@num

Evaluate exact rational arithmetic, truncate the final result toward zero, and check its 256-bit integer range.

Returns: number

Syntax

@num(...tokens)

Arguments

Name	Type	Description
[...tokens]	any	Arithmetic expression (e.g. $a + $b * 2)

Examples

# Basic arithmetic
set $sum @num(1 + 2)

# Exponentiation
set $pow @num(2 ^ 10)

# Expression with variables
set $a 10
set $b 3
set $result @num($a * $b + 1)

# Convert a string to number
set $n @num("42")

See Also

• @num.format — format with decimals (like formatUnits)
• @num.parse — parse a decimal string (like parseUnits)
• @bool — boolean expressions

Exact evaluation and final conversion

num computes exact rational intermediates, then truncates the final result toward zero. The final nonnegative integer must fit uint256; negative integers must fit int256. Use floor or ceil to choose another final rounding direction. Use calc and calc! for checked integer arithmetic, with // for division.

Modular powers and inverses

a ^ e % m (or (a ^ e) % m) computes an integer modular power without materializing the intermediate power. A negative exponent uses the modular inverse: 3 ^ -1 % 11 is 4, and 3 ^ -2 % 11 is 5. The inverse exists only when the base and modulus are coprime; otherwise the expression fails. Composite moduli are supported. Modulus zero fails, modulus 1 or -1 returns zero, and exponent zero returns 1 % m, including 0 ^ 0.

For a negative base, odd exponents (including negative odd exponents) return a negative remainder: -3 ^ -1 % 11 is -4. The modulus's sign is ignored. This uses signed remainders, not a normalized nonnegative residue convention.

Only a power immediately followed by % receives modular semantics; an intervening operation or nested helper establishes a separate evaluation boundary.

These rules apply when the base, exponent, and modulus evaluate to integers. num still permits arbitrary-precision operands and checks only the final integer's range. Without a following modulus, 3 ^ -1 remains the exact rational 1/3 before final truncation; for example, @num(3 ^ -1 * 3) is 1. floor and ceil share these expression rules.