diff --git a/include/mbedtls/poly1305.h b/include/mbedtls/poly1305.h
index b02f968..f0ec44c 100644
--- a/include/mbedtls/poly1305.h
+++ b/include/mbedtls/poly1305.h
@@ -34,7 +34,7 @@
 #define MBEDTLS_POLY1305_H
 
 #if !defined(MBEDTLS_CONFIG_FILE)
-#include "mbedtls/config.h"
+#include "config.h"
 #else
 #include MBEDTLS_CONFIG_FILE
 #endif
@@ -84,14 +84,18 @@
  *                  \c mbedtls_poly1305_finish(), then finally
  *                  \c mbedtls_poly1305_free().
  *
- * \param ctx       The Poly1305 context to initialize.
+ * \param ctx       The Poly1305 context to initialize. This must
+ *                  not be \c NULL.
  */
 void mbedtls_poly1305_init( mbedtls_poly1305_context *ctx );
 
 /**
- * \brief           This function releases and clears the specified Poly1305 context.
+ * \brief           This function releases and clears the specified
+ *                  Poly1305 context.
  *
- * \param ctx       The Poly1305 context to clear.
+ * \param ctx       The Poly1305 context to clear. This may be \c NULL, in which
+ *                  case this function is a no-op. If it is not \c NULL, it must
+ *                  point to an initialized Poly1305 context.
  */
 void mbedtls_poly1305_free( mbedtls_poly1305_context *ctx );
 
@@ -102,11 +106,11 @@
  *                  invocation of Poly1305.
  *
  * \param ctx       The Poly1305 context to which the key should be bound.
- * \param key       The buffer containing the 256-bit key.
+ *                  This must be initialized.
+ * \param key       The buffer containing the \c 32 Byte (\c 256 Bit) key.
  *
  * \return          \c 0 on success.
- * \return          #MBEDTLS_ERR_POLY1305_BAD_INPUT_DATA
- *                  if ctx or key are NULL.
+ * \return          A negative error code on failure.
  */
 int mbedtls_poly1305_starts( mbedtls_poly1305_context *ctx,
                              const unsigned char key[32] );
@@ -120,13 +124,14 @@
  *                  It can be called repeatedly to process a stream of data.
  *
  * \param ctx       The Poly1305 context to use for the Poly1305 operation.
- * \param ilen      The length of the input data (in bytes). Any value is accepted.
+ *                  This must be initialized and bound to a key.
+ * \param ilen      The length of the input data in Bytes.
+ *                  Any value is accepted.
  * \param input     The buffer holding the input data.
- *                  This pointer can be NULL if ilen == 0.
+ *                  This pointer can be \c NULL if `ilen == 0`.
  *
  * \return          \c 0 on success.
- * \return          #MBEDTLS_ERR_POLY1305_BAD_INPUT_DATA
- *                  if ctx or input are NULL.
+ * \return          A negative error code on failure.
  */
 int mbedtls_poly1305_update( mbedtls_poly1305_context *ctx,
                              const unsigned char *input,
@@ -137,12 +142,12 @@
  *                  Authentication Code (MAC).
  *
  * \param ctx       The Poly1305 context to use for the Poly1305 operation.
- * \param mac       The buffer to where the MAC is written. Must be big enough
- *                  to hold the 16-byte MAC.
+ *                  This must be initialized and bound to a key.
+ * \param mac       The buffer to where the MAC is written. This must
+ *                  be a writable buffer of length \c 16 Bytes.
  *
  * \return          \c 0 on success.
- * \return          #MBEDTLS_ERR_POLY1305_BAD_INPUT_DATA
- *                  if ctx or mac are NULL.
+ * \return          A negative error code on failure.
  */
 int mbedtls_poly1305_finish( mbedtls_poly1305_context *ctx,
                              unsigned char mac[16] );
@@ -154,16 +159,16 @@
  * \warning         The key must be unique and unpredictable for each
  *                  invocation of Poly1305.
  *
- * \param key       The buffer containing the 256-bit key.
- * \param ilen      The length of the input data (in bytes). Any value is accepted.
+ * \param key       The buffer containing the \c 32 Byte (\c 256 Bit) key.
+ * \param ilen      The length of the input data in Bytes.
+ *                  Any value is accepted.
  * \param input     The buffer holding the input data.
- *                  This pointer can be NULL if ilen == 0.
- * \param mac       The buffer to where the MAC is written. Must be big enough
- *                  to hold the 16-byte MAC.
+ *                  This pointer can be \c NULL if `ilen == 0`.
+ * \param mac       The buffer to where the MAC is written. This must be
+ *                  a writable buffer of length \c 16 Bytes.
  *
  * \return          \c 0 on success.
- * \return          #MBEDTLS_ERR_POLY1305_BAD_INPUT_DATA
- *                  if key, input, or mac are NULL.
+ * \return          A negative error code on failure.
  */
 int mbedtls_poly1305_mac( const unsigned char key[32],
                           const unsigned char *input,