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Re: basic formats
Date: Sun, 29 Mar 2009 01:32:58 +0100
From: Vincent Lefevre <vincent@xxxxxxxxxx>
To: stds-754@xxxxxxxxxxxxxxxxx
Subject: basic formats
Hi,
The standard says:
2.1.4 basic format: One of five floating-point representations,
three binary and two decimal, whose encodings are specified by this
standard, and which can be used for arithmetic. One or more of the
basic formats is implemented in any conforming implementation.
and
3.1.1 Formats
This clause defines floating-point formats, which are used to
represent a finite subset of real numbers (see 3.2). Formats are
characterized by their radix, precision, and exponent range, and
each format can represent a unique set of floating-point data
(see 3.3).
All formats can be supported as arithmetic formats; that is, they
may be used to represent floating-point operands or results for
the operations described in later clauses of this standard.
Specific fixed-width encodings for binary and decimal formats
are defined in this clause for a subset of the formats (see 3.4
and 3.5). These interchange formats are identified by their size
(see 3.6) and can be used for the exchange of floating-point
data between implementations.
Five basic formats are defined in this clause:
-- Three binary formats, with encodings in lengths of 32, 64,
and 128 bits.
-- Two decimal formats, with encodings in lengths of 64 and
128 bits.
Additional arithmetic formats are recommended for extending these
basic formats (see 3.7).
This is not clear. It seems that both binary16 and decimal32 satisfy
the conditions of the "basic format" definition: their encodings are
specified and they can be used for arithmetic (second paragraph of
3.1.1). In some drafts, they were declared as "storage formats". but
this notion seems to have disappeared. So, what is their status?
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
Vincent,
I think you have it.
The 5 basic formats are, as stated, Binary32, Binary64,
Binary128, Decimal64, & Decimal128. They qualify as all
of formats, fixed-width encodings, arithmetic formats, &
interchange formats.
While the name "storage format" was eliminated during the
public comment phase, the concept of a format that can be
read from, written to, & converted to & from, but otherwise
supports no arithmetic still exists.
I think that pretty much covers it.
Enjoy,
Dan