A floating point conversion algorithm for mixed precision computations

2012 ◽  
Vol 13 (9) ◽  
pp. 711-718
Author(s):  
Choon Lih Hoo ◽  
Sallehuddin Mohamed Haris ◽  
Nik Abdullah Nik Mohamed
Keyword(s):  
Floating Point ◽  
Conversion Algorithm ◽  
Mixed Precision

Rigorous floating-point mixed-precision tuning

2017 ◽  
Author(s):  
Wei-Fan Chiang ◽  
Mark Baranowski ◽  
Ian Briggs ◽  
Alexey Solovyev ◽  
Ganesh Gopalakrishnan ◽  
...  
Keyword(s):  
Floating Point ◽  
Mixed Precision

Regime Inference for Sound Floating-Point Optimizations

2021 ◽  
Vol 20 (5s) ◽  
pp. 1-23
Author(s):  
Robert Rabe ◽  
Anastasiia Izycheva ◽  
Eva Darulova
Keyword(s):  
Floating Point ◽  
Improve Performance ◽  
Rounding Errors ◽  
Proper Functioning ◽  
Mixed Precision ◽  
Input Domain ◽  
Different Parts

Efficient numerical programs are required for proper functioning of many systems. Today’s tools offer a variety of optimizations to generate efficient floating-point implementations that are specific to a program’s input domain. However, sound optimizations are of an “all or nothing” fashion with respect to this input domain—if an optimizer cannot improve a program on the specified input domain, it will conclude that no optimization is possible. In general, though, different parts of the input domain exhibit different rounding errors and thus have different optimization potential. We present the first regime inference technique for sound optimizations that automatically infers an effective subdivision of a program’s input domain such that individual sub-domains can be optimized more aggressively. Our algorithm is general; we have instantiated it with mixed-precision tuning and rewriting optimizations to improve performance and accuracy, respectively. Our evaluation on a standard benchmark set shows that with our inferred regimes, we can, on average, improve performance by 65% and accuracy by 54% with respect to whole-domain optimizations.

Efficient Multiple-Precision Floating-Point Fused Multiply-Add with Mixed-Precision Support

2019 ◽  
Vol 68 (7) ◽  
pp. 1035-1048 ◽  
Author(s):  
Hao Zhang ◽  
Dongdong Chen ◽  
Seok-Bum Ko
Keyword(s):  
Floating Point ◽  
Multiple Precision ◽  
Mixed Precision

Fine-grained floating-point precision analysis

2016 ◽  
Vol 32 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Michael O Lam ◽  
Jeffrey K Hollingsworth
Keyword(s):  
High Performance ◽  
Floating Point ◽  
Data Sets ◽  
Double Precision ◽  
Precision Analysis ◽  
Memory Space ◽  
Incremental Search ◽  
Fine Grained ◽  
Mixed Precision ◽  
Application Developers

Floating-point computation is ubiquitous in high-performance scientific computing, but rounding error can compromise the results of extended calculations, especially at large scales. In this paper, we present new techniques that use binary instrumentation and modification to do fine-grained floating-point precision analysis, simulating any level of precision less than or equal to the precision of the original program. These techniques have an average of 40–70% lower overhead and provide more fine-grained insights into a program’s sensitivity than previous mixed-precision analyses. We also present a novel histogram-based visualization of a program’s floating-point precision sensitivity, as well as an incremental search technique that allows developers to incrementally trade off analysis time for detail, including the ability to restart analyses from where they left off. We present results from several case studies and experiments that show the efficacy of these techniques. Using our tool and its novel visualization, application developers can more quickly determine for specific data sets whether their application could be run using fewer double precision variables, saving both time and memory space.

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