P0245r0: Initial proposal.
Changes from P0245r0 to P0245r1:
There is a base-2 scientific notation for floating point values: 0x3.ABCp-10.
The significand is given in hexadecimal, and the exponent is given in decimal and interpreted
with respect to base 2. This notation is convenient for certain uses. For example, the smallest
normal IEEE-754 single precision value is readily written as 0x1.0p-126. More
generally, this notation can be used when an exact object representation is desired (and the
floating point implementation uses a base-2 or base-2n representation).
The standard library outputs this representation via the hexfloat manipulator
for ostreams, and via the a/A conversion specifiers in
printf. Similarly,
formatted input works because strtod recognises this representation (and
the semantics of formatted istream input operations and scanf are defined in
terms of strtod, but see below for a detail). We should also allow this
representation as a literal in the core language.
Note that the C language which is referenced by the C++ standard also allows this literal syntax.
This is a core language extension that adds a new numeric literal syntax. The proposed
syntax is ill-formed in the current working draft. Note that non-standard user-defined
literals must start with an underscore, and the standard library does not define a UDL
operator named p or P.
In section [lex.fcon] (2.13.4 in the working draft), change the grammar as follows (cf. C11 6.4.4.2/1).
. digit-sequence
digit-sequence .
(追記) hexadecimal-fraction-constant: (追記ここまで)
(追記) hexadecimal-digit-sequenceopt . hexadecimal-digit-sequence (追記ここまで)
(追記) hexadecimal-digit-sequence . (追記ここまで)
exponent-part:
e signopt digit-sequence
E signopt digit-sequence
(追記) binary-exponent-part: (追記ここまで)
(追記) p signopt digit-sequence (追記ここまで)
(追記) P signopt digit-sequence (追記ここまで)
sign: one of
+ -
digit-sequence:
digit
digit-sequence 'opt digit
(追記) hexadecimal-digit-sequence: (追記ここまで)
(追記) hexadecimal-digit (追記ここまで)
(追記) hexadecimal-digit-sequence 'opt hexadecimal-digit (追記ここまで)
(追記) hexadecimal-prefix: one of (追記ここまで)
(追記) 0x 0X (追記ここまで)
floating-suffix: one of
f l F LChange the subsequent paragraph 1 in the following way:
e or E, (削除ここまで)e, E, p or P, (追記ここまで)
an optionally
signed integer exponent, and an optional type suffix. The integer and
fraction parts both consist of a sequence of decimal (base ten) digits
0x or 0X. The literal is a decimal
floating literal in the former case and a hexadecimal floating literal
in the latter case. (追記ここまで)
Optional separating single quotes in a
digit-sequence (追記) or hexadecimal-digit-sequence (追記ここまで)
are ignored when determining its value.
[Example. The literals 1.602'176'565e-19 and
1.602176565e-19 have the same value. – end example]
Either the integer part or the fraction part (not both) can be
omittede E ) (削除ここまで)E (追記ここまで)
and the exponent (not both) can be omitted (追記) from a decimal floating literal (追記ここまで).
(追記) The radix point (but not the exponent) can be omitted from a hexadecimal floating literal. (追記ここまで)
The integer part, the optional 49.625
and 0xC.68p+2 have the same value. – end example] (追記ここまで)
If the scaled value is in
the range of representable values for its type, the result is the scaled
value if representable, else the larger or smaller representable value
nearest the scaled value, chosen in an implementation-defined manner.
The type of a floating literal is double
unless explicitly specified by a suffix. The suffixes f and
F specify float, the suffixes l and
L specify long double. If the scaled value is not
in the range of representable values for its type, the program is ill-formed.
Drafting note. We changed “significant part” to “significand” and “decimal point” to “radix point”.
Also change the grammar in section [lex.ext] (2.13.8):
Although the library rules in [facet.num.get.members] say that formatted floating
point input uses the conversion rules of strtod etc., the section also
restricts the set of characters permissible for floating point parsing to
"0123456789abcdefxABCDEFX+-", which is missing the values p
and P. Should the present proposal succeed, we plan to either create a new
library proposal, or revisit LWG issue 2381
to add support for parsing hexadecimal floating point literals to the standard library.
Hexadecimal float literals are already supported as a vendor extension by several compilers: Clang, EDG, Embarcadero, GCC. Formatted input via iostreams is supported by libc++.