By Martin Bohner, Allan C. Peterson
Very good introductory fabric at the calculus of time scales and dynamic equations.; quite a few examples and workouts illustrate the varied software of dynamic equations on time scales.; Unified and systematic exposition of the subjects permits solid transitions from bankruptcy to chapter.; participants contain Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this box of study.; worthy as a complete source of time scales and dynamic equations for natural and utilized mathematicians.; entire bibliography and index entire this article.
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The problem, however, lies in the fact that the actual number of bits is still system- and compiler-dependent: switching hardware vendors and compilers is normal, and surprises due to improper number representation (which can often go unnoticed) are better avoided when possible. The concept of kind is the modern Fortran response to this problem, and it deprecates the double precision type. 18 Even better, the programmer need not be concerned with the lower-level details, since two special intrinsic functions (discussed shortly) allow querying for the most economic types that meet some natural requirements.
18 Compilers are required to provide a default kind for each of the 5 intrinsic types, but they may (and most do) support additional kinds. 19 In practice, it is more convenient to use shorter denominators for the kind-parameters. 3 Scalar Values and Constants 17 will guarantee that the compiler selects a suitable type of integer to fit values of t in the interval (−1018 , 1018 ). 2. selected_real_kind(requestedPrecision, requestedExponentRange), where both arguments are integers, returns the appropriate kindparameter for representing numbers with a decimal exponent range of at least requestedExponentRange, and a decimal precision of at least requestedPrecision20 after the decimal point.
13 However, numerical algorithms also vary with respect to the precision they need to function correctly. To balance these factors, most computer systems support several sub-types for integer and real values. Modern Fortran has a very convenient mechanism for specifying the numerical requirements of a program in a portable way, without forcing developers (or, worse, users) to study each CPU in-depth. We discuss this feature in Sect. 4. It is important that programmers keep in mind the limitations of the internal representations, since these are an endless source of bugs.