# 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.

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)

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)

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.