the equivalent of its most significant three bits are in one-hot form, and recycled into the dividend/recycled remainder register  411  as a partial remainder (PR). 
     Each predicted quotient digit  416  is assembled in a quotient assembly register  420 . This process is iterated until all desired quotient bits have been assembled. When all desired quotient bits are assembled, redundancy in the quotient is removed by propagating carry in the quotient assembly register  420  to form a raw mantissa quotient  420   a ; and carry may optionally be propagated by carry propagator  421  on the contents of the dividend/recycled remainder register  411  to form a remainder  422 . The raw mantissa quotient  420   a  and the raw quotient exponent  405  are then normalized by Normalizer and Exception Generator  425  to form a floating point quotient  426 . In event of divide overflow or other error conditions, Normalizer and Exception Generator  425  generates an exception or error flag and an error or not-a-number code for the floating point quotient  426  according to the rules of IEEE 754. 
     The MSB recoder  410 , Dividend/recycled remainder register  411 , quotient digit predictor  413 , CSA Multiplier and Subtractor array  414 , multiplexor array  415 , shifter  417 , quotient assembly register  420 , and carry propagator  421 , with associated control logic including an iteration counter to control iteration of the division, together comprise the SRT divider  430 . 
     The primary advantage of this SRT divider is that, with one-hot coding of the most significant bits of dividend/recycled remainder register  411 , fewer levels of logic are required for paths through the quotient digit predictor  413 , CSA Multiplier &amp; subtractor array  414 , Multiplexor array  415 , and shifter  417  than with ordinary binary coding. This results in part because carry propagation is inherent during subtraction of the one-hot encoded most significant bits of the dividend/recycled remainder, the only bits over which carry must be propagated during each cycle. A multiplexor array, or barrel, shifter is used for this one-hot encoded subtractor. 
     FIG. 4 portrays a basic SRT divider that produces one quotient bit per cycle of the iterative division process. The iterative process may be, and preferably is, unrolled to provide for generation of two, three, or more bits of quotient per cycle. 
     The core of an SRT divider embodying one-hot coding of the most significant bits of the dividend and unrolled to generate two bits of quotient per cycle is detailed in FIG.  5 . The divisor  500  enters a divisor multiplier  501  that generates the possible products of possible quotient digits times the divisor, including negative one times the divisor  502  and one times the divisor  503 . A third possible product, zero, equal to a possible quotient digit of zero times the divisor, is optimized out of the logic. The divider is divided into a control section  504  that operates upon the one-hot coded portion  506  of the dividend or partial remainder  515 , and a datapath section  504   a  that operates upon the binary encoded portion  507  of the dividend or partial remainder. 
     A dividend  505  enters with its most significant binary three bits recoded into eight lines of one-hot encoded form  506 . Remaining bits of dividend  505  remain in binary-encoded form  507 . A top few bits  508  of the divisor  500  may, but are not required to, enter each of two quotient selection logic blocks  509  and  510  in the control section  504  of the divider, these divisor bits are necessary for quotient digit estimation for all radixes greater than two and are optional in the radix-two divider stages of FIG. 5. A pipeline latch for the dividend during a first iteration and for a partial remainder during further iterations of the division is shown at  515  and  516 . 
     The one-hot encoded portion  517  of the dividend enters the first quotient selection logic  509 , which generates a quotient digit  519 , here q(i+1), selected from the set {−1,0,+1}, as this embodiment comprises two cascaded stages of radix-2 SRT division. The dividend enters the control section  504  of the divider through a one-hot pipeline register  515 , the output  517  of which enters the first quotient selection logic  509 . A group of one-hot adders  520  subtract the upper portion of the possible divisor products  502  and  503  from the dividend or partial remainder  517  upper portion, the outputs of which are fed to partial remainder selection multiplexor  521 , with the output  517  of pipeline register  515  that is the sum when the quotient digit  519  is zero. A barrel shifter array of multiplexers is used for one-hot addition and subtraction, with output remaining in one-hot form. Partial remainder selection multiplexor  521  produces a partial remainder  522  most significant portion. 
     The low, binary encoded, portion of the dividend enters the datapath  504   a  section of the divider through quotient/partial remainder low portion pipeline register  516 . The quotient digit  519  also controls a partial remainder selection multiplexor  525  in the datapath  504   a  portion of the divider. Multiplexor  525  selects between the pipeline register  516  and the sums of the possible products  526  (formed by subtracting the lesser bits of the divisor products  502  and  503  from the contents of the pipeline register  516  in an array of carry-save adders  527 ). This multiplexor  525  produces a low, binary encoded, portion of a partial remainder  528 . 
     The most significant bit, both of the sum vector and carry vector, of the low portion partial remainder  528  are considered by the second stage quotient selection logic  510 . 
     The most significant bit portion  522  of the first partial remainder enters the second quotient selection logic  510 , generating a second quotient digit  530 . A one-hot adder array  531  produces a set of possible partial remainders  532 , which, along with the most significant bit portion  522  of the first partial remainder, are selected according to the second quotient digit  530  by a second high portion partial remainder selection multiplexor  533  to produce a second partial remainder high portion  534 . 
     The low, binary encoded, partial remainder portion  528  also enters a set of adders  540  that produce a set of possible differences  541  of quotient digit times the divisor. The second quotient digit  530  selects between these possible differences  541  in multiplexor  542  to produce a low, binary encoded, portion of a second partial remainder  543 . This low portion of the second partial remainder is shifted by a partial remainder shifter (not shown) and redeposited in the dividend/partial remainder low portion pipeline register  516 . Since the partial remainder shifter need shift only by a constant number of bit positions, it is implemented by wiring partial remainder  543  bits N to input bits N+n of dividend/partial remainder register  516 . 
     A few upper bits  544  of the low portion of the second partial remainder  543 , together with the second partial remainder high portion  534 , are processed into a shifted, one-hot encoded top portion  545  by a propagator  546 , and deposited into one-hot pipeline register  515 . 
     The quotient digits  519  and  530  are assembled into a quotient by a quotient assembly register (not shown). 
     An alternative embodiment having a two-bit merged datapath section is portrayed in FIG.  6 . In this embodiment, divisor  600  enters through a multiplier array  601  that provides all the possible products of a pair of single quotient digits times the divisor  602 : minus three times the divisor, minus two times the divisor, minus the divisor, the divisor, two times the divisor, and three times the divisor. Zero times the divisor is optimized out of the logic. 
     The dividend  605  enters the alternative embodiment of FIG. 6 into dividend/partial remainder high part one-hot encoded pipeline register  606  and dividend/partial remainder low portion pipeline register  607 . The most significant three bits  608  of dividend  605  enter the pipeline register  606  through a one-hot encoder  609 . 
     As with the embodiment of FIG. 5, the most significant bits  615  (FIG. 6) of the divisor  600  may enter the control section  616  of the embodiment of FIG. 6 into a first  617  and a second  618  quotient selection logic element. The contents  620  of the high part pipeline register  606  also enter the first  617  quotient selection logic and a one-hot encoded adder array  621 . Adder array  621  adds the high portions of the minus divisor and plus divisor terms of the possible products of a pair of single quotient digits times the divisor  602  to the contents  620  of the high part pipeline register  606 , producing an array of sums  622 . 
     The first quotient selection logic  617  produces a first quotient digit  625 , that controls a first partial remainder top portion multiplexor  626  to generate a first partial remainder top portion  627 . Unlike the embodiment of FIG. 5, no first partial remainder lower portion is produced. 
     The first partial remainder top portion  627  is fed to the second quotient digit selection logic  618  to generate a second quotient digit  630 , and to a one-hot encoded adder barrel shifter array  631  that adds the high portions of the minus divisor and plus divisor terms of the possible products of a pair of single quotient digits times the divisor  602 , producing an array of sums  632 . 
     The second quotient digit  630  then controls a second partial remainder top portion multiplexor  635  to generate a second partial remainder top portion  636 . 
     In the datapath  640  portion of the divider of FIG. 6, a binary-encoded portion of the low portion pipeline register  607  is fed to a carry-save adder array  641  and to a low portion partial remainder selection multiplexor  642 . The array of possible products of a pair of single quotient digits times the divisor  602  is also fed to carry-save adder array  641 , which produces an array of all the possible differences  643  of the low portion pipeline register  607  and the possible products of a pair of single quotient digits times the divisor  602 . 
     The first  625  and second  630  quotient digits are combined  645  to control the low portion partial remainder selection multiplexor  642 , which selects a low portion partial remainder  646 . The low portion partial remainder  646  is shifted by a shifter  647 , before being latched in the low portion pipeline register  607 . The most significant bits of the low portion partial remainder  646  and the second partial remainder top portion  636  are combined and shifted in propagator  650  to produce a new one-hot encoded partial remainder high portion  651  that is latched into the high part pipeline register  606 . 
     In operation, in a preliminary cycle, the dividend mantissa portion from an exponent/mantissa splitter has its most significant bits one-hot encoded by encoder  609  and is latched into the pipeline registers  606  and  607 , and the divisor  600  is presented to the multiplier array  601 . 
     In a first iteration, a first two, most significant, bits of quotient are generated by quotient selection logic elements  617  and  618 , these quotient bits then generate a first iteration partial remainder one-hot encoded high portion at propagator  650  and a binary-encoded first iteration partial remainder low portion at shifter  647 , these first iteration partial remainders are latched into pipeline registers  606  and  607 . This quotient bit pair is latched into the quotient assembly register most significant bits. 
     In a second and subsequent iterations, additional quotient bit pairs are generated by quotient selection logic elements  617  and  618 , these quotient bits being used to generate further iteration partial remainder one-hot encoded high portions at the output of propagator  650  and a binary-encoded further iteration partial remainder low portions at the output of shifter  647 . The further iteration partial remainders are latched into the pipeline registers  606  and  607 . These quotient bit pairs are latched into the quotient assembly register next most significant bits. A counter and appropriate control logic (not shown) control which bits of the quotient assembly register are loaded in each iteration and the number of iterations. 
     In this implementation, the second quotient selection logic  618  requires information equivalent to the result of the most significant bits of the lower portion subtraction. This is obtained by duplication logic  650 , that uses the most significant two bits of the lower section dividend/partial remainder register  607 , a few bits from the −D and +D possible digit products times the divisor  602 , and the first quotient selection logic  617  output  625 , to generate the equivalent  651  of the most significant bit of an intermediate partial remainder lower portion. 
     Upon completion of sufficient iterations, an assembled quotient is present in the quotient assembly register. The redundancies in the assembled quotient are reduced by carry propagation logic of the type known in the art of SRT dividers and normalized as required. 
     A one-hot encoded SRT divider embodying the present invention may also be used to perform integer division, as shown in FIG.  7 . In this embodiment, positive integers are assumed, signed integers may be converted to positive integers by logic well known in the art, or the divider may be designed to handle signed integers by converting the one-bit detectors disclosed to detectors of the first bit that does not match the sign bit. 
     An integer divisor  700  enters through a one-bit detector  701 , that detects the identity of the most significant bit that does not match the sign (zero for positive integers) of the divisor. A barrel shifter  702  left-shifts the divisor  700  such that the most significant bit that does not match the sign is in the most significant bit position of a shifted divisor  703 . 
     Similarly, an integer dividend  705  enters through a one-bit detector  706 , that detects the identity of the most significant bit that does not match the sign (zero for positive integers) of the dividend. A barrel shifter  707  left-shifts the dividend  705  such that the most significant bit that does not match the sign is in the most significant bit position of a shifted dividend  708 . 
     The shifted divisor  703  and shifted dividend  708  then enter a divider core  710 , such as the divider core of FIG. 6, that performs the division iterations and produces a sequence of quotient digits  711 . The quotient digits  711  are assembled in a quotient digit assembler  712 , and redundancy is removed to form a binary quotient in carry propagator  713  to form a raw quotient  714 . 
     An adjustment calculator and exception generator  720  examines the bit count of the most significant bits of both divisor and dividend as reported by the one-bit detectors  701  and  706 . The adjustment calculator determine a count  721  of bit positions by which the raw quotient  714  must be shifted by a barrel shifter  722  to form a correct integer quotient  723 . The adjustment calculator and exception generator  720  also determines when a divide by zero error condition must be reported. 
     The core of an SRT divider embodying one-hot coding of the most significant bits of the dividend, unrolled to generate two bits of quotient per cycle, and without speculative execution in subtraction to form the next partial remainder is detailed in FIG.  8 . The divisor  800  enters a divisor multiplier  801  that generates the possible products of possible quotient digits times the divisor, including negative one times the divisor  802  and one times the divisor  803 . A third possible product, zero, equal to a possible quotient digit of zero times the divisor, is optimized out of the logic. The divider is divided into a control section  804  that operates upon the one-hot coded portion  806  of the dividend or partial remainder  805 , and a datapath section  804   a  that operates upon the binary encoded portion  807  of the dividend or partial remainder. 
     A dividend  805  enters with its most significant binary three bits recoded into eight lines of one-hot encoded form  806 . Remaining bits of dividend  805  remain in binary-encoded form  807 . A top few bits  808  of the divisor  800  may enter each of two quotient selection logic blocks  809  and  810  in the control section  804  of the divider, these bits must enter the quotient selection logic in divider stages having radix greater than two, the may optionally enter the quotient selection logic in the divider having two cascaded radix-two stages illustrated in FIG. 8. A pipeline latch for the dividend during a first iteration and for a partial remainder during further iterations of the division is shown at  815  and  816 . 
     The one-hot encoded portion  817  of the dividend enters the first quotient selection logic  809 , which generates a quotient digit  819 , here q(i+l), selected from the set {−1,0,+1}, as this embodiment comprises two cascaded stages of radix-2 SRT division. The quotient enters the control section  804  of the divider through a one-hot pipeline register  815 , the output  817  of which enters the first quotient selection logic  809 . A group of one-hot adders  820  add the most significant bits of the possible divisor products  802  and  803 , the outputs of which are fed to partial remainder selection multiplexor  821 , with the output  817  of pipeline register  815  that is the sum when the quotient digit  819  is zero. A barrel shifter array of multiplexers is used for one-hot addition or subtraction, as required, with output remaining in one-hot form. Partial remainder selection multiplexor  821  produces a partial remainder  822  most significant portion. This embodiment therefore uses speculative execution in computing the high, one-hot encoded, bits of each partial remainder. 
     The low, binary encoded, portion of the dividend enters the datapath  804   a  section of the divider through quotient/partial remainder low portion pipeline register  816 . The quotient digit  819  also controls an operand selection multiplexor  825  in the datapath  504   a  portion of the divider. Multiplexor  825  selects between the possible products of the quotient digit times the divisor, including minus the divisor  802 , zero, and the divisor  803 . The selected product of the quotient digit times the divisor is subtracted from the partial remainder low portion in the pipeline latch  816  by a carry save adder  826 . Carry save adder  826  produces a low, binary encoded, portion of a partial remainder  828  without speculative execution of the subtraction. The most significant bits of the low portion partial remainder  828  are considered by the second quotient selection logic  810 . 
     The most significant bit portion  822  of the first partial remainder enters the second quotient selection logic  810 , generating a second quotient digit  830 . A one-hot adder array  831  produces a set of possible partial remainders  832 , which, along with the most significant bit portion  822  of the first partial remainder, are selected according to the second quotient digit  830  by a second high portion partial remainder selection multiplexor  833  to produce a second partial remainder high portion  834 . 
     The second quotient digit  830  selects between the possible products −D,  802 , zero, and +D  803  of a quotient digit and the divisor  800  in a multiplexor  840  to form a selected product  841 . Selected product  841  is subtracted by a carry-save adder  842  from the intermediate partial remainder  828  to produce a low, binary encoded, portion of a second partial remainder  843 . This low portion of the second partial remainder is shifted by a partial remainder shifter (not shown) and redeposited in the dividend/partial remainder low portion pipeline register  816 . Since the partial remainder shifter need shift only by a constant number of bit positions, it is implemented by wiring partial remainder  843  bits N to input bits N+n of dividend/partial remainder register  816 . 
     A few upper bits  844  of the low portion of the second partial remainder  843 , together with the second partial remainder high portion  834 , are processed into a shifted, one-hot encoded top portion  845  by a propagator  846 , and deposited into one-hot pipeline register  815 . 
     The quotient digits  819  and  830  are assembled into a quotient by a quotient assembly register (not shown). 
     The invention has been shown with reference to particular preferred embodiments. It will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention. For example, the number of dividend and partial remainder most significant bits that are one-hot encoded may be increased from three to a higher number such as six (for radix four operation), as may be desirable in operating at an effective radix. The number of bits of quotient, divisor, and dividend may vary from the embodiments set forth, the effective radix may be some other value than two or four, and the number of iterations will vary with effective radix and operand lengths. Further, the multiport register file may be divided into separate register arrays for the integer and for the floating point pipelines. It is understood that the invention is defined by the scope of the following claims.