  We present a C++ library, TLoops, which uses a hierarchy of expression
templates to represent operations upon tensorial quantities in single lines of
C++ code that resemble analytic equations. These expressions may be run as-is,
but may also be used to emit equivalent low-level C or CUDA code, which either
performs the operations more quickly on the CPU, or allows them to be rapidly
ported to run on NVIDIA GPUs. We detail the expression template and C++-class
hierarchy that represents the expressions and which makes automatic
code-generation possible. We then present benchmarks of the expression-template
code, the automatically generated C code, and the automatically generated CUDA
code running on several generations of NVIDIA GPU.
