Parallel RAM

In computer science, a parallel random-access machine (parallel RAM or PRAM) is a shared-memory abstract machine. As its name indicates, the PRAM is intended as the parallel-computing analogy to the random-access machine (RAM) (not to be confused with random-access memory). In the same way that the RAM is used by sequential-algorithm designers to model algorithmic performance (such as time complexity), the PRAM is used by parallel-algorithm designers to model parallel algorithmic performance (such as time complexity, where the number of processors assumed is typically also stated). Similar to the way in which the RAM model neglects practical issues, such as access time to cache memory versus main memory, the PRAM model neglects such issues as synchronization and communication, but provides any (problem-size-dependent) number of processors. Algorithm cost, for instance, is estimated using two parameters O(time) and O(time × processor_number).
Read/write conflicts.
Read/write conflicts, commonly termed interlocking in accessing the same shared memory location simultaneously are resolved by one of the following strategies:
Here, E and C stand for 'exclusive' and 'concurrent' respectively. The read causes no discrepancies while the concurrent write is further defined as:
Several simplifying assumptions are made while considering the development of algorithms for PRAM. They are:
These kinds of algorithms are useful for understanding the exploitation of concurrency, dividing the original problem into similar sub-problems and solving them in parallel. The introduction of the formal 'P-RAM' model in Wyllie's 1979 thesis had the aim of quantifying analysis of parallel algorithms in a way analogous to the Turing Machine. The analysis focused on a MIMD model of programming using a CREW model but showed that many variants, including implementing a CRCW model and implementing on an SIMD machine, were possible with only constant overhead.
Implementation.
PRAM algorithms cannot be parallelized with the combination of CPU and dynamic random-access memory (DRAM) because DRAM does not allow concurrent access; but they can be implemented in hardware or read/write to the internal static random-access memory (SRAM) blocks of a field-programmable gate array (FPGA), it can be done using a CRCW algorithm.
However, the test for practical relevance of PRAM (or RAM) algorithms depends on whether their cost model provides an effective abstraction of some computer; the structure of that computer can be quite different than the abstract model. The knowledge of the layers of software and hardware that need to be inserted is beyond the scope of this article. But, articles such as demonstrate how a PRAM-like abstraction can be supported by the explicit multi-threading (XMT) paradigm and articles such as demonstrate that a PRAM algorithm for the maximum flow problem can provide strong speedups relative to the fastest serial program for the same problem. The article demonstrated that PRAM algorithms as-is can achieve competitive performance even without any additional effort to cast them as mutli-threaded programs on XMT.
Example code.
This is an example of SystemVerilog code which finds the maximum value in the array in only 2 clock cycles. It compares all the combinations of the elements in the array at the first clock, and merges the result at the second clock. It uses CRCW memory; codice_1 and codice_2 are written concurrently. The concurrency causes no conflicts because the algorithm guarantees that the same value is written to the same memory. This code can be run on FPGA hardware.
module FindMax #(parameter int len = 8)
 (input bit clock, resetN, input bit[7:0] data[len], output bit[7:0] maxNo);
 typedef enum bit[1:0] {COMPARE, MERGE, DONE} State;
 State state;
 bit m[len];
 int i, j;
 always_ff @(posedge clock, negedge resetN) begin
 if (!resetN) begin
 for (i = 0; i < len; i++) m[i] <= 0;
 state <= COMPARE;
 end else begin
 case (state)
 COMPARE: begin
 for (i = 0; i < len; i++) begin
 for (j = 0; j < len; j++) begin
 if (data[i] < data[j]) m[i] <= 1;
 end
 end
 state <= MERGE;
 end
 MERGE: begin
 for (i = 0; i < len; i++) begin
 if (m[i] == 0) maxNo <= data[i];
 end
 state <= DONE;
 end
 endcase
 end
 end
endmodule