Addressing Mode and Bit Extensions to the Thumb-2 Instruction Set Architecture

Thumb-2 is the most recent instruction set architecture for ARM processors which are one of the most widely used embedded processors. In this paper, two extensions are proposed to improve the performance of the Thumb-2 instruction set architecture, which are addressing mode extensions and sign/zero extensions combined with data processing instructions. To speed up access to an element of an aggregated data, the proposed approach first introduces three new addressing modes for load and store instructions. They are register-plus-immediate offset addressing mode, negative register offset addressing mode, and post-increment register offset addressing mode. Register-plus-immediate offset addressing mode permits two offsets and negative register offset allows offset to be a negative value of a register content. Post-increment register offset mode automatically modifies the offset address after the memory operation. The second is the sign/zero extension combined with a data processing instruction which allows the result of a data processing operation to be sign/zero extended to accelerate a type conversion. Several least frequently used instructions are reduced to provide the encoding space for the new extensions. Experiments show that the proposed approach improves performance by an average of 8.6% when compared to the Thumb-2 instruction set architecture.

Border Handling for 2D Transpose Filter Structures on an FPGA

It is sometimes desirable to implement filters using a transpose-form filter structure. However, managing image borders is generally considered more complex than it is with the more commonly used direct-form structure. This paper explores border handling for transpose-form filters, and proposes two novel mechanisms: transformation coalescing, and combination chain modification. For linear filters, coefficient coalescing can effectively exploit the digital signal processing blocks, resulting in the smallest resources requirements. Combination chain modification requires similar resources to direct-form border handling. It is demonstrated that the combination chain multiplexing can be split into two stages, consisting of a combination network followed by the transpose-form combination chain. The resulting transpose-form border handling networks are of similar complexity to the direct-form networks, enabling the transpose-form filter structure to be used where required. The transpose form is also significantly faster, being automatically pipelined by the filter structure. Of the border extension methods, zero-extension requires the least resources.

EQUIVARIANT CALCULUS OF FUNCTORS AND-ANALYTICITY OF REAL ALGEBRAIC -THEORY

We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial $G$-sets to symmetric $G$-spectra, where $G$ is a finite group. We extend a notion of $G$-linearity suggested by Blumberg to define stably excisive and ${\it\rho}$-analytic homotopy functors, as well as a $G$-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected $G$-maps to $G$-equivalences. It is analogous to the classical result of Goodwillie that ‘functors with zero derivative are locally constant’. As the main example, we show that Hesselholt and Madsen’s Real algebraic $K$-theory of a split square zero extension of Wall antistructures defines an analytic functor in the $\mathbb{Z}/2$-equivariant setting. We further show that the equivariant derivative of this Real $K$-theory functor is $\mathbb{Z}/2$-equivalent to Real MacLane homology.

Characterizations for fractional Hardy inequality

We provide a Maz'ya-type characterization for a fractional Hardy inequality. As an application, we show that a bounded open set G admits a fractional Hardy inequality if and only if the associated fractional capacity is quasiadditive with respect to Whitney cubes of G and the zero extension operator acting on Cc(G) is bounded in an appropriate manner.

A Unified Bifurcation Analysis of Sheet Metal Forming Limits

The purpose of this study is to determine analytically the orientations of localized necks occurring in sheet metal forming processes, and obtain the corresponding forming limit diagrams (FLDs). In addition to the force equilibrium condition as adopted by other researchers, we include the moment equilibrium in this study. The shear terms due to the perturbation are found to vanish inside the localized neck of a region of deformation. This simplifies the two-dimensional problem to a one-dimensional problem. Furthermore, it is found that there are only three possible orientations for the initiation of a localized neck, i.e., two principal directions and one zero extension direction (which applies only to negative strain ratio deformations). A special case study using the von Mises yield criterion is also presented in this paper. Predictions from our unified analysis matches with the results of Hill, R., 1952, “On Discontinuous Plastic States, With Special Reference to Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 1, pp. 19–30. For the negative strain ratio regime (left-hand side of the FLDs), and with the results of Storen, S., and Rice, R., 1975, “Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 23, pp. 421–441. For the positive strain ratio regime (right hand-side of the FLD). When the localized neck is assumed to be in the zero extension direction for the negative strain ratio deformation, deformation theory and flow theory of plasticity give the same limit strains, and a unified solution to the limit strain is obtained. This solution is independent of the specific yield criterion used.