Contents
What Every Computer Scientist Should Know floating-point?
Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow.
Why do we need floating-point arithmetic?
Floating point representation makes numerical computation much easier. You could write all your programs using integers or fixed-point representations, but this is tedious and error-prone. This is the same as an understanding that the integer the bits represent should be divided by a particular power of two.
What is a floating point number in computer science?
In programming, a floating-point or float is a variable type that is used to store floating-point number values. A floating-point number is one where the position of the decimal point can “float” rather than being in a fixed position within a number. Examples of floating-point numbers are 1.23, 87.425, and 9039454.2.
Why are they called floating point numbers?
The term floating point is derived from the fact that there is no fixed number of digits before and after the decimal point; that is, the decimal point can float. There are also representations in which the number of digits before and after the decimal point is set, called fixed-pointrepresentations.
What is the point of floating-point?
A floating-point system can be used to represent, with a fixed number of digits, numbers of different orders of magnitude: e.g. the distance between galaxies or the diameter of an atomic nucleus can be expressed with the same unit of length.
How do you do floating point operations?
Floating-point numbers have decimal points in them. The number 2.0 is a floating-point number because it has a decimal in it. The number 2 (without a decimal point) is a binary integer. Floating-point operations involve floating-point numbers and typically take longer to execute than simple binary integer operations.
What do you need to know about floating point arithmetic?
Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computationby Pat Sterbenz, is long out of print.
Are there floating point compilers in every language?
Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow.
Why is the result of a floating point calculation rounded?
Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation. The section Relative Error and Ulpsdescribes how it is measured.
Which is the unique representation of a floating point?
Floating-point representations are not necessarily unique. For example, both 0.01 × 101and 1.00 ×10-1represent 0.1. If the leading digit is nonzero (d00 in equation (1)above), then the representation is said to be normalized. The floating-point number 1.00 ×10-1is normalized, while 0.01 ×101is not.