DIVIDE

Divide the left operand by the right operand to calculate a quotient and optional remainder.

Opcode	Bytes	Cycles	Form	Example
$a5	3	29	divide i:_, {s_byte}	divide i:4, 123
$a7	3	29	divide i:_, i:_	divide i:4, i:8
$dc	4	29	divide i:_, {s_byte}, remainder i:_	divide i:4, 123, remainder i:8
$de	4	29	divide i:_, i:_, remainder i:_	divide i:4, i:8, remainder i:12

Condition flag	Output
zero (ZF)	If the quotient is zero, this flag is 1; otherwise it is 0.
negative (NF)	If the signed quotient is a negative number, this flag is 1; otherwise it is 0.
overflow (OF)	If the divisor is zero, this flag is 1; otherwise it is 0.
carry (CF)	This flag is always 0.

Notes

• Terminology: If we write a / b = q, a is called the dividend, b is the divisor, and q is the quotient. If the division is not exact, the remainder will be nonzero.

• For example, divide i:4, i:8, remainder i:12 divides i:4 (the dividend) by i:8 (the divisor), storing the quotient back into i:4. The remainder is stored in i:12.

• The remainder's register will always be assigned after the quotient's register. This allows a modulus expression such as x <- x %% 123 to be compiled as divide i:4, 123, remainder i:4 without need for a temporary register to discard the quotient.

• If the divisor is zero, the quotient and remainder will always be zero.

• To trap division-by-zero, you can use the fail if overflow instruction.

Euclidean division

For historical reasons, most CPUs and programming languages such as C and Rust implement truncated division, where the remainder can be a negative number if the dividend is negative. Chombit's divide instruction performs truncated division by default. The Hybrix language's / and % operators are implemented this way.

Euclidean division ensures that the remainder is always a positive number. It is the most mathematically correct way to divide. This method is selected if a with euclid instruction immediately precedes the divide instruction. The Hybrix language's // and %% operators are implemented this way.

The table below illustrates the differences:

Truncated quotient	Truncated remainder
17 / 5 = 3	17 % 5 = 2
-17 / 5 = -3	-17 % 5 = -2
17 / -5 = -3	17 % -5 = 2
-17 / -5 = 3	-17 % -5 = -2

Euclidean quotient	Euclidean remainder
17 // 5 = 3	17 %% 5 = 2
-17 // 5 = -4	-17 %% 5 = 3
17 // -5 = -3	17 %% -5 = 2
-17 // -5 = 4	-17 %% -5 = 3