Assembly x64 Intro - Horner Polynomial Evaluation

; horner_64.asm  Horners method of evaluating polynomials
;
; given a polynomial  Y = a_n X^n + a_n-1 X^n-1 + ... a_1 X + a_0
; a_n is the coefficient 'a' with subscript n. X^n is X to nth power
; compute y_1 = a_n * X + a_n-1
; compute y_2 = y_1 * X + a_n-2
; compute y_i = y_i-1 * X + a_n-i   i=3..n
; thus    y_n = Y = value of polynomial
;
; in assembly language:
;   load some register with a_n, multiply by X
;   add a_n-1, multiply by X, add a_n-2, multiply by X, ...
;   finishing with the add  a_0
;
; output from execution:
; a  6319
; aa 6319
; af 6.319000e+03

extern printf
section .data
global main

section .data
fmta: db "a  %ld",10,0
fmtaa: db "aa %ld",10,0
fmtflt: db "af %e",10,0

section .text
main: push rbp ; set up stack

; evaluate an integer polynomial, X=7, using a count

section .data
a: dq 2,5,-7,22,-9 ; coefficients of polynomial, a_n first
X: dq 7 ; X = 7
; n=4, 8 bytes per coefficient
section .text
mov rax,[a] ; accumulate value here, get coefficient a_n
mov rdi,1 ; subscript initialization
mov rcx,4 ; loop iteration count initialization, n
h3loop: imul rax,[X] ; * X     (ignore edx)
add rax,[a+8*rdi] ; + a_n-i
inc rdi ; increment subscript
loop h3loop ; decrement rcx, jump on non zero

mov rsi, rax ; print rax
mov rdi, fmta ; format
mov rax, 0 ; no float
call printf


; evaluate an integer polynomial, X=7, using a count as index
; optimal organization of data allows a three instruction loop

section .data
aa: dq -9,22,-7,5,2 ; coefficients of polynomial, a_0 first
n: dq 4 ; n=4, 8 bytes per coefficient
section .text
mov rax,[aa+4*8] ; accumulate value here, get coefficient a_n
mov rcx,[n] ; loop iteration count initialization, n
h4loop: imul rax,[X] ; * X     (ignore edx)
add rax,[aa+8*rcx-8]; + aa_n-i
loop h4loop ; decrement rcx, jump on non zero

mov rsi, rax ; print rax
mov rdi, fmtaa ; format
mov rax, 0 ; no float
call printf

; evaluate a double floating polynomial, X=7.0, using a count as index
; optimal organization of data allows a three instruction loop

section .data
af: dq -9.0,22.0,-7.0,5.0,2.0 ; coefficients of polynomial, a_0 first
XF: dq 7.0
Y: dq 0.0
N: dd 4

section .text
mov rcx,[N] ; loop iteration count initialization, n
fld qword [af+8*rcx]; accumulate value here, get coefficient a_n
h5loop: fmul qword [XF] ; * XF
fadd qword [af+8*rcx-8] ; + aa_n-i
loop h5loop ; decrement rcx, jump on non zero

fstp qword [Y] ; store Y in order to print Y
movq xmm0, qword [Y] ; well, may just mov reg
mov rdi, fmtflt ; format
mov rax, 1 ; one float
call printf

pop rbp ; restore stack
mov rax,0 ; normal return
ret ; return

a  6319
aa 6319
af 6.319000e+03