1,746 research outputs found
High Performance and Optimal Configuration of Accurate Heterogeneous Block-Based Approximate Adder
Approximate computing is an emerging paradigm to improve power and
performance efficiency for error-resilient application. Recent approximate
adders have significantly extended the design space of accuracy-power
configurable approximate adders, and find optimal designs by exploring the
design space. In this paper, a new energy-efficient heterogeneous block-based
approximate adder (HBBA) is proposed; which is a generic/configurable model
that can be transformed to a particular adder by defining some configurations.
An HBBA, in general, is composed of heterogeneous sub-adders, where each
sub-adder can have a different configuration. A set of configurations of all
the sub-adders in an HBBA defines its configuration. The block-based adders are
approximated through inexact logic configuration and truncated carry chains.
HBBA increases design space providing additional design points that fall on the
Pareto-front and offer better power-accuracy trade-off compared to other
configurations. Furthermore, to avoid Mont-Carlo simulations, we propose an
analytical modelling technique to evaluate the probability of error and
Probability Mass Function (PMF) of error value. Moreover, the estimation method
estimates delay, area and power of heterogeneous block-based approximate
adders. Thus, based on the analytical model and estimation method, the optimal
configuration under a given error constraint can be selected from the whole
design space of the proposed adder model by exhaustive search. The simulation
results show that our HBBA provides improved accuracy in terms of error metrics
compared to some state-of-the-art approximate adders. HBBA with 32 bits length
serves about 15% reduction in area and up to 17% reduction in energy compared
to state-of-the-art approximate adders.Comment: Submitted to the IEEE-TCAD journal, 16 pages, 16 figure
Latency Optimized Asynchronous Early Output Ripple Carry Adder based on Delay-Insensitive Dual-Rail Data Encoding
Asynchronous circuits employing delay-insensitive codes for data
representation i.e. encoding and following a 4-phase return-to-zero protocol
for handshaking are generally robust. Depending upon whether a single
delay-insensitive code or multiple delay-insensitive code(s) are used for data
encoding, the encoding scheme is called homogeneous or heterogeneous
delay-insensitive data encoding. This article proposes a new latency optimized
early output asynchronous ripple carry adder (RCA) that utilizes single-bit
asynchronous full adders (SAFAs) and dual-bit asynchronous full adders (DAFAs)
which incorporate redundant logic and are based on the delay-insensitive
dual-rail code i.e. homogeneous data encoding, and follow a 4-phase
return-to-zero handshaking. Amongst various RCA, carry lookahead adder (CLA),
and carry select adder (CSLA) designs, which are based on homogeneous or
heterogeneous delay-insensitive data encodings which correspond to the
weak-indication or the early output timing model, the proposed early output
asynchronous RCA that incorporates SAFAs and DAFAs with redundant logic is
found to result in reduced latency for a dual-operand addition operation. In
particular, for a 32-bit asynchronous RCA, utilizing 15 stages of DAFAs and 2
stages of SAFAs leads to reduced latency. The theoretical worst-case latencies
of the different asynchronous adders were calculated by taking into account the
typical gate delays of a 32/28nm CMOS digital cell library, and a comparison is
made with their practical worst-case latencies estimated. The theoretical and
practical worst-case latencies show a close correlation....Comment: arXiv admin note: text overlap with arXiv:1704.0761
Asynchronous Early Output Dual-Bit Full Adders Based on Homogeneous and Heterogeneous Delay-Insensitive Data Encoding
This paper presents the designs of asynchronous early output dual-bit full
adders without and with redundant logic (implicit) corresponding to homogeneous
and heterogeneous delay-insensitive data encoding. For homogeneous
delay-insensitive data encoding only dual-rail i.e. 1-of-2 code is used, and
for heterogeneous delay-insensitive data encoding 1-of-2 and 1-of-4 codes are
used. The 4-phase return-to-zero protocol is used for handshaking. To
demonstrate the merits of the proposed dual-bit full adder designs, 32-bit
ripple carry adders (RCAs) are constructed comprising dual-bit full adders. The
proposed dual-bit full adders based 32-bit RCAs incorporating redundant logic
feature reduced latency and area compared to their non-redundant counterparts
with no accompanying power penalty. In comparison with the weakly indicating
32-bit RCA constructed using homogeneously encoded dual-bit full adders
containing redundant logic, the early output 32-bit RCA comprising the proposed
homogeneously encoded dual-bit full adders with redundant logic reports
corresponding reductions in latency and area by 22.2% and 15.1% with no
associated power penalty. On the other hand, the early output 32-bit RCA
constructed using the proposed heterogeneously encoded dual-bit full adder
which incorporates redundant logic reports respective decreases in latency and
area than the weakly indicating 32-bit RCA that consists of heterogeneously
encoded dual-bit full adders with redundant logic by 21.5% and 21.3% with nil
power overhead. The simulation results obtained are based on a 32/28nm CMOS
process technology
Indicating Asynchronous Array Multipliers
Multiplication is an important arithmetic operation that is frequently
encountered in microprocessing and digital signal processing applications, and
multiplication is physically realized using a multiplier. This paper discusses
the physical implementation of many indicating asynchronous array multipliers,
which are inherently elastic and modular and are robust to timing, process and
parametric variations. We consider the physical realization of many indicating
asynchronous array multipliers using a 32/28nm CMOS technology. The
weak-indication array multipliers comprise strong-indication or weak-indication
full adders, and strong-indication 2-input AND functions to realize the partial
products. The multipliers were synthesized in a semi-custom ASIC design style
using standard library cells including a custom-designed 2-input C-element. 4x4
and 8x8 multiplication operations were considered for the physical
implementations. The 4-phase return-to-zero (RTZ) and the 4-phase return-to-one
(RTO) handshake protocols were utilized for data communication, and the
delay-insensitive dual-rail code was used for data encoding. Among several
weak-indication array multipliers, a weak-indication array multiplier utilizing
a biased weak-indication full adder and the strong-indication 2-input AND
function is found to have reduced cycle time and power-cycle time product with
respect to RTZ and RTO handshaking for 4x4 and 8x8 multiplications. Further,
the 4-phase RTO handshaking is found to be preferable to the 4-phase RTZ
handshaking for achieving enhanced optimizations of the design metrics.Comment: arXiv admin note: text overlap with arXiv:1903.0943
Efficiency analysis methodology of FPGAs based on lost frequencies, area and cycles
We propose a methodology to study and to quantify efficiency and the impact of overheads on runtime performance. Most work on High-Performance Computing (HPC) for FPGAs only studies runtime performance or cost, while we are interested in how far we are from peak performance and, more importantly, why. The efficiency of runtime performance is defined with respect to the ideal computational runtime in absence of inefficiencies. The analysis of the difference between actual and ideal runtime reveals the overheads and bottlenecks. A formal approach is proposed to decompose the efficiency into three components: frequency, area and cycles. After quantification of the efficiencies, a detailed analysis has to reveal the reasons for the lost frequencies, lost area and lost cycles. We propose a taxonomy of possible causes and practical methods to identify and quantify the overheads. The proposed methodology is applied on a number of use cases to illustrate the methodology. We show the interaction between the three components of efficiency and show how bottlenecks are revealed
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