This paper presents a summary of the 2nd Latent in the Wild Fingerprint Recognition Competition held at the 2025 International Joint Conference on Biometrics. The competition has two tracks: latent fingerprint 1) recognition, and 2) quality assessment. It attracted a total of 12 participating teams from academia and industry for both tracks, representing 10 countries. In total, 8 valid submissions were evaluated by the organizers. The competition aimed to advance the state-of-the-art in latent fingerprint recognition and quality assessment by providing a challenging dataset of latent fingerprints collected in natural, non-ideal conditions. This paper summarizes the dataset, evaluation protocols, submitted methods, and the competition results.

We introduce a new accurate summation algorithm based on the error-free summation into floating-point buckets. Our algorithm exploits ideas from Zhu and Hayes’ OnlineExactSum , but it uses a significantly smaller number of accumulators and has a better instruction-level parallelism. In the default setting, our implementation aaaSum returns a faithfully rounded floating-point approximation of the true sum. We also discuss possible modifications for the computation of reproducible, correctly rounded, and multiple precision floating-point approximations. The computational overhead for any of these modifications is kept comparably small. Numerical tests demonstrate that aaaSum performs well for very small to large problem sizes, independent of the condition number of the problem. We compare our algorithm with other accurate and high-precision summation approaches.

We present a pair arithmetic for the four basic operations and square root. It can be regarded as a simplified, more-efficient double-double arithmetic. The central assumption on the underlying arithmetic is the first standard model for error analysis for operations on a discrete set of real numbers. Neither do we require a floating-point grid nor a rounding to nearest property. Based on that, we define a relative rounding error unit u and prove rigorous error bounds for the computed result of an arbitrary arithmetic expression depending on u, the size of the expression, and possibly a condition measure. In the second part of this note, we extend the error analysis by examining requirements to ensure faithfully rounded outputs and apply our results to IEEE 754 standard conform floating-point systems. For a class of mathematical expressions, using an IEEE 754 standard conform arithmetic with base β , the result is proved to be faithfully rounded for up to 1 / √ β u - 2 operations. Our findings cover a number of previously published algorithms to compute faithfully rounded results, among them Horner’s scheme, products, sums, dot products, or Euclidean norm. Beyond that, several other problems can be analyzed, such as polynomial interpolation, orientation problems, Householder transformations, or the smallest singular value of Hilbert matrices of large size.