scholarly journals Branch Divergence Reduction Based on Code Motion

2020 ◽  
Vol 28 (0) ◽  
pp. 302-309 ◽  
Author(s):  
Junji Fukuhara ◽  
Munehiro Takimoto
Keyword(s):  
Code Motion ◽  
Branch Divergence

scholarly journals Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

2014 ◽  
Vol 25 (2) ◽  
pp. 177-212 ◽  
Author(s):  
WILLIAM T. SHAW ◽  
THOMAS LUU ◽  
NICK BRICKMAN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Processing Unit ◽  
Model Risk ◽  
Change Of Variables ◽  
Special Cases ◽  
Wide Range ◽  
Branch Divergence

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function.

Code motion of control structures in high-level languages

1986 ◽  
Author(s):  
Ron Cytron ◽  
Andy Lowry ◽  
F. Kenneth Zadeck
Keyword(s):  
Control Structures ◽  
High Level ◽  
Code Motion

An SSA-based algorithm for optimal speculative code motion under an execution profile

2012 ◽  
Vol 47 (6) ◽  
pp. 98
Author(s):  
Hucheng Zhou ◽  
Wenguang Chen ◽  
Fred Chow
Keyword(s):  
Code Motion
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