Quadruple-precision floating-point format

In computing, quadruple precision (also commonly shortened to quad precision) is a binary floating-point-based computer number format that occupies 16 bytes (128 bits) in computer memory and whose precision is about twice the 53-bit double precision.

This 128 bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables: as William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed."

Floating point

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.

Floating Point

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.

Track listing

Personnel

Reception

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".

Format

Format may refer to:

Computing:

Format (Common Lisp)

FORMAT is a function in Common Lisp that can produce formatted text using a format string similar to the printf format string. It provides more functionality than printf, allowing the user to output numbers in English, apply certain format specifiers only under certain conditions, iterate over data structures, and output in a tabular format. This functionally originates in MIT's Lisp Machine Lisp, where it was based on Multics ioa_.

Example

An example of a C printf call is the following:

Using Common Lisp, this is equivalent to:

Another example would be to print every element of list delimited with commas, which can be done using the ~{, ~^ and ~} directives:

Note that not only is the list of values iterated over directly by FORMAT, but the commas correctly are printed between items, not after them. A yet more complex example would be printing out a list using customary English phrasing:

Whilst FORMAT is somewhat infamous for its tendency to become opaque and hard to read, it provides a remarkably concise yet powerful syntax for a specialised and common need.

Format (magazine)

Format is a German weekly finance and business magazine published in Austria and headquartered in Vienna.

History and profile

Format was established in 1998. The magazine has its headquarters in Vienna and is published weekly on Fridays. The publisher is the Verlagsgruppe NEWS.Gruner + Jahr has a stake in the magazine.

Format covers topics mainly on business, politics, culture and lifestyles. The magazine also features the views of bankers, trade experts and financiers. One of its former editors-in-chief is Peter Pelinka.

Format had a circulation of 68,000 copies in 2003. Its circulation was 50,000 copies in 2007. The sold circulation of the weekly was 47,155 copies in 2009. Its circulation in 2012 was 31,021 copies. The circulation of the magazine during the first half of 2013 was 39,296 copies.

See also

List of magazines in Austria

References