chore(c_api): add the c_api code from the docs as a test

tfhe/c_api_tests/test_c_doc.c

@@ -0,0 +1,68 @@
+// If this test break the c_api doc needs to be updated
+
+#include <tfhe.h>
+
+#include <assert.h>
+#include <stdio.h>
+
+int main(void)
+{
+    int ok = 0;
+    // Prepare the config builder for the high level API and choose which types to enable
+    ConfigBuilder *builder;
+    Config *config;
+
+    // Put the builder in a default state without any types enabled
+    config_builder_all_disabled(&builder);
+    // Enable the uint128 type using the small LWE key for encryption
+    config_builder_enable_default_integers_small(&builder);
+    // Populate the config
+    config_builder_build(builder, &config);
+
+    ClientKey *client_key = NULL;
+    ServerKey *server_key = NULL;
+
+    // Generate the keys using the config
+    generate_keys(config, &client_key, &server_key);
+    // Set the server key for the current thread
+    set_server_key(server_key);
+
+    FheUint128 *lhs = NULL;
+    FheUint128 *rhs = NULL;
+    FheUint128 *result = NULL;
+    // A 128-bit unsigned integer containing value: 20 << 64 | 10
+    U128 clear_lhs = { .w0 = 10, .w1 = 20 };
+    // A 128-bit unsigned integer containing value: 2 << 64 | 1
+    U128 clear_rhs = { .w0 = 1, .w1 = 2 };
+
+    ok = fhe_uint128_try_encrypt_with_client_key_u128(clear_lhs, client_key, &lhs);
+    assert(ok == 0);
+
+    ok = fhe_uint128_try_encrypt_with_client_key_u128(clear_rhs, client_key, &rhs);
+    assert(ok == 0);
+
+    // Compute the subtraction
+    ok = fhe_uint128_sub(lhs, rhs, &result);
+    assert(ok == 0);
+
+    U128 clear_result;
+    // Decrypt
+    ok = fhe_uint128_decrypt(result, client_key, &clear_result);
+    assert(ok == 0);
+
+    // Here the subtraction allows us to compare each word
+    assert(clear_result.w0 == 9);
+    assert(clear_result.w1 == 18);
+
+    // Destroy the ciphertexts
+    fhe_uint128_destroy(lhs);
+    fhe_uint128_destroy(rhs);
+    fhe_uint128_destroy(result);
+
+    // Destroy the keys
+    client_key_destroy(client_key);
+    server_key_destroy(server_key);
+
+    printf("FHE computation successful!\n");
+    return EXIT_SUCCESS;
+}