By Ayan Palchaudhuri, Rajat Subhra Chakraborty
This publication describes the optimized implementations of numerous mathematics datapath, controlpath and pseudorandom series generator circuits for attention of excessive functionality mathematics circuits special in the direction of a selected relatives of the high-end box Programmable Gate Arrays (FPGAs). It explores typical, modular, cascadable and bit-sliced architectures of those circuits, through at once instantiating the objective FPGA-specific primitives within the HDL. each proposed structure is justified with distinctive mathematical analyses. at the same time, limited placement of the circuit construction blocks is played, by means of putting the logically similar primitives in shut proximity to each other by means of delivering appropriate placement constraints within the Xilinx proprietary “User Constraints File”. The e-book covers the implementation of a GUI-based CAD instrument named FlexiCore built-in with the Xilinx built-in software program setting (ISE) for layout automation of platform-specific high-performance mathematics circuits from user-level requisites. This software has been used to enforce the proposed circuits, in addition to implementations of integer mathematics algorithms the place a number of of the proposed circuits are used as construction blocks. Implementation effects display better functionality and more advantageous operand-width scalability for the proposed circuits, with admire to implementations derived via different latest ways. This ebook will end up precious to researchers, scholars and pros engaged within the area of FPGA circuit optimization and implementation.
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Extra info for High Performance Integer Arithmetic Circuit Design on FPGA: Architecture, Implementation and Design Automation
Sample text
The philosophy behind estimating the hardware resource requirement in terms of the number of LUTs used [4] may not reflect its actual implementation on hardware. For example, let us consider the Boolean logic functionality of an 8 : 1 multiplexer, which is essentially an 11-input 1-output combinational logic function. 1), lut(x) = 2 for k = 6. This information indicates that the first six variables go as input to the first LUT and the remaining five variables along with the output of the first LUT go as input to the second LUT.
Ym ) with Y = {y1 , . . 5) Here, the sets X and Y are called the support [2] of the functions g and h. , g and h are orthogonal) • 2 ≤ |X | + |Y | ≤ 10; if X ∩ Y = ∅ where |X | and |Y | are the cardinality of the sets X and Y . 22 3 A Fabric Component Based Design Approach … Fig. 1 Architecture mapping for Boolean logic that can be decomposed with respect to a single variable 3. Let f be a Boolean function of n variables (8 ≤ n ≤ 13) which can be represented in the following form (see Fig. 1): f (i 1 , i 2 , .
4. Let f be a function of n variables (17 ≤ n ≤ 26) such that we can apply recursive decomposition twice on it as shown below: f (i 1 , i 2 , . . 7) • Here, f x1 x2 , f x1 x2 , f x1 x3 and f x1 x3 are each 6 (or less)-input combinational functions that can individually be realized using one LUT each. • Three wide function multiplexers present in the same slice as that of the LUTs computes the final expression as shown in Fig. 2. 3 Guidelines for High-Performance Realization 23 Fig. 1) however evaluates to lut(x) = 6, where x = xmax = 27 (6 × 4 (four six-input LUTs) + 3 (select lines)) and k = 6.