How to resolve the algorithm 9 billion names of God the integer step by step in the AArch64 Assembly programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm 9 billion names of God the integer step by step in the AArch64 Assembly programming language
Table of Contents
Problem Statement
This task is a variation of the short story by Arthur C. Clarke. (Solvers should be aware of the consequences of completing this task.) In detail, to specify what is meant by a “name”:
Display the first 25 rows of a number triangle which begins: Where row
n
{\displaystyle n}
corresponds to integer
n
{\displaystyle n}
, and each column
C
{\displaystyle C}
in row
m
{\displaystyle m}
from left to right corresponds to the number of names beginning with
C
{\displaystyle C}
. A function
G ( n )
{\displaystyle G(n)}
should return the sum of the
n
{\displaystyle n}
-th row. Demonstrate this function by displaying:
G ( 23 )
{\displaystyle G(23)}
,
G ( 123 )
{\displaystyle G(123)}
,
G ( 1234 )
{\displaystyle G(1234)}
, and
G ( 12345 )
{\displaystyle G(12345)}
.
Optionally note that the sum of the
n
{\displaystyle n}
-th row
P ( n )
{\displaystyle P(n)}
is the integer partition function. Demonstrate this is equivalent to
G ( n )
{\displaystyle G(n)}
by displaying:
P ( 23 )
{\displaystyle P(23)}
,
P ( 123 )
{\displaystyle P(123)}
,
P ( 1234 )
{\displaystyle P(1234)}
, and
P ( 12345 )
{\displaystyle P(12345)}
.
If your environment is able, plot
P ( n )
{\displaystyle P(n)}
against
n
{\displaystyle n}
for
n
1 … 999
{\displaystyle n=1\ldots 999}
.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm 9 billion names of God the integer step by step in the AArch64 Assembly programming language
Source code in the aarch64 programming language
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program integerName64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ MAXI, 524
/*********************************/
/* Initialized data */
/*********************************/
.data
sMessResult: .asciz "Total : @ pour @ \n"
szMessError: .asciz "Number too large !!.\n"
szCarriageReturn: .asciz "\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
sZoneConv: .skip 24
tbNames: .skip 8 * MAXI
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
mov x0,#5
bl functionG
mov x0,#23
bl functionG
mov x0,#123
bl functionG
mov x0,#524
bl functionG
mov x0,#1234
bl functionG
100: // standard end of the program
mov x0, #0 // return code
mov x8, #EXIT // request to exit program
svc #0 // perform the system call
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessResult: .quad sMessResult
qAdrtbNames: .quad tbNames
qAdrsZoneConv: .quad sZoneConv
/******************************************************************/
/* compute function G */
/******************************************************************/
/* x0 contains N */
functionG:
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
cmp x0,#MAXI + 1
bge 2f
mov x3,x0
mov x2,#1
1: // loop compute every item
mov x0,x2
bl computeNumber
add x2,x2,#1
cmp x2,x3
ble 1b
ldr x1,qAdrsZoneConv // result display
bl conversion10 // call decimal conversion
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv // insert conversion in message
bl strInsertAtCharInc
mov x4,x0
mov x0,x3
ldr x1,qAdrsZoneConv // result display
bl conversion10 // call decimal conversion
mov x0,x4
ldr x1,qAdrsZoneConv // insert conversion in message
bl strInsertAtCharInc
bl affichageMess
mov x0,#0
b 100f
2:
ldr x0,qAdrszMessError
bl affichageMess
mov x0,#-1
100:
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrszMessError: .quad szMessError
/******************************************************************/
/* random door test strategy */
/******************************************************************/
/* x0 contains N */
computeNumber:
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
ldr x6,qAdrtbNames // table address
mov x1,#1
str x1,[x6] // init item 0
mov x1,#0
str x1,[x6,x0,lsl #3] // init item N
mov x2,#1 // indice
1:
add x3,x2,x2, lsl #1
sub x4,x3,#1
mul x4,x2,x4
lsr x4,x4,#1
subs x3,x0,x4 // compute new indice
blt 90f
tst x2,#1 // indice owen ?
beq 2f
ldr x4,[x6,x3,lsl #3]
ldr x5,[x6,x0,lsl #3]
add x5,x5,x4 // addition
str x5,[x6,x0,lsl #3]
b 3f
2: // else substrac
ldr x4,[x6,x3,lsl #3]
ldr x5,[x6,x0,lsl #3]
sub x5,x5,x4
str x5,[x6,x0,lsl #3]
3:
subs x3,x3,x2 // compute new indice
blt 90f
tst x2,#1 // owen ?
beq 4f
ldr x4,[x6,x3,lsl #3]
ldr x5,[x6,x0,lsl #3]
add x5,x5,x4
str x5,[x6,x0,lsl #3]
b 5f
4:
ldr x4,[x6,x3,lsl #3]
ldr x5,[x6,x0,lsl #3]
sub x5,x5,x4
str x5,[x6,x0,lsl #3]
5:
add x2,x2,#1
cmp x2,x0
ble 1b
90:
ldr x0,[x6,x0,lsl #3] // return last item of table
100:
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
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