decimal32

Decimal32 is one of the decimal floating-point formats defined by the IEEE 754-2008 standard. It represents decimal numbers with about seven decimal digits of precision, offering a compact option for decimal arithmetic in memory-constrained environments. It is part of the decimal family that also includes decimal64 (16 digits) and decimal128 (34 digits), providing different trade-offs between precision and range.

The 32-bit representation encodes a sign, an exponent, and a significand. The significand stores the decimal digits, while the exponent scales the significand by powers of ten. There are two common encoding forms for decimal32: densely packed decimal (DPD) and binary integer decimal (BID). In practice, either encoding may be used depending on platform and library support.

Decimal32 supports the standard IEEE 754 rounding modes, including round-to-nearest with ties to even, as well as toward zero, toward +infinity, and toward −infinity. It provides the usual special values such as Infinity, NaN, and signed zero. As with other decimal floating-point formats, arithmetic follows rules that aim to produce correctly rounded results under the chosen rounding mode. Operations include addition, subtraction, multiplication, division, and square root, all performed in decimal.

Use cases for decimal32 focus on scenarios where memory efficiency is important but decimal precision is required, such as certain financial or business applications with tight storage constraints. Hardware and software implementations vary; decimal floating-point support has been added in various processor architectures and numerical libraries, alongside the larger decimal formats decimal64 and decimal128, to accommodate different precision needs and performance considerations.