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Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.
The arithmetical difference between two consecutive representable floating-point numbers which have the same exponent is called a unit in the last place (ULP). For example, if there is no representable number lying between the representable numbers 1.45a70c22 hex and 1.45a70c24 hex, the ULP is 2×16 −8, or 2 −31.
Sign bit: 1 bit; Exponent width: 5 bits; Significand precision: 11 bits (10 explicitly stored) The format is laid out as follows: The format is assumed to have an implicit lead bit with value 1 unless the exponent field is stored with all zeros. Thus, only 10 bits of the significand appear in the memory format but the total precision is 11 bits.
The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. The leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand are combined into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field.
The implicit leading 1 is nothing but the hidden bit in IEEE 754 floating point, and the bitfield storing the remainder is thus the mantissa. However, whether or not the implicit 1 is included is a major point of confusion with both terms—and especially so with mantissa. In keeping with the original usage in the context of log tables, it ...
The mantissa x (where log2(x) is between -1/2 and 1/2) is then compared to a table and intervals for further reduction into a z with known log2 and an in-range x/z, along with polynomial coefficients used for the interval x/z is in. The result is then log(z) + log(x/z) + k. [7]
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).
Mantissa (/ m æ n ˈ t ɪ s ə /) may refer to: Mantissa (logarithm) , the fractional part of the common (base-10) logarithm Significand (also commonly called mantissa), the significant digits of a floating-point number or a number in scientific notation