Function Evaluation in Unnormalized Arithmetic

Abstract

The evaluation of a function of one argument is a standard computationaI task. When an unnormMized number representation is used, it is appropriate that function evaluation be subject to certain "adjustrcmnt" criteria, defined independently of the computing method. In this paper some such criteria are developed, and their application described.In particular, consideration is given to questions of the extent to which general principles apply (i.e. for large classes of functions of a single argument) and the manner in which particular properties of the functions involved (e.g. the functions evaluated by standard library subroutines) may be invoked. The analysis, although framed in terms of unnormalized arithmetic, gives insight into the general nature of significance propagation through function evaluation, and provides a means for analyzing calculations carried out in the usual normalized arithmetic, particularly in the case where an "index of signifi. canoe" is employed.

Comparing Student and Generative Artificial Intelligence Chatbot Responses to Organic Chemistry Writing-to-Learn Assignments

“…For example, the racemization of thalidomide is written about with reference to stereochemistry and the reaction medium on various sources which are readily available online (e.g., refs and ); this may explain the tendency for all three chatbots to include the reaction medium , stereochemistry , and stereochemistry formation features more often for the thalidomide assignment relative to the Wittig assignment. As for the Wittig assignment, various online sources discuss ylides (compounds with opposite charges on adjacent atoms) and the role of nucleophilic attacks (e.g., refs and ); this may explain the tendency for the chatbots to include discussion of charges , nonelectronic mechanisms (e.g., the word “attacks”), and implicit properties (e.g., nucleophilicity) more so than the chatbot responses to the thalidomide assignment.…”

Uncovering the Binder Interactions with S-PAN and MXene for Room Temperature Na–S Batteries

“…This is due to the presence of fluorine atoms in PVDF, the oxygen and hydrogen atoms in both PAA and CMC, the nitrogen and hydrogen atoms in S-PAN, and fluorine, oxygen, and hydroxyl terminations in Ti 3 C 2 T x . From the Fourier transform infrared (FTIR) spectra, PAA-SM exhibits an absorption peak at 3425 cm –1 , and CMC-SM exhibits a strong peak at 3427 cm –1 , corresponding to O–H hydrogen bonding . However, PVDF-SM does not showcase any significant absorption peaks between 3600 and 3900 cm –1 , which is the region corresponding to H–F hydrogen bonding (Figure f–h) .…”