Add all-your-base exercise (#47)

Author: keiravillekode

config.json

@@ -214,6 +214,14 @@
         "prerequisites": [],
         "difficulty": 3
       },
+      {
+        "slug": "all-your-base",
+        "name": "All Your Base",
+        "uuid": "8e88bcf3-a492-4a09-8c3c-33718446ec1a",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
+      },
       {
         "slug": "armstrong-numbers",
         "name": "Armstrong Numbers",

exercises/practice/all-your-base/.docs/instructions.md

@@ -0,0 +1,28 @@
+# Instructions
+
+Convert a sequence of digits in one base, representing a number, into a sequence of digits in another base, representing the same number.
+
+~~~~exercism/note
+Try to implement the conversion yourself.
+Do not use something else to perform the conversion for you.
+~~~~
+
+## About [Positional Notation][positional-notation]
+
+In positional notation, a number in base **b** can be understood as a linear combination of powers of **b**.
+
+The number 42, _in base 10_, means:
+
+`(4 × 10¹) + (2 × 10⁰)`
+
+The number 101010, _in base 2_, means:
+
+`(1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)`
+
+The number 1120, _in base 3_, means:
+
+`(1 × 3³) + (1 × 3²) + (2 × 3¹) + (0 × 3⁰)`
+
+_Yes. Those three numbers above are exactly the same. Congratulations!_
+
+[positional-notation]: https://en.wikipedia.org/wiki/Positional_notation

exercises/practice/all-your-base/.docs/introduction.md

@@ -0,0 +1,8 @@
+# Introduction
+
+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.

exercises/practice/all-your-base/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "all_your_base.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "blurb": "Convert a number, represented as a sequence of digits in one base, to any other base."
+}

exercises/practice/all-your-base/.meta/example.fut

@@ -0,0 +1,17 @@
+def unify (input_base: i32) (digits: []i32): i32 =
+  let n = loop n = 0 for digit in digits do
+    assert (digit >= 0 && digit < input_base) (n * input_base + digit)
+  in
+    n
+
+def separate (output_base: i32) (number: i32): []i32 =
+  if number == 0 then [0] else
+  let (_, a, i) = loop (n, a, i) = (number, replicate 32 0, 32) while n > 0 do
+    (n / output_base, a with [i - 1] = n % output_base, i - 1)
+  in
+    a[i:]
+
+def rebase (input_base: i32) (digits: []i32) (output_base: i32): []i32 =
+  assert (input_base >= 2 && output_base >= 2) digits
+  |> unify input_base
+  |> separate output_base

exercises/practice/all-your-base/.meta/tests.toml

@@ -0,0 +1,73 @@
+# 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.
+
+[5ce422f9-7a4b-4f44-ad29-49c67cb32d2c]
+description = "single bit one to decimal"
+
+[0cc3fea8-bb79-46ac-a2ab-5a2c93051033]
+description = "binary to single decimal"
+
+[f12db0f9-0d3d-42c2-b3ba-e38cb375a2b8]
+description = "single decimal to binary"
+
+[2c45cf54-6da3-4748-9733-5a3c765d925b]
+description = "binary to multiple decimal"
+
+[65ddb8b4-8899-4fcc-8618-181b2cf0002d]
+description = "decimal to binary"
+
+[8d418419-02a7-4824-8b7a-352d33c6987e]
+description = "trinary to hexadecimal"
+
+[d3901c80-8190-41b9-bd86-38d988efa956]
+description = "hexadecimal to trinary"
+
+[5d42f85e-21ad-41bd-b9be-a3e8e4258bbf]
+description = "15-bit integer"
+
+[d68788f7-66dd-43f8-a543-f15b6d233f83]
+description = "empty list"
+
+[5e27e8da-5862-4c5f-b2a9-26c0382b6be7]
+description = "single zero"
+
+[2e1c2573-77e4-4b9c-8517-6c56c5bcfdf2]
+description = "multiple zeros"
+
+[3530cd9f-8d6d-43f5-bc6e-b30b1db9629b]
+description = "leading zeros"
+
+[a6b476a1-1901-4f2a-92c4-4d91917ae023]
+description = "input base is one"
+
+[e21a693a-7a69-450b-b393-27415c26a016]
+description = "input base is zero"
+
+[54a23be5-d99e-41cc-88e0-a650ffe5fcc2]
+description = "input base is negative"
+
+[9eccf60c-dcc9-407b-95d8-c37b8be56bb6]
+description = "negative digit"
+
+[232fa4a5-e761-4939-ba0c-ed046cd0676a]
+description = "invalid positive digit"
+
+[14238f95-45da-41dc-95ce-18f860b30ad3]
+description = "output base is one"
+
+[73dac367-da5c-4a37-95fe-c87fad0a4047]
+description = "output base is zero"
+
+[13f81f42-ff53-4e24-89d9-37603a48ebd9]
+description = "output base is negative"
+
+[0e6c895d-8a5d-4868-a345-309d094cfe8d]
+description = "both bases are negative"

exercises/practice/all-your-base/all_your_base.fut

@@ -0,0 +1 @@
+def rebase (input_base: i32) (digits: []i32) (output_base: i32): []i32 = ???

exercises/practice/all-your-base/test.fut

@@ -0,0 +1,109 @@
+import "all_your_base"
+
+-- single bit one to decimal
+-- ==
+-- input { 2 [1] 10 }
+-- output { [1] }
+
+-- binary to single decimal
+-- ==
+-- input { 2 [1, 0, 1] 10 }
+-- output { [5] }
+
+-- single decimal to binary
+-- ==
+-- input { 10 [5] 2 }
+-- output { [1, 0, 1] }
+
+-- binary to multiple decimal
+-- ==
+-- input { 2 [1, 0, 1, 0, 1, 0] 10 }
+-- output { [4, 2] }
+
+-- decimal to binary
+-- ==
+-- input { 10 [4, 2] 2 }
+-- output { [1, 0, 1, 0, 1, 0] }
+
+-- trinary to hexadecimal
+-- ==
+-- input { 3 [1, 1, 2, 0] 16 }
+-- output { [2, 10] }
+
+-- hexadecimal to trinary
+-- ==
+-- input { 16 [2, 10] 3 }
+-- output { [1, 1, 2, 0] }
+
+-- 15-bit integer
+-- ==
+-- input { 97 [3, 46, 60] 73 }
+-- output { [6, 10, 45] }
+
+-- empty list
+-- ==
+-- input { 2 empty([0]i32) 10 }
+-- output { [0] }
+
+-- single zero
+-- ==
+-- input { 10 [0] 2 }
+-- output { [0] }
+
+-- multiple zeros
+-- ==
+-- input { 10 [0, 0, 0] 2 }
+-- output { [0] }
+
+-- leading zeros
+-- ==
+-- input { 7 [0, 6, 0] 10 }
+-- output { [4, 2] }
+
+-- input base is one
+-- ==
+-- input { 1 [0] 10 }
+-- error: Error*
+
+-- input base is zero
+-- ==
+-- input { 0 empty([0]i32) 10 }
+-- error: Error*
+
+-- input base is negative
+-- ==
+-- input { -2 [1] 10 }
+-- error: Error*
+
+-- negative digit
+-- ==
+-- input { 2 [1, -1, 1, 0, 1, 0] 10 }
+-- error: Error*
+
+-- invalid positive digit
+-- ==
+-- input { 2 [1, 2, 1, 0, 1, 0] 10 }
+-- error: Error*
+
+-- output base is one
+-- ==
+-- input { 2 [1, 0, 1, 0, 1, 0] 1 }
+-- error: Error*
+
+-- output base is zero
+-- ==
+-- input { 10 [7] 0 }
+-- error: Error*
+
+-- output base is negative
+-- ==
+-- input { 2 [1] -7 }
+-- error: Error*
+
+-- both bases are negative
+-- ==
+-- input { -2 [1] -7 }
+-- error: Error*
+
+def main (input_base: i32) (digits: []i32) (output_base: i32): []i32 =
+  rebase input_base digits output_base