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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 the e)
    • 0x1.2p123 (optional + or - after the p)
  • Digit separators (_) may be used, but only in conventional locations

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 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

If digit separators (_) are included in literals, they must meet the respective condition:

  • For decimal integers, the digit separators shall occur every three digits starting from the right. For example, 2_147_483_648.
  • For hexadecimal integers, the digit separators shall occur every four digits starting from the right. For example, 0x7FFF_FFFF.
  • For real-number literals, digit separators can appear in the decimal and hexadecimal integer portions (prior to the period and after the optional e or mandatory p) as described in the previous bullets. For example, 2_147.483648e12_345 or 0x1_00CA.FEF00Dp+24
  • For binary literals, digit separators can appear between any two digits. For example, 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