FLOATING POINT NUMBERS

Defining Floating Point Numbers

To define floating-point numbers, I can use the dd directive in the data section to represent 32-bit floating-point values.

x dd 3.14
y dd 2.1

These lines define two floating-point numbers, x and y, with the respective values of 3.14 and 2.1.

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Loading Values into Registers

To load these values into registers, I utilize the movss instruction (Scalar Single-Precision Floating-Point Value).

movss xmm0, [x]
movss xmm1, [y]

xmm0 and xmm1 are special registers designed for storing floating-point numbers (can use up to xmm15). The square brackets indicate fetching the value stored at the memory address of x and y, respectively.

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Performing Operations

Performing arithmetic operations like addition, subtraction, multiplication, and division follows similar principles.

addss xmm0, xmm1

This instruction adds the values stored in xmm0 and xmm1, storing the result back into xmm0.

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Precision Considerations

One crucial consideration when working with floating-point numbers is precision. Floating-point values are stored using IEEE floating-point notation, which can lead to slight inaccuracies in representation. For example, 3.14 might be stored as 3.1400001 due to these limitations.

In the 32 bit IEEE format:

• 1 bit is allocated as the sign bit;
• The next 8 bits are allocated as the exponent field;
• The last 23 bits are the fractional parts of the normalized number;
• A sign bit of 0 indicates a positive number, and a 1 is negative;

section .data
    x DD 3.14
    y DD 2.1

section .text

global _start

_start:
        movss xmm0, [x] ; scalar single precision floating point move
                        ; scalar because i are moving a single decimal value
                        ; single precision meaning is a 32-bit floating point number
        
        movss xmm1, [y]
        addss xmm0, xmm1
        mov ebx, 1
        int 80h

        ; xmm0 = 3.1400001 IEEE
        ; xmm1 = 2.0999999 IEEE
        ; result = 5.2399977 IEEE

To print the value of xmm0 in GDB, use the command p $xmm0.v4_float[0].

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Compare Floating Point Numbers

Comparing floating-point numbers is a bit more complex than comparing integers. The cmp instruction doesn’t work with floating-point numbers, so I use the ucomiss instruction instead.

section .data
    x DD 3.14
    y DD 2.1

section .text

global _start

_start:
        movss xmm0, [x]
        movss xmm1, [y]
        ucomiss xmm0, xmm1  ; cmp doesn't work
        ja above            ; jump if above
        jmp end

above:
        mov ecx, 1

end:
        mov eax, 1
        mov ebx, 1
        int 80h

Also, ja (jump above) instead of jg (jump greater) because I compare floating point numbers. The only jump condition equal to integers is je (jump equal). The rest is as follows: jb (jump below), jae (jump above or equal), jbe (jump below or equal), jne (jump not equal).