Is it possible to use extended precision for decimal number using 64 bit defined by IEEE 754 standard in MATLAB 7.11 (R2010b) ?

I want to use the extended and extendable precision defined in the IEEE 754 standard for representing decimal numbers using 64 bit in MATLAB 7.11 (R2010b).

The normal level of precision for the radix 10 64 bit format is only 16 digits. The Standard states that the precision for the radix 10 64 bit format can be extended to 22 digits, which would enable greater quantization present in the data. Does MATLAB support this extension, and if so, how do we implement it and what are the consequences in processing time.

Answer 1

[MathWorks Support Team]

MATLAB 7.11 (R2010b) strictly follows the number representation based on the IEEE 754 standard. However, MATLAB does not support extending the precision for the decimal representation of a number in a 64 bit format, which is mentioned in the standard. The following link depicts the representation that MATLAB uses for floating point number arithmetic (both single and double precision):

 <http://www.mathworks.com/help/toolbox/fixpoint/ug/f15882.html>

The Symbolic Math Toolbox in the MATLAB product family, which is an add on product with MATLAB allows setting the number of digits for precision of a given number. It consists of functions like VPA that enable control of precision digits for a number. However, the difference while using a datatype in Symbolic Math Toolbox is its representation as a 'sym' type which uses much larger memory than the fundamental datatype 'double' in MATLAB. An example that illustrates this case is as follows:

% Using the VPA command in Symbolic Math Toolbox gives 25 digits of precision in this example

p = vpa(pi);

p =

3.1415926535897932384626433832795

% 'sym' type uses 112 bytes of memory

whos p

Name      Size            Bytes  Class    Attributes

   p         1x1               112  sym 

% Using fundamental datatype representation in MATLAB 

p = pi

p =

     3.1416

% 'double' type uses 8 bytes of memory

whos p

   Name      Size            Bytes  Class     Attributes

   p         1x1                 8  double

You can find more information about the VPA (Variable point Arithmetic) function in the Symbolic Math Toolbox and few demos of this product at the following link:

 <http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/vpa.html>

 <http://www.mathworks.com/products/symbolic/demos.html>