Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient, arbitrarily high precision hardware logarithmic arithmetic
  for linear algebra   The logarithmic number system (LNS) is arguably not broadly used due to
exponential circuit overheads for summation tables relative to arithmetic
precision. Methods to reduce this overhead have been proposed, yet still yield
designs with high chip area and power requirements. Use remains limited to
lower precision or high multiply/add ratio cases, while much of linear algebra
(near 1:1 multiply/add ratio) does not qualify. We present a dual-base
approximate logarithmic arithmetic comparable to floating point in use, yet
unlike LNS it is easily fully pipelined, extendable to arbitrary precision with
$O(n^2)$ overhead, and energy efficient at a 1:1 multiply/add ratio. Compared
to float32 or float64 vector inner product with FMA, our design is respectively
2.3x and 4.6x more energy efficient in 7 nm CMOS. It depends on exp and log
evaluation 5.4x and 3.2x more energy efficient, at 0.23x and 0.37x the chip
area for equivalent accuracy versus standard hyperbolic CORDIC using
shift-and-add and approximated ODE integration in the style of Revol and
Yakoubsohn. This technique is a novel design alternative for low power, high
precision hardened linear algebra in computer vision, graphics and machine
learning applications.

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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph