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Our RLibm project has recently proposed methods to generate a single implementation for an elementary function that produces correctly rounded results for multiple rounding modes and representations with up to 32-bits. They are appealing for developing fast reference libraries without double rounding issues. The key insight is to build polynomial approximations that produce the correctly rounded result for a representation with two additional bits when compared to the largest target representation and with the “non-standard” round-to-odd rounding mode, which makes double rounding the RLibm math library result to any smaller target representation innocuous. The resulting approximations generated by the RLibm approach are implemented with machine supported floating-point operations with the round-to-nearest rounding mode. When an application uses a rounding mode other than the round-to-nearest mode, the RLibm math library saves the application’s rounding mode, changes the system’s rounding mode to round-to-nearest, computes the correctly rounded result, and restores the application’s rounding mode. This frequent change of rounding modes has a performance cost. This paper proposes two new methods, which we call rounding-invariant outputs and rounding-invariant input bounds, to avoid the frequent changes to the rounding mode and the dependence on the round-to-nearest mode. First, our new rounding-invariant outputs method proposes using the round-to-zero rounding mode to implement RLibm’s polynomial approximations. We propose fast, error-free transformations to emulate a round-to-zero result from any standard rounding mode without changing the rounding mode. Second, our rounding-invariant input bounds method factors any rounding error due to different rounding modes using interval bounds in the RLibm pipeline. Both methods make a different set of trade-offs and improve the performance of resulting libraries by more than 2× 

Inducibly degradable polymers present new opportunities to integrate tough hydrogels into a wide range of biomaterials. Rapid and inducible degradation enables fast transition in material properties without sacrificing material integrity prior to removal. In pursuit of bioorthogonal chemical modalities that will enable inducible polymer degradation in biologically relevant environments, enamine N-oxide crosslinkers are developed for double network acrylamide-based polymer/alginate hydrogels. Bioorthogonal dissociation initiated by the application of aqueous diboron solution through several delivery mechanisms effectively lead to polymer degradation. Their degradation by aqueous B2(OH)4 solution results in a fracture energy half-life of <10 min. The biocompatibility of the degradable hydrogels and B2(OH)4 reagent is assessed, and the removability of strongly adhered tough hydrogels on mice skin is evaluated. Thermoresponsive PNiPAAm/Alg hydrogels are fabricated and application of the hydrogels as a chemically inducible degradable intraoral wound dressing is demonstrated. It is demonstrated through in vivo maximum tolerated dose studies that diboron solution administered to mice by oral gavage is well tolerated. Successful integration of enamine N-oxides within the tough double network hydrogels as chemically degradable motifs demonstrates the applicability of enamine N-oxides in the realm of polymer chemistry and highlights the importance of chemically induced bioorthogonal dissociation reactions for materials science. 

Electrostatic capacitors are foundational components of advanced electronics and high-power electrical systems owing to their ultrafast charging-discharging capability. Ferroelectric materials offer high maximum polarization, but high remnant polarization has hindered their effective deployment in energy storage applications. Previous methodologies have encountered problems because of the deteriorated crystallinity of the ferroelectric materials. We introduce an approach to control the relaxation time using two-dimensional (2D) materials while minimizing energy loss by using 2D/3D/2D heterostructures and preserving the crystallinity of ferroelectric 3D materials. Using this approach, we were able to achieve an energy density of 191.7 joules per cubic centimeter with an efficiency greater than 90%. This precise control over relaxation time holds promise for a wide array of applications and has the potential to accelerate the development of highly efficient energy storage systems.