Numeric literals

Table of contents

Overview

The following syntaxes are supported:

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 lexed as two separate tokens: 0.(Util.Abs)() and tuple.3 both treat the period as member or element access, not as a radix point.

To support tuple indexing, a real number literal is never formed immediately following a . token with no intervening whitespace. Instead, the result is an integer literal.

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_345 or 0x1_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