numeric_literals.md 6.4 KB
Numeric literals
Table of contents
Overview
The following syntaxes are supported:
- Integer literals
12345(decimal)0x1FE(hexadecimal)0b1010(binary)
- Real-number literals
123.456(digits on both sides of the.)123.456e789(optional+or-after thee)0x1.2p123(optional+or-after thep)
- Digit separators (
_)
Note that real-number literals always contain a . with digits on both sides,
and integer literals never contain a ..
Literals are case-sensitive. Unlike in C++, literals do not have a suffix to indicate their type.
Details
Integer literals
Decimal integers are written as a non-zero decimal digit followed by zero or
more additional decimal digits, or as a single 0.
Integers in other bases are written as a 0 followed by a base specifier
character, followed by a sequence of one or more digits in the corresponding
base. The available base specifiers and corresponding bases are:
| Base specifier | Base | Digits |
|---|---|---|
b |
2 | 0 and 1 |
x |
16 | 0 ... 9, A ... F |
The above table is case-sensitive. For example, 0b1 and 0x1A are valid, and
0B1, 0X1A, and 0x1a are invalid.
A zero at the start of a literal can never be followed by another digit: either
the literal is 0, the 0 begins a base specifier, or the next character is a
decimal point (see below). No support is provided for octal literals, and any C
or C++ octal literal (other than 0) is invalid in Carbon.
Real-number literals
Real numbers are written as a decimal or hexadecimal integer followed by a
period (.) followed by a sequence of one or more decimal or hexadecimal
digits, respectively. A digit is required on each side of the period. 0. and
.3 are both invalid.
A real number can be followed by an exponent character, an optional + or -
(defaulting to + if absent), and a character sequence matching the grammar of
a decimal integer with some value N. For a decimal real number, the exponent
character is e, and the effect is to multiply the given value by
10±N. For a hexadecimal real number, the exponent character
is p, and the effect is to multiply the given value by
2±N. The exponent suffix is optional for both decimal and
hexadecimal real numbers.
Note that a decimal integer followed by e is not a real-number literal. For
example, 3e10 is not a valid literal.
When a real-number literal is interpreted as a value of a real-number type, its value is the representable real number closest to the value of the literal. In the case of a tie, the nearest value whose mantissa is even is selected.
The decimal real number syntax allows for any decimal fraction to be expressed -- that is, any number of the form a x 10-b, where a is an integer and b is a non-negative integer. Because the decimal fractions are dense in the reals and the set of values of the real-number type is assumed to be discrete, every value of the real-number type can be expressed as a real number literal. However, for certain applications, directly expressing the intended real-number representation may be more convenient than producing a decimal equivalent that is known to convert to the intended value. Hexadecimal real-number literals are provided in order to permit values of binary floating or fixed point real-number types to be expressed directly.
Digit separators
A digit separator (_) may occur between any two digits within a literal. For
example:
- Decimal integers:
1_23_456_7890 - Hexadecimal integers:
0x7_F_FF_FFFF - Real-number literals:
2_147.48_3648e12_345or0x1_00CA.FE_F00Dp+2_4 - Binary literals:
0b1_000_101_11
Divergence from other languages
The design provides a syntax that is deliberately close to that used both by C++ and many other languages, so it should feel familiar to developers. However, it selects a reasonably minimal subset of the syntaxes. This minimal approach provides benefits directly in line with the goal that Carbon code should be easy to read, understand, and write:
- Reduces unnecessary choices for programmers.
- Simplifies the syntax rules of the language.
- Improves consistency of written Carbon code.
That said, it still provides sufficient variations to address important use cases for the goal of not leaving room for a lower level language:
- Hexadecimal and binary integer literals.
- Scientific notation floating point literals.
- Hexadecimal (scientific) floating point literals.
Alternatives considered
References
- Proposal #143: Numeric literals
- Proposal #866: Allow ties in floating literals
- Proposal #1983: Weaken digit separator placement rules