# 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`):
LDA #\$2A ; 42
STA \$4202
LDA #\$81 ; 129
STA \$4203
NOP ; Wait 8 machine cycles
NOP
NOP
NOP
LDA \$4216 ; A = \$2A (result low byte)
LDA \$4217 ; A = \$15 (result high byte)

## 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` to `8,388,607`.
• 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`):
LDA #\$D0 ; Low byte of \$8AD0
STA \$211B
LDA #\$8A ; High byte of \$8AD0
STA \$211B ; This sets up the multiplicand
LDA #\$09 ; \$09
STA \$211C ; This sets up multiplier
LDA \$2134 ; A = \$50 (result low byte)
LDA \$2135 ; A = \$E1 (result middle byte)
LDA \$2136 ; A = \$FB (result high byte)
; (= \$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`):
LDA #\$00
STA \$4204
LDA #\$01 ; Write \$0100 to dividend
STA \$4205
LDA #\$02 ; Write \$02 to divisor
STA \$4206
NOP ; Wait 16 machine cycles
NOP
NOP
NOP
NOP
NOP
NOP
NOP
LDA \$4214 ; A = \$80 (result low byte)
LDA \$4215 ; A = \$00 (result high byte)
LDA \$4216 ; A = \$00, as there are no remainders
LDA \$4217 ; A = \$00, as there are no remainders
Here's an example demonstrating modulo: `257 / 2 = 128, remainder 1` (in hexadecimal: `\$0101 / \$02 = \$0080, remainder \$0001`)
LDA #\$01
STA \$4204
LDA #\$01 ; Write \$0101 to dividend
STA \$4205
LDA #\$02 ; Write \$02 to divisor
STA \$4206
NOP ; Wait 16 machine cycles
NOP
NOP
NOP
NOP
NOP
NOP
NOP
LDA \$4214 ; A = \$80 (result low byte)
LDA \$4215 ; A = \$00 (result high byte)
LDA \$4216 ; A = \$01, as there is a remainder (remainder low byte)
LDA \$4217 ; A = \$00 (remainder high byte)
There is no hardware signed division.