12,120 research outputs found
Certification of Bounds of Non-linear Functions: the Templates Method
The aim of this work is to certify lower bounds for real-valued multivariate
functions, defined by semialgebraic or transcendental expressions. The
certificate must be, eventually, formally provable in a proof system such as
Coq. The application range for such a tool is widespread; for instance Hales'
proof of Kepler's conjecture yields thousands of inequalities. We introduce an
approximation algorithm, which combines ideas of the max-plus basis method (in
optimal control) and of the linear templates method developed by Manna et al.
(in static analysis). This algorithm consists in bounding some of the
constituents of the function by suprema of quadratic forms with a well chosen
curvature. This leads to semialgebraic optimization problems, solved by
sum-of-squares relaxations. Templates limit the blow up of these relaxations at
the price of coarsening the approximation. We illustrate the efficiency of our
framework with various examples from the literature and discuss the interfacing
with Coq.Comment: 16 pages, 3 figures, 2 table
Ithemal: Accurate, Portable and Fast Basic Block Throughput Estimation using Deep Neural Networks
Predicting the number of clock cycles a processor takes to execute a block of
assembly instructions in steady state (the throughput) is important for both
compiler designers and performance engineers. Building an analytical model to
do so is especially complicated in modern x86-64 Complex Instruction Set
Computer (CISC) machines with sophisticated processor microarchitectures in
that it is tedious, error prone, and must be performed from scratch for each
processor generation. In this paper we present Ithemal, the first tool which
learns to predict the throughput of a set of instructions. Ithemal uses a
hierarchical LSTM--based approach to predict throughput based on the opcodes
and operands of instructions in a basic block. We show that Ithemal is more
accurate than state-of-the-art hand-written tools currently used in compiler
backends and static machine code analyzers. In particular, our model has less
than half the error of state-of-the-art analytical models (LLVM's llvm-mca and
Intel's IACA). Ithemal is also able to predict these throughput values just as
fast as the aforementioned tools, and is easily ported across a variety of
processor microarchitectures with minimal developer effort.Comment: Published at 36th International Conference on Machine Learning (ICML)
201
Optimization and sensitivity analysis of computer simulation models by the score function method
Experimental Design;Simulation;Optimization;Queueing Theory
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