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# Instructions | ||
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Convert a sequence of digits in one base, representing a number, into a sequence of digits in another base, representing the same number. | ||
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~~~~exercism/note | ||
Try to implement the conversion yourself. | ||
Do not use something else to perform the conversion for you. | ||
~~~~ | ||
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## About [Positional Notation][positional-notation] | ||
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In positional notation, a number in base **b** can be understood as a linear combination of powers of **b**. | ||
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The number 42, _in base 10_, means: | ||
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`(4 × 10¹) + (2 × 10⁰)` | ||
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The number 101010, _in base 2_, means: | ||
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`(1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)` | ||
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The number 1120, _in base 3_, means: | ||
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`(1 × 3³) + (1 × 3²) + (2 × 3¹) + (0 × 3⁰)` | ||
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_Yes. Those three numbers above are exactly the same. Congratulations!_ | ||
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[positional-notation]: https://en.wikipedia.org/wiki/Positional_notation |
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# Introduction | ||
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You've just been hired as professor of mathematics. | ||
Your first week went well, but something is off in your second week. | ||
The problem is that every answer given by your students is wrong! | ||
Luckily, your math skills have allowed you to identify the problem: the student answers _are_ correct, but they're all in base 2 (binary)! | ||
Amazingly, it turns out that each week, the students use a different base. | ||
To help you quickly verify the student answers, you'll be building a tool to translate between bases. |
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{ | ||
"authors": [ | ||
"keiravillekode" | ||
], | ||
"files": { | ||
"solution": [ | ||
"all_your_base.s" | ||
], | ||
"test": [ | ||
"all_your_base_test.c" | ||
], | ||
"example": [ | ||
".meta/example.s" | ||
] | ||
}, | ||
"blurb": "Convert a number, represented as a sequence of digits in one base, to any other base." | ||
} |
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.equ BAD_BASE, -1 | ||
.equ BAD_DIGIT, -2 | ||
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.text | ||
.globl rebase | ||
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/* extern int rebase(int32_t in_base, const int32_t* in_digits, int in_digit_count, int32_t out_base, int32_t* out_digits); */ | ||
rebase: | ||
cmp w0, #2 /* minimum valid base */ | ||
blt .bad_base | ||
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cmp w3, #2 | ||
blt .bad_base | ||
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mov x5, #0 /* value represented by digits */ | ||
mov x7, x4 /* output pointer */ | ||
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.read: | ||
cbz x2, .write | ||
ldr w6, [x1], 4 /* load input digit, post-increment */ | ||
cmp w6, w0 | ||
bhs .bad_digit /* unsigned >= */ | ||
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madd x5, x0, x5, x6 /* in_base * value + digit */ | ||
sub x2, x2, #1 /* decrement number of digits remaining */ | ||
b .read | ||
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.bad_base: | ||
mov x0, BAD_BASE | ||
ret | ||
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.bad_digit: | ||
mov x0, BAD_DIGIT | ||
ret | ||
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.write: | ||
udiv x1, x5, x3 /* divide value by out_base */ | ||
msub x6, x1, x3, x5 /* remainder, i.e. output digit */ | ||
str w6, [x7], #4 /* store, post-increment */ | ||
mov x5, x1 | ||
cbnz x5, .write /* loop until value is 0 */ | ||
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sub x0, x7, x4 /* length of output, in bytes */ | ||
lsr x0, x0, #2 | ||
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.reverse: | ||
ldr w1, [x7, #-4]! /* load, pre-decrement */ | ||
cmp x7, x4 | ||
beq .return | ||
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ldr w2, [x4] | ||
str w2, [x7] | ||
str w1, [x4], #4 /* store, post-increment */ | ||
cmp x7, x4 | ||
bne .reverse | ||
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.return: | ||
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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[5ce422f9-7a4b-4f44-ad29-49c67cb32d2c] | ||
description = "single bit one to decimal" | ||
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[0cc3fea8-bb79-46ac-a2ab-5a2c93051033] | ||
description = "binary to single decimal" | ||
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[f12db0f9-0d3d-42c2-b3ba-e38cb375a2b8] | ||
description = "single decimal to binary" | ||
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[2c45cf54-6da3-4748-9733-5a3c765d925b] | ||
description = "binary to multiple decimal" | ||
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[65ddb8b4-8899-4fcc-8618-181b2cf0002d] | ||
description = "decimal to binary" | ||
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[8d418419-02a7-4824-8b7a-352d33c6987e] | ||
description = "trinary to hexadecimal" | ||
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[d3901c80-8190-41b9-bd86-38d988efa956] | ||
description = "hexadecimal to trinary" | ||
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[5d42f85e-21ad-41bd-b9be-a3e8e4258bbf] | ||
description = "15-bit integer" | ||
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[d68788f7-66dd-43f8-a543-f15b6d233f83] | ||
description = "empty list" | ||
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[5e27e8da-5862-4c5f-b2a9-26c0382b6be7] | ||
description = "single zero" | ||
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[2e1c2573-77e4-4b9c-8517-6c56c5bcfdf2] | ||
description = "multiple zeros" | ||
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[3530cd9f-8d6d-43f5-bc6e-b30b1db9629b] | ||
description = "leading zeros" | ||
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[a6b476a1-1901-4f2a-92c4-4d91917ae023] | ||
description = "input base is one" | ||
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[e21a693a-7a69-450b-b393-27415c26a016] | ||
description = "input base is zero" | ||
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[54a23be5-d99e-41cc-88e0-a650ffe5fcc2] | ||
description = "input base is negative" | ||
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[9eccf60c-dcc9-407b-95d8-c37b8be56bb6] | ||
description = "negative digit" | ||
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[232fa4a5-e761-4939-ba0c-ed046cd0676a] | ||
description = "invalid positive digit" | ||
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[14238f95-45da-41dc-95ce-18f860b30ad3] | ||
description = "output base is one" | ||
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[73dac367-da5c-4a37-95fe-c87fad0a4047] | ||
description = "output base is zero" | ||
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[13f81f42-ff53-4e24-89d9-37603a48ebd9] | ||
description = "output base is negative" | ||
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[0e6c895d-8a5d-4868-a345-309d094cfe8d] | ||
description = "both bases are negative" |
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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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.equ BAD_BASE, -1 | ||
.equ BAD_DIGIT, -2 | ||
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.text | ||
.globl rebase | ||
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rebase: | ||
ret |
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