- published: 22 Jan 2014
- views: 520048
In computing, floating point is the formulaic representation that approximates a real number so as to support a trade-off between range and precision. A number is, in general, represented approximately to a fixed number of significant digits (the significand) and scaled using an exponent; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:
where significand ∈ Z, base ∈ N, and exponent ∈ Z.
For example:
The term floating point refers to the fact that a number's radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated as the exponent component, and thus the floating-point representation can be thought of as a kind of scientific notation.
A floating-point system can be used to represent, with a fixed number of digits, numbers of different orders of magnitude: e.g. the distance between galaxies or the diameter of an atomic nucleus can be expressed with the same unit of length. The result of this dynamic range is that the numbers that can be represented are not uniformly spaced; the difference between two consecutive representable numbers grows with the chosen scale.
Sam Shepherd is an English electronic musician and neuroscientist, who records and performs music under the name Floating Points. Shepherd is also a co-founder of the label Eglo Records.
After several EPs, singles and live appearances, Shepherd released Floating Points' debut studio album, Elaenia, in November 2015, to widespread critical acclaim.
Raised in Manchester, England, Shepherd studied piano at Chetham's School of Music before completing a PhD in neuroscience and epigenetics at University College London.
Shepherd has previously performed with a sixteen-piece live incarnation of Floating Points, entitled the Floating Points Ensemble. The group won an award for "Best BBC Radio 1 Maida Vale Session".
Floating Point is an album by John McLaughlin, released in 2008 through the record label Abstract Logix. The album reached number fourteen on Billboard's Top Jazz Albums chart.
Michael G. Nastos of AllMusic calls the album "a surprisingly fine effort, ebbing and flowing from track to track, with McLaughlin's high-level musicianship shining through, same as it ever was." John Kelman in All About Jazz wrote "One of the most fluent, evocative and powerful albums in a career filled with high points" and concludes "McLaughlin's Indian friends may not have jazz in their blood the way it is in the guitarist's, but by approaching unmistakably western-informed music with an eastern mindset, they make Floating Point an album that, in McLaughlin's lengthy discography, is one of his most successful fusion records".
Floating may refer to:
The Algorithm is the musical project of French musician Rémi Gallego (born October 7, 1989). Gallego is from Perpignan and his style is a combination of electronic music with features of progressive metal and djent. Gallego chose the name The Algorithm to highlight the music's complexity and its electronic nature.
After the demise of his former band Dying Breath, Rémi Gallego decided in 2009 to look for potential members for a band that focused on mathcore, which came as an inspiration from The Dillinger Escape Plan. After a futile search for new members, with the help of his guitar and a DAW, Gallego began to produce his own music.
In December 2009 and July 2010, he published the two demos "The Doppler Effect" and "CRITICAL.ERROR", which were / released via his own website for free download. Towards the end of 2010, he announced that he was working on a new EP named "Identity" (it was never completed). Also, he was preparing for his first live appearances.
Why can't floating point do money? It's a brilliant solution for speed of calculations in the computer, but how and why does moving the decimal point (well, in this case binary or radix point) help and how does it get currency so wrong? 3D Graphics Playlist: http://www.youtube.com/playlist?list=PLzH6n4zXuckrPkEUK5iMQrQyvj9Z6WCrm The Trouble with Timezones: http://youtu.be/-5wpm-gesOY More from Tom Scott: http://www.youtube.com/user/enyay and https://twitter.com/tomscott http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
A short tutorial to explain how floating point numbers are stored in computer memory. Starting with a decimal number and converting to a binary representation. Please Note: I made an error @09:48 - 0.125 is NOT 0.001. 0.0125 is more like 0.00000011...
http://KEXP.ORG presents Floating Points performing live in the KEXP studio. Recorded May 3, 2016. Songs: Silhouettes Argente Kuiper Host: Larry Rose Audio Engineer: Michael Parker & Kevin Suggs Cameras: Jim Beckmann, Alaia D'Alessandro & Scott Holpainen Editor: Scott Holpainen Photo thumbnail by Matthew B. Thompson http://kexp.org http://www.floatingpoints.co.uk
http://www.Cppcon.org — Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/cppcon/cppcon2015 — Every day we develop software that relies on math while we often overlook the importance of understanding the implications of using our IEEE floats. From the often cited “floating point error” to unstable algorithms, this talk will explain the importance of floats, understanding their storage, the impact of the IEEE floats on math, and designing algorithms better. Finally, the talk will conclude with a quick case study of storing time for games and simulations. — John Farrier is a software engineer, researcher, and musician. He designs software architectures for military modeling and simulation activities. His projects support efforts across...
New Floating Points album available now: http://bit.ly/FloatyPElaenia This is probably the most substantial and also darkest FP dispatch to date, and though a couple of numbers have been kicking around on dubplate for a while, it's good to have all in one place and sounding this spruce. 'Myrtle Avenue' is an out-and-out epic at 10 minutes long, using the time to go super-deep; it's fundamentally a stripped house groover, but with clustered drum-swing and warm, boogie-funked keys very much in the vein of Theo. It really goes at its own pace and is unpressured by the demands of the dancefloor, and is undoubtedly one of the most mature Floating Points productions to date. 'Obfuse' goes for a more minimal, broken flex, scuffed 808s underscored by discreet, cosmic-tinged synth patterns. 'Reali...
A tutorial on floating point representation of numbers.
‘Silhouettes’ is comprised of music from ’Silhouettes (I, II & III) which is taken from the debut album 'Elaenia', out now on Pluto in the UK / ROW, Luaka Bop in N&S; America, Inertia in AU / NZ & Beatink in Japan. Get ‘Elaenia’: iTunes: http://found.ee/ElaeniaiTunes Vinyl: http://found.ee/ElaeniaLP CD: http://found.ee/ElaeniaCD Download: http://found.ee/ElaeniaDL Rough Trade: http://found.ee/ElaeniaRoughTrade A message from the Directors: An oscillating stream of light attempts to intrude on an arid natural landscape, abstract light and a living environment merge, reacting to the dynamics of the music. The luminous abstract forms are produced by a light painting machine that, frame by frame, draws in a real environment the 3D animated figures. This is an experimental video created by P...
Order BRUTE FORCE at: http://fixtstore.com/thealgorithm New Algorithm Music & Merch Now Available Song: floating point Album: Brute Force Artist: The Algorithm Label: FiXT Follow FiXT: FACEBOOK: http://www.facebook.com/fixtmusic TWITTER: http://www.twitter.com/fixtmusic Follow The Algorithm! FACEBOOK: https://www.facebook.com/TheAlg0r1thm... TWITTER: https://twitter.com/The_Algorithm SOUNDCLOUD :https://soundcloud.com/the-algorithm WEB: http://www.the-algorithm.net/ Want to use this track in your YouTube videos? Find out at http://fixtmusic.tv
Why can't floating point do money? It's a brilliant solution for speed of calculations in the computer, but how and why does moving the decimal point (well, in this case binary or radix point) help and how does it get currency so wrong? 3D Graphics Playlist: http://www.youtube.com/playlist?list=PLzH6n4zXuckrPkEUK5iMQrQyvj9Z6WCrm The Trouble with Timezones: http://youtu.be/-5wpm-gesOY More from Tom Scott: http://www.youtube.com/user/enyay and https://twitter.com/tomscott http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
A short tutorial to explain how floating point numbers are stored in computer memory. Starting with a decimal number and converting to a binary representation. Please Note: I made an error @09:48 - 0.125 is NOT 0.001. 0.0125 is more like 0.00000011...
http://KEXP.ORG presents Floating Points performing live in the KEXP studio. Recorded May 3, 2016. Songs: Silhouettes Argente Kuiper Host: Larry Rose Audio Engineer: Michael Parker & Kevin Suggs Cameras: Jim Beckmann, Alaia D'Alessandro & Scott Holpainen Editor: Scott Holpainen Photo thumbnail by Matthew B. Thompson http://kexp.org http://www.floatingpoints.co.uk
http://www.Cppcon.org — Presentation Slides, PDFs, Source Code and other presenter materials are available at: https://github.com/cppcon/cppcon2015 — Every day we develop software that relies on math while we often overlook the importance of understanding the implications of using our IEEE floats. From the often cited “floating point error” to unstable algorithms, this talk will explain the importance of floats, understanding their storage, the impact of the IEEE floats on math, and designing algorithms better. Finally, the talk will conclude with a quick case study of storing time for games and simulations. — John Farrier is a software engineer, researcher, and musician. He designs software architectures for military modeling and simulation activities. His projects support efforts across...
New Floating Points album available now: http://bit.ly/FloatyPElaenia This is probably the most substantial and also darkest FP dispatch to date, and though a couple of numbers have been kicking around on dubplate for a while, it's good to have all in one place and sounding this spruce. 'Myrtle Avenue' is an out-and-out epic at 10 minutes long, using the time to go super-deep; it's fundamentally a stripped house groover, but with clustered drum-swing and warm, boogie-funked keys very much in the vein of Theo. It really goes at its own pace and is unpressured by the demands of the dancefloor, and is undoubtedly one of the most mature Floating Points productions to date. 'Obfuse' goes for a more minimal, broken flex, scuffed 808s underscored by discreet, cosmic-tinged synth patterns. 'Reali...
A tutorial on floating point representation of numbers.
‘Silhouettes’ is comprised of music from ’Silhouettes (I, II & III) which is taken from the debut album 'Elaenia', out now on Pluto in the UK / ROW, Luaka Bop in N&S; America, Inertia in AU / NZ & Beatink in Japan. Get ‘Elaenia’: iTunes: http://found.ee/ElaeniaiTunes Vinyl: http://found.ee/ElaeniaLP CD: http://found.ee/ElaeniaCD Download: http://found.ee/ElaeniaDL Rough Trade: http://found.ee/ElaeniaRoughTrade A message from the Directors: An oscillating stream of light attempts to intrude on an arid natural landscape, abstract light and a living environment merge, reacting to the dynamics of the music. The luminous abstract forms are produced by a light painting machine that, frame by frame, draws in a real environment the 3D animated figures. This is an experimental video created by P...
Order BRUTE FORCE at: http://fixtstore.com/thealgorithm New Algorithm Music & Merch Now Available Song: floating point Album: Brute Force Artist: The Algorithm Label: FiXT Follow FiXT: FACEBOOK: http://www.facebook.com/fixtmusic TWITTER: http://www.twitter.com/fixtmusic Follow The Algorithm! FACEBOOK: https://www.facebook.com/TheAlg0r1thm... TWITTER: https://twitter.com/The_Algorithm SOUNDCLOUD :https://soundcloud.com/the-algorithm WEB: http://www.the-algorithm.net/ Want to use this track in your YouTube videos? Find out at http://fixtmusic.tv
Introduction to Floating Point Numbers and conversions