An official website of the United States government
Abstract Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision.
more »
« less
Accelerated fixed-point iterative reconstruction for fiber borescope imaging
Computational imaging systems with embedded processing have potential advantages in power consumption, computing speed, and cost. However, common processors in embedded vision systems have limited computing capacity and low level of parallelism. The widely used iterative algorithms for image reconstruction rely on floating-point processors to ensure calculation precision, which require more computing resources than fixed-point processors. Here we present a regularized Landweber fixed-point iterative solver for image reconstruction, implemented on a field programmable gated array (FPGA). Compared with floating-point embedded uniprocessors, iterative solvers implemented on the fixed-point FPGA gain 1 to 2 orders of magnitude acceleration, while achieving the same reconstruction accuracy in comparable number of effective iterations. Specifically, we have demonstrated the proposed fixed-point iterative solver in fiber borescope image reconstruction, successfully correcting the artifacts introduced by the lenses and fiber bundle.
more »
« less
- Award ID(s):
- 1932858
- PAR ID:
- 10471736
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 31
- Issue:
- 23
- ISSN:
- 1094-4087; OPEXFF
- Format(s):
- Medium: X Size: Article No. 38355
- Size(s):
- Article No. 38355
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Brain-inspired Hyperdimensional (HD) computing models cognition by exploiting properties of high dimensional statistics– high-dimensional vectors, instead of working with numeric values used in contemporary processors. A fundamental weakness of existing HD computing algorithms is that they require to use floating point models in order to provide acceptable accuracy on realistic classification problems. However, working with floating point values significantly increases the HD computation cost. To address this issue, we proposed QuantHD, a novel framework for quantization of HD computing model during training. QuantHD enables HD computing to work with a low-cost quantized model (binary or ternary model) while providing a similar accuracy as the floating point model. We accordingly propose an FPGA implementation which accelerates HD computing in both training and inference phases. We evaluate QuantHD accuracy and efficiency on various real-world applications, and observe that QuantHD can achieve on average 17.2% accuracy improvement as compared to the existing binarized HD computing algorithms which provide a similar computation cost. In terms of efficiency, QuantHD FPGA implementation can achieve on average 42.3× and 4.7× (34.1× and 4.1×) energy efficiency improvement and speedup during inference (training) as compared to the state-of-the-art HD computing algorithms.more » « less
-
Though photonic computing systems offer advantages in speed, scalability, and power consumption, they often have a limited dynamic encoding range due to low signal-to-noise ratios. Compared to digital floating-point encoding, photonic fixed-point encoding limits the precision of photonic computing when applied to scientific problems. In the case of iterative algorithms such as those commonly applied in machine learning or differential equation solvers, techniques like precision decomposition and residue iteration can be applied to increase accuracy at a greater computing cost. However, the analog nature of photonic symbols allows for modulation of both amplitude and frequency, opening the possibility of encoding both the significand and exponent of floating-point values on photonic computing systems to expand the dynamic range without expending additional energy. With appropriate schema, element-wise floating-point multiplication can be performed intrinsically through the interference of light. Herein, we present a method for configurable, signed, floating-point encoding and multiplication on a limited precision photonic primitive consisting of a directly modulated Mach–Zehnder interferometer. We demonstrate this method using Newton's method to find the Golden Ratio within ±0.11%, with six-level exponent encoding for a signed trinary digit-equivalent significand, corresponding to an effective increase of 243× in the photonic primitive's dynamic range.more » « less
-
null (Ed.)With ever-increasing volumes of scientific floating-point data being produced by high-performance computing applications, significantly reducing scientific floating-point data size is critical, and error-controlled lossy compressors have been developed for years. None of the existing scientific floating-point lossy data compressors, however, support effective fixed-ratio lossy compression. Yet fixed-ratio lossy compression for scientific floating-point data not only compresses to the requested ratio but also respects a user-specified error bound with higher fidelity. In this paper, we present FRaZ: a generic fixed-ratio lossy compression framework respecting user-specified error constraints. The contribution is twofold. (1) We develop an efficient iterative approach to accurately determine the appropriate error settings for different lossy compressors based on target compression ratios. (2) We perform a thorough performancemore » « less
-
With ever-increasing volumes of scientific floating-point data being produced by high-performance computing applications, significantly reducing scientific floating-point data size is critical, and error-controlled lossy compressors have been developed for years. None of the existing scientific floating-point lossy data compressors, however, support effective fixed-ratio lossy compression. Yet fixed-ratio lossy compression for scientific floating-point data not only compresses to the requested ratio but also respects a user-specified error bound with higher fidelity. In this paper, we present FRaZ: a generic fixed-ratio lossy compression framework respecting user-specified error constraints. The contribution is twofold. (1) We develop an efficient iterative approach to accurately determine the appropriate error settings for different lossy compressors based on target compression ratios. (2) We perform a thorough performance and accuracy evaluation for our proposed fixed-ratio compression framework with multiple state-of-the-art error-controlled lossy compressors, using several real-world scientific floating-point datasets from different domains. Experiments show that FRaZ effectively identifies the optimum error setting in the entire error setting space of any given lossy compressor. While fixed-ratio lossy compression is slower than fixed-error compression, it provides an important new lossy compression technique for users of very large scientific floating-point datasets.more » « less
