11.1.6 The decimal type
The decimal type is a 128-bit data type suitable for financial and monetary
calculations. The decimal type
can represent values ranging from 1.0 × 10.28 to approximately 7.9 × 1028
with 28.29 significant digits.
The finite set of values of type decimal are of the form (.1)s × c ×
10-e, where the sign s is 0 or 1, the
coefficient c is given by 0 ≤ c < 296, and the scale e is such that 0 ≤ e
≤ 28. The decimal type does not
support signed zeros, infinities, or NaN’s.
A decimal is represented as a 96-bit integer scaled by a power of ten. For
decimals with an absolute value
less than 1.0m, the value is exact to the 28th decimal place, but no
further. For decimals with an absolute
value greater than or equal to 1.0m, the value is exact to 28 or 29 digits.
Contrary to the float and double
data types, decimal fractional numbers such as 0.1 can be represented
exactly in the decimal
representation. In the float and double representations, such numbers are
often infinite fractions, making
those representations more prone to round-off errors.
If one of the operands of a binary operator is of type decimal, then the
other operand must be of an integral
type or of type decimal. If an integral type operand is present, it is
converted to decimal before the
operation is performed.
The result of an operation on values of type decimal is that which would
result from calculating an exact
result (preserving scale, as defined for each operator) and then rounding
to fit the representation. Results are
rounded to the nearest representable value, and, when a result is equally
close to two representable values, to
the value that has an even number in the least significant digit position
(this is known as .banker.s
rounding.). That is, results are exact to 28 or 29 digits, but to no more
than 28 decimal places. A zero result
always has a sign of 0 and a scale of 0.
If a decimal arithmetic operation produces a value that is too small for
the decimal format after rounding, the
result of the operation becomes zero. If a decimal arithmetic operation
produces a result that is too large
for the decimal format, a System.OverflowException is thrown.
The decimal type has greater precision but smaller range than the
floating-point types. Thus, conversions
from the floating-point types to decimal might produce overflow exceptions,
and conversions from
decimal to the floating-point types might cause loss of precision. For
these reasons, no implicit conversions
exist between the floating-point types and decimal, and without explicit
casts, it is not possible to mix
floating-point and decimal operands in the same expression.