The R10000 , code-named "T5", is a RISC microprocessor implementation of the MIPS IV instruction set architecture (ISA) developed by MIPS Technologies, Inc. (MTI), then a division of Silicon Graphics, Inc. (SGI). The chief designers are Chris Rowen and Kenneth C. Yeager. The R10000 microarchitecture is known as ANDES, an abbreviation for Architecture with Non-sequential Dynamic Execution Scheduling. The R10000 largely replaces the R8000 in the high-end and the R4400 elsewhere. MTI was a fabless semiconductor company ; the R10000 was fabricated by NEC and Toshiba . Previous fabricators of MIPS microprocessors such as Integrated Device Technology (IDT) and three others did not fabricate the R10000 as it was more expensive to do so than the R4000 and R4400.
77-501: The R10000 was introduced in January 1996 at clock frequencies of 175 MHz and 195 MHz. A 150 MHz version was introduced in the O2 product line in 1997, but discontinued shortly after due to customer preference for the 175 MHz version. The R10000 was not available in large volumes until later in the year due to fabrication problems at MIPS's foundries. The 195 MHz version
154-516: A barrel shifter and hardware for confirming the prediction of conditional branches. The second pipeline is used to access the multiplier and divider. Multiplies are pipelined, and have a six-cycle latency for 32-bit integers and ten for 64-bit integers. Division is not pipelined. The divider uses a non-restoring algorithm that produces one bit per cycle. Latencies for 32-bit and 64-bit divides are 35 and 67 cycles, respectively. The floating-point unit (FPU) consists of four functional units, an adder,
231-467: A 0.25 μm CMOS process with four levels of aluminum interconnect . The use of a new process does not mean that the R12000 was a simple die shrink with a tweaked microarchitecture; the layout of the die is optimized to take advantage of the 0.25 μm process. The NEC fabricated VR12000 contained 7.15 million transistors and measured 15.7 by 14.6 mm (229.22 mm). The R12000A is a derivative of
308-654: A 0.25 μm process enabled the microprocessor to reach 250 MHz. Users of the R10000 include: The R10000 is a four-way superscalar design that implements register renaming and executes instructions out-of-order . Its design is a departure from previous MTI microprocessors such as the R4000, which is a much simpler scalar in-order design that relies largely on high clock rates for performance. The R10000 fetches four instructions every cycle from its instruction cache . These instructions are decoded and then placed into
385-527: A 144-bit bus, of which 128 bits are for data and 16 bits for ECC. The L3 cache's clock rate would be programmable. The R18000 was to be fabricated in NEC's UX5 process, a 0.13 μm CMOS process with nine levels of copper interconnect . It would have used 1.2 V power supply and dissipated less heat than contemporary server microprocessors in order to be densely packed into systems. Superscalar A superscalar processor (or multiple-issue processor )
462-477: A 32 KB instruction cache and a 32 KB data cache. The instruction cache is two-way set-associative and has a 128-byte line size. Instructions are partially decoded by appending four bits to each instruction (which have a length of 32 bits) before they are placed in the cache. The 32 KB data cache is dual-ported through two-way interleaving. It consists of two 16 KB banks , and each bank are two-way set-associative. The cache has 64-byte lines, uses
539-406: A close approximation to the final quotient and produce twice as many digits of the final quotient on each iteration. Newton–Raphson and Goldschmidt algorithms fall into this category. Variants of these algorithms allow using fast multiplication algorithms . It results that, for large integers, the computer time needed for a division is the same, up to a constant factor, as the time needed for
616-437: A computation point of view, the expressions X i + 1 = X i + X i ( 1 − D X i ) {\displaystyle X_{i+1}=X_{i}+X_{i}(1-DX_{i})} and X i + 1 = X i ( 2 − D X i ) {\displaystyle X_{i+1}=X_{i}(2-DX_{i})} are not equivalent. To obtain
693-493: A full-width subtraction. This simplification in turn allows a radix higher than 2 to be used. Like non-restoring division, the final steps are a final full-width subtraction to resolve the last quotient bit, and conversion of the quotient to standard binary form. The Intel Pentium processor's infamous floating-point division bug was caused by an incorrectly coded lookup table. Five of the 1066 entries had been mistakenly omitted. Newton–Raphson uses Newton's method to find
770-669: A given CPU): Seymour Cray 's CDC 6600 from 1964 is often mentioned as the first superscalar design. The 1967 IBM System/360 Model 91 was another superscalar mainframe. The Intel i960 CA (1989), the AMD 29000 -series 29050 (1990), and the Motorola MC88110 (1991), microprocessors were the first commercial single-chip superscalar microprocessors. RISC microprocessors like these were the first to have superscalar execution, because RISC architectures free transistors and die area which can be used to include multiple execution units and
847-413: A multiplexed bus to a system controller, which would interface the microprocessors to their local memory and the rest of the system via a hypercube network. The R18000 improved the floating-point instruction queues and revised the floating-point unit to feature two multiply–add units, quadrupling the peak FLOPS count. Division and square-root would be performed in separate non-pipelined units in parallel to
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#1732787330757924-462: A multiplication, whichever multiplication algorithm is used. Discussion will refer to the form N / D = ( Q , R ) {\displaystyle N/D=(Q,R)} , where is the input, and is the output. The simplest division algorithm, historically incorporated into a greatest common divisor algorithm presented in Euclid's Elements , Book VII, Proposition 1, finds
1001-636: A multiplier, divide unit and square root unit. The adder and multiplier are pipelined, but the divide and square root units are not. Adds and multiplies have a latency of three cycles and the adder and multiplier can accept a new instruction every cycle. The divide unit has a 12- or 19-cycle latency, depending on whether the divide is single precision or double precision, respectively. The square root unit executes square root and reciprocal square root instructions. Square root instructions have an 18- or 33-cycle latency for single precision or double precision, respectively. A new square root instruction can be issued to
1078-445: A property that becomes extremely valuable when the numbers involved have many digits (e.g. in the large integer domain). But it also means that the initial convergence of the method can be comparatively slow, especially if the initial estimate X 0 {\displaystyle X_{0}} is poorly chosen. For the subproblem of choosing an initial estimate X 0 {\displaystyle X_{0}} , it
1155-409: A result with a precision of 2 n bits while making use of the second expression, one must compute the product between X i {\displaystyle X_{i}} and ( 2 − D X i ) {\displaystyle (2-DX_{i})} with double the given precision of X i {\displaystyle X_{i}} ( n bits). In contrast,
1232-439: A single processor. Thus a multicore CPU is possible where each core is an independent processor containing multiple parallel pipelines, each pipeline being superscalar. Some processors also include vector capability. Division algorithm#SRT division A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or remainder ,
1309-442: A standard recurrence equation where: Restoring division operates on fixed-point fractional numbers and depends on the assumption 0 < D < N . The quotient digits q are formed from the digit set {0,1}. The basic algorithm for binary (radix 2) restoring division is: Non-performing restoring division is similar to restoring division except that the value of 2R is saved, so D does not need to be added back in for
1386-436: A superscalar CPU the dispatcher reads instructions from memory and decides which ones can be run in parallel, dispatching each to one of the several execution units contained inside a single CPU. Therefore, a superscalar processor can be envisioned as having multiple parallel pipelines, each of which is processing instructions simultaneously from a single instruction thread. Most modern superscalar CPUs also have logic to reorder
1463-527: A unit of time) than would otherwise be possible at a given clock rate . Each execution unit is not a separate processor (or a core if the processor is a multi-core processor ), but an execution resource within a single CPU such as an arithmetic logic unit . While a superscalar CPU is typically also pipelined , superscalar and pipelining execution are considered different performance enhancement techniques. The former (superscalar) executes multiple instructions in parallel by using multiple execution units, whereas
1540-478: A zero at X = 1 / D {\displaystyle X=1/D} . The obvious such function is f ( X ) = D X − 1 {\displaystyle f(X)=DX-1} , but the Newton–Raphson iteration for this is unhelpful, since it cannot be computed without already knowing the reciprocal of D {\displaystyle D} (moreover it attempts to compute
1617-486: Is 640 MB/s as it requires some cycles to transmit addresses. The system interface controller supports glue-less symmetrical multiprocessing (SMP) of up to four microprocessors. Systems using the R10000 with external logic can scale to hundreds of processors. An example of such a system is the Origin 2000 . The R10000 consists of approximately 6.8 million transistors, of which approximately 4.4 million are contained in
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#17327873307571694-459: Is R >> n. (As with restoring division, the low-order bits of R are used up at the same rate as bits of the quotient Q are produced, and it is common to use a single shift register for both.) SRT division is a popular method for division in many microprocessor implementations. The algorithm is named after D. W. Sweeney of IBM , James E. Robertson of University of Illinois , and K. D. Tocher of Imperial College London . They all developed
1771-494: Is a CPU that implements a form of parallelism called instruction-level parallelism within a single processor. In contrast to a scalar processor , which can execute at most one single instruction per clock cycle, a superscalar processor can execute more than one instruction during a clock cycle by simultaneously dispatching multiple instructions to different execution units on the processor. It therefore allows more throughput (the number of instructions that can be executed in
1848-673: Is a derivative of the R10000 started by MIPS and completed by SGI. It was fabricated by NEC and Toshiba. The version fabricated by NEC is called the VR12000. The microprocessor was introduced in November 1998. It is available at 270, 300 and 360 MHz. The R12000 was developed as a stop-gap solution following the cancellation of the "Beast" project, which intended to deliver a successor to the R10000. R12000 users include NEC, Siemens-Nixdorf , SGI and Tandem Computers (and later Compaq, after their acquisition of Tandem). The R12000 improves upon
1925-426: Is an 800 MHz version, introduced on 4 February 2004. Later, a 900 MHz version was introduced, and this version was, for some time, the fastest publicly known R16000A—SGI later revealed there were 1.0 GHz R16000s shipped to selected customers. R16000 users included HP and SGI. SGI used the microprocessor in their Fuel and Tezro workstations; and the Origin 3000 servers and supercomputers. HP used
2002-424: Is chosen from five possibilities: { −2, −1, 0, +1, +2 }. Because of this, the choice of a quotient digit need not be perfect; later quotient digits can correct for slight errors. (For example, the quotient digit pairs (0, +2) and (1, −2) are equivalent, since 0×4+2 = 1×4−2.) This tolerance allows quotient digits to be selected using only a few most-significant bits of the dividend and divisor, rather than requiring
2079-496: Is convenient to apply a bit-shift to the divisor D to scale it so that 0.5 ≤ D ≤ 1; by applying the same bit-shift to the numerator N , one ensures the quotient does not change. Then one could use a linear approximation in the form to initialize Newton–Raphson. To minimize the maximum of the absolute value of the error of this approximation on interval [ 0.5 , 1 ] {\displaystyle [0.5,1]} , one should use The coefficients of
2156-412: Is exponentially slower than even slow division algorithms like long division. It is useful if Q is known to be small (being an output-sensitive algorithm ), and can serve as an executable specification. Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting
2233-426: Is no assurance otherwise and failure to detect a dependency would produce incorrect results. No matter how advanced the semiconductor process or how fast the switching speed, this places a practical limit on how many instructions can be simultaneously dispatched. While process advances will allow ever greater numbers of execution units (e.g. ALUs), the burden of checking instruction dependencies grows rapidly, as does
2310-427: Is protected by 9-bits of error correcting code (ECC). The cache and bus operate at the same clock rate as the R10000, whose maximum frequency was 200 MHz. At 200 MHz, the bus yielded a peak bandwidth of 3.2 GB/s. The cache is two-way set associative, but to avoid a high pin count, the R10000 predicts which way is accessed. MIPS IV is a 64-bit architecture, but to reduce cost the R10000 does not implement
2387-454: Is removed and delegated to the compiler . Explicitly parallel instruction computing (EPIC) is like VLIW with extra cache prefetching instructions. Simultaneous multithreading (SMT) is a technique for improving the overall efficiency of superscalar processors. SMT permits multiple independent threads of execution to better utilize the resources provided by modern processor architectures. The fact that they are independent means that we know that
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2464-480: Is the difference between scalar and vector arithmetic. A superscalar processor is a mixture of the two. Each instruction processes one data item, but there are multiple execution units within each CPU thus multiple instructions can be processing separate data items concurrently. Superscalar CPU design emphasizes improving the instruction dispatcher accuracy and allowing it to keep the multiple execution units in use at all times. This has become increasingly important as
2541-585: Is the last derivative of the R10000. It is developed by SGI and fabricated by NEC in their 0.11 μm process with eight levels of copper interconnect. The microprocessor was introduced on 9 January 2003, debuting at 700 MHz for the Fuel and also used in their Onyx4 Ultimate Vision . In April 2003, a 600 MHz version was introduced for the Origin 350 . Improvements are 64 KB instruction and data caches. The R16000A refers to R16000 microprocessors with clock rates higher than 700 MHz. The first R16000A
2618-430: Is trivial: perform a ones' complement (bit by bit complement) on the original Q {\displaystyle Q} . Finally, quotients computed by this algorithm are always odd, and the remainder in R is in the range −D ≤ R < D. For example, 5 / 2 = 3 R −1. To convert to a positive remainder, do a single restoring step after Q is converted from non-standard form to standard form: The actual remainder
2695-644: The ALU , integer multiplier , integer shifter, FPU , etc. There may be multiple versions of each execution unit to enable the execution of many instructions in parallel. This differs from a multi-core processor that concurrently processes instructions from multiple threads, one thread per processing unit (called "core"). It also differs from a pipelined processor , where the multiple instructions can concurrently be in various stages of execution, assembly-line fashion. The various alternative techniques are not mutually exclusive—they can be (and frequently are) combined in
2772-621: The convergence is exactly quadratic, it follows that steps are enough to calculate the value up to P {\displaystyle P\,} binary places. This evaluates to 3 for IEEE single precision and 4 for both double precision and double extended formats. The following computes the quotient of N and D with a precision of P binary places: For example, for a double-precision floating-point division, this method uses 10 multiplies, 9 adds, and 2 shifts. The Newton-Raphson division method can be modified to be slightly faster as follows. After shifting N and D so that D
2849-480: The reciprocal of D {\displaystyle D} and multiply that reciprocal by N {\displaystyle N} to find the final quotient Q {\displaystyle Q} . The steps of Newton–Raphson division are: In order to apply Newton's method to find the reciprocal of D {\displaystyle D} , it is necessary to find a function f ( X ) {\displaystyle f(X)} that has
2926-420: The write-back protocol, and is virtually indexed and physically tagged to enable the cache to be indexed in the same clock cycle and to maintain coherency with the secondary cache. The external secondary unified cache supported capacities between 512 KB and 16 MB. It is implemented with commodity synchronous static random access memory (SSRAM). The cache is accessed via its own 128-bit bus that
3003-423: The R10000 microarchitecture by: inserting an extra pipeline stage to improve clock frequency by resolving a critical path; increasing the number of entries in the branch history table, improving prediction; modifying the instruction queues so they take into account the age of a queued instruction, enabling older instructions to be executed before newer ones if possible. The R12000 was fabricated by NEC and Toshiba in
3080-461: The R12000 developed by SGI. Introduced in July 2000, it operates at 400 MHz and was fabricated by NEC a 0.18 μm process with aluminum interconnects . The R14000 is a further development of the R12000 announced in July 2001. The R14000 operates at 500 MHz, enabled by the 0.13 μm CMOS process with five levels of copper interconnect it is fabricated with. It features improvements to
3157-531: The R16000A in their NonStop Himalaya S-Series fault-tolerant servers inherited from Tandem via Compaq. The R18000 is a canceled further development of the R10000 microarchitecture that featured major improvements by Silicon Graphics, Inc. described at the Hot Chips symposium in 2001. The R18000 was designed specifically for SGI's ccNUMA servers and supercomputers. Each node would have two R18000s connected via
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3234-531: The SysAD or Avalanche configuration for backwards compatibility with R10000 systems. The R18000 would have a 1 MB four-way set-associative secondary cache to be included on-die; supplemented by an optional tertiary cache built from single data rate (SDR) or double data rate (DDR) SSRAM or DDR SDRAM with capacities of 2 to 64 MB. The L3 cache would have its cache tags, equivalent to 400 KB, located on-die to reduce latency. The L3 cache would be accessed via
3311-519: The algorithm independently at approximately the same time (published in February 1957, September 1958, and January 1958 respectively). SRT division is similar to non-restoring division, but it uses a lookup table based on the dividend and the divisor to determine each quotient digit. The most significant difference is that a redundant representation is used for the quotient. For example, when implementing radix-4 SRT division, each quotient digit
3388-553: The case of R < 0. Non-restoring division uses the digit set {−1, 1} for the quotient digits instead of {0, 1}. The algorithm is more complex, but has the advantage when implemented in hardware that there is only one decision and addition/subtraction per quotient bit; there is no restoring step after the subtraction, which potentially cuts down the numbers of operations by up to half and lets it be executed faster. The basic algorithm for binary (radix 2) non-restoring division of non-negative numbers is: Following this algorithm,
3465-402: The complexity of register renaming circuitry to mitigate some dependencies. Collectively the power consumption , complexity and gate delay costs limit the achievable superscalar speedup. However even given infinitely fast dependency checking logic on an otherwise conventional superscalar CPU, if the instruction stream itself has many dependencies, this would also limit the possible speedup. Thus
3542-419: The degree of intrinsic parallelism in the code stream forms a second limitation. Collectively, these limits drive investigation into alternative architectural changes such as very long instruction word (VLIW), explicitly parallel instruction computing (EPIC), simultaneous multithreading (SMT), and multi-core computing . With VLIW, the burdensome task of dependency checking by hardware logic at run time
3619-447: The divide unit every 20 or 35 cycles for single precision and double precision respectively. Reciprocal square roots have longer latencies, 30 to 52 cycles for single precision (32-bit) and double precision (64-bit) respectively. The floating-point register file contains sixty-four 64-bit registers, of which thirty-two are architectural and the remaining are rename registers. The adder has its own dedicated read and write ports, whereas
3696-517: The entire physical or virtual address . Instead, it has a 40-bit physical address and a 44-bit virtual address, thus it is capable of addressing 1 TB of physical memory and 16 TB of virtual memory . The R10000 uses the Avalanche bus , a 64-bit bus that operates at frequencies up to 100 MHz. Avalanche is a multiplexed address and data bus, so at 100 MHz it yields a maximum theoretical bandwidth of 800 MB/s, but its peak bandwidth
3773-422: The error is defined as ε i = 1 − D X i {\displaystyle \varepsilon _{i}=1-DX_{i}} , then: This squaring of the error at each iteration step – the so-called quadratic convergence of Newton–Raphson's method – has the effect that the number of correct digits in the result roughly doubles for every iteration ,
3850-459: The exact reciprocal in one step, rather than allow for iterative improvements). A function that does work is f ( X ) = ( 1 / X ) − D {\displaystyle f(X)=(1/X)-D} , for which the Newton–Raphson iteration gives which can be calculated from X i {\displaystyle X_{i}} using only multiplication and subtraction, or using two fused multiply–adds . From
3927-550: The function at the endpoints, namely, F ( 1 / 2 ) = F ( 1 ) = − F ( − T 1 / ( 2 T 2 ) ) {\displaystyle F(1/2)=F(1)=-F(-T_{1}/(2T_{2}))} . The two equations in the two unknowns have a unique solution T 1 = 48 / 17 {\displaystyle T_{1}=48/17} and T 2 = − 32 / 17 {\displaystyle T_{2}=-32/17} , and
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#17327873307574004-448: The instruction of one thread can be executed out of order and/or in parallel with the instruction of a different one. Also, one independent thread will not produce a pipeline bubble in the code stream of a different one, for example, due to a branch. Superscalar processors differ from multi-core processors in that the several execution units are not entire processors. A single processor is composed of finer-grained execution units such as
4081-512: The instruction queues can accept up to four instructions from the decoder, avoiding any bottlenecks. The instruction queues issue their instructions to their execution units dynamically depending on the availability of operands and resources. Each of the queues except for the load/store queue can issue up to two instructions every cycle to its execution units. The load/store queue can only issue one instruction. The R10000 can thus issue up to five instructions every cycle. The integer unit consists of
4158-452: The instructions to try to avoid pipeline stalls and increase parallel execution. Available performance improvement from superscalar techniques is limited by three key areas: Existing binary executable programs have varying degrees of intrinsic parallelism. In some cases instructions are not dependent on each other and can be executed simultaneously. In other cases they are inter-dependent: one instruction impacts either resources or results of
4235-405: The integer register file and three pipelines , two integer, one load store. The integer register file is 64 bits wide and contains 64 entries, of which 32 are architectural registers and 32 are rename registers which implement register renaming. The register file has seven read ports and three write ports. Both integer pipelines have an adder and a logic unit. However, only the first pipeline has
4312-412: The integer, floating-point or load/store instruction queues depending on the type of the instruction. The decode unit is assisted by the pre-decoded instructions from the instruction cache, which append five bits to every instruction to enable the unit to quickly identify which execution unit the instruction is executed in, and rearrange the format of the instruction to optimize the decode process. Each of
4389-444: The largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder. When used with a binary radix, this method forms the basis for the (unsigned) integer division with remainder algorithm below. Short division is an abbreviated form of long division suitable for one-digit divisors. Chunking – also known as
4466-441: The latter (pipeline) executes multiple instructions in the same execution unit in parallel by dividing the execution unit into different phases. In the "Simple superscalar pipeline" figure, fetching two instructions at the same time is superscaling, and fetching the next two before the first pair has been written back is pipelining. The superscalar technique is traditionally associated with several identifying characteristics (within
4543-1066: The linear approximation are determined as follows. The absolute value of the error is | ε 0 | = | 1 − D ( T 1 + T 2 D ) | {\displaystyle |\varepsilon _{0}|=|1-D(T_{1}+T_{2}D)|} . The minimum of the maximum absolute value of the error is determined by the Chebyshev equioscillation theorem applied to F ( D ) = 1 − D ( T 1 + T 2 D ) {\displaystyle F(D)=1-D(T_{1}+T_{2}D)} . The local minimum of F ( D ) {\displaystyle F(D)} occurs when F ′ ( D ) = 0 {\displaystyle F'(D)=0} , which has solution D = − T 1 / ( 2 T 2 ) {\displaystyle D=-T_{1}/(2T_{2})} . The function at that minimum must be of opposite sign as
4620-552: The maximum error is F ( 1 ) = 1 / 17 {\displaystyle F(1)=1/17} . Using this approximation, the absolute value of the error of the initial value is less than It is possible to generate a polynomial fit of degree larger than 1, computing the coefficients using the Remez algorithm . The trade-off is that the initial guess requires more computational cycles but hopefully in exchange for fewer iterations of Newton–Raphson. Since for this method
4697-479: The microarchitecture of the R12000 by supporting double data rate (DDR) SSRAMs for the secondary cache and a 200 MHz system bus. The R14000A is a further development of the R14000 announced in February 2002. It operates at 600 MHz, dissipates approximately 17 W, and was fabricated by NEC Corporation in a 0.13 μm CMOS process with seven levels of copper interconnect. The R16000, code-named "N0",
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#17327873307574774-463: The more rigid methods used in the simpler P5 Pentium ; it also simplified speculative execution and allowed higher clock frequencies compared to designs such as the advanced Cyrix 6x86 . The simplest processors are scalar processors. Each instruction executed by a scalar processor typically manipulates one or two data items at a time. By contrast, each instruction executed by a vector processor operates simultaneously on many data items. An analogy
4851-522: The multiplier shares its with the divider and square root unit. The divide and square root units use the SRT algorithm. The MIPS IV ISA has a multiply–add instruction. This instruction is implemented by the R10000 with a bypass — the result of the multiply can bypass the register file and be delivered to the add pipeline as an operand, thus it is not a fused multiply–add , and has a four-cycle latency. The R10000 has two comparatively large on-chip caches,
4928-472: The multiply–add units. The system interface and memory hierarchy was also significantly reworked. It would have a 52-bit virtual address and a 48-bit physical address. The bidirectional multiplexed address and data system bus of the earlier models would be replaced by two unidirectional DDR links, a 64-bit multiplexed address and write path and a 128-bit read path. The paths could be shared with another R18000 through multiplexing. The bus could also be configured in
5005-753: The number of units has increased. While early superscalar CPUs would have two ALUs and a single FPU , a later design such as the PowerPC 970 includes four ALUs, two FPUs, and two SIMD units. If the dispatcher is ineffective at keeping all of these units fed with instructions, the performance of the system will be no better than that of a simpler, cheaper design. A superscalar processor usually sustains an execution rate in excess of one instruction per machine cycle . But merely processing multiple instructions concurrently does not make an architecture superscalar, since pipelined , multiprocessor or multi-core architectures also achieve that, but with different methods. In
5082-468: The other. The instructions a = b + c; d = e + f can be run in parallel because none of the results depend on other calculations. However, the instructions a = b + c; b = e + f might not be runnable in parallel, depending on the order in which the instructions complete while they move through the units. Although the instruction stream may contain no inter-instruction dependencies, a superscalar CPU must nonetheless check for that possibility, since there
5159-407: The partial quotients method or the hangman method – is a less-efficient form of long division which may be easier to understand. By allowing one to subtract more multiples than what one currently has at each stage, a more freeform variant of long division can be developed as well. The following algorithm, the binary version of the famous long division , will divide N by D , placing
5236-470: The possibility of using a 339-pin multi-chip module (MCM) containing the microprocessor die and 1 MB of cache. The R10000 was extended by multiple successive derivatives. All derivatives after the R12000 have their clock frequency kept as low as possible to maintain power dissipation in the 15 to 20 W range so they can be densely packaged in SGI's high performance computing (HPC) systems. The R12000
5313-482: The primary caches. The die measures 16.640 by 17.934 mm, for a die area of 298.422 mm. It is fabricated in a 0.35 μm process and packaged in 599-pad ceramic land grid array (LGA). Before the R10000 was introduced, the Microprocessor Report , covering the 1994 Microprocessor Forum, reported that it was packaged in a 527-pin ceramic pin grid array (CPGA); and that vendors also investigated
5390-413: The product between X i {\displaystyle X_{i}} and ( 1 − D X i ) {\displaystyle (1-DX_{i})} need only be computed with a precision of n bits, because the leading n bits (after the binary point) of ( 1 − D X i ) {\displaystyle (1-DX_{i})} are zeros. If
5467-988: The quotient in Q and the remainder in R . In the following pseudo-code, all values are treated as unsigned integers. If we take N=1100 2 (12 10 ) and D=100 2 (4 10 ) Step 1 : Set R=0 and Q=0 Step 2 : Take i=3 (one less than the number of bits in N) Step 3 : R=00 (left shifted by 1) Step 4 : R=01 (setting R(0) to N(i)) Step 5 : R < D, so skip statement Step 2 : Set i=2 Step 3 : R=010 Step 4 : R=011 Step 5 : R < D, statement skipped Step 2 : Set i=1 Step 3 : R=0110 Step 4 : R=0110 Step 5 : R>=D, statement entered Step 5b : R=10 (R−D) Step 5c : Q=10 (setting Q(i) to 1) Step 2 : Set i=0 Step 3 : R=100 Step 4 : R=100 Step 5 : R>=D, statement entered Step 5b : R=0 (R−D) Step 5c : Q=11 (setting Q(i) to 1) end Q=11 2 (3 10 ) and R=0. Slow division methods are all based on
5544-418: The quotient is in a non-standard form consisting of digits of −1 and +1. This form needs to be converted to binary to form the final quotient. Example: If the −1 digits of Q {\displaystyle Q} are stored as zeros (0) as is common, then P {\displaystyle P} is Q {\displaystyle Q} and computing M {\displaystyle M}
5621-421: The remainder given two positive integers using only subtractions and comparisons: The proof that the quotient and remainder exist and are unique (described at Euclidean division ) gives rise to a complete division algorithm, applicable to both negative and positive numbers, using additions, subtractions, and comparisons: This procedure always produces R ≥ 0. Although very simple, it takes Ω(Q) steps, and so
5698-437: The result of Euclidean division . Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring , non-performing restoring, non-restoring , and SRT division. Fast division methods start with
5775-477: The traditional uniformity of the instruction set favors superscalar dispatch (this was why RISC designs were faster than CISC designs through the 1980s and into the 1990s, and it's far more complicated to do multiple dispatch when instructions have variable bit length). Except for CPUs used in low-power applications, embedded systems , and battery -powered devices, essentially all general-purpose CPUs developed since about 1998 are superscalar. The P5 Pentium
5852-431: Was in short supply throughout 1996, and was priced at US$ 3,000 as a result. On 25 September 1996, SGI announced that R10000s fabricated by NEC between March and the end of July that year were faulty, drawing too much current and causing systems to shut down during operation. SGI recalled 10,000 R10000s that had shipped in systems as a result, which impacted the company's earnings. In 1997, a version of R10000 fabricated in
5929-459: Was the first superscalar x86 processor; the Nx586 , P6 Pentium Pro and AMD K5 were among the first designs which decode x86 -instructions asynchronously into dynamic microcode -like micro-op sequences prior to actual execution on a superscalar microarchitecture ; this opened up for dynamic scheduling of buffered partial instructions and enabled more parallelism to be extracted compared to
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