Add difference-of-squares exercise (#70)

config.json

@@ -58,6 +58,14 @@
         "prerequisites": [],
         "difficulty": 2
       },
+      {
+        "slug": "difference-of-squares",
+        "name": "Difference of Squares",
+        "uuid": "88ebf02b-e19b-4058-a48b-2e1560345dd0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 3
+      },
       {
         "slug": "eliuds-eggs",
         "name": "Eliud's Eggs",

exercises/practice/difference-of-squares/.docs/instructions.md

@@ -0,0 +1,14 @@
+# Instructions
+
+Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
+
+The square of the sum of the first ten natural numbers is
+(1 + 2 + ... + 10)² = 55² = 3025.
+
+The sum of the squares of the first ten natural numbers is
+1² + 2² + ... + 10² = 385.
+
+Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.
+
+You are not expected to discover an efficient solution to this yourself from first principles; research is allowed, indeed, encouraged.
+Finding the best algorithm for the problem is a key skill in software engineering.

exercises/practice/difference-of-squares/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "difference_of_squares.s"
+    ],
+    "test": [
+      "difference_of_squares_test.c"
+    ],
+    "example": [
+      ".meta/example.s"
+    ]
+  },
+  "blurb": "Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.",
+  "source": "Problem 6 at Project Euler",
+  "source_url": "https://projecteuler.net/problem=6"
+}

exercises/practice/difference-of-squares/.meta/example.s

@@ -0,0 +1,35 @@
+.text
+.globl square_of_sum
+.globl sum_of_squares
+.globl difference_of_squares
+
+/* extern uint64_t square_of_sum(uint64_t number); */
+square_of_sum:
+        add     x1, x0, #1
+        mul     x0, x0, x1
+        lsr     x0, x0, #1              /* number (number + 1) / 2 */
+        mul     x0, x0, x0              /* number**2 (number + 1)**2 / 4 */
+        ret
+
+/* extern uint64_t sum_of_squares(uint64_t number); */
+sum_of_squares:
+        add     x1, x0, #1
+        mul     x2, x0, x1              /* number (number + 1) */
+        add     x0, x0, x1              /* 2 * number + 1 */
+        mul     x0, x0, x2
+        mov     x1, #6
+        udiv    x0, x0, x1              /* number (number + 1) (2 * number + 1) / 6 */
+        ret
+
+/* extern uint64_t difference_of_squares(uint64_t number); */
+difference_of_squares:
+        add     x1, x0, #1
+        add     x2, x0, x1              /* 2 * number + 1 */
+        mul     x0, x0, x1
+        lsr     x0, x0, #1              /* number (number + 1) / 2 */
+        mul     x2, x0, x2
+        mov     x1, #3
+        udiv    x2, x2, x1              /* number (number + 1) (2 * number + 1) / 6 */
+        mul     x0, x0, x0              /* number**2 (number + 1)**2 / 4 */
+        sub     x0, x0, x2
+        ret

exercises/practice/difference-of-squares/.meta/tests.toml

@@ -0,0 +1,37 @@
+# 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.
+
+[e46c542b-31fc-4506-bcae-6b62b3268537]
+description = "Square the sum of the numbers up to the given number -> square of sum 1"
+
+[9b3f96cb-638d-41ee-99b7-b4f9c0622948]
+description = "Square the sum of the numbers up to the given number -> square of sum 5"
+
+[54ba043f-3c35-4d43-86ff-3a41625d5e86]
+description = "Square the sum of the numbers up to the given number -> square of sum 100"
+
+[01d84507-b03e-4238-9395-dd61d03074b5]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 1"
+
+[c93900cd-8cc2-4ca4-917b-dd3027023499]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 5"
+
+[94807386-73e4-4d9e-8dec-69eb135b19e4]
+description = "Sum the squares of the numbers up to the given number -> sum of squares 100"
+
+[44f72ae6-31a7-437f-858d-2c0837adabb6]
+description = "Subtract sum of squares from square of sums -> difference of squares 1"
+
+[005cb2bf-a0c8-46f3-ae25-924029f8b00b]
+description = "Subtract sum of squares from square of sums -> difference of squares 5"
+
+[b1bf19de-9a16-41c0-a62b-1f02ecc0b036]
+description = "Subtract sum of squares from square of sums -> difference of squares 100"

exercises/practice/difference-of-squares/Makefile

@@ -0,0 +1,36 @@
+AS = aarch64-linux-gnu-as
+CC = aarch64-linux-gnu-gcc
+
+CFLAGS = -g -Wall -Wextra -pedantic -Werror
+LDFLAGS =
+
+ALL_LDFLAGS = -pie -Wl,--fatal-warnings
+
+ALL_CFLAGS = -std=c99 -fPIE $(CFLAGS)
+ALL_LDFLAGS += $(LDFLAGS)
+
+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)
+
+CC_CMD = $(CC) $(ALL_CFLAGS) -c -o $@ $<
+
+all: tests
+	qemu-aarch64 -L /usr/aarch64-linux-gnu ./$<
+
+tests: $(ALL_OBJS)
+	@$(CC) $(ALL_CFLAGS) $(ALL_LDFLAGS) -o $@ $(ALL_OBJS)
+
+%.o: %.s
+	@$(AS) -o $@ $<
+
+%.o: %.c
+	@$(CC_CMD)
+
+vendor/unity.o: vendor/unity.c vendor/unity.h vendor/unity_internals.h
+	@$(CC_CMD)
+
+clean:
+	@rm -f *.o vendor/*.o tests
+
+.PHONY: all clean

exercises/practice/difference-of-squares/difference_of_squares.s

@@ -0,0 +1,13 @@
+.text
+.globl square_of_sum
+.globl sum_of_squares
+.globl difference_of_squares
+
+square_of_sum:
+    ret
+
+sum_of_squares:
+    ret
+
+difference_of_squares:
+    ret

exercises/practice/difference-of-squares/difference_of_squares_test.c

@@ -0,0 +1,91 @@
+#include "vendor/unity.h"
+
+#include <stdint.h>
+
+extern uint64_t square_of_sum(uint64_t number);
+
+extern uint64_t sum_of_squares(uint64_t number);
+
+extern uint64_t difference_of_squares(uint64_t number);
+
+void setUp(void) {
+}
+
+void tearDown(void) {
+}
+
+void test_square_of_sum_1(void) {
+    TEST_ASSERT_EQUAL_UINT64(1U, square_of_sum(1));
+}
+
+void test_square_of_sum_5(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(225U, square_of_sum(5));
+}
+
+void test_square_of_sum_100(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(25502500U, square_of_sum(100));
+}
+
+void test_sum_of_squares_1(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(1U, sum_of_squares(1));
+}
+
+void test_sum_of_squares_5(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(55U, sum_of_squares(5));
+}
+
+void test_sum_of_squares_100(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(338350U, sum_of_squares(100));
+}
+
+void test_difference_of_squares_1(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(0U, difference_of_squares(1));
+}
+
+void test_difference_of_squares_5(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(170U, difference_of_squares(5));
+}
+
+void test_difference_of_squares_100(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(25164150U, difference_of_squares(100));
+}
+
+void test_square_of_sum_90000(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(16402864502025000000U, square_of_sum(90000));
+}
+
+void test_sum_of_squares_90000(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(243004050015000U, sum_of_squares(90000));
+}
+
+void test_difference_of_squares_90000(void) {
+    TEST_IGNORE();
+    TEST_ASSERT_EQUAL_UINT64(16402621497974985000U, difference_of_squares(90000));
+}
+
+int main(void) {
+    UNITY_BEGIN();
+    RUN_TEST(test_square_of_sum_1);
+    RUN_TEST(test_square_of_sum_5);
+    RUN_TEST(test_square_of_sum_100);
+    RUN_TEST(test_sum_of_squares_1);
+    RUN_TEST(test_sum_of_squares_5);
+    RUN_TEST(test_sum_of_squares_100);
+    RUN_TEST(test_difference_of_squares_1);
+    RUN_TEST(test_difference_of_squares_5);
+    RUN_TEST(test_difference_of_squares_100);
+    RUN_TEST(test_square_of_sum_90000);
+    RUN_TEST(test_sum_of_squares_90000);
+    RUN_TEST(test_difference_of_squares_90000);
+    return UNITY_END();
+}