Home > By category > Scripts >Development Tools > XSum



XSum

  • Downloads: 
  • Views: 
  • Rating:

XSum - SUM with error compensation

The accuracy of the sum of floating point numbers is limited by the truncation error. E.g. SUM([1e16, 1, -1e16]) replies 0 instead of 1 and the error of SUM(RANDN(N, 1)) is about EPS*(N / 10).
Kahan, Knuth, Dekker, Ogita and Rump (and others) have derived some methods to reduce the influence of rounding errors, which are implemented here as fast C-Mex: XSum(RANDN(N, 1), 'Knuth') is exact to all 15 digits.

Y = XSum(X, N, Method)
INPUT:
X: Double array of any size.
N: Dimension to operate on.
Method: String: 'Double', 'Long', 'Kahan', 'Knuth', 'KnuthLong', 'Knuth2'.

OUTPUT:
Y: Double array, equivalent to SUM, but with compensated error depending
on the Method. The high-precision result is rounded to double precision.

METHODS: (speed and accuracy compared to SUM)
- Double: A thread-safe implementation of Matlab's SUM. At least in Matlab 2008a to 2009b the results of the multi-threaded SUM can differ slightly from call to call. 50% faster than single-threaded SUM (MSVC++ 2008), equivalent accuracy.
- Long: Accumulated in a 80 bit long double, if the compiler support this (e.g. LCC v3.8). 3.5 more valid digits, 40% slower.
- Kahan: The local error is subtracted from the next element. 1 to 3 more valid digits, 10% slower.
- Knuth: As if the sum is accumulated in a 128 bit float: about 15 more valid digits. About the same speed (MSVC++2008 compiler). This is suitable for the most real world problems.
- Knuth2: 30 more valid digits as if it is accumulated in a 196 bit float. 60% slower.
- KnuthLong: As Knuth, but using long doubles to get about 21 more valid digits, if supported by the compiler. 2.5 times slower.

Free download from Shareware Connection - XSum - SUM with error compensation

Publisher: Jan Simon | License: Shareware
Version: 1.0 | Size: 10 KB | Platform: Matlab, Scripts
Released Date: 19-05-2013 | Rating: 0 | Title: XSum

Author Url: http://www.mathworks.com
Program Info Url: http://www.mathworks.com
Download Url: http://www.mathworks.com/matlabcentral/fx_files/26800/1/XSum.zip

More downloads from XSum publisher Jan Simon:

ScaleTime - ScaleTime - fast linear matrix interpolation

DateStr2Num - DATESTR2NUM - Fast conversion of DATESTR to DATENUM

strncmpr - Compare last N chars of strings or cell strings

Patch FILTFILT - If applied to a matrix, the function FILTFILT (Signal Processing Toolbox) calls itself recursively for each column.

fSGolayFilt - fSGolayFilt is a fast polynomial smoothing filter for uniformly spaced signals

XSum keywords:
XSum related downloads:

VIDEO TUTORIAL: PUBLISHING MATLAB RESULTS TO HTML, WORD, LATEX, ETC - VIDEO TUTORIAL: PUBLISHING MATLAB RESULTS TO HTML, WORD, LATEX, ETC.(Narration in Spanish)

Crop vidoe to sub elements - This functions allows the user to crop the input movie to several (unlimited) fragments of his choice.

Text message / E-mail Matlab! - Have you ever had a need to invert a matrix while out for dinner? Have you ever had the need to solve a second-order differential equation while stuck in traffic but didn't have access to Matlab? Well, now you can!

N-dimensional histogram - Like histc but for n-dimension.

Efficient K-Means Clustering using JIT - This is a tool for K-means clustering.

Shareware Connection periodically updates pricing and software information of 'XSum' from company source 'Jan Simon' , so some information may be slightly out-of-date. You should confirm all information before relying on it. Software piracy is theft,  Using 'XSum' crack, password, serial numbers, registration codes, key generators is illegal and prevent future development of XSum.

New Reviews

Serif CraftArtist 2 Professional - There are plenty of image editing tools available for Windows users but the number of scrapbooking apps is not much. However, with Serif CraftArtist Professional you can create sleek looking greeting card, digital albums and scrapbooks without ...

Eset Cyber Security Pro - There was a time Mac users were simply oblivious to the existence of malware and viruses, partially encouraged by Apple’s claim that Mac’s do not fall prey to malicious code. In last few years, that perception has been shattered owing ...

Autodesk Smoke - Autodesk is the company well known for making some of the most feature rich and versatile tools for 3D modeling, animation and engineering design related work. Its Smoke is a Mac OS specific app that is aimed at professionals involved in ...

Avast Endpoint Protection Suite Plus - PC security has become a vital aspect of computing nowadays and business users face the heat more than home users. While installing and handling a standalone antivirus suite is neither tedious nor time consuming, the scenario is different in ...

NovaBench - PC performance benchmarking is something that may not interest average users much but tech savvy lot resort to such apps to find out prowess and capability of their laptops and desktops. While there are quite a few PC benchmarking apps in market, ...

Backup Dwarf Home Edition - Making backups of data and media content has become extremely important for computer users nowadays. Owing to hardware failure, you may end up losing gigabytes of precious data. Besides, you may not want to leave sensitive data accessible to all ...

Stellar Insta Backup - Data Backup Software - Taking backup of data stored in your PC is quite essential these days, given the fact average PC users deal with tons of data and hardware failure or OS corruption can happen. However, it is also necessary that you pick the right software for ...

CyberFence - Technological innovations play a pivotal role in changing human lives but they also come with their pitfalls. Perhaps, nothing can be a bigger example of this than the web. You need the internet for education, work, monetary transactions and ...

Autodesk MotionBuilder 2015 - 3D animators and post production setups need to use Motion capturing technology extensively for making stunning films, ads and tutorials etc. Over the years, both software and hardware technology used in this segment have evolved by leaps and ...

Adobe Media Encoder - Almost every PC user faces a situation where he or she needs to convert an audio or video file fast into a format of choice. There are several free and commercial apps, but the abundance of options can actually make selection difficult. If you ...




New Downloads

game_solve

The input to this function is
a matrix A in which A(i,j)
represents the payoff from the
"column" player to the "row"
...

VideoDB for PHPkode

VideoDB is a database to
manage your personal video
collection

uContext - Clickbank
In-Text Affiliate Links

uContext is a free service
that locates keywords in your
content and turns them into
affiliate links that take your
...

Mojo Clicks for Scripts

Mojo Clicks is a simple click
tracker easily installed in
just 4 steps.

Save and load data as
multi-frame TIFF format

You can easily save and load a
variety types of data as
multi-frame TIFF format by
using this.

Rohde & Schwarz CMD55
Digital Radiocom Tester

This is a MATLAB™ instrument
driver for use with v2.0 of
the Instrument Control
Toolboxd-OC?D? and higher

Patterns

Complex websites and web
applications can be created by
combining configurations of
Modules, Content Types (CCK,)
Views, ...

Tweet Manager

Create Your Own Custom Twitter
Application and Publish to
Your Twitter account 'Via Your
Custom Twitter Application'

Image Gallery Management

This is an add-on module for
Image Gallery

i-trax for Scripts

i-trax is a simple and easy to
use software system for your
mobile device.

ASP.NET Ajax Grid and Pager

ASP.NET Ajax Grid and Pager
allows you to create a custom
Ajax Grid and Pager with the
Microsoft ASP.NET AJAX
platform.

INITools

Tools for parsing and using
INI-style files A set of
tools for parsing and using
.ini-style files, including an
abstract ...