tailieunhanh - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 167

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 167', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 28 Chapter 1. Preliminaries Error Accuracy and Stability Althoughwe assume no prior training of the reader informal numerical analysis we will need to presume a common understanding of a few key concepts. We will define these briefly in this section. Computers store numbers not with infinite precision but rather in some approximation that can be packed into a fixed number of bits binary digits or bytes groups of 8 bits . Almost all computers allow the programmer a choice among several different such representations or data types. Data types can differ in the number of bits utilized the wordlength but also in the more fundamental respect of whether the stored number is represented in fixed-point int or long or floating-point float or double format. A number in integer representation is exact. Arithmetic between numbers in integer representation is also exact with the provisos that i the answer is not outside the range of usually signed integers that can be represented and ii that division is interpreted as producing an integer result throwing away any integer remainder. In floating-point representation a number is represented internally by a sign bit s interpreted as plus or minus an exact integer exponent e and an exact positive integer mantissa M. Taken together these represent the number s x M x Be-E where B is the base of the representation usually B 2 but sometimes B 16 and E is the bias of the exponent a fixed integer constant for any given machine and representation. An example is shown in Figure . Several floating-point bit patterns can represent the same number. If B 2 for example a mantissa with leading high-order zero bits can be left-shifted . multiplied by a power of 2 if the exponent is decreased by a compensating amount. Bit patterns that are as left-shifted as they can be are termed normalized. Most computers always produce normalized results since these don t waste any bits of the mantissa and thus allow a greater accuracy of the .