Calculate sqrt using newton iteration method

newton_sqrt.asm

;;
; Calculate sqrt using newton iteration method
; Assembly version of https://gist.github.com/Lukas0025/b6aacb8d2a5d79d51d2f9ca7cd5af2ab with fixed iteration count
; @autor Lukáš Plevač <lukas@plevac.eu>
; @date 6.8.2021
; Under CC0
;

%include "io.inc"

section .data

myx dd 3.0

section .text
global CMAIN

;;
; @param eax number for sqrt
; @return eax = sqrt(eax)
NSQRT:
    FINIT
    ;LOAD X
    push eax
    FLD dword [esp]
    ;FLD2
    FLD1
    FLD1
    FADD
    ; initial estimate
    FDIV ; x / 2
    ; 3 iterations
    mov ecx, 3
NSQRT_LOOP:
    ; x{n} = x{n-1} - (x{n-1} ** 2 - x) / (2 * x{n-1})
    FLD st0 ; load x{n-1}
    FLD st0 ; load x{n-1}
    FMUL ; x{n-1} ** 2
    FLD dword [esp] ; load x{0}
    FSUB ; - n
    
    ; FLD2
    FLD1
    FLD1
    FADD
    
    FLD st2 ; load x{n-1}
    FMUL
    
    FDIV
    FSUB
    
    ; debug
    ; FST dword [myx]
    
    LOOP NSQRT_LOOP
    
    FSTP dword [esp]
    pop eax
    ret
    
CMAIN:
    mov ebp, esp; for correct debugging
    ;write your code here
    xor eax, eax
    mov eax, [myx]
    call NSQRT
    ret