Abstract. Mixed-precision approaches can provide substantial speed-ups for both computing- and memory-bound codes requiring little effort. Most scientific codes have overengineered the numerical precision leading to a situation where models are using more resources than required without having a clue about where these resources are unnecessary and where are really needed. Consequently, there is the possibility to obtain performance benefits from using a more appropriate choice of precision and the only thing that is needed is a method to determine which real variables can be represented with fewer bits without affecting the accuracy of the results. This paper presents a novel method to enable modern and legacy codes to benefit from a reduction of precision without sacrificing accuracy. It consists in a simple idea: if we can measure how reducing the precision of a group of variables affects the outputs, we can evaluate the level of precision this group of variables need. Modifying and recompiling the code for each case that has to be evaluated would require an amount of effort that makes this task prohibitive. Instead, the method presented in this paper relies on the use of a tool called Reduced Precision Emulator (RPE) that can significantly streamline the process . Using the RPE and a list of parameters containing the precisions that will be used for each real variable in the code, it is possible within a single binary to emulate the effect on the outputs of a specific choice of precision. Once we have the potential of emulating the effects of reduced precision, we can proceed with the design of the tests required to obtain knowledge about all the variables in the model. The number of possible combinations is prohibitively large and impossible to explore. The alternative of performing a screening of the variables individually can give certain insight about the precision needed by the variables, but on the other hand some more complex interactions that involve several variables may remain hidden. Instead, we use a divide-and-conquer algorithm that identifies the parts that cannot handle reduced precision and builds a set of variables that can. The method has been put to proof using two state-of-the-art ocean models, NEMO and ROMS, with very promising results. Obtaining this information is crucial to build afterwards an actual mixed precision version of the code that will bring the promised performance benefits.
A divide-and-conquer algorithm for quantum state preparation
