Performance of stencil computations can be significantly improved through smart implementations that improve memory locality, computation reuse, or parallelize the computation. Unfortunately, efficient implementations are hard to obtain because they often involve non-traditional transformations, which means that they cannot be produced by optimizing the reference stencil with a compiler. In fact, many stencils are produced by code generators that were tediously handcrafted.

Sketching is a software synthesis approach where the programmer develops a partial implementation - a sketch - and a separate specification of the desired functionality. The synthesizer then completes the sketch to behave like the specification. The correctness of the synthesized implementation is guaranteed by the compiler, which allows, among other benefits, rapid development of highly tuned implementations without the fear of introducing bugs.We develop SKETCH, a language for finite programs with linguistic support for sketching. Finite programs include many highperformance kernels, including cryptocodes. In contrast to prior synthesizers, which had to be equipped with domain-specific rules, SKETCH completes sketches by means of a combinatorial search based on generalized boolean satisfiability. Consequently, our combinatorial synthesizer is complete for the class of finite programs: it is guaranteed to complete any sketch in theory, and in practice has scaled to realistic programming problems.Freed from domain rules, we can now write sketches as simpleto-understand partial programs, which are regular programs in which difficult code fragments are replaced with holes to be filled by the synthesizer. Holes may stand for index expressions, lookup tables, or bitmasks, but the programmer can easily define new kinds of holes using a single versatile synthesis operator.We have used SKETCH to synthesize an efficient implementation of the AES cipher standard. The synthesizer produces the most complex part of the implementation and runs in about an hour.

Many traditional techniques for "looking inside" volumetric data involve removing portions of the data, for example using various cutting tools, to reveal the interior. This allows the user to see hidden parts of the data, but has the disadvantage of removing potentially important surrounding contextual information. We explore an alternate strategy for browsing that uses deformations, where the user can cut into and open up, spread apart, or peel away parts of the volume in real time, making the interior visible while still retaining surrounding context. We consider various deformation strategies and present a number of interaction techniques based on different metaphors. Our designs pay special attention to the semantic layers that might compose a volume (e.g. the skin, muscle, bone in a scan of a human). Users can apply deformations to only selected layers, or apply a given deformation to a different degree to each layer, making browsing more flexible and facilitating the visualization of relationships between layers. Our interaction techniques are controlled with direct, "in place" manipulation, using pop-up menus and 3D widgets, to avoid the divided attention and awkwardness that would come with panels of traditional widgets. Initial user feedback indicates that our techniques are valuable, especially for showing portions of the data spatially situated in context with surrounding data.