Thursday, March 03, 2011

Perils of floating point arithmetic

A recent discussion on stackoverflow brought up the issue of results of floating point arithmetic being non-reproducible

A reader asked what one could do to guarantee that result of floating point computation is always the same, and Daniel Lichtblau, a veteran developer at the kernel group of WRI replied that "it is impossible with current hardware and software"

One problem is that IEEE 754 standard is ambiguous, and different implementations of it give slightly different results. See page 250 of What Every Computer Scientist Should Know About Floating Point Arithmetic for specific examples. This means that compiling code on a different system can produce slightly different results.

Another issue is that even when you run the same computation on the same system, results can be slightly different on reruns. This has to do with how low-level optimization is scheduled.

This means that if you want your results to be reproducible, you should avoid things like testing floating point numbers for equality. John D Cook gives some more advice in Five Tips for Floating Point Programming

73 comments:

svrtechnologies said...

Good One...Salesforce Training Online

QuickBooks Support Phone Number said...

People working with accounts, transaction, banking transaction need our service. Some of you are employing excel sheets for a few calculations. QuickBooks Tech Support Number all the above has a certain use.

htop said...

thanks for sharing this informations
best angularjs training in chennai
angular js training in sholinganallur
angularjs training in chennai
azure training in chennai
best java training in chennai
selenium training in chennai

bestonlinetraining said...

nice article thanks for sharing the post...!

sumathikits said...

nice article thanks for sharing the post...!
Sql and Plsql Training

Tableau Training

Teradata Training

Testing Tools Training

remo said...

THANKS FOR THE INFORMATION...
<a href="http://www.chloros.in/digital-marketing-internship.htmlhttp://www.chloros.in/digital-marketing-internship.html>Digital Marketing Internship Program in Bangalore</a>

https://tagifind.com/ips-officer-kaise-bane/ said...

https://tagifind.com/ips-officer-kaise-bane/

https://tagifind.com/what-is-computer-cmos/ said...

https://tagifind.com/what-is-computer-cmos/

winner77bet said...

agen bola terpercaya
judi bola terpercaya
daftar joker123

qb enterprise support number said...

Hey! What a remarkable blog. I really like your work, since it has all the properties of a good blog. Keep writing such a blog. QuickBooks is easy to use and highly customizable accounting software. You can easily install this software. You can even get instant help at QuickBooks Error Support Phone Number +1-888-238-7409. Visit us: - https://www.error.enetquickbookenterprise.com/

Nandhini said...

thanks for sharing the nice article, keep posting
Python training in bangalore
Python training in Bangalore
Data science with python training in Bangalore
Angular js training in bangalore
Hadoop training in bangalore
DevOPs training in bangalore
Agile and scrum training in bangalore

Nandhini said...

thanks for sharing the nice article, keep posting
Python training in bangalore
Python training in Bangalore
Data science with python training in Bangalore
Angular js training in bangalore
Hadoop training in bangalore
DevOPs training in bangalore
Agile and scrum training in bangalore

gautham said...

Thanks for your post. learn on cyber security online training india

Unknown said...

It's an amazing post with informative data shared, hope you will share such more valuable post in future. Great work from

Dubai City Sightseeing

mahi said...

Please refer below if you are looking for best project center in coimbatore

Hadoop Training in Coimbatore | CCNA Training in Coimbatore | AWS Training in Coimbatore | AngularJS Training in Coimbatore | Dotnet Training In Coimbatore | SAS Training In Coimbatore | R-Programming Training In Coimbatore

Thank you for excellent article.

preethi minion said...

nice...
india shared web hosting
italy web hosting
suden web hosting
tunisia hosting
uruguay web hosting
inplant training in chennai

desert safari tours said...

This is very nice one and gives in-depth information.

svrtechnologies said...

Pretty article! I found some useful information in your blog, it was awesome to read, thanks for sharing this great content to my vision, keep sharing.

oracle pl sql training

svrtechnologies said...

This is so elegant and logical and clearly explained. Brilliantly goes through what could be a complex process and makes it obvious...

online cyber security training

Maze Tech said...

SEO Service in Chennai

KITS Technologies said...


Nice .....!
R Programming Online Training

PHP Online Training

SAP Fico Online Training

Sailpoint Online Training

Core Java Online Training

Business Analysis Online Training

Amazon Web Server Online Training

Burak said...

fairtilt get the bio, wiki, age, height, net worth & more facts about your favourite celebrity, personality, sportsperson, etc.
Ozge Torer BioOzge Torer Bio

Sophia said...

Thanks for sharing the article, Check out
FPSC Patrol Officer Past Papers

subha said...

Nice and good article. It is very useful for me to learn and understand easily. Thanks for sharing your valuable information and time. Please keep updating ....nice page to growth ur knowledge.
Ai & Artificial Intelligence Course in Chennai
PHP Training in Chennai
Ethical Hacking Course in Chennai Blue Prism Training in Chennai
UiPath Training in Chennai

Agen Slot777 Mobile said...

This blog is very good information. Thanks for share ^^

Slot777
Sbobet365
Link Login Sbobet369
Daftar Sbobet777 Mobile
Agen Slot88 Indonesia
Agen Slotbet88 Mobile
Www-sbobet.com

Video Teraveloka said...

Freechip Tanpa Deposit Bulan September 2020 (COMING SOON)

• Daftar >> Freechip Gratis

Follow on Twitter @s1288poker
Follow on Instagram @s128poker.ofc
Follow on Facebook @s128cash.biz

Python said...

Thank you for sharing this. It is worth reading for everyone.
Data Science Online Training
python Online Training

sedenvans said...

Good post.keeping sharing such valuable informations.

Staff transportation buses on rent

Toy shops in Dubai said...

Great information !!! Instead of learning from classrooms, encourage the creativity of children. It helps them discover their passion for a specific field they want to do. Eg:-doctor’s set, kitchen sets, Diecast items and clay activities. With our personalised wholesale services, Purchase Toys Online.
Visit Website >> Toys & Games for Kids UAE

Management consultancy Dubai said...

UBL Accounting and Taxation is a professional accounting firm of experienced Chartered Accountants for best auditing Dubai. Located at Dubai we are a team of hardcore professionals qualified in the field of Auditing, Accounting, Taxation, System Audits, and Management Consultancy. We also provide all services for business setup in Dubai, UAE. All the solutions we offer are very cost-effective and reliable. we the auditing companies in Dubai provide all services for you.
Click to know about the best chartered accountants in Dubai

SEO experts in Dubai said...

Digital and social media marketing services are also responsible for your brand promotion and website traffic. New news and viral videos are bringing social media to the forefront. Many people search on social media sites to find social media content. Social connections give you a new way to do business. Using social media for marketing can increase your services worldwide. Visit >> Social media marketing company in Dubai

SAGEK said...

GOOD BLOG..... I LIKE IT!!!
Link Sbobet188 Asia Login Apk
Sbobet88 Bola Slot Mobile Asia

SHIVANGI said...

Nice Information Check out the best online platform where you will get CBSE Previous Year Question Papers
Previous year sample papers
Previous year sample papers
Previous year sample papers
Previous year sample papers
Previous year sample papers
sample papers
sample papers

DIAN said...

Thank you for your post, myself very happy to read it because it can give me more insight, thanks.. Visit my blog..thankyou
Sbobet369
Joker388 Slot
Slot88
Maxbet388
Joker118

Dewi said...

Your blog has always been great. I read your every blog, Reading your blog helps a lot.
Thankyou for sharing with us!! :)


Joker388
Sbobet99
Sbobet888
Joker388
Slot88 Bola

Rohman said...

I like this topic.This site has lots of advantage.I found many interesting things from this site. It helps me in many ways.

Daftar S128 Net
Sbobet1388
Sbowin
http://139.59.252.210/
Sbobet365

Thank you for this article.
Have a nice day!! ^_^

DIAN said...

Thank you for your post, myself very happy to read it because it can give me more insight, thanks.. Visit my blog..thankyou
Sbobet88

Dewey Does said...

hey such great information you have shared with us about digital marketing i'm also a digital marketing person here is some service we are providing in india please check
search engine optimisation company in india
social media marketing company in india
bulk email marketing company in india
search engine marketing company in india
content marketing company in india
ppc advertising company in india
web devlopment company in india

SHIVANGI said...

Top Immigration lawyers/Consultants in Delhi for all your immigration needs. Our legal advisors/lawyers have
considerable experience handling complex NRI Legal matters.
https://lexmove1.blogspot.com/2021/05/looking-for-top-notch-immigration.html
Top Immigration lawyers/Consultants

Sandra Kristianti said...

It’s really a great and helpful piece of information.
I’m satisfied that you simply shared this useful info
with us. Please keep us informed like this. Thank you for
sharing.

Buat Akun Sbobet88
Slot Joker123
Sbobet88 Agen Judi Online Terpercaya
Daftar Akun Sbobet88 Mobile
Login Sbobet88 Mobile Indonesia

Iwan Januardi said...

Someone essentially lend a hand to make critically
posts I would state. That is the very first time I frequented your website page and up to now?
I surprised with the research you made to create this particular submit
incredible. Wonderful task!

Cara Login Sbobet777 Indonesia
Casino88
Judi Dingdong Online
Joker88 Slot
Sbobet128

Dedi Akbar said...

Oh my goodness! Impressive article dude! Thank you, However I am going through
difficulties with your RSS. I don’t know the reason why I am
unable to join it. Is there anybody else having the same RSS problems?
Anyone that knows the solution will you kindly respond?
Thanks!!

Judi Dadu Online
Sbobet168
Sbobet303
Sbobet188
Sbobet365

Dorothi Amelia said...

Howdy! I could have sworn I’ve visited this blog before but after browsing through many of the articles I realized it’s new to me. Anyways, I’m certainly delighted I discovered it and I’ll be book-marking it and checking back frequently!

Daftar Sbowin Wap Mobile
Daftar Sbobet99 Slot
Daftar Sbobetcc Slot
Daftar Bola888 Slot
Daftar Sbobet Slot

Silviana Mo said...

Nice post. I was checking constantly this blog and I am impressed!
Extremely useful information specifically the last part 🙂 I care for such information a lot.
I was seeking this certain info for a very long time.
Thank you and good luck.

Daftar S128 Net
Daftar Sbobet88 Slot
Daftar Judi Slot Online
Dewa Hoki
Dewahoki

Alexander Adi said...

Hi, i tһink that і saw you visited my website thus і
came to “return the favor”.I am attempting to find things to impгove my website!I ѕuppoѕe its ok to use a few
of your iԁeas!!

Slot777
Poker77
Daftar Sky777 Slot
Mega888 Slot
Mega77 Slot

Aurellia Anin said...

Its like you read my mind! You appear to know so much about this, like you wrote the book in it or something. I think that you could do with some pics to drive the message home a little bit, but instead of that, this is magnificent blog. A great read. I’ll definitely be back.

Login Wap Winsbotop Com
Sbobet Mobile Login
Login Sbotop Euro
Daftar Joker388 Slot Mobile
Digmaan Live

Fanny Ariesta said...

Hi there, i read your blog from time to time
and i own a similar one and i was just wondering if you get a lot of spam feedback?
If so how do you reduce it, any plugin or anything you can suggest?
I get so much lately it’s driving me insane so any assistance is very much appreciated.

Live22 Slot
Dewahoki Slot 777
Game Slot 777
Joker Slot 388
Permainan Menembak Ikan

Sandra Yustika said...

Hi there, i read your blog from time to time
and i own a similar one and i was just wondering if you get a lot of spam feedback?
If so how do you reduce it, any plugin or anything you can suggest?
I get so much lately it’s driving me insane so any assistance is very much appreciated.

Agen 1388 Bet
Situs Joker1999
Daftar Fa Fa Slot
Download Apklive22
Royal Slot 777

Nelson said...

Thanks for taking the time to discuss this, I feel strongly about it and love learning more on this topic. If possible, as you gain expertise, would you mind updating your blog with extra information? It is extremely helpful for me,for more slot online terbaru

The Home Dekor said...

Hey Its Really Nice Blog, Information you have Shared With Us Its Litrally Helpful for People, and Here's some links of my site We are leading company wooden of wooden furniture
buy dining tables online
solid wood dining table
dining table online
small dining table
wooden dining table
dining tables online
extension dining table
dining table set online
living room furniture online
furniture for living room
furniture latest design
Solid wood furniture for living room
latest design of furniture
buy living room furniture
Solid wood furniture for living room
Buy furniture for living room
Study room furniture
study table for kids
sofa for study room
study room furnitures
buy dining table set
buy dining furniture
dining room furniture online
dining sets online

Agen Slot Online Terpercaya said...

APA ITU AGEN SLOT ONLINE WARUNG168
Warungmewah Agen Slot Online Terpercaya Pada zaman yang sangat modern seperti ini, Kita dimudahkan dalam melakukan setiap kegiatan Sehari-hari entah itu Bertransaksi Jual/Beli, Nonton, Mendengar kan Musik, Bermain game Bahkan ketika pandemi seperti saat ini Pembelajaran juga dilakukan secara online melalui Internet. Kemudahan Teknologi juga bisa kalian rasakan Saat bermain Situs Judi Slot online / Joker Gaming . Slot merupakan Permainan yang berisi gambar maupun simbol menarik, menggunakan gulungan vertikal untuk membuat sebuah kombinasi, Permainan ini sangat sederhana.


CASINO ONLINE
SLOT ONLINE
WARUNG168
POKER ONLINE

mpo slot said...

Thanks for sharing this excellent post, I am going to share it as an external reference link in a post I am writing on Guest Posting.

Sexy Lingerie Dubai said...

Lingerie Dubai , a pioneer in comfort and style for everyday essentials for women. We offer only the best lingerie brands in the world that ooze ultimate confidence and sophistication. Our products are aptly suited for women who embrace a multitude of roles and goals in her life.

Jumanto said...

"Oh my goodness! Impressive article dude! Thank you, However I am going through difficulties with your RSS. I don’t know the reason why I am unable to join it. Is there anybody else having the same RSS problems?
Anyone that knows the solution will you kindly respond? Thanks!!"

Sbobet slot
Slot77
88 Sbobet

Anonymous said...

I have a loyalty that runs in my bloodstream, when I lock into someone or something inside McDonald's menu, you can't get me away from it because I commit that thoroughly. That's in friendship, that's a deal, that's a commitment. Don't give me paper with Burger King menu, Wendy's menu, Sonic menu, Olive Garden menu, Starbucks menu, Dunkin Donuts menu, Popeyes menu, Pizza Hut menu and Papa John's menu - I can get the same lawyer who drew it up to break it. But if you shake my hand, that's for life.

HOBI4D said...


Pokoknya Bakalan Jackpot Sensational & Scatter di Hobi4D !!!
Daftar Sekarang Juga di Hobi4D !!!

Deposit via Pulsa Tanpa Potongan !!!

Bonus New Member 10%
Bonus Harian 10%
dan Banyak Bonus Lainnya !!!

Link: hobisenang,org
Whatsapp +6281219567330

Karavilent said...

This site is very helpful and gives me a lot of inspiration, so I want to say thank you.. I hope this site continues to grow.

Slot Macau
Bola365
Raja88 Slot
Daftar Judi Bola
Live22 Slot
Sbowin Login Sbobet Mobile

Sexy Lingerie Dubai said...

We at Sexy Lingerie Dubai emphasize authenticity, freedom, creativity, and evolution. Our online lingerie store designs are vastly revolutionary as well as trendy, where any queen can find her lingerie online. These mottos are reflected in every product that we have manufactured. Through these incredible collections of women’s lingerie, we have become the most beloved online lingerie store in Dubai.
Visit: https://sexylingeriedubai.com/

Juandra said...

Great work !! Looking forward to more of such good work, Thanks for sharing this helpful information with us.

Hokislot 188
Mpo33 Login Apk

Lingerie Abudhabi said...

Lingerie Abudhabi
We at Lingerie Abudhabi emphasize authenticity, freedom, creativity, and evolution. Our online lingerie store designs are vastly revolutionary as well as trendy, where any queen can find her lingerie online. These mottos are reflected in every product that we have manufactured. Through these incredible collections of women’s lingerie, we have become the most beloved online lingerie store in Abudhabi.

https://lingerie-abudhabi.ae/

Lingerie UAE said...

Lingerie UAE
We at Lingerie UAE emphasize authenticity, freedom, creativity, and evolution. Our online lingerie store designs are vastly revolutionary as well as trendy, where any queen can find her lingerie online. These mottos are reflected in every product that we have manufactured. Through these incredible collections of women’s lingerie, we have become the most beloved online lingerie store in UAE.

Lingerie Dubai said...

Lingerie Dubai … We at Lingerie Dubai emphasize authenticity, freedom, creativity, and evolution. Our online lingerie store designs are vastly revolutionary as well as trendy, where any queen can find her lingerie online. These mottos are reflected in every product that we have manufactured. Through these incredible collections of women’s lingerie, we have become the most beloved online lingerie store in Dubai.

Katherine Byrne said...

This article post so great. Thankyou for sharing this news guys !

Lux88
Joker888
777slot
Joker777

Careerera said...

This is a really fascinating and useful blog. I've read a lot of blogs lately, but your writing style is quite distinct and insightful. If you've read my articles, please go to the next step.

Cyber Security Course

Online Edu Tech said...


This is excellent news for me; thank you for sharing it, buddy!

Cyber Security Interview Questions

Sophia Jones said...

Nice Articles. Advantage of Cyber Security

Gebyar123 said...

bermain di Gebyar123
dengan modal ceban jadi tuan.
link pendaftaran : https://bit.ly/vincenzo88

Sophia Jones said...

I love this Articles. Thanx for Sharing. Best Cyber Security Course

Anonymous said...

this blog is very helpful
https://www.joy-toy.ae/

Agile Interview Questions said...

Great Blog.

Chaukor Studio Ghaziabad said...

Great Blog. I love this Articles. Best Interior Designers In Noida

Viswadhika said...

Hey, thanks for the blog article. Really looking forward to reading more. Cool.

Hyperion Essbase Planning Certification Online Training from Hyderabad
Oracle EBS R12 SCM Online Live Classes
SSIS Online Training from India
Oracle Fusion Planning Central Certification Online Training from Hyderabad

Budi Indriyani said...

After the syrup has simmered for 10-15 minutes, remove the saucepan from the heat and let it cool for a few minutes. Using a fine-mesh strainer, strain the syrup into a clean container, pressing on the lavender flowers to extract as much flavor as possible. Discard the lavender flowers. pabrik batu alam cirebon