Virtually all real-valued computations are carried out using floating-point data types and operations. The precision of these data types must be set with the goals of reducing the overall round-off error, but also emphasizing performance improvements. Often, a mixed-precision allocation achieves this optimum; unfortunately, there are no techniques available to compute such allocations and conservatively meet a given error target across all program inputs. In this work, we present a rigorous approach to precision allocation based on formal analysis via Symbolic Taylor Expansions, and error analysis based on interval functions. This approach is implemented in an automated tool called FPTuner that generates and solves a quadratically constrained quadratic program to obtain a precision-annotated version of the given expression. FPTuner automatically introduces all the requisite precision up and down casting operations. It also allows users to flexibly control precision allocation using constraints to cap the number of high precision operators as well as group operators to allocate the same precision to facilitate vectorization. We evaluate FPTuner by tuning several benchmarks and measuring the proportion of lower precision operators allocated as we increase the error threshold. We also measure the reduction in energy consumption resulting from executing mixed-precision tuned code on a real hardware platform. We observe significant energy savings in response to mixed-precision tuning, but also observe situations where unexpected compiler behaviors thwart intended optimizations.

Tools for floating-point error estimation are fundamental to program understanding and optimization. In this paper, we focus on tools for determining the input settings to a floating point routine that maximizes its result error. Such tools can help support activities such as precision allocation, performance optimization, and auto-tuning. We benchmark current abstraction-based precision analysis methods, and show that they often do not work at scale, or generate highly pessimistic error estimates, often caused by non-linear operators or complex input constraints that define the set of legal inputs. We show that while concrete-testing-based error estimation methods based on maintaining shadow values at higher precision can search out higher error-inducing inputs, suit able heuristic search guidance is key to finding higher errors. We develop a heuristic search algorithm called Binary Guided Random Testing (BGRT). In 45 of the 48 total benchmarks, including many real-world routines, BGRT returns higher guaranteed errors. We also evaluate BGRT against two other heuristic search methods called ILS and PSO, obtaining better results.

In this paper we present JST, a tool that automatically generates a high coverage test suite for industrial strength Java applications. This tool uses a numeric-string hybrid symbolic execution engine at its core which is based on the Symbolic Java PathFinder platform. However, in order to make the tool applicable to industrial applications the existing generic platform had to be enhanced in numerous ways that we describe in this paper. The JST tool consists of newly supported essential Java library components and widely used data structures; novel solving techniques for string constraints, regular expressions, and their interactions with integer and floating point numbers; and key optimizations that make the tool more efficient. We present a methodology to seamlessly integrate the features mentioned above to make the tool scalable to industrial applications that are beyond the reach of the original platform in terms of both applicability and performance. We also present extensive experimental data to illustrate the effectiveness of our tool.