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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.sysarc.2006.03.002 Byline: Ahmet AkkaA (a), Michael J. Schulte (b) Keywords: Quadruple precision; Double precision; Single precision; Multiplier; Floating-point; Computer arithmetic; Rounding; Normalization Abstract: Although most modern processors have hardware support for double precision or double-extended precision floating-point multiplication, this support is inadequate for many scientific computations. This paper presents the architecture of a quadruple precision floating-point multiplier that also supports two parallel double precision multiplications. Since hardware support for quadruple precision arithmetic is expensive, a new technique is presented that requires much less hardware than a fully parallel quadruple precision multiplier. With this architecture, quadruple precision multiplication has a latency of three cycles and two parallel double precision multiplications have latencies of only two cycles. The multiplier is pipelined so that two double precision multiplications can begin every cycle or a quadruple precision multiplication can begin every other cycle. The technique used for the dual-mode quadruple precision multiplier is also applied to the design of a dual-mode double precision floating-point multiplier that performs a double precision multiplication or two single precision multiplications in parallel. Synthesis results show that the dual-mode double precision multiplier requires 43% less area than a conventional double precision multiplier. The correctness of all the multipliers presented in this paper is tested and verified through extensive simulation. Author Affiliation: (a) Computer Engineering Department, Koc University, 34450 Sariyer, Istanbul, Turkey (b) Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA Article History: Received 21 September 2004; Revised 10 March 2006; Accepted 24 March 2006

Time-resolved contrast-enhanced magnetic resonance (MR) angiography (CE-MRA) has gained in popularity relative to X-ray Digital Subtraction Angiography because it provides three-dimensional (3-D) spatial resolution and it is less invasive. We have previously presented methods that improve temporal resolution in CE-MRA while providing high spatial resolution by employing an undersampled 3-D projection (3D PR) trajectory. The increased coverage and isotropic resolution of the 3D PR acquisition simplify visualization of the vasculature from any perspective. We present a new algorithm to develop a set of time-resolved 3-D image volumes by preferentially weighting the 3D PR data according to its acquisition time. An iterative algorithm computes a series of density compensation functions for a regridding reconstruction, one for each time frame, that exploit the variable sampling density in 3D PR. The iterative weighting procedure simplifies the calculation of appropriate density compensation for arbitrary sampling patterns, which improve sampling efficiency and, thus, signal-to-noise ratio and contrast-to-noise ratio, since it is does not require a closed-form calculation based on geometry. Current medical workstations can display these large four-dimensional studies, however, interactive cine animation of the data is only possible at significantly degraded resolution. Therefore, we also present a method for interactive visualization using powerful graphics cards and distributed processing. Results from volunteer and patient studies demonstrate the advantages of dynamic imaging with high spatial resolution. Index Terms--Animation, image reconstruction, magnetic resonance imaging, temporal filtering.