5.4. Numbers#

Syntax#

HexNumberExpression = (* literal: *) HEX_LITERAL
                      (* unit: *) NumberUnit?; (* Deprecated in 0.5.0 *)

DecimalNumberExpression = (* literal: *) DECIMAL_LITERAL
                          (* unit: *) NumberUnit?;

HEX_LITERAL = "0x" «HEX_CHARACTER»+ ("_" «HEX_CHARACTER»+)*;

(* Deprecated in 0.5.0 *)
HEX_LITERAL = "0X" «HEX_CHARACTER»+ ("_" «HEX_CHARACTER»+)*;

DECIMAL_LITERAL = "." «DECIMAL_DIGITS» «DECIMAL_EXPONENT»?;

DECIMAL_LITERAL = «DECIMAL_DIGITS» «DECIMAL_EXPONENT»?;

(* Deprecated in 0.5.0 *)
DECIMAL_LITERAL = «DECIMAL_DIGITS» "." «DECIMAL_EXPONENT»?;

(* Deprecated in 0.5.0 *)
DECIMAL_LITERAL = «DECIMAL_DIGITS» "." «DECIMAL_DIGITS» «DECIMAL_EXPONENT»?;

(* Introduced in 0.5.0 *)
DECIMAL_LITERAL = «DECIMAL_DIGITS» ("." «DECIMAL_DIGITS»)? «DECIMAL_EXPONENT»?;

«DECIMAL_DIGITS» = ("0"…"9")+ ("_" ("0"…"9")+)*;

«DECIMAL_EXPONENT» = ("e" | "E") "-"? «DECIMAL_DIGITS»;

NumberUnit = (* variant: *) WEI_KEYWORD
           | (* variant: *) GWEI_KEYWORD (* Introduced in 0.6.11 *)
           | (* variant: *) SZABO_KEYWORD (* Deprecated in 0.7.0 *)
           | (* variant: *) FINNEY_KEYWORD (* Deprecated in 0.7.0 *)
           | (* variant: *) ETHER_KEYWORD
           | (* variant: *) SECONDS_KEYWORD
           | (* variant: *) MINUTES_KEYWORD
           | (* variant: *) HOURS_KEYWORD
           | (* variant: *) DAYS_KEYWORD
           | (* variant: *) WEEKS_KEYWORD
           | (* variant: *) YEARS_KEYWORD; (* Deprecated in 0.5.0 *)

Integers#

Signed (int8..int256) and unsigned (uint8..uint256) integers of various sizes, from 8 to 256 bits, moving up in steps of 8 bits. uint and int are aliases for uint256 and int256, respectively.

Integers in Solidity are restricted to a certain range. For example, with uint32, this is 0 up to 2**32 - 1.

Integer literals are formed from a sequence of digits in the range 0-9. They are interpreted as decimals. For example, 69 means sixty nine.

Decimals#

Decimal fractional literals are formed by a . with at least one number on one side. Examples include 1., .1 and 1.3.

Fixed Point Numbers#

Signed fixed and unsigned fixed ufixed point number of various sizes. Keywords ufixedMxN and fixedMxN, where M represents the number of bits taken by the type and N represents how many decimal points are available. M must be divisible by 8 and goes from 8 to 256 bits. N must be between 0 and 80, inclusive. ufixed and fixed are aliases for ufixed128x18 and fixed128x18, respectively.

Scientific Notation#

Scientific notation in the form of 2e10 is also supported, where the mantissa can be fractional but the exponent has to be an integer. The literal MeE is equivalent to M * 10**E. Examples include 2e10, -2e10, 2e-10, 2.5e1.

Using Underscores#

Underscores can be used to separate the digits of a numeric literal to aid readability. For example, decimal 123_000, hexadecimal 0x2eff_abcde, scientific decimal notation 1_2e345_678 are all valid. Underscores are only allowed between two digits and only one consecutive underscore is allowed. There is no additional semantic meaning added to a number literal containing underscores, the underscores are ignored.

Ether Units#

A literal number can take a suffix of wei, gwei or ether to specify a sub-denomination of Ether, where Ether numbers without a postfix are assumed to be Wei.

assert(1 wei == 1);
assert(1 gwei == 1e9);
assert(1 szabo == 1e12);
assert(1 finney == 1e15);
assert(1 ether == 1e18);

Time Units#

Suffixes that can be used to specify units of time where seconds are the base unit and units are considered naively in the following way:

assert(1 == 1 seconds);
assert(1 minutes == 60 seconds);
assert(1 hours == 60 minutes);
assert(1 days == 24 hours);
assert(1 weeks == 7 days);