ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

Instructions

Test suite

Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

- take the next available unmarked number in your list (it is prime)
- mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.

Make sure you have read the C page on the Exercism site. This covers the basic information on setting up the development environment expected by the exercises.

Get the first test compiling, linking and passing by following the three rules of test-driven development.

The included makefile can be used to create and run the tests using the `test`

task.

```
make test
```

Create just the functions you need to satisfy any compiler errors and get the test to fail. Then write just enough code to get the test to pass. Once you've done that, move onto the next test.

As you progress through the tests, take the time to refactor your implementation for readability and expressiveness and then go on to the next test.

Try to use standard C99 facilities in preference to writing your own low-level algorithms or facilities by hand.

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
#include <string.h>
#include "vendor/unity.h"
#include "../src/sieve.h"
static primes_array_t result_array;
#define ARRAY_LENGTH(x) sizeof(x)/sizeof(x[0])
void setUp(void)
{
}
void tearDown(void)
{
}
void test_no_primes_under_two(void)
{
const unsigned int limit = 1;
const unsigned int expected_prime_count = 0;
unsigned int result_prime_count;
memset(result_array, 0, sizeof(result_array));
result_prime_count = sieve(limit, result_array);
TEST_ASSERT_EQUAL(expected_prime_count, result_prime_count);
}
void test_find_first_prime(void)
{
TEST_IGNORE(); // delete this line to run test
const unsigned int limit = 2;
const primes_array_t expected_prime_array = { 2 };
const unsigned int expected_prime_count = 1;
unsigned int result_prime_count;
memset(result_array, 0, sizeof(result_array));
result_prime_count = sieve(limit, result_array);
TEST_ASSERT_EQUAL(expected_prime_count, result_prime_count);
TEST_ASSERT_EQUAL_UINT_ARRAY(expected_prime_array, result_array,
ARRAY_LENGTH(expected_prime_array));
}
void test_find_primes_up_to_10(void)
{
TEST_IGNORE();
const unsigned int limit = 10;
const primes_array_t expected_prime_array = { 2, 3, 5, 7 };
const unsigned int expected_prime_count = 4;
unsigned int result_prime_count;
memset(result_array, 0, sizeof(result_array));
result_prime_count = sieve(limit, result_array);
TEST_ASSERT_EQUAL(expected_prime_count, result_prime_count);
TEST_ASSERT_EQUAL_UINT_ARRAY(expected_prime_array, result_array,
ARRAY_LENGTH(expected_prime_array));
}
void test_limit_is_prime(void)
{
TEST_IGNORE();
const unsigned int limit = 13;
const primes_array_t expected_prime_array = { 2, 3, 5, 7, 11, 13 };
const unsigned int expected_prime_count = 6;
unsigned int result_prime_count;
memset(result_array, 0, sizeof(result_array));
result_prime_count = sieve(limit, result_array);
TEST_ASSERT_EQUAL(expected_prime_count, result_prime_count);
TEST_ASSERT_EQUAL_UINT_ARRAY(expected_prime_array, result_array,
ARRAY_LENGTH(expected_prime_array));
}
void test_find_primes_up_to_1000(void)
{
TEST_IGNORE();
const unsigned int limit = 1000;
const primes_array_t expected_prime_array = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269,
271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431,
433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673,
677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857,
859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
953, 967, 971, 977, 983, 991, 997
};
const unsigned int expected_prime_count = 168;
unsigned int result_prime_count;
memset(result_array, 0, sizeof(result_array));
result_prime_count = sieve(limit, result_array);
TEST_ASSERT_EQUAL(expected_prime_count, result_prime_count);
TEST_ASSERT_EQUAL_UINT_ARRAY(expected_prime_array, result_array,
ARRAY_LENGTH(expected_prime_array));
}
int main(void)
{
UnityBegin("test/test_sum_of_multiples.c");
RUN_TEST(test_no_primes_under_two);
RUN_TEST(test_find_first_prime);
RUN_TEST(test_find_primes_up_to_10);
RUN_TEST(test_limit_is_prime);
RUN_TEST(test_find_primes_up_to_1000);
UnityEnd();
return 0;
}
```

```
#include "sieve.h"
#include <math.h>
/* https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes */
unsigned int sieve(const unsigned int limit, primes_array_t primes)
{
if (!limit || !primes)
return 0;
int sieve[limit + 1];
unsigned int i, j, upto;
for (i = 2; i <= limit; i++)
sieve[i] = 1;
upto = (unsigned int) sqrt(limit);
for (i = 2; i <= upto; i++)
if (sieve[i] == 1)
for (j = i*i; j <= limit; j += i)
sieve[j] = 0;
i = 0;
for (j = 2; j <= limit; j++)
if (sieve[j] == 1)
primes[i++] = j;
return i;
}
```

```
#ifndef SIEVE_H
#define SIEVE_H
#define MAX_LIMIT_TESTED (1000)
typedef unsigned int primes_array_t[MAX_LIMIT_TESTED];
unsigned int sieve(const unsigned int limit, primes_array_t primes);
#endif
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

Level up your programming skills with 3,450 exercises across 52 languages, and insightful discussion with our volunteer team of welcoming mentors.
Exercism is
**100% free forever**.

## Community comments