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# Instructions | ||
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Given a number determine whether or not it is valid per the Luhn formula. | ||
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The [Luhn algorithm][luhn] is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers. | ||
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The task is to check if a given string is valid. | ||
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## Validating a Number | ||
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Strings of length 1 or less are not valid. | ||
Spaces are allowed in the input, but they should be stripped before checking. | ||
All other non-digit characters are disallowed. | ||
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### Example 1: valid credit card number | ||
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```text | ||
4539 3195 0343 6467 | ||
``` | ||
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The first step of the Luhn algorithm is to double every second digit, starting from the right. | ||
We will be doubling | ||
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```text | ||
4539 3195 0343 6467 | ||
↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ (double these) | ||
``` | ||
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If doubling the number results in a number greater than 9 then subtract 9 from the product. | ||
The results of our doubling: | ||
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```text | ||
8569 6195 0383 3437 | ||
``` | ||
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Then sum all of the digits: | ||
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```text | ||
8+5+6+9+6+1+9+5+0+3+8+3+3+4+3+7 = 80 | ||
``` | ||
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If the sum is evenly divisible by 10, then the number is valid. | ||
This number is valid! | ||
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### Example 2: invalid credit card number | ||
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```text | ||
8273 1232 7352 0569 | ||
``` | ||
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Double the second digits, starting from the right | ||
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```text | ||
7253 2262 5312 0539 | ||
``` | ||
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Sum the digits | ||
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```text | ||
7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57 | ||
``` | ||
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57 is not evenly divisible by 10, so this number is not valid. | ||
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[luhn]: https://en.wikipedia.org/wiki/Luhn_algorithm |
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{ | ||
"authors": [ | ||
"keiravillekode" | ||
], | ||
"files": { | ||
"solution": [ | ||
"luhn.s" | ||
], | ||
"test": [ | ||
"luhn_test.c" | ||
], | ||
"example": [ | ||
".meta/example.s" | ||
] | ||
}, | ||
"blurb": "Given a number determine whether or not it is valid per the Luhn formula.", | ||
"source": "The Luhn Algorithm on Wikipedia", | ||
"source_url": "https://en.wikipedia.org/wiki/Luhn_algorithm" | ||
} |
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.text | ||
.globl valid | ||
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/* extern int valid(const char *value); */ | ||
valid: | ||
mov x1, x0 | ||
mov x2, #0 /* digit count */ | ||
mov x3, #0 /* digit sum */ | ||
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.first_scan: | ||
ldrb w4, [x1], #1 /* load byte, post-increment */ | ||
cbz w4, .end_first_scan | ||
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cmp w4, #' ' | ||
beq .first_scan | ||
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sub w4, w4, #'0' | ||
cmp w4, #10 | ||
bhs .reject /* unsigned >= */ | ||
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add x2, x2, #1 | ||
b .first_scan | ||
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.end_first_scan: | ||
mov x1, x0 | ||
cmp x2, #2 | ||
blt .reject | ||
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.second_scan: | ||
ldrb w4, [x1], #1 /* load byte, post-increment */ | ||
cbz w4, .end_second_scan | ||
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cmp w4, #' ' | ||
beq .second_scan | ||
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sub w4, w4, #'0' | ||
tst x2, #1 | ||
bne .add | ||
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lsl w4, w4, #1 /* multiply by 2 */ | ||
cmp w4, #10 | ||
blo .add /* unsigned < */ | ||
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sub w4, w4, #9 | ||
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.add: | ||
add x3, x3, x4 | ||
sub x2, x2, #1 | ||
b .second_scan | ||
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.end_second_scan: | ||
mov x6, #10 | ||
udiv x7, x3, x6 /* divide value by 10 */ | ||
msub x0, x7, x6, x3 /* remainder */ | ||
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cmp x0, xzr | ||
cset x0, eq | ||
ret | ||
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.reject: | ||
mov x0, #0 | ||
ret |
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# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[792a7082-feb7-48c7-b88b-bbfec160865e] | ||
description = "single digit strings can not be valid" | ||
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[698a7924-64d4-4d89-8daa-32e1aadc271e] | ||
description = "a single zero is invalid" | ||
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[73c2f62b-9b10-4c9f-9a04-83cee7367965] | ||
description = "a simple valid SIN that remains valid if reversed" | ||
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[9369092e-b095-439f-948d-498bd076be11] | ||
description = "a simple valid SIN that becomes invalid if reversed" | ||
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[8f9f2350-1faf-4008-ba84-85cbb93ffeca] | ||
description = "a valid Canadian SIN" | ||
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[1cdcf269-6560-44fc-91f6-5819a7548737] | ||
description = "invalid Canadian SIN" | ||
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[656c48c1-34e8-4e60-9a5a-aad8a367810a] | ||
description = "invalid credit card" | ||
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[20e67fad-2121-43ed-99a8-14b5b856adb9] | ||
description = "invalid long number with an even remainder" | ||
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[7e7c9fc1-d994-457c-811e-d390d52fba5e] | ||
description = "invalid long number with a remainder divisible by 5" | ||
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[ad2a0c5f-84ed-4e5b-95da-6011d6f4f0aa] | ||
description = "valid number with an even number of digits" | ||
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[ef081c06-a41f-4761-8492-385e13c8202d] | ||
description = "valid number with an odd number of spaces" | ||
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[bef66f64-6100-4cbb-8f94-4c9713c5e5b2] | ||
description = "valid strings with a non-digit added at the end become invalid" | ||
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[2177e225-9ce7-40f6-b55d-fa420e62938e] | ||
description = "valid strings with punctuation included become invalid" | ||
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[ebf04f27-9698-45e1-9afe-7e0851d0fe8d] | ||
description = "valid strings with symbols included become invalid" | ||
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[08195c5e-ce7f-422c-a5eb-3e45fece68ba] | ||
description = "single zero with space is invalid" | ||
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[12e63a3c-f866-4a79-8c14-b359fc386091] | ||
description = "more than a single zero is valid" | ||
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[ab56fa80-5de8-4735-8a4a-14dae588663e] | ||
description = "input digit 9 is correctly converted to output digit 9" | ||
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[b9887ee8-8337-46c5-bc45-3bcab51bc36f] | ||
description = "very long input is valid" | ||
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[8a7c0e24-85ea-4154-9cf1-c2db90eabc08] | ||
description = "valid luhn with an odd number of digits and non zero first digit" | ||
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[39a06a5a-5bad-4e0f-b215-b042d46209b1] | ||
description = "using ascii value for non-doubled non-digit isn't allowed" | ||
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[f94cf191-a62f-4868-bc72-7253114aa157] | ||
description = "using ascii value for doubled non-digit isn't allowed" | ||
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[8b72ad26-c8be-49a2-b99c-bcc3bf631b33] | ||
description = "non-numeric, non-space char in the middle with a sum that's divisible by 10 isn't allowed" |
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AS = aarch64-linux-gnu-as | ||
CC = aarch64-linux-gnu-gcc | ||
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CFLAGS = -g -Wall -Wextra -pedantic -Werror | ||
LDFLAGS = | ||
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ALL_LDFLAGS = -pie -Wl,--fatal-warnings | ||
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ALL_CFLAGS = -std=c99 -fPIE $(CFLAGS) | ||
ALL_LDFLAGS += $(LDFLAGS) | ||
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C_OBJS = $(patsubst %.c,%.o,$(wildcard *.c)) | ||
AS_OBJS = $(patsubst %.s,%.o,$(wildcard *.s)) | ||
ALL_OBJS = $(filter-out example.o,$(C_OBJS) $(AS_OBJS) vendor/unity.o) | ||
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CC_CMD = $(CC) $(ALL_CFLAGS) -c -o $@ $< | ||
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all: tests | ||
qemu-aarch64 -L /usr/aarch64-linux-gnu ./$< | ||
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tests: $(ALL_OBJS) | ||
@$(CC) $(ALL_CFLAGS) $(ALL_LDFLAGS) -o $@ $(ALL_OBJS) | ||
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%.o: %.s | ||
@$(AS) -o $@ $< | ||
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%.o: %.c | ||
@$(CC_CMD) | ||
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vendor/unity.o: vendor/unity.c vendor/unity.h vendor/unity_internals.h | ||
@$(CC_CMD) | ||
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clean: | ||
@rm -f *.o vendor/*.o tests | ||
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.PHONY: all clean |
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.text | ||
.globl valid | ||
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valid: | ||
ret |
Oops, something went wrong.