ISO/IEC JTC1 SC22 WG21 P00245r0

Date: 2016-02-09


Thomas Köppe <>

Hexadecimal floating literals for C++


  1. Summary
  2. Impact
  3. Proposed wording
  4. An iostreams issue
  5. Existing practice and implementation experience


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.

Proposed wording

In section [lex.fcon] (2.13.4 in the working draft), change the grammar as follows (cf. C11

floating-literal:   decimal-floating-literal   hexadecimal-floating-literal decimal-floating-literal:   fractional-constant exponent-partopt floating-suffixopt   digit-sequence exponent-part floating-suffixopt hexadecimal-floating-literal:   hexadecimal-prefix hexadecimal-fractional-constant binary-exponent-part floating-suffixopt   hexadecimal-prefix hexadecimal-digit-sequence binary-exponent-part floating-suffixopt fractional-constant:   digit-sequenceopt . digit-sequence   digit-sequence . hexadecimal-fraction-constant:   hexadecimal-digit-sequenceopt . hexadecimal-digit-sequence   hexadecimal-digit-sequence . exponent-part:   e signopt digit-sequence   E signopt digit-sequence binary-exponent-part:   p signopt digit-sequence   P signopt digit-sequence sign: one of   + - digit-sequence:   digit   digit-sequence 'opt digit hexadecimal-digit-sequence:   hexadecimal-digit   hexadecimal-digit-sequence 'opt hexadecimal-digit hexadecimal-prefix: one of   0x 0X floating-suffix: one of   f l F L

Change the subsequent paragraph 1 in the following way:

A floating literal consists of an integer part, a decimalradix point, a fraction part, an e or E, e, E, p or P, an optionally signed integer exponent, and an optional type suffix. The integer and fraction parts both consist of either a sequence of decimal (base ten) digits ., or they include the hexadecimal-prefix and consist of a sequence of hexadecimal (base sixteen) digits. The literal is a decimal floating literal in the former case and a hexadecimal floating literal in the latter case. Optional separating single quotes in a digit-sequence or hexadecimal-digit-sequence are ignored when determining its value. [Example. The literals 1.602'176'565e-19 and 1.602176565e-19 have the same value.] Either the integer part or the fraction part (not both) can be omitted; either. Either the decimalradix point or the letter e (or E )or E and the exponent (not both) can be omitted from a decimal floating literal. The radix point (but not the exponent) can be omitted from a hexadecimal floating literal. The integer part, the optional decimalradix point and the optional fraction part form the significantsignificand part of the floating literal. TheIn a decimal floating literal, the exponent, if present, indicates the power of 10 by which the significantsignificand part is to be scaled. In a hexadecimal floating literal, the exponent indicates the power of 2 by which the significand part is to be scaled. 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” to “significand” and “decimal point” to “radix point”.

Also change the grammar in section [lex.ext] (2.13.8):

user-defined-floating-literal:   fractional-constant exponent-partopt ud-suffix   digit-sequence exponent-part ud-suffix   hexadecimal-prefix hexadecimal-fractional-constant binary-exponent-part ud-suffix   hexadecimal-prefix hexadecimal-digit-sequence binary-exponent-part ud-suffix

An iostreams issue

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.

Existing practice and implementation experience

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++.