A Study of High Performance Multiple Precision Arithmetic on Graphics Processing Units

Multiple precision (MP) arithmetic is a core building block of a wide variety of algorithms in computational mathematics and computer science. In mathematics MP is used in computational number theory, geometric computation, experimental mathematics, and in some random matrix problems. In computer science, MP arithmetic is primarily used in cryptographic algorithms: securing communications, digital signatures, and code breaking. In most of these application areas, the factor that limits performance is the MP arithmetic. The focus of our research is to build and analyze highly optimized libraries that allow the MP operations to be offloaded from the CPU to the GPU. Our goal is to achieve an order of magnitude improvement over the CPU in three key metrics: operations per second per socket, operations per watt, and operation per second per dollar. What we find is that the SIMD design and balance of compute, cache, and bandwidth resources on the GPU is quite different from the CPU, so libraries such as GMP cannot simply be ported to the GPU. New approaches and algorithms are required to achieve high performance and high utilization of GPU resources. Further, we find that low-level ISA differences between GPU generations means that an approach that works well on one generation might not run well on the next. Here we report on our progress towards MP arithmetic libraries on the GPU in four areas: (1) large integer addition, subtraction, and multiplication; (2) high performance modular multiplication and modular exponentiation (the key operations for cryptographic algorithms) across generations of GPUs; (3) high precision floating point addition, subtraction, multiplication, division, and square root; (4) parallel short division, which we prove is asymptotically optimal on EREW and CREW PRAMs

Immunocytochemical study of cell type distribution in the pituitary of Barbus barbus (Teleostei, Cyprindidae)

Antisera to mammalian pituitary and placental hormones have been used to identify and localize the different cell types in the pituitary of the barbel (Barbus barbus, L.). The immunocytochemical labeling employed the immunoperoxidase technique or the immunogold silver staining procedure. Corticotrophic and prolactin cells, visualized using antisera to human adrenocorticotropic hormone and ovine prolactin (PRL), respectively, occur in the rostral pars distalis (RPD). Antisera against mammalian gonadotropins [ovine folliclestimulating hormone (FSH); bovine luteinizing hormone] or porcine growth hormone selectively cross-react with two different cell populations occupying the major part of the proximal pars distalis (PPD). Thyrotropic cells, stained by an antiserum to whole human thyroidstimulating hormone preabsorbed with porcine FSH, are scattered throughout the PPD and found amongst growth hormone and gonadotrophic cells. The majority of pars intermedia cells are stained with anti-melanophore stimulating hormone whereas the scattered PAS positive cells are revealed by both anti-ovine PRL and anti-bovine placental lactogen (or chorionic somatomammotropin). The latter antiserum also cross-reacts with the PRL cells of the RPD. Our results indicate that the distribution of the different cell types in Barbus barbus is similar to that described in other families of teleosts. This report is also the first demonstration of antigenic similarity between mammalian placental lactogen and fish prolactin