# X86 Assembly/Arithmetic

All arithmetic instructions are executed in (one of) the ALUs. The ALU can only perform integer arithmetics, for floating point instructions see chapter “Floating Point”.

## Basic operations

Arithmetic instructions take two operands: a destination and a source.
* The destination must be a register or a memory location.
* The source may be either a memory location, a register, or a constant value.
Note that at most one operand may be a memory location.

### Addition and Subtraction

This adds addend to destination and stores the result in destination.
Like add, only it subtracts subtrahend from destination instead. In C: destination -= subtrahend;

### Multiplication
#### Unsigned Multiplication

mul multiplicand
This multiplies multiplicand by the value of corresponding byte-length in the accumulator.
result registers used by mul :
| width of multiplicand | 1 byte | 2 bytes | 4 bytes | 8 bytes |
| corresponding multiplier | AL | AX | EAX | RAX |
| product higher part stored in | AH | DX | EDX | RDX |
| product lower part stored in | AL | AX | EAX | RAX |
In the second case, the target is not EAX for backward compatibility with code written for older processors.
Affected flags are:
* OF ≔ higher part of product ≠ 0
* CF ≔ higher part of product ≠ 0
All other flags are undefined.

#### Signed Multiplication

imul multiplicand
This instruction is almost like mul, but it treats the sign bit (the MSB), differently.
The imul instruction also accepts two other formats:
This multiplies destination by multiplicand and puts the result, the product, in destination.
This multiplies multiplier by multiplicand and places it into product.

### Division

div divisor
This divides the value in the dividend register(s) by divisor, see table below.
idiv arg
As div, only signed.
result registers for div :
| width of divisor | 1 byte | 2 bytes | 4 bytes | 8 bytes |
| dividend | AX | DX ￮ AX | EDX ￮ EAX | RDX ￮ RAX |
| remainder stored in | AH | DX | EDX | RDX |
| quotient stored in | AL | AX | EAX | RAX |
The circle (￮) means concatenation. With divisor size 4, this means that EDX are the bits 32-63 and EAX are bits 0-31 of the input number (with lower bit numbers being less significant, in this example).
As you typically have 32 or 64-bit input values for signed division, you often need to use CDQ or CQO to sign-extend EAX into EDX or RAXinto RDX just before the division.
If quotient does not fit into quotient register, arithmetic overflow interrupt occurs. All flags are in undefined state after the operation.

### Sign Inversion

neg arg
Arithmetically negates the argument (i.e. two's complement negation).

## Carry Arithmetic Instructions

Add with carry. Adds src + CF to dest, storing result in dest. Usually follows a normal add instruction to deal with values twice as large as the size of the register. In the following example, source contains a 64-bit number which will be added to destination.
Subtract with borrow. Subtracts src + CF from dest, storing result in dest. Usually follows a normal sub instruction to deal with values twice as large as the size of the register.

## Increment and Decrement
### Increment

inc augend
This instruction increments the register value augend by 1. It performs much faster than add arg, 1, but it does not affect the CF.

### Decrement

dec minuend

#### Operation

Decrements the value in minuend by 1, but this is much faster than the semantically equivalent sub minuend, 1.

#### Operands

Minuend may be either a register or memory operand.

#### Application

* Some programming language represent Boolean values with either all bits zero, or all bits set to one. When you are programming Boolean functions you need to take account of this. The dec instruction can help you with this. Very often you set the final (Boolean) result based on flags. By choosing an instruction that is opposite of the intended and then decrementing the resulting value you will obtain a value satisfying the programming language’s requirements. Here is a trivial example testing for zero. xor rax, rax ; rax ≔ false (ensure result is not wrong due to any residue) test rdi, rdi ; rdi ≟ 0 (ZF ≔ rax = 0) setnz al ; al ≔ ¬ZF dec rax ; rax ≔ rax − 1 If you intend to set false the “erroneously” set 1 will be “fixed” by dec. If you intend to set true, which is represented by −1, you will decrement the value zero, the “underflow” of which causing all bits to flip. Note, some architectures execute dec slowly, because of the fact that the flags register is overwritten only partially. It therefore is usually more efficient to use negsetz al   ; al ≔ ZF neg rax   ; rax ≔ 0 − rax which will affect the CF too, though.
* Since inc and dec do not affect the CF, you can use these instructions to update a loop’s counting variable without overwriting some information stored in it. If you need an instruction that does not affect any flags while implicitly also performing a dec, you could use the rather slow loop.

## Pointer arithmetic

The lea instruction can be used for arithmetic, especially on pointers. See chapter “data transfer”, § “load effective address”.