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 childrens developing interests and abilities.”
—David Elkind (20th century)
“Gradually the village murmur subsided, and we seemed to be embarked on the placid current of our dreams, floating from past to future as silently as one awakes to fresh morning or evening thoughts.”
—Henry David Thoreau (18171862)
“Consider a man riding a bicycle. Whoever he is, we can say three things about him. We know he got on the bicycle and started to move. We know that at some point he will stop and get off. Most important of all, we know that if at any point between the beginning and the end of his journey he stops moving and does not get off the bicycle he will fall off it. That is a metaphor for the journey through life of any living thing, and I think of any society of living things.”
—William Golding (b. 1911)