diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -934,6 +934,10 @@
 "An optional starting value can be specified.  The returned checksum is\n"
 "an integer.");
 
+fdef HAVE_SSIZE_T
+typedef ssize_t         Py_ssize_t;
+#elif SIZEOF_VOID_P == SIZEOF_SIZE_T
+
 static PyObject *
 PyZlib_adler32(PyObject *self, PyObject *args)
 {
@@ -942,11 +946,24 @@
 
     if (!PyArg_ParseTuple(args, "y*|I:adler32", &pbuf, &adler32val))
         return NULL;
+
     /* Releasing the GIL for very small buffers is inefficient
        and may lower performance */
     if (pbuf.len > 1024*5) {
+        Py_ssize_t len = pbuf.len, rest = 0;
         Py_BEGIN_ALLOW_THREADS
-        adler32val = adler32(adler32val, pbuf.buf, pbuf.len);
+        if ((size_t)len >= UINT_MAX) {
+            rest = len;
+            len = UINT_MAX;
+        }
+        for (;;) {
+            adler32val = adler32(adler32val, pbuf.buf, len);
+            rest -= len;
+            if (rest <= 0)
+                break;
+            if (rest < len)
+                len = rest;
+        }
         Py_END_ALLOW_THREADS
     } else {
         adler32val = adler32(adler32val, pbuf.buf, pbuf.len);
@@ -970,11 +987,24 @@
 
     if (!PyArg_ParseTuple(args, "y*|I:crc32", &pbuf, &crc32val))
         return NULL;
+
     /* Releasing the GIL for very small buffers is inefficient
        and may lower performance */
     if (pbuf.len > 1024*5) {
+        Py_ssize_t len = pbuf.len, rest = 0;
         Py_BEGIN_ALLOW_THREADS
-        signed_val = crc32(crc32val, pbuf.buf, pbuf.len);
+        if ((size_t)len >= UINT_MAX) {
+            rest = len;
+            len = UINT_MAX;
+        }
+        for (;;) {
+            adler32val = crc32(crc32val, pbuf.buf, len);
+            rest -= len;
+            if (rest <= 0)
+                break;
+            if (rest < len)
+                len = rest;
+        }
         Py_END_ALLOW_THREADS
     } else {
         signed_val = crc32(crc32val, pbuf.buf, pbuf.len);