Double-precision floating point arithmetic

It should be kept in mind that the format command does not affect how MATLAB computations are done. Computations on float variables, namely, single or double, are done in appropriate floating point precision, no matter how those variables are displayed. Computations on integer variables are done natively in integer. MATLAB uses double-precision floating point arithmetic, which is accurate to approximately 15 digits and can work with the following data types tTable 1.21. 

The parameter eg is a small positive number such as 10-8. A reasonable choice is around the order of the square root of machine precision, em, defined as the smallest number x such that the floating point value of (1 + x) is greater than the floating representation of 1. This precision-dependent (i.e., double versus single) and machine-dependent quantity is approximately the value of the unit roundoff, or 2 ( +D for binary computer arithmetic involving t binary digits (or bits) in the fractional part of the number. For example, for double-precision computations on a DEC VAX, t = 52 and m 10 16. As computational errors will enter from sources other than finite arithmetic, a suitable eg is then a number greater than or equal to 10 8. 

Double precision arithmetic was employed during data acquisition and the software included a floating point Fourier transform capability. 

Uses floating point double precision arithmetic for all computations. 

Decimal number Decimal numbers are represented using a floating point representation with the most important one being the IEEE Standard 754, which provides both a 32-bit single and a 64-bit double precision representation with 8-bit and 11-bit exponents and 23-bit and 52-bit fractions, respectively. The IEEE standard has become widely accepted, and is used in most contemporary processors and arithmetic coprocessors. 

Almost all operations in MATLAB are performed in double-precision arithmetic conforming to IEEE Standard 754 (double precision calls for 52 mantissa bits). This represents the highest degree of resolution by which MATLAB can see two very close numbers as two different entities. The following examples illustrate the concept of floating point-related computational problems. 

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