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Strong gravitational lensing is a powerful probe of cosmology and the darkmatter distribution. Efficient lensing software is already a necessity to fullyuse its potential and the performance demands will only increase with theupcoming generation of telescopes. In this paper, we study the possible impactof High Performance Computing techniques on a performance-critical part of thewidely used lens modeling software LENSTOOL. We implement the algorithm once asa highly optimized CPU version and once with graphics card acceleration for asimple parametric lens model. In addition, we study the impact of finitemachine precision on the lensing algorithm. While double precision is thedefault choice for scientific applications, we find that single precision canbe sufficiently accurate for our purposes and lead to a big speedup. Thereforewe develop and present a mixed precision algorithm which only uses doubleprecision when necessary. We measure the performance of the differentimplementations and find that the use of High Performance Computing Techniquesdramatically improves the code performance both on CPUs and GPUs. Compared tothe current LENSTOOL implementation on 12 CPU cores, we obtain speedup factorsof up to 170. We achieve this optimal performance by using our mixed precisionalgorithm on a high-end GPU which is common in modern supercomputers. We alsoshow that these techniques reduce the energy consumption by up to 98%.Furthermore, we demonstrate that a highly competitive speedup can be reachedwith consumer GPUs. While they are an order of magnitude cheaper than thehigh-end graphics cards, they are rarely used for scientific computations dueto their low double precision performance. Our mixed precision algorithmunlocks their full potential. The consumer GPU delivers a speedup which is onlya factor of four lower than the best speedup achieved by a high-end GPU.

High Performance Computing for gravitational lens modeling: single vs double precision on GPUs and CPUs