4.1 IEEE Arithmetic

MATLAB carries out all its arithmetic computations in double precision floating point arithmetic, conforming to the IEEE standard [32]. The logical function isieee returns a result of 1 (true) if MATLAB is using IEEE arithmetic and 0 (false) if not. For MATLAB 6 isieee is always true, but earlier versions of MATLAB were available for certain machines that did not support IEEE arithmetic. The function computer returns the type of computer on which MATLAB is running. The machine used to produce all the output shown in this book gives

   <span class="unicode">?</span> computer   ans =   PCWIN   <span class="unicode">?</span> isieee   ans =        1

In MATLAB's double data type each number occupies a 64-bit word. Nonzero numbers range in magnitude between approximately 10 ^?308 and 10 ⁺³⁰⁸ and the unit roundoff is 2 ^?53 ? 1.11 10 ^?16. (See [30, Chap. 2] for a detailed explanation of floating point arithmetic.) The significance of the unit roundoff is that it is a bound for the relative error in converting a real number to floating point form and also a bound for the relative error in adding, subtracting, multiplying or dividing two floating point numbers or taking the square root of a floating point number. In simple terms, MATLAB stores floating point numbers and carries out elementary operations to an accuracy of about...