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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.
Chapter 9.3 of The Art of Assembly by Randall Hyde discusses multiprecision arithmetic, with examples in x86-assembly. Rosetta Code task Arbitrary-precision integers Case studies in the style in which over 95 programming languages compute the value of 5**4**3**2 using arbitrary precision arithmetic.
Example: the decimal number () = (¯) can be rearranged into + ⏟ … Since the 53rd bit to the right of the binary point is a 1 and is followed by other nonzero bits, the round-to-nearest rule requires rounding up, that is, add 1 bit to the 52nd bit.
If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string.
All integers with seven or fewer decimal digits, and any 2 n for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754 standard , the 32-bit base-2 format is officially referred to as binary32 ; it was called single in IEEE 754-1985 .
"PIC S9999", for example, would require a signed variable of four decimal digits precision. If specified as a binary field, this would select a 16-bit signed type on most platforms. If specified as a binary field, this would select a 16-bit signed type on most platforms.
Truncation of positive real numbers can be done using the floor function.Given a number + to be truncated and , the number of elements to be kept behind the decimal point, the truncated value of x is
This gives from 33 to 36 significant decimal digits precision. If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string.