By Ayan Palchaudhuri, Rajat Subhra Chakraborty
This e-book describes the optimized implementations of a number of mathematics datapath, controlpath and pseudorandom series generator circuits for awareness of excessive functionality mathematics circuits distinct in the direction of a selected relations of the high-end box Programmable Gate Arrays (FPGAs). It explores average, modular, cascadable and bit-sliced architectures of those circuits, via at once instantiating the objective FPGA-specific primitives within the HDL. each proposed structure is justified with certain mathematical analyses. at the same time, limited placement of the circuit development blocks is played, through putting the logically comparable primitives in shut proximity to each other via delivering suitable placement constraints within the Xilinx proprietary “User Constraints File”. The booklet covers the implementation of a GUI-based CAD software named FlexiCore built-in with the Xilinx built-in software program surroundings (ISE) for layout automation of platform-specific high-performance mathematics circuits from user-level requisites. This device has been used to enforce the proposed circuits, in addition to implementations of integer mathematics algorithms the place numerous of the proposed circuits are used as construction blocks. Implementation effects reveal greater functionality and more suitable operand-width scalability for the proposed circuits, with admire to implementations derived via different latest techniques. This e-book will turn out helpful to researchers, scholars and execs engaged within the area of FPGA circuit optimization and implementation.
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Extra resources for High Performance Integer Arithmetic Circuit Design on FPGA: Architecture, Implementation and Design Automation
G i: j equals 1 when a carry 36 4 Architecture of Datapath Circuits Fig. , the outgoing carry ci+1 =1 . Pi: j = Pi , Pi Pi−1: j if i = j. if i ≥ j. 6) G i: j = Gi , if i = j. G i + Pi G i−1: j if i ≥ j. 7) where Pi = ai ⊕ bi and G i = ai bi . 9) where i ≥ m ≥ j + 1. 2 Integer Adder/Subtractor Architecture 37 Fig. 6 Architecture for fast carry generator  In the architecture depicted in Fig. 6, the logic functions G i: j and Pi: j are calculated using the 6-input LUTs where i = j + 1, and m = i + 1 = j + 2 and cm is calculated using the carry chain.
B1 b0 , where A = −an−1 2n−1 + n−2 ai 2i and B = −bm−1 2m−1 + i=0 Ptc (= − pm+n−1 2m+n−1 + m−2 b j 2 j , and their product j=0 m+n−2 pk 2k ) is represented as pm+n−1 pm+n−2 . . p1 p0 . k=0 We shall now prove the two’s complement product P in the same light as suggested in  for the original Baugh-Wooley Multiplication Algorithm . The main idea is Fig. 10 A 6 × 6 unsigned array multiplication 50 4 Architecture of Datapath Circuits to convert a two’s complement multiplication to an equivalent parallel array addition problem in which all partial product bits are positive.
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.
High Performance Integer Arithmetic Circuit Design on FPGA: Architecture, Implementation and Design Automation by Ayan Palchaudhuri, Rajat Subhra Chakraborty