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Decimal128
In computing, decimal128 is a decimal floating-point computer number format, number format that occupies 128 bits in computer memory, memory. Formally introduced in IEEE 754-2008, it is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Format The decimal128 format supports 34 decimal digits of significand and an exponent range of −6143 to +6144, i.e. to . Because the significand is not normalized, most values with less than 34 significant digits have multiple possible representations; , etc. This set of representations for a same value is called a ''Cohort (floating point), cohort''. Zero has 12288 possible representations (24576 if both signed zeros are included, in two different cohorts). Encoding of decimal128 values The IEEE 754 standard allows two alternative encodings for decimal128 values: * The binary encoding, based on binary integer decimal (BID): The significand is encoded as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard #Design rationale, addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and Software portability, portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of Binary code, binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinity, infinities, and special "not a number" values (NaNs) * ''interchange formats:'' encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form * ''rounding rules:'' properties to be satisfied when rounding numbers during arithmetic and conversions * ''operations:'' arithmetic and other operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Floating-point
Decimal floating-point (DFP) 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 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 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 alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
