Decimal floating point arithmetic refers to both a representation and operations on decimal floating point numbers. Working directly with decimal (base 10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base 2) fractions.
The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates eight decimal digits and two decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with eight decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on. This wider range can dramatically slow the accumulation of rounding errors during successive calculations; for example, the Kahan summation algorithm can be used in floating point to add many numbers with no asymptotic accumulation of rounding error.
Read more about Decimal Floating Point: Implementations, IEEE 754-2008 Encoding, Floating Point Arithmetic Operations
Famous quotes containing the words decimal, floating and/or point:
“It makes little sense to spend a month teaching decimal fractions to fourth-grade pupils when they can be taught in a week, and better understood and retained, by sixth-grade students. Child-centeredness does not mean lack of rigor or standards; it does mean finding the best match between curricula and children’s developing interests and abilities.”
—David Elkind (20th century)
“I myself have seen the floating ships
And nothing will ever be the same
The shouts,
The harrowing voices within the house.
I stand apart with an army:
My mind is graven with ships.”
—Hilda Doolittle (1886–1961)
“The town is divided into various groups, which form so many little states, each with its own laws and customs, its jargon and its jokes. While the association holds and the fashion lasts, they admit nothing well said or well done except by one of themselves, and they are incapable of appeciating anything from another source, to the point of despising those who are not initiated into their mysteries.”
—Jean De La Bruyère (1645–1696)