Note:Decimal floating-point is not part of the IEEE standards.
Decimal Floating Point (L extension) is a tentative standard
RISC-V extension for base-10 representations (decimal32, decimal64,
decimal128), and it is not supported in RARS.
"L" Standard Extension for Decimal
(pdf)
Decimal Floating-Point, Version 0.0
- Standard DFP Interchange Format
The draft standard defined three main widths for exchanging data,
which match modern C/C++ types (such as _Decimal32, _Decimal64,
and _Decimal128).
Format
Name |
Total
bits |
Significant
Range |
Exponent
Range |
Purpose | C-Type
|
|---|
| decimal32 |
32 bits |
7 decimal
digits |
(-95) to (+96) |
Storage economy | (rarely used for arithmetic) |
| decimal64 |
64 bits |
16 decimal
digits |
(-383) to (+384) |
Standard Precision | (_Decimal64) |
| decimal128 |
128 bits |
34 decimal
digits |
(-6143) to (+6144) |
Extended Precision | (_Decimal128) |
- Encoding the Significant (DPD vs. BID)
Because computers are fundamentally binary, saving base-10 digits efficiently
into binary bits required a new approach. The standard allows two encoding
schemes:
- Densely Packed Decimal (DPD): Compresses groups of 3 decimal digits into
10 bits (whereas standard BCD would require 12 bits). This is the
preferred standard for IBM hardware (z/Architecture and POWER processors).
- Binary Integer Decimal (BID): Encodes the significant directly as a massive
standard binary integer. This scheme is favored by software-based math
libraries and Intel/AMD architectures.
Both encodings store the exact same mathematical value and range; they
only differ in how the bits are organized on the chip.
- Special Values and States
Just like binary floating-point, the decimal standard reserves specific bit
patterns for boundary cases:
- Signed Zeros: Both (+0.0) and (-0.0) are supported.
- Infinities: (+infty) and (-infty) handle overflow conditions.
- NaN (Not a Number): Divided into Quiet NaNs (qNaN) and Signaling
NaNs (sNaN) to represent invalid operations.