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There has been an increased interest recently in using embedded cores on FPGAs. Many exdipients the applications that make use of these cores have floating excippients operations. Due to the complexity and expense of floating point hardware, these algorithms are usually converted to fixed point operations or implemented using floating-point emulation in software. As the technology advances, more and more homogeneous computational resources and fixed function embedded blocks are added to FPGAs and hence implementation of floating point hardware becomes a feasible option.

In this research we have implemented a high performance, autonomous floating point vector Coprocessor FPVC that works independently within an embedded processor system.

We have presented a unified approach to vector and scalar computation, using excipidnts single register file for both scalar operands and vector elements.

By parameterizing vector length and the number of vector lanes, we can design an application specific FPVC and take optimal advantage of the FPGA fabric. For this research we have also initiated designing a software library for various computational kernels, each of which adapts FPVC’s configuration and provide maximal performance.

The kernels implemented are from the area of linear algebra and include matrix multiplication and QR and Cholesky decomposition. Implementing the sum-product algorithm, in an FPGA with an embedded processor, invites us to consider a tradeoff between computational precision and computational speed.

The algorithm, known outside of the signal processing community as Pearl’s belief propagation, is used for iterative soft-decision decoding of LDPC codes. We determined the feasibility of a coprocessor that will perform product computations. Our FPGA-based coprocessor design performs computer algebra with significantly less precision than the standard e.

Using synthesis, targeting a 3, LUT Xilinx FPGA, we show that key components of a decoder are feasible and that the full single-precision decoder could be constructed using a larger part. Soft-decision decoding by the iterative belief propagation algorithm is impacted both positively and negatively by a reduction in the precision of the computation. Reducing precision reduces the coding gain, but the limited-precision computation can operate faster.

A proposed solution offers custom logic to perform computations with less precision, yet uses the floating-point format to interface with the software. Simulation results show the achievable coding gain. Synthesis results help theorize the the full capacity and performance of an FPGA-based coprocessor.

Toward a formal verification of a floating-point coprocessor and its composition with a central processing unit. Discussed here is work to formally specify and verify a floating point coprocessor based on the MC The coprocessor consists of two independent units: Reasoning about the interaction and synchronization among processes using higher order logic is demonstrated.

The control laws program was executed in 7. The software emulator execution times for these two tasks were The space, weight and cost reductions achieved in the present, aircraft control application of this combination of a bit microprocessor with an bit floating point coprocessor may be obtainable in other real time control applications.

Floating point multiplication is a critical part in high dynamic range and computational intensive digital signal processing applications which require high precision and low power. Rounding has not been implemented to suit high precision applications. The novelty of the research is that it is the first ever NULL convention logic multiplier, designed to perform floating point multiplication.

The proposed multiplier offers substantial decrease in power consumption when compared with its synchronous version. Performance attributes of the NULL convention logic floating point multiplier, obtained from Xilinx simulation and Cadence, are compared with its equivalent synchronous implementation. NULL convention floating point multiplier.


Floating-point function generation routines for bit microcomputers.

floating point coprocessor: Topics by

Several computer subroutines have been developed that interpolate three types of nonanalytic functions: The routines use data in floating-point form. However, because they are ezcipients for use on a bit Intel system with an mathematical coprocessorfoprocessor execute as fast as routines using data in scaled integer form.

Although all of the routines are written in assembly language, they have been implemented in a modular fashion so as to facilitate their use with high-level languages. Floating point arithmetic in future supercomputers.

Considerations in the floating-point design of a supercomputer are discussed. Particular attention is given to word size, hardware support for extended precision, format, and accuracy characteristics. The features believed to be most important for a future supercomputer floating-point design include: Verification of floating-point software.

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is excipienys further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error.

ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

This is done by reading bytes bit by bit, converting them to floating-point numbers, then writing results to another file. Useful when data files created by VAX computer must be used on other machines. Written in C language. Rational Arithmetic in Floating-Point.


An integrated circuit floating coprkcessor accumulator. Goddard Space Flight Center has developed a large scale integrated circuit type which can perform pulse counting, storage, floating point compression, and serial transmission, using a single monolithic device. Counts of 27 or 19 bits can be converted to transmitted values of 12 or 8 bits respectively. Use of the has resulted in substantial savaings in weight, volume, and dollar resources on at least 11 scientific instruments to be flown coprrocessor 4 NASA spacecraft.

The design, construction, and application of the are described. High-performance floating-point image computing workstation for medical applications. Each add-in board provides an expansion connector to which an optional image computing coprocessor board may be added.

Coprocesor coprocessors can execute programs from external high-speed microcode memory as well as built-in internal microcode routines. The internal microcode routines provide support for 2-D and 3-D graphics operations, matrix and vector arithmetic, and image processing in integer, IEEE single-precision floating pointor IEEE double-precision floating point.

In addition to providing a library of C functions which links the NeXT computer to the add-in coprocesssor and supports its various operational modes, algorithms and medical imaging application programs are being developed and implemented for image display and enhancement.

The worst of these problems is the absence of Slang constructs for coding separate chip component Another related problem was the inability to explicitly declare the size of Slang node values. Environment parameters and basic functions for floating-point computation. A language-independent proposal for environment parameters and basic functions for floating-point computation is presented. Basic functions are proposed to analyze, synthesize, and scale floating-point numbers.

The model provides a small set of parameters and a small set of axioms along coproceswor sharp measures of roundoff error. The parameters and functions can be used to write portable and robust codes that deal intimately with the floating-point representation. Subject to underflow and overflow constraints, a number can be scaled by a power of the floating-point radix inexpensively and without loss of precision. The medical, military, scientific and exciipients communities have come to rely on imaging and computer graphics for solutions to many types of problems.


Systems based on imaging technology are used to acquire and process images, and analyze and extract data from images that would otherwise be of little use. Images can be transformed and enhanced to reveal detail and meaning that would go undetected without imaging techniques.

The success of imaging has increased the demand for faster and less coprpcessor imaging systems and as these systems become available, more and more applications are discovered and more demands are made. From the designer’s perspective the challenge to meet these demands forces him to attack the problem of imaging from a different perspective. The computing demands of imaging algorithms must be balanced against the desire for affordability and flexibility.

Systems must be flexible and easy to use, ready for current applications but at the same time anticipating new, unthought of uses. Here at the University of Washington Image Processing Systems Lab IPSL we are focusing our attention on imaging and graphics systems that implement imaging algorithms for use in an interactive environment.

We have developed a PC-based imaging workstation with the goal to provide powerful and flexible, floating point processing capabilities, along with graphics functions in an affordable package suitable for diverse environments and many applications. This collection of PVS theories provides a basis for machine checked verification of floating-point systems.

This formal definition illustrates that formal specification techniques are sufficiently advanced that is is reasonable to consider their use in the development of future standards.

Design of a reversible single precision floating point subtractor. In recent years, Reversible logic has emerged as a major area of research due to its ability to reduce the power dissipation which is the main requirement in the low power digital circuit design. However, few designs exist on efficient reversible BCD subtractors but no work on reversible floating point subtractor.

In this paper, it is proposed to present an efficient reversible single precision floating-point subtractor. The proposed design requires reversible designs of an 8-bit and a coprcoessor comparator unit, an 8-bit and a bit subtractor, and a normalization unit. For normalization, a bit Reversible Leading Zero Detector and a bit reversible shift register is implemented to shift the mantissas.

To realize a reversible 1-bit comparator, in this paper, two new 3×3 reversible gates are proposed The proposed reversible 1-bit comparator is better and optimized in terms of the number of reversible gates used, the number of transistor count and the number of garbage coprocessot. The proposed work is analysed in terms of number of reversible gates, garbage coorocessor, constant inputs and quantum costs. Using these modules, an efficient design of a reversible single precision floating point subtractor is proposed.

Proposed circuits have been simulated using Modelsim and synthesized using Xilinx Virtex5vlx30tff The total on-chip power consumed by the proposed bit reversible floating point subtractor is 0. Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed- point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed- point specification are required to reduce the application time-to-market.

In this paper, a new methodology for the floating -to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed- point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach exci;ients into account the DSP architecture to optimise the fixed- point formats and the floating-to-fixed-point conversion process is coupled with the code generation process.

The fixed- point data types and the position of the scaling operations are optimised to reduce the code execution time.