Use "" not <> for internal/ includes

Reviewed-by: Richard Levitte <levitte@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/4217)

crypto/asn1/bio_asn1.c

@@ -14,7 +14,7 @@
  */
 
 #include <string.h>
-#include <internal/bio.h>
+#include "internal/bio.h"
 #include <openssl/asn1.h>
 #include "internal/cryptlib.h"
 

crypto/async/async.c

@@ -19,7 +19,7 @@
 #include "async_locl.h"
 
 #include <openssl/err.h>
-#include <internal/cryptlib_int.h>
+#include "internal/cryptlib_int.h"
 #include <string.h>
 
 #define ASYNC_JOB_RUNNING   0

crypto/async/async_locl.h

@@ -20,7 +20,7 @@
 # include <windows.h>
 #endif
 
-#include <internal/async.h>
+#include "internal/async.h"
 #include <openssl/crypto.h>
 
 typedef struct async_ctx_st async_ctx;

crypto/bio/b_addr.c

@@ -16,7 +16,7 @@
 #ifndef OPENSSL_NO_SOCK
 #include <openssl/err.h>
 #include <openssl/buffer.h>
-#include <internal/thread_once.h>
+#include "internal/thread_once.h"
 
 CRYPTO_RWLOCK *bio_lookup_lock;
 static CRYPTO_ONCE bio_lookup_init = CRYPTO_ONCE_STATIC_INIT;

crypto/bio/bio_lcl.h

@@ -87,7 +87,7 @@ union bio_addr_st {
 /* END BIO_ADDRINFO/BIO_ADDR stuff. */
 
 #include "internal/cryptlib.h"
-#include <internal/bio.h>
+#include "internal/bio.h"
 
 typedef struct bio_f_buffer_ctx_struct {
     /*-

crypto/bio/bio_meth.c

@@ -8,7 +8,7 @@
  */
 
 #include "bio_lcl.h"
-#include <internal/thread_once.h>
+#include "internal/thread_once.h"
 
 CRYPTO_RWLOCK *bio_type_lock = NULL;
 static CRYPTO_ONCE bio_type_init = CRYPTO_ONCE_STATIC_INIT;

crypto/bn/bn_srp.c

@@ -13,7 +13,7 @@
 #ifndef OPENSSL_NO_SRP
 
 #include <openssl/srp.h>
-#include <internal/bn_srp.h>
+#include "internal/bn_srp.h"
 
 # if (BN_BYTES == 8)
 #  if (defined(_WIN32) || defined(_WIN64)) && !defined(__MINGW32__)

crypto/conf/conf_lib.c

@@ -9,7 +9,7 @@
 
 #include <stdio.h>
 #include <string.h>
-#include <internal/conf.h>
+#include "internal/conf.h"
 #include <openssl/crypto.h>
 #include <openssl/err.h>
 #include <openssl/conf.h>

crypto/conf/conf_sap.c

@@ -10,7 +10,7 @@
 #include <stdio.h>
 #include <openssl/crypto.h>
 #include "internal/cryptlib.h"
-#include <internal/conf.h>
+#include "internal/conf.h"
 #include <openssl/x509.h>
 #include <openssl/asn1.h>
 #include <openssl/engine.h>

crypto/engine/eng_int.h

@@ -12,8 +12,8 @@
 # define HEADER_ENGINE_INT_H
 
 # include "internal/cryptlib.h"
-# include <internal/engine.h>
-# include <internal/thread_once.h>
+# include "internal/engine.h"
+# include "internal/thread_once.h"
 # include "internal/refcount.h"
 
 #ifdef  __cplusplus

crypto/engine/eng_openssl.c

@@ -11,7 +11,7 @@
 #include <stdio.h>
 #include <openssl/crypto.h>
 #include "internal/cryptlib.h"
-#include <internal/engine.h>
+#include "internal/engine.h"
 #include <openssl/pem.h>
 #include <openssl/evp.h>
 #include <openssl/rand.h>

crypto/engine/eng_rdrand.c

@@ -11,7 +11,7 @@
 
 #include <stdio.h>
 #include <string.h>
-#include <internal/engine.h>
+#include "internal/engine.h"
 #include <openssl/rand.h>
 #include <openssl/err.h>
 #include <openssl/crypto.h>

crypto/err/err.c

@@ -10,16 +10,16 @@
 #include <stdio.h>
 #include <stdarg.h>
 #include <string.h>
-#include <internal/cryptlib_int.h>
-#include <internal/err.h>
-#include <internal/err_int.h>
+#include "internal/cryptlib_int.h"
+#include "internal/err.h"
+#include "internal/err_int.h"
 #include <openssl/lhash.h>
 #include <openssl/err.h>
 #include <openssl/crypto.h>
 #include <openssl/buffer.h>
 #include <openssl/bio.h>
 #include <openssl/opensslconf.h>
-#include <internal/thread_once.h>
+#include "internal/thread_once.h"
 
 static int err_load_strings(const ERR_STRING_DATA *str);
 

crypto/evp/c_allc.c

@@ -10,7 +10,7 @@
 #include <stdio.h>
 #include "internal/cryptlib.h"
 #include <openssl/evp.h>
-#include <internal/evp_int.h>
+#include "internal/evp_int.h"
 #include <openssl/pkcs12.h>
 #include <openssl/objects.h>
 

crypto/evp/c_alld.c

@@ -10,7 +10,7 @@
 #include <stdio.h>
 #include "internal/cryptlib.h"
 #include <openssl/evp.h>
-#include <internal/evp_int.h>
+#include "internal/evp_int.h"
 #include <openssl/pkcs12.h>
 #include <openssl/objects.h>
 

crypto/evp/e_rc5.c

@@ -13,7 +13,7 @@
 #ifndef OPENSSL_NO_RC5
 
 # include <openssl/evp.h>
-# include <internal/evp_int.h>
+# include "internal/evp_int.h"
 # include <openssl/objects.h>
 # include "evp_locl.h"
 # include <openssl/rc5.h>

crypto/evp/names.c

@@ -10,7 +10,7 @@
 #include <stdio.h>
 #include "internal/cryptlib.h"
 #include <openssl/evp.h>
-#include <internal/objects.h>
+#include "internal/objects.h"
 #include <openssl/x509.h>
 #include "internal/evp_int.h"
 

crypto/evp/pbe_scrypt.c

@@ -12,7 +12,7 @@
 #include <string.h>
 #include <openssl/evp.h>
 #include <openssl/err.h>
-#include <internal/numbers.h>
+#include "internal/numbers.h"
 
 #ifndef OPENSSL_NO_SCRYPT
 

crypto/init.c

@@ -7,24 +7,24 @@
  * https://www.openssl.org/source/license.html
  */
 
-#include <internal/cryptlib_int.h>
+#include "internal/cryptlib_int.h"
 #include <openssl/err.h>
-#include <internal/rand_int.h>
-#include <internal/bio.h>
+#include "internal/rand_int.h"
+#include "internal/bio.h"
 #include <openssl/evp.h>
-#include <internal/evp_int.h>
-#include <internal/conf.h>
-#include <internal/async.h>
-#include <internal/engine.h>
-#include <internal/comp.h>
-#include <internal/err.h>
-#include <internal/err_int.h>
-#include <internal/objects.h>
+#include "internal/evp_int.h"
+#include "internal/conf.h"
+#include "internal/async.h"
+#include "internal/engine.h"
+#include "internal/comp.h"
+#include "internal/err.h"
+#include "internal/err_int.h"
+#include "internal/objects.h"
 #include <stdlib.h>
 #include <assert.h>
-#include <internal/thread_once.h>
-#include <internal/dso.h>
-#include <internal/store.h>
+#include "internal/thread_once.h"
+#include "internal/dso.h"
+#include "internal/store.h"
 
 static int stopped = 0;
 

crypto/objects/o_names.c

@@ -16,7 +16,7 @@
 #include <openssl/objects.h>
 #include <openssl/safestack.h>
 #include <openssl/e_os2.h>
-#include <internal/thread_once.h>
+#include "internal/thread_once.h"
 #include "obj_lcl.h"
 
 /*

crypto/x509/x509_vfy.c

@@ -22,8 +22,8 @@
 #include <openssl/x509.h>
 #include <openssl/x509v3.h>
 #include <openssl/objects.h>
-#include <internal/dane.h>
-#include <internal/x509_int.h>
+#include "internal/dane.h"
+#include "internal/x509_int.h"
 #include "x509_lcl.h"
 
 /* CRL score values */

e_os.h

@@ -14,7 +14,7 @@
 
 # include <openssl/e_os2.h>
 # include <openssl/crypto.h>
-# include <internal/nelem.h>
+# include "internal/nelem.h"
 
 /*
  * <openssl/e_os2.h> contains what we can justify to make visible to the

include/internal/dso.h

@@ -11,7 +11,7 @@
 # define HEADER_DSO_H
 
 # include <openssl/crypto.h>
-# include <internal/dsoerr.h>
+# include "internal/dsoerr.h"
 
 #ifdef __cplusplus
 extern "C" {

test/asn1_internal_test.c

@@ -16,7 +16,7 @@
 #include <openssl/evp.h>
 #include <openssl/objects.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 /**********************************************************************
  *

test/asn1_time_test.c

@@ -16,7 +16,7 @@
 #include <openssl/evp.h>
 #include <openssl/objects.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 struct testdata {
     char *data;             /* TIME string value */

test/bad_dtls_test.c

@@ -37,10 +37,8 @@
 #include <openssl/err.h>
 #include <openssl/rand.h>
 #include <openssl/kdf.h>
-
 #include "../ssl/packet_locl.h"
-#include <internal/nelem.h>
-
+#include "internal/nelem.h"
 #include "testutil.h"
 
 /* For DTLS1_BAD_VER packets the MAC doesn't include the handshake header */

test/bftest.c

@@ -16,11 +16,9 @@
 #include <string.h>
 #include <stdlib.h>
 #include <openssl/opensslconf.h> /* To see if OPENSSL_NO_BF is defined */
-
 #include "testutil.h"
 
-#include <internal/nelem.h>
-
+#include "internal/nelem.h"
 #ifndef OPENSSL_NO_BF
 # include <openssl/blowfish.h>
 

test/bntest.c

@@ -12,9 +12,9 @@
 #include <string.h>
 #include <ctype.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "../e_os.h"
-#include <internal/numbers.h>
+#include "internal/numbers.h"
 #include <openssl/bn.h>
 #include <openssl/crypto.h>
 #include <openssl/err.h>

test/casttest.c

@@ -12,7 +12,7 @@
 #include <stdlib.h>
 
 #include <openssl/opensslconf.h> /* To see if OPENSSL_NO_CAST is defined */
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_CAST

test/cipher_overhead_test.c

@@ -7,7 +7,7 @@
  * https://www.openssl.org/source/license.html
  */
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifdef __VMS

test/cipherbytes_test.c

@@ -18,7 +18,7 @@
 #include <openssl/ssl3.h>
 #include <openssl/tls1.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 static SSL_CTX *ctx;

test/cipherlist_test.c

@@ -18,7 +18,7 @@
 #include <openssl/ssl3.h>
 #include <openssl/tls1.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 typedef struct cipherlist_test_fixture {

test/ciphername_test.c

@@ -19,7 +19,7 @@
 #include <openssl/ssl3.h>
 #include <openssl/tls1.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 typedef struct cipher_id_name {

test/constant_time_test.c

@@ -10,7 +10,7 @@
 #include <stdio.h>
 #include <stdlib.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "internal/constant_time_locl.h"
 #include "testutil.h"
 #include "internal/numbers.h"

test/crltest.c

@@ -7,7 +7,7 @@
  * https://www.openssl.org/source/license.html
  */
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include <string.h>
 #include <openssl/bio.h>
 #include <openssl/crypto.h>

test/d2i_test.c

@@ -20,7 +20,7 @@
 #include <openssl/err.h>
 #include <openssl/x509.h>
 #include <openssl/x509v3.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 static const ASN1_ITEM *item_type;
 static const char *test_file;

test/danetest.c

@@ -24,7 +24,7 @@
 #endif
 #include "testutil.h"
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #define _UC(c) ((unsigned char)(c))
 
@@ -422,7 +422,7 @@ int setup_tests(void)
     return 1;
 }
 
-#include <internal/dane.h>
+#include "internal/dane.h"
 
 static void store_ctx_dane_init(X509_STORE_CTX *store_ctx, SSL *ssl)
 {

test/dhtest.c

@@ -11,7 +11,7 @@
 #include <stdlib.h>
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include <openssl/crypto.h>
 #include <openssl/bio.h>
 #include <openssl/bn.h>

test/drbgtest.c

@@ -8,7 +8,7 @@
  */
 
 #include <string.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include <openssl/crypto.h>
 #include <openssl/err.h>
 #include <openssl/rand.h>

test/dsatest.c

@@ -19,7 +19,7 @@
 #include <openssl/dsa.h>
 
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #ifndef OPENSSL_NO_DSA
 static int dsa_cb(int p, int n, BN_GENCB *arg);

test/dtlsv1listentest.c

@@ -12,7 +12,7 @@
 #include <openssl/bio.h>
 #include <openssl/err.h>
 #include <openssl/conf.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_SOCK

test/ecstresstest.c

@@ -8,7 +8,7 @@
  * or in the file LICENSE in the source distribution.
  */
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #include <stdio.h>

test/ectest.c

@@ -8,7 +8,7 @@
  * https://www.openssl.org/source/license.html
  */
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_EC

test/evp_extra_test.c

@@ -16,7 +16,7 @@
 #include <openssl/rsa.h>
 #include <openssl/x509.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 /*
  * kExampleRSAKeyDER is an RSA private key in ASN.1, DER format. Of course, you

test/exptest.c

@@ -11,7 +11,7 @@
 #include <stdlib.h>
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #include <openssl/bio.h>
 #include <openssl/bn.h>

test/handshake_helper.c

@@ -18,7 +18,7 @@
 
 #ifndef OPENSSL_NO_SOCK
 # define USE_SOCKETS
-# include <internal/nelem.h>
+# include "internal/nelem.h"
 #endif
 
 #include "handshake_helper.h"

test/hmactest.c

@@ -11,7 +11,7 @@
 #include <string.h>
 #include <stdlib.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 # include <openssl/hmac.h>
 # include <openssl/sha.h>

test/ideatest.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_IDEA

test/igetest.c

@@ -12,7 +12,7 @@
 #include <openssl/rand.h>
 #include <stdio.h>
 #include <string.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #define TEST_SIZE       128

test/lhash_test.c

@@ -16,7 +16,7 @@
 #include <openssl/err.h>
 #include <openssl/crypto.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 /*

test/md2test.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_MD2

test/mdc2_internal_test.c

@@ -14,7 +14,7 @@
 
 #include <openssl/mdc2.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 typedef struct {
     const char *input;

test/mdc2test.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #if defined(OPENSSL_NO_DES) && !defined(OPENSSL_NO_MDC2)

test/modes_internal_test.c

@@ -16,7 +16,7 @@
 #include <openssl/modes.h>
 #include "../crypto/modes/modes_lcl.h"
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 typedef struct {
     size_t size;

test/poly1305_internal_test.c

@@ -15,7 +15,7 @@
 #include "testutil.h"
 #include "internal/poly1305.h"
 #include "../crypto/poly1305/poly1305_local.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 typedef struct {
     size_t size;

test/rc2test.c

@@ -7,7 +7,7 @@
  * https://www.openssl.org/source/license.html
  */
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_RC2

test/rc4test.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_RC4

test/rc5test.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #ifndef OPENSSL_NO_RC5

test/rsa_test.c

@@ -12,7 +12,7 @@
 #include <stdio.h>
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #include <openssl/crypto.h>
 #include <openssl/err.h>

test/sanitytest.c

@@ -8,7 +8,7 @@
  */
 
 #include <string.h>
-#include <internal/numbers.h>
+#include "internal/numbers.h"
 
 #include "testutil.h"
 

test/servername_test.c

@@ -21,7 +21,7 @@
 #include "../ssl/packet_locl.h"
 
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #define CLIENT_VERSION_LEN      2
 

test/siphash_internal_test.c

@@ -16,7 +16,7 @@
 #include "testutil.h"
 #include "internal/siphash.h"
 #include "../crypto/siphash/siphash_local.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 static BIO* b_stderr = NULL;
 static BIO* b_stdout = NULL;

test/ssl_cert_table_internal_test.c

@@ -14,7 +14,7 @@
 
 #include <openssl/ssl.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #ifdef __VMS
 # pragma names save

test/ssl_test_ctx.c

@@ -12,7 +12,7 @@
 #include <openssl/e_os2.h>
 #include <openssl/crypto.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "../e_os.h"
 #include "ssl_test_ctx.h"
 #include "testutil.h"

test/ssl_test_ctx_test.c

@@ -15,7 +15,7 @@
 #include <stdio.h>
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "ssl_test_ctx.h"
 #include "testutil.h"
 #include <openssl/e_os2.h>

test/sslapitest.c

@@ -17,7 +17,7 @@
 
 #include "ssltestlib.h"
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "../ssl/ssl_locl.h"
 
 static char *cert = NULL;

test/ssltest_old.c

@@ -25,7 +25,7 @@
 #include <string.h>
 #include <time.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 #define USE_SOCKETS
 #include "e_os.h"

test/ssltestlib.c

@@ -9,7 +9,7 @@
 
 #include <string.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "ssltestlib.h"
 #include "testutil.h"
 

test/stack_test.c

@@ -16,7 +16,7 @@
 #include <openssl/err.h>
 #include <openssl/crypto.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 /* The macros below generate unused functions which error out one of the clang

test/test_test.c

@@ -16,7 +16,7 @@
 #include <openssl/crypto.h>
 #include <openssl/bn.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 #define TEST(expected, test) test_case((expected), #test, (test))

test/testutil/driver.c

@@ -14,7 +14,7 @@
 #include <string.h>
 #include <assert.h>
 
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include <openssl/bio.h>
 
 /*

test/testutil/format_output.c

@@ -13,7 +13,7 @@
 
 #include <string.h>
 #include <ctype.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 /* The size of memory buffers to display on failure */
 #define MEM_BUFFER_SIZE     (2000)

test/testutil/main.c

@@ -8,7 +8,7 @@
  */
 
 #include "../testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "output.h"
 #include "tu_local.h"
 

test/testutil/tests.c

@@ -14,7 +14,7 @@
 #include <errno.h>
 #include <string.h>
 #include <ctype.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 /*
  * Output a failed test first line.

test/time_offset_test.c

@@ -16,7 +16,7 @@
 #include <openssl/asn1.h>
 #include <openssl/x509.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 typedef struct {
     const char *data;

test/v3nametest.c

@@ -8,7 +8,7 @@
  */
 
 #include <string.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "../e_os.h"
 #include <openssl/x509.h>
 #include <openssl/x509v3.h>

test/x509_internal_test.c

@@ -15,7 +15,7 @@
 #include <openssl/x509.h>
 #include <openssl/x509v3.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 /**********************************************************************
  *

test/x509_time_test.c

@@ -15,7 +15,7 @@
 #include <openssl/asn1.h>
 #include <openssl/x509.h>
 #include "testutil.h"
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 
 typedef struct {
     const char *data;

test/x509aux.c

@@ -16,7 +16,7 @@
 #include <openssl/pem.h>
 #include <openssl/conf.h>
 #include <openssl/err.h>
-#include <internal/nelem.h>
+#include "internal/nelem.h"
 #include "testutil.h"
 
 static int test_certs(int num)