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The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
C# has a built-in data type decimal consisting of 128 bits resulting in 28–29 significant digits. It has an approximate range of ±1.0 × 10 −28 to ±7.9228 × 10 28. [1] Starting with Python 2.4, Python's standard library includes a Decimal class in the module decimal. [2] Ruby's standard library includes a BigDecimal class in the module ...
The otherwise binary Wang VS machine supported a 64-bit decimal floating-point format in 1977. [2] The Motorola 68881 supported a format with 17 digits of mantissa and 3 of exponent in 1984, with the floating-point support library for the Motorola 68040 processor providing a compatible 96-bit decimal floating-point storage format in 1990. [2]
8 bits Byte, octet, minimum size of char in C99( see limits.h CHAR_BIT) −128 to +127 0 to 255 2 bytes 16 bits x86 word, minimum size of short and int in C −32,768 to +32,767 0 to 65,535 4 bytes 32 bits x86 double word, minimum size of long in C, actual size of int for most modern C compilers, [8] pointer for IA-32-compatible processors
^ PHP will unserialize any floating-point number correctly, but will serialize them to their full decimal expansion. For example, 3.14 will be serialized to 3.140 000 000 000 000 124 344 978 758 017 532 527 446 746 826 171 875 .
The 8 decimal values whose digits are all 8s or 9s have four codings each. The bits marked x in the table above are ignored on input, but will always be 0 in computed results. (The 8 × 3 = 24 non-standard encodings fill in the gap from 10 3 = 1000 and 2 10 - 1 = 1023.)
The 2008 revision extended the previous standard where it was necessary, added decimal arithmetic and formats, tightened up certain areas of the original standard which were left undefined, and merged in IEEE 854 (the radix-independent floating-point standard). In a few cases, where stricter definitions of binary floating-point arithmetic might ...
In decimal interchange formats they require no special encoding because the format supports unnormalized numbers directly. Mathematically speaking, the normalized floating-point numbers of a given sign are roughly logarithmically spaced, and as such any finite-sized normal float cannot include zero. The subnormal floats are a linearly spaced ...