Arithmetic

1 + 1; // 2

Standard operators are

op	name
+	addition
-	subtraction and unary negation
*	multiplication
/	division
%	modulus
**	exponentiation
gcd	greatest common denominator
lcm	least common multiplier

It might seem odd to have gcd and lcm as primitives, but they are needed internally for rationals so there is no real overhead adding them as primitives.

F♮ supports the following numeric types:

• arbitrary sized integers - ints are promoted individually to bigints if an arithmetic operation overflows.
• rationals - precision-preserving rational numbers - division of integers where the result is not an integer produces a rational, and arithmetic on rationals produces a rational or an integer: 2 + 1/2 is 5/2, 1/2 + 1/2 is 1 etc.
• irrationals - floating point numbers.
• complex numbers - -1 ** (1/2) results in 1i, complex numbers can be input as i.e. (1 + 2i).

The standard formats for literal floating point and integer decimals are recognised, hexadecimal integers are prefixed by 0x or 0X, additionally imaginary numbers (decimal, hex or float) have the suffix i (no space) and you can use underscores _ within any sequence of digits to improve readability. It's probably worth pointing out that you have to write 1i to get i, i by itself is not treated specially.

Coercion is as follows, somewhat complicated by complex numbers which can have integer, float or rational components.

• int $\sqsubset$ rational $\sqsubset$ float $\sqsubset$ complex

But to be clear as far as type-checking is concerned, there is only the single type number.

Plans are afoot to support trig and log functions over the above, and there are already some built-in functions to help with complex number manipulation, see Builtins.

Next: Booleans