389 lines
12 KiB
Plaintext
389 lines
12 KiB
Plaintext
/* ARM assembly AARCH64 Raspberry PI 3B */
|
|
/* program totient.s */
|
|
|
|
/************************************/
|
|
/* Constantes */
|
|
/************************************/
|
|
.include "../includeConstantesARM64.inc"
|
|
.equ MAXI, 25
|
|
|
|
/*********************************/
|
|
/* Initialized data */
|
|
/*********************************/
|
|
.data
|
|
szMessNumber: .asciz " number @ totient @ @ \n"
|
|
szCarriageReturn: .asciz "\n"
|
|
szMessPrime: .asciz " is prime."
|
|
szMessSpace: .asciz " "
|
|
szMessCounterPrime: .asciz "Number of primes to @ : @ \n"
|
|
szMessOverflow: .asciz "Overflow function isPrime.\n"
|
|
/*********************************/
|
|
/* UnInitialized data */
|
|
/*********************************/
|
|
.bss
|
|
sZoneConv: .skip 24
|
|
/*********************************/
|
|
/* code section */
|
|
/*********************************/
|
|
.text
|
|
.global main
|
|
main:
|
|
mov x4,#1 // start number
|
|
1:
|
|
mov x0,x4
|
|
bl totient // compute totient
|
|
mov x5,x0
|
|
mov x0,x4
|
|
bl isPrime // control if number is prime
|
|
mov x6,x0
|
|
mov x0,x4 // display result
|
|
ldr x1,qAdrsZoneConv
|
|
bl conversion10 // call décimal conversion
|
|
ldr x0,qAdrszMessNumber
|
|
ldr x1,qAdrsZoneConv // insert conversion in message
|
|
bl strInsertAtCharInc
|
|
mov x7,x0
|
|
mov x0,x5
|
|
ldr x1,qAdrsZoneConv
|
|
bl conversion10 // call décimal conversion
|
|
mov x0,x7
|
|
ldr x1,qAdrsZoneConv // insert conversion in message
|
|
bl strInsertAtCharInc
|
|
mov x7,x0
|
|
cmp x6,#1
|
|
ldr x1,qAdrszMessPrime
|
|
ldr x8,qAdrszMessSpace
|
|
csel x1,x1,x8,eq
|
|
mov x0,x7
|
|
bl strInsertAtCharInc
|
|
bl affichageMess // display message
|
|
|
|
add x4,x4,#1 // increment number
|
|
cmp x4,#MAXI // maxi ?
|
|
ble 1b // and loop
|
|
|
|
mov x4,#2 // first number
|
|
mov x5,#0 // prime counter
|
|
ldr x6,iCst1000 // load constantes
|
|
ldr x7,iCst10000
|
|
ldr x8,iCst100000
|
|
2:
|
|
mov x0,x4
|
|
bl isPrime
|
|
cmp x0,#0
|
|
beq 3f
|
|
add x5,x5,#1
|
|
3:
|
|
add x4,x4,#1
|
|
cmp x4,#100
|
|
bne 4f
|
|
mov x0,#100
|
|
mov x1,x5
|
|
bl displayCounter
|
|
b 7f
|
|
4:
|
|
cmp x4,x6 // 1000
|
|
bne 5f
|
|
mov x0,x6
|
|
mov x1,x5
|
|
bl displayCounter
|
|
b 7f
|
|
5:
|
|
cmp x4,x7 // 10000
|
|
bne 6f
|
|
mov x0,x7
|
|
mov x1,x5
|
|
bl displayCounter
|
|
b 7f
|
|
6:
|
|
cmp x4,x8 // 100000
|
|
bne 7f
|
|
mov x0,x8
|
|
mov x1,x5
|
|
bl displayCounter
|
|
7:
|
|
cmp x4,x8
|
|
ble 2b // and loop
|
|
|
|
100: // standard end of the program
|
|
mov x0, #0 // return code
|
|
mov x8,EXIT
|
|
svc #0 // perform the system call
|
|
qAdrszCarriageReturn: .quad szCarriageReturn
|
|
qAdrsZoneConv: .quad sZoneConv
|
|
qAdrszMessNumber: .quad szMessNumber
|
|
qAdrszMessCounterPrime: .quad szMessCounterPrime
|
|
qAdrszMessPrime: .quad szMessPrime
|
|
qAdrszMessSpace: .quad szMessSpace
|
|
iCst1000: .quad 1000
|
|
iCst10000: .quad 10000
|
|
iCst100000: .quad 100000
|
|
/******************************************************************/
|
|
/* display counter */
|
|
/******************************************************************/
|
|
/* x0 contains limit */
|
|
/* x1 contains counter */
|
|
displayCounter:
|
|
stp x1,lr,[sp,-16]! // save registers
|
|
stp x2,x3,[sp,-16]! // save registers
|
|
mov x2,x1
|
|
ldr x1,qAdrsZoneConv
|
|
bl conversion10 // call décimal conversion
|
|
ldr x0,qAdrszMessCounterPrime
|
|
ldr x1,qAdrsZoneConv // insert conversion in message
|
|
bl strInsertAtCharInc
|
|
mov x3,x0
|
|
mov x0,x2
|
|
ldr x1,qAdrsZoneConv
|
|
bl conversion10 // call décimal conversion
|
|
mov x0,x3
|
|
ldr x1,qAdrsZoneConv // insert conversion in message
|
|
bl strInsertAtCharInc
|
|
bl affichageMess
|
|
100:
|
|
ldp x2,x3,[sp],16 // restaur registers
|
|
ldp x1,lr,[sp],16 // restaur registers
|
|
ret
|
|
/******************************************************************/
|
|
/* compute totient of number */
|
|
/******************************************************************/
|
|
/* x0 contains number */
|
|
totient:
|
|
stp x1,lr,[sp,-16]! // save registers
|
|
stp x2,x3,[sp,-16]! // save registers
|
|
stp x4,x5,[sp,-16]! // save registers
|
|
mov x4,x0 // totient
|
|
mov x5,x0 // save number
|
|
mov x1,#0 // for first divisor
|
|
1: // begin loop
|
|
mul x3,x1,x1 // compute square
|
|
cmp x3,x5 // compare number
|
|
bgt 4f // end
|
|
add x1,x1,#2 // next divisor
|
|
udiv x2,x5,x1
|
|
msub x3,x1,x2,x5 // compute remainder
|
|
cmp x3,#0 // remainder null ?
|
|
bne 3f
|
|
2: // begin loop 2
|
|
udiv x2,x5,x1
|
|
msub x3,x1,x2,x5 // compute remainder
|
|
cmp x3,#0
|
|
csel x5,x2,x5,eq // new value = quotient
|
|
beq 2b
|
|
|
|
udiv x2,x4,x1 // divide totient
|
|
sub x4,x4,x2 // compute new totient
|
|
3:
|
|
cmp x1,#2 // first divisor ?
|
|
mov x0,1
|
|
csel x1,x0,x1,eq // divisor = 1
|
|
b 1b // and loop
|
|
4:
|
|
cmp x5,#1 // final value > 1
|
|
ble 5f
|
|
mov x0,x4 // totient
|
|
mov x1,x5 // divide by value
|
|
udiv x2,x4,x5 // totient divide by value
|
|
sub x4,x4,x2 // compute new totient
|
|
5:
|
|
|
|
mov x0,x4
|
|
100:
|
|
ldp x4,x5,[sp],16 // restaur registers
|
|
ldp x2,x3,[sp],16 // restaur registers
|
|
ldp x1,lr,[sp],16 // restaur registers
|
|
ret
|
|
/***************************************************/
|
|
/* Verification si un nombre est premier */
|
|
/***************************************************/
|
|
/* x0 contient le nombre à verifier */
|
|
/* x0 retourne 1 si premier 0 sinon */
|
|
isPrime:
|
|
stp x1,lr,[sp,-16]! // save registres
|
|
stp x2,x3,[sp,-16]! // save registres
|
|
mov x2,x0
|
|
sub x1,x0,#1
|
|
cmp x2,0
|
|
beq 99f // retourne zéro
|
|
cmp x2,2 // pour 1 et 2 retourne 1
|
|
ble 2f
|
|
mov x0,#2
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
cmp x2,3
|
|
beq 2f
|
|
mov x0,#3
|
|
bl moduloPur64
|
|
blt 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f
|
|
|
|
cmp x2,5
|
|
beq 2f
|
|
mov x0,#5
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
|
|
cmp x2,7
|
|
beq 2f
|
|
mov x0,#7
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
|
|
cmp x2,11
|
|
beq 2f
|
|
mov x0,#11
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
|
|
cmp x2,13
|
|
beq 2f
|
|
mov x0,#13
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
|
|
cmp x2,17
|
|
beq 2f
|
|
mov x0,#17
|
|
bl moduloPur64
|
|
bcs 100f // erreur overflow
|
|
cmp x0,#1
|
|
bne 99f // Pas premier
|
|
2:
|
|
cmn x0,0 // carry à zero pas d'erreur
|
|
mov x0,1 // premier
|
|
b 100f
|
|
99:
|
|
cmn x0,0 // carry à zero pas d'erreur
|
|
mov x0,#0 // Pas premier
|
|
100:
|
|
ldp x2,x3,[sp],16 // restaur des 2 registres
|
|
ldp x1,lr,[sp],16 // restaur des 2 registres
|
|
ret // retour adresse lr x30
|
|
|
|
/**************************************************************/
|
|
/********************************************************/
|
|
/* Calcul modulo de b puissance e modulo m */
|
|
/* Exemple 4 puissance 13 modulo 497 = 445 */
|
|
/********************************************************/
|
|
/* x0 nombre */
|
|
/* x1 exposant */
|
|
/* x2 modulo */
|
|
moduloPur64:
|
|
stp x1,lr,[sp,-16]! // save registres
|
|
stp x3,x4,[sp,-16]! // save registres
|
|
stp x5,x6,[sp,-16]! // save registres
|
|
stp x7,x8,[sp,-16]! // save registres
|
|
stp x9,x10,[sp,-16]! // save registres
|
|
cbz x0,100f
|
|
cbz x1,100f
|
|
mov x8,x0
|
|
mov x7,x1
|
|
mov x6,1 // resultat
|
|
udiv x4,x8,x2
|
|
msub x9,x4,x2,x8 // contient le reste
|
|
1:
|
|
tst x7,1
|
|
beq 2f
|
|
mul x4,x9,x6
|
|
umulh x5,x9,x6
|
|
//cbnz x5,99f
|
|
mov x6,x4
|
|
mov x0,x6
|
|
mov x1,x5
|
|
bl divisionReg128U
|
|
cbnz x1,99f // overflow
|
|
mov x6,x3
|
|
2:
|
|
mul x8,x9,x9
|
|
umulh x5,x9,x9
|
|
mov x0,x8
|
|
mov x1,x5
|
|
bl divisionReg128U
|
|
cbnz x1,99f // overflow
|
|
mov x9,x3
|
|
lsr x7,x7,1
|
|
cbnz x7,1b
|
|
mov x0,x6 // result
|
|
cmn x0,0 // carry à zero pas d'erreur
|
|
b 100f
|
|
99:
|
|
ldr x0,qAdrszMessOverflow
|
|
bl affichageMess
|
|
cmp x0,0 // carry à un car erreur
|
|
mov x0,-1 // code erreur
|
|
|
|
100:
|
|
ldp x9,x10,[sp],16 // restaur des 2 registres
|
|
ldp x7,x8,[sp],16 // restaur des 2 registres
|
|
ldp x5,x6,[sp],16 // restaur des 2 registres
|
|
ldp x3,x4,[sp],16 // restaur des 2 registres
|
|
ldp x1,lr,[sp],16 // restaur des 2 registres
|
|
ret // retour adresse lr x30
|
|
qAdrszMessOverflow: .quad szMessOverflow
|
|
/***************************************************/
|
|
/* division d un nombre de 128 bits par un nombre de 64 bits */
|
|
/***************************************************/
|
|
/* x0 contient partie basse dividende */
|
|
/* x1 contient partie haute dividente */
|
|
/* x2 contient le diviseur */
|
|
/* x0 retourne partie basse quotient */
|
|
/* x1 retourne partie haute quotient */
|
|
/* x3 retourne le reste */
|
|
divisionReg128U:
|
|
stp x6,lr,[sp,-16]! // save registres
|
|
stp x4,x5,[sp,-16]! // save registres
|
|
mov x5,#0 // raz du reste R
|
|
mov x3,#128 // compteur de boucle
|
|
mov x4,#0 // dernier bit
|
|
1:
|
|
lsl x5,x5,#1 // on decale le reste de 1
|
|
tst x1,1<<63 // test du bit le plus à gauche
|
|
lsl x1,x1,#1 // on decale la partie haute du quotient de 1
|
|
beq 2f
|
|
orr x5,x5,#1 // et on le pousse dans le reste R
|
|
2:
|
|
tst x0,1<<63
|
|
lsl x0,x0,#1 // puis on decale la partie basse
|
|
beq 3f
|
|
orr x1,x1,#1 // et on pousse le bit de gauche dans la partie haute
|
|
3:
|
|
orr x0,x0,x4 // position du dernier bit du quotient
|
|
mov x4,#0 // raz du bit
|
|
cmp x5,x2
|
|
blt 4f
|
|
sub x5,x5,x2 // on enleve le diviseur du reste
|
|
mov x4,#1 // dernier bit à 1
|
|
4:
|
|
// et boucle
|
|
subs x3,x3,#1
|
|
bgt 1b
|
|
lsl x1,x1,#1 // on decale le quotient de 1
|
|
tst x0,1<<63
|
|
lsl x0,x0,#1 // puis on decale la partie basse
|
|
beq 5f
|
|
orr x1,x1,#1
|
|
5:
|
|
orr x0,x0,x4 // position du dernier bit du quotient
|
|
mov x3,x5
|
|
100:
|
|
ldp x4,x5,[sp],16 // restaur des 2 registres
|
|
ldp x6,lr,[sp],16 // restaur des 2 registres
|
|
ret // retour adresse lr x30
|
|
|
|
|
|
/***************************************************/
|
|
/* ROUTINES INCLUDE */
|
|
/***************************************************/
|
|
.include "../includeARM64.inc"
|