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For example, 32 contiguous bits may be treated as an array of 32 Booleans, a 4-byte string, an unsigned 32-bit integer or an IEEE single precision floating point value. Because the stored bits are never changed, the programmer must know low level details such as representation format, byte order, and alignment needs, to meaningfully cast.
With the example in view, a number of details can be discussed. The most important is the choice of the representation of the big number. In this case, only integer values are required for digits, so an array of fixed-width integers is adequate. It is convenient to have successive elements of the array represent higher powers of the base.
IEEE single/double, BigDecimal: Length-prefixed "short" Strings (up to 64 bytes), marker-terminated "long" Strings and (optional) back-references Arbitrary-length heterogenous arrays with end-marker Arbitrary-length key/value pairs with end-marker Structured Data eXchange Formats (SDXF) Big-endian signed 24-bit or 32-bit integer
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Data conversion is the conversion of computer data from one format to another. Throughout a computer environment, data is encoded in a variety of ways. For example, computer hardware is built on the basis of certain standards, which requires that data contains, for example, parity bit checks.
On some PowerPC systems, [11] long double is implemented as a double-double arithmetic, where a long double value is regarded as the exact sum of two double-precision values, giving at least a 106-bit precision; with such a format, the long double type does not conform to the IEEE floating-point standard.
The range of a double-double remains essentially the same as the double-precision format because the exponent has still 11 bits, [4] significantly lower than the 15-bit exponent of IEEE quadruple precision (a range of 1.8 × 10 308 for double-double versus 1.2 × 10 4932 for binary128).
The C99 and C11 standards of the C language family, in their annex F ("IEC 60559 floating-point arithmetic"), recommend such an extended format to be provided as "long double". [18] A format satisfying the minimal requirements (64-bit significand precision, 15-bit exponent, thus fitting on 80 bits) is provided by the x86 architecture.