Cuda Floating Point Error
Contents |
Fused Multiply-Add (FMA) 3.Dot Product: An Accuracy Example 3.1.Example Algorithms 3.2.Comparison 4.CUDA and Floating Point 4.1.Compute Capability 2.0 and Above 4.2.Rounding Modes 4.3.Controlling Fused cuda floating point exception Multiply-add 4.4.Compiler Flags 4.5.Differences from x86 5.Considerations for a Heterogeneous World
Cuda Float Overflow
5.1.Mathematical Function Accuracy 5.2.x87 and SSE 5.3.Core Counts 5.4.Verifying GPU Results 6.Concrete Recommendations A.Acknowledgements B.References Search floating point rounding error Results This document includes math equations (highlighted in red) which are best viewed with Firefox version 4.0 or higher, or another MathML-aware browser. There is also a
Floating Point Relative Error
PDF version of this document. Floating Point and IEEE 754 (PDF) - v8.0 (older) - Last updated September 27, 2016 - Send Feedback - Floating Point and IEEE 754 Compliance for NVIDIA GPUs A number of issues related to floating point accuracy and compliance are a frequent source of confusion on both CPUs invalid floating point operation error and GPUs. The purpose of this white paper is to discuss the most common issues related to NVIDIA GPUs and to supplement the documentation in the CUDA C Programming Guide. 1.Introduction Since the widespread adoption in 1985 of the IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754-1985 [1]) virtually all mainstream computing systems have implemented the standard, including NVIDIA with the CUDA architecture. IEEE 754 standardizes how arithmetic results should be approximated in floating point. Whenever working with inexact results, programming decisions can affect accuracy. It is important to consider many aspects of floating point behavior in order to achieve the highest performance with the precision required for any specific application. This is especially true in a heterogeneous computing environment where operations will be performed on different types of hardware. Understanding some of the intricacies of floating point and the specifics of how NVIDIA hardware handles floating point is obviously important to CUDA programmers striving to implement correct numerical
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Floating Point Error Calculator
Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 million floating point error fortran programmers, just like you, helping each other. Join them; it only takes a minute: Sign up Division of floating point numbers on GPU different from that on CPU up vote 4 down vote favorite 3 When I http://docs.nvidia.com/cuda/floating-point/ divide 2 floating point numbers on the GPU, i get .196405. When i divide them on CPU , i get .196404. The acutal value using the calculator is .196404675. How do i make the division on the GPU and the CPU same? cuda gpu share|improve this question asked Dec 18 '12 at 16:28 Programmer 2,41995390 4 Why do you need them to be the same? My gut says that if you need http://stackoverflow.com/questions/13937328/division-of-floating-point-numbers-on-gpu-different-from-that-on-cpu them to be equivalent, you should adjust your significant digits when interpreting the results, not when calculating them. –Patrick87 Dec 18 '12 at 16:38 3 What precision, what GPU, what source numbers and most importantly why? –talonmies Dec 18 '12 at 16:47 2 Please show code and compiler options and identify the GPU. Double-precision division in CUDA always uses IEEE-754 rounding, however the CPU may use extended precision internally, leading to a problem called double rounding when it returns the double precision result. Single-precision division in CUDA uses IEEE-754 rounding by default for sm_20 and up. Various compiler options can lead to the use of approximate single-precision division, and sm_1x platforms always use approximate division for the single-precision division operator (you can use intrinsics to get IEEE-754 rounded division). –njuffa Dec 18 '12 at 18:59 @talonmies: I am doing floating point division. The GPU is GeForce GT 540M. As for the why, I know my CPU implementation is correct. Just want to check if my GPU implementaion is correct by comparing outputs. –Programmer Dec 19 '12 at 9:43 @Programmer: single or double precision is what I was asking –talonmies Dec 19 '12 at 9:47 | show 2 more comments 3 Answers 3 active oldest votes up vote 9 down vote accepted As t
fixed-point? What will be the difference in execution time on an Nvidia TESLA? I currently have an OpenCL code that uses double precision floating point in massively parallel https://www.researchgate.net/post/GPU_floating-point_double_precision_vs_64-bits_fixed-point_What_will_be_the_difference_in_execution_time_on_an_Nvidia_TESLA filtering functions (i.e. a lot of multiply-accumulate instructions). Since it does not meet a time deadline, I was wondering how much time I can save if I used 64-bits fixed-point integers rather than 64-bits floating-point. The accuracy will only be marginally affected. The main problem I have is execution time. Before doing the transition I would like to hear from some experts. floating point Topics Scientific Computing (Computational Science) × 127 Questions 3,002 Followers Follow Open Source Scientific Software × 198 Questions 8,736 Followers Follow OpenCL × 29 Questions 237 Followers Follow Parallel and Distributed Computing × 144 Questions 13,390 Followers Follow GPU Programming × 77 Questions 1,573 Followers Follow Jun 17, 2013 Share Facebook Twitter LinkedIn Google+ 3 / 0 Popular Answers John Gustafson · floating point error Ceranovo, Inc. Mario, I am very glad to hear you raising this question. 64-bit precision is being blindly used as a panacea in so many applications, when the input arguments have only three or four decimals of accuracy and the only accuracy needed in the outputs is also three or four decimals. But numerically-ignorant programmers invoke 15 decimals of accuracy throughout a calculation, just to be safe. YES, there is massive savings possible over using 15-decimal "scratch" variables for the entire calculation, which is usually done because no one has the time or expertise to think about rounding error any more. You can increase speed and accuracy at the same time as you decrease memory footprint, pressure on bandwidth, energy usage, and power consumption, just by right-sizing the precision and dynamic range to what you need. Any possibility of quantifying the error in your output as a function of errors in inputs? It's usually not easy to figure out, but if you can, you may be astonished at the economy of storage that the knowledge presents to you. Double-precision IEEE floats provide over 60
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