Hardware math
The SNES processor is capable of basic multiplication and division by 2ⁿ, but if you'd like to multiply or divide by other numbers, you'll have to make use of certain SNES hardware registers.
Hardware Unsigned Multiplication
The SNES has a set of hardware registers used for unsigned multiplication:
Register | Access | Description |
$4202 | Write | Multiplicand, 8-bit, unsigned. |
$4203 | Write | Multiplier, 8-bit, unsigned. Writing to this also starts the multiplication process. |
$4216 | Read | Unsigned multiply 16-bit product, low byte |
$4217 | Read | Unsigned multiply 16-bit product, high byte |
After you write to $4203
to start the multiplication process, you will need to wait 8 machine cycles, which is typically done by adding four NOP
instructions to the code. If you don't wait 8 machine cycles, the results are unpredictable.
Here's an example of 42 * 129 = 5418
(in hexadecimal: $2A * $81 = $152A
):
Hardware Signed Multiplication
There's a set of hardware registers which can be used for fast, signed multiplication:
Register | Access | Description |
$211B | Write twice | Multiplicand, 16-bit, signed. First write: Low byte of multiplicand. Second write: High byte of multiplicand |
$211C | Write | Multiplier, 8-bit. |
$2134 | Read | Signed multiply 24-bit product, low byte |
$2135 | Read | Signed multiply 24-bit product, middle byte |
$2136 | Read | Signed multiply 24-bit product, high byte |
There's a catch to using these hardware registers, however, as they double as certain Mode 7 registers as well:
You can only use them for signed multiplication
The result is signed 24-bit, meaning the results range from
-8,388,608
to8,388,607
.
The results are instant. That means you don't have to use
NOP
to wait for the results.You cannot use them when Mode 7 graphics are being rendered on the screen.
This means that when Mode 7 is enabled, you can only use them inside NMI (V-blank).
This also means that you can use them without any restrictions, outside of Mode 7.
Note that register $211B
is "write twice". This means that you have to write an 8-bit value twice to this same register which in total makes up a 16-bit value. First, you write the low byte, then the high byte of the 16-bit value.
Here's an example of -30000 * 9 = -270000
(in hexadecimal: $8AD0 * $09 = $FBE150
):
Hardware Unsigned Division
The SNES has a set of hardware registers used for unsigned division. They are laid out as follows:
Register | Access | Description |
$4204 | Write | Dividend, 16-bit, unsigned, low byte. |
$4205 | Write | Dividend, 16-bit, unsigned, high byte. |
$4206 | Write | Divisor, 8-bit, unsigned. Writing to this also starts the division process. |
$4214 | Read | Unsigned division 16-bit quotient, low byte |
$4215 | Read | Unsigned division 16-bit quotient, high byte |
$4216 | Read | Unsigned division remainder, low byte |
$4217 | Read | Unsigned division remainder, high byte |
Quotient means how many times the dividend can "fit" in the divisor. For example: 6 / 3 = 2
. Thus, the quotient is 2. Another way you can read this is: You can extract 3 two times from 6 and end up with exactly 0 as leftover.
Modulo is an operation that determines the remainder of the dividend that couldn't "fit" into the divisor. For example: 8 / 3 = 2
. You can subtract 3 two times from 8, but in the end, you have a 2 as a remainder. Thus, the modulo for this operation is 2
. Because there are hardware registers that support remainders, the SNES also supports the modulo operation.
After you write to $4206
to start the division process, you will need to wait 16 machine cycles, which is typically done by adding eight NOP
instructions to the code. If you don't wait 16 machine cycles, the results are unpredictable.
Here's an example of 256 / 2 = 128
(in hexadecimal: $0100 / $02 = $0080
):
Here's an example demonstrating modulo: 257 / 2 = 128, remainder 1
(in hexadecimal: $0101 / $02 = $0080, remainder $0001
)
There is no hardware signed division.
Last updated