diff --git a/Include/longintrepr.h b/Include/longintrepr.h
index 1296849..a3b74b4 100644
--- a/Include/longintrepr.h
+++ b/Include/longintrepr.h
@@ -42,10 +42,10 @@
 */
 
 #if PYLONG_BITS_IN_DIGIT == 30
-typedef PY_UINT32_T digit;
-typedef PY_INT32_T sdigit; /* signed variant of digit */
-typedef PY_UINT64_T twodigits;
-typedef PY_INT64_T stwodigits; /* signed variant of twodigits */
+typedef uint32_t digit;
+typedef int32_t sdigit; /* signed variant of digit */
+typedef uint64_t twodigits;
+typedef int64_t stwodigits; /* signed variant of twodigits */
 #define PyLong_SHIFT	30
 #define _PyLong_DECIMAL_SHIFT	9 /* max(e such that 10**e fits in a digit) */
 #define _PyLong_DECIMAL_BASE	((digit)1000000000) /* 10 ** DECIMAL_SHIFT */
diff --git a/Include/pyhash.h b/Include/pyhash.h
index a7ca937..a814af6 100644
--- a/Include/pyhash.h
+++ b/Include/pyhash.h
@@ -36,14 +36,14 @@
  * memory layout on 64 bit systems
  *   cccccccc cccccccc cccccccc  uc -- unsigned char[24]
  *   pppppppp ssssssss ........  fnv -- two Py_hash_t
- *   k0k0k0k0 k1k1k1k1 ........  siphash -- two PY_UINT64_T
+ *   k0k0k0k0 k1k1k1k1 ........  siphash -- two uint64_t
  *   ........ ........ ssssssss  djbx33a -- 16 bytes padding + one Py_hash_t
  *   ........ ........ eeeeeeee  pyexpat XML hash salt
  *
  * memory layout on 32 bit systems
  *   cccccccc cccccccc cccccccc  uc
  *   ppppssss ........ ........  fnv -- two Py_hash_t
- *   k0k0k0k0 k1k1k1k1 ........  siphash -- two PY_UINT64_T (*)
+ *   k0k0k0k0 k1k1k1k1 ........  siphash -- two uint64_t (*)
  *   ........ ........ ssss....  djbx33a -- 16 bytes padding + one Py_hash_t
  *   ........ ........ eeee....  pyexpat XML hash salt
  *
@@ -59,13 +59,11 @@
         Py_hash_t prefix;
         Py_hash_t suffix;
     } fnv;
-#ifdef PY_UINT64_T
     /* two uint64 for SipHash24 */
     struct {
-        PY_UINT64_T k0;
-        PY_UINT64_T k1;
+        uint64_t k0;
+        uint64_t k1;
     } siphash;
-#endif
     /* a different (!) Py_hash_t for small string optimization */
     struct {
         unsigned char padding[16];
@@ -121,8 +119,7 @@
  * configure script.
  *
  * - FNV is available on all platforms and architectures.
- * - SIPHASH24 only works on plaforms that provide PY_UINT64_T and doesn't
- *   require aligned memory for integers.
+ * - SIPHASH24 only works on plaforms that don't require aligned memory for integers.
  * - With EXTERNAL embedders can provide an alternative implementation with::
  *
  *     PyHash_FuncDef PyHash_Func = {...};
@@ -134,8 +131,7 @@
 #define Py_HASH_FNV 2
 
 #ifndef Py_HASH_ALGORITHM
-#  if (defined(PY_UINT64_T) && defined(PY_UINT32_T) \
-       && !defined(HAVE_ALIGNED_REQUIRED))
+#  ifndef HAVE_ALIGNED_REQUIRED
 #    define Py_HASH_ALGORITHM Py_HASH_SIPHASH24
 #  else
 #    define Py_HASH_ALGORITHM Py_HASH_FNV
diff --git a/Include/pytime.h b/Include/pytime.h
index 859321b..595fafc 100644
--- a/Include/pytime.h
+++ b/Include/pytime.h
@@ -13,16 +13,12 @@
 extern "C" {
 #endif
 
-#ifdef PY_INT64_T
 /* _PyTime_t: Python timestamp with subsecond precision. It can be used to
    store a duration, and so indirectly a date (related to another date, like
    UNIX epoch). */
-typedef PY_INT64_T _PyTime_t;
+typedef int64_t _PyTime_t;
 #define _PyTime_MIN PY_LLONG_MIN
 #define _PyTime_MAX PY_LLONG_MAX
-#else
-#  error "_PyTime_t need signed 64-bit integer type"
-#endif
 
 typedef enum {
     /* Round towards minus infinity (-inf).
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index fd6b230..63a060c 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -69,10 +69,6 @@
 #include "Python.h"
 #include <time.h>               /* for seeding to current time */
 
-#ifndef PY_UINT32_T
-#  error "Failed to find an exact-width 32-bit integer type"
-#endif
-
 /* Period parameters -- These are all magic.  Don't change. */
 #define N 624
 #define M 397
@@ -83,7 +79,7 @@
 typedef struct {
     PyObject_HEAD
     int index;
-    PY_UINT32_T state[N];
+    uint32_t state[N];
 } RandomObject;
 
 static PyTypeObject Random_Type;
@@ -95,13 +91,13 @@
 
 
 /* generates a random number on [0,0xffffffff]-interval */
-static PY_UINT32_T
+static uint32_t
 genrand_int32(RandomObject *self)
 {
-    PY_UINT32_T y;
-    static const PY_UINT32_T mag01[2] = {0x0U, MATRIX_A};
+    uint32_t y;
+    static const uint32_t mag01[2] = {0x0U, MATRIX_A};
     /* mag01[x] = x * MATRIX_A  for x=0,1 */
-    PY_UINT32_T *mt;
+    uint32_t *mt;
 
     mt = self->state;
     if (self->index >= N) { /* generate N words at one time */
@@ -141,16 +137,16 @@
 static PyObject *
 random_random(RandomObject *self)
 {
-    PY_UINT32_T a=genrand_int32(self)>>5, b=genrand_int32(self)>>6;
+    uint32_t a=genrand_int32(self)>>5, b=genrand_int32(self)>>6;
     return PyFloat_FromDouble((a*67108864.0+b)*(1.0/9007199254740992.0));
 }
 
 /* initializes mt[N] with a seed */
 static void
-init_genrand(RandomObject *self, PY_UINT32_T s)
+init_genrand(RandomObject *self, uint32_t s)
 {
     int mti;
-    PY_UINT32_T *mt;
+    uint32_t *mt;
 
     mt = self->state;
     mt[0]= s;
@@ -170,10 +166,10 @@
 /* init_key is the array for initializing keys */
 /* key_length is its length */
 static PyObject *
-init_by_array(RandomObject *self, PY_UINT32_T init_key[], size_t key_length)
+init_by_array(RandomObject *self, uint32_t init_key[], size_t key_length)
 {
     size_t i, j, k;       /* was signed in the original code. RDH 12/16/2002 */
-    PY_UINT32_T *mt;
+    uint32_t *mt;
 
     mt = self->state;
     init_genrand(self, 19650218U);
@@ -181,14 +177,14 @@
     k = (N>key_length ? N : key_length);
     for (; k; k--) {
         mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525U))
-                 + init_key[j] + (PY_UINT32_T)j; /* non linear */
+                 + init_key[j] + (uint32_t)j; /* non linear */
         i++; j++;
         if (i>=N) { mt[0] = mt[N-1]; i=1; }
         if (j>=key_length) j=0;
     }
     for (k=N-1; k; k--) {
         mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941U))
-                 - (PY_UINT32_T)i; /* non linear */
+                 - (uint32_t)i; /* non linear */
         i++;
         if (i>=N) { mt[0] = mt[N-1]; i=1; }
     }
@@ -208,7 +204,7 @@
 {
     PyObject *result = NULL;            /* guilty until proved innocent */
     PyObject *n = NULL;
-    PY_UINT32_T *key = NULL;
+    uint32_t *key = NULL;
     size_t bits, keyused;
     int res;
     PyObject *arg = NULL;
@@ -220,7 +216,7 @@
         time_t now;
 
         time(&now);
-        init_genrand(self, (PY_UINT32_T)now);
+        init_genrand(self, (uint32_t)now);
         Py_INCREF(Py_None);
         return Py_None;
     }
@@ -248,7 +244,7 @@
     keyused = bits == 0 ? 1 : (bits - 1) / 32 + 1;
 
     /* Convert seed to byte sequence. */
-    key = (PY_UINT32_T *)PyMem_Malloc((size_t)4 * keyused);
+    key = (uint32_t *)PyMem_Malloc((size_t)4 * keyused);
     if (key == NULL) {
         PyErr_NoMemory();
         goto Done;
@@ -267,7 +263,7 @@
         size_t i, j;
         /* Reverse an array. */
         for (i = 0, j = keyused - 1; i < j; i++, j--) {
-            PY_UINT32_T tmp = key[i];
+            uint32_t tmp = key[i];
             key[i] = key[j];
             key[j] = tmp;
         }
@@ -329,7 +325,7 @@
         element = PyLong_AsUnsignedLong(PyTuple_GET_ITEM(state, i));
         if (element == (unsigned long)-1 && PyErr_Occurred())
             return NULL;
-        self->state[i] = (PY_UINT32_T)element;
+        self->state[i] = (uint32_t)element;
     }
 
     index = PyLong_AsLong(PyTuple_GET_ITEM(state, i));
@@ -349,8 +345,8 @@
 random_getrandbits(RandomObject *self, PyObject *args)
 {
     int k, i, words;
-    PY_UINT32_T r;
-    PY_UINT32_T *wordarray;
+    uint32_t r;
+    uint32_t *wordarray;
     PyObject *result;
 
     if (!PyArg_ParseTuple(args, "i:getrandbits", &k))
@@ -366,7 +362,7 @@
         return PyLong_FromUnsignedLong(genrand_int32(self) >> (32 - k));
 
     words = (k - 1) / 32 + 1;
-    wordarray = (PY_UINT32_T *)PyMem_Malloc(words * 4);
+    wordarray = (uint32_t *)PyMem_Malloc(words * 4);
     if (wordarray == NULL) {
         PyErr_NoMemory();
         return NULL;
diff --git a/Modules/_testcapimodule.c b/Modules/_testcapimodule.c
index 290797f..8d2cf31 100644
--- a/Modules/_testcapimodule.c
+++ b/Modules/_testcapimodule.c
@@ -98,14 +98,14 @@
     CHECK_SIGNNESS(Py_UCS1, 0);
     CHECK_SIGNNESS(Py_UCS2, 0);
     CHECK_SIGNNESS(Py_UCS4, 0);
-    CHECK_SIZEOF(PY_INT32_T, 4);
-    CHECK_SIGNNESS(PY_INT32_T, 1);
-    CHECK_SIZEOF(PY_UINT32_T, 4);
-    CHECK_SIGNNESS(PY_UINT32_T, 0);
-    CHECK_SIZEOF(PY_INT64_T, 8);
-    CHECK_SIGNNESS(PY_INT64_T, 1);
-    CHECK_SIZEOF(PY_UINT64_T, 8);
-    CHECK_SIGNNESS(PY_UINT64_T, 0);
+    CHECK_SIZEOF(int32_t, 4);
+    CHECK_SIGNNESS(int32_t, 1);
+    CHECK_SIZEOF(uint32_t, 4);
+    CHECK_SIGNNESS(uint32_t, 0);
+    CHECK_SIZEOF(int64_t, 8);
+    CHECK_SIGNNESS(int64_t, 1);
+    CHECK_SIZEOF(uint64_t, 8);
+    CHECK_SIGNNESS(uint64_t, 0);
 
     /* pointer/size types */
     CHECK_SIZEOF(size_t, sizeof(void *));
diff --git a/Modules/audioop.c b/Modules/audioop.c
index ed1eca3..c11506c 100644
--- a/Modules/audioop.c
+++ b/Modules/audioop.c
@@ -297,7 +297,7 @@
 
 #define GETINT8(cp, i)          GETINTX(signed char, (cp), (i))
 #define GETINT16(cp, i)         GETINTX(short, (cp), (i))
-#define GETINT32(cp, i)         GETINTX(PY_INT32_T, (cp), (i))
+#define GETINT32(cp, i)         GETINTX(int32_t, (cp), (i))
 
 #if WORDS_BIGENDIAN
 #define GETINT24(cp, i)  (                              \
@@ -314,7 +314,7 @@
 
 #define SETINT8(cp, i, val)     SETINTX(signed char, (cp), (i), (val))
 #define SETINT16(cp, i, val)    SETINTX(short, (cp), (i), (val))
-#define SETINT32(cp, i, val)    SETINTX(PY_INT32_T, (cp), (i), (val))
+#define SETINT32(cp, i, val)    SETINTX(int32_t, (cp), (i), (val))
 
 #if WORDS_BIGENDIAN
 #define SETINT24(cp, i, val)  do {                              \
@@ -1129,7 +1129,7 @@
             val = ((unsigned int)GETINT24(fragment->buf, i)) & 0xffffffu;
         else {
             assert(width == 4);
-            val = GETINTX(PY_UINT32_T, fragment->buf, i);
+            val = GETINTX(uint32_t, fragment->buf, i);
         }
 
         val += (unsigned int)bias;
@@ -1144,7 +1144,7 @@
             SETINT24(ncp, i, (int)val);
         else {
             assert(width == 4);
-            SETINTX(PY_UINT32_T, ncp, i, val);
+            SETINTX(uint32_t, ncp, i, val);
         }
     }
     return rv;
diff --git a/Objects/unicodeobject.c b/Objects/unicodeobject.c
index 4256d05..86f23c9 100644
--- a/Objects/unicodeobject.c
+++ b/Objects/unicodeobject.c
@@ -5330,7 +5330,7 @@
     const void *data;
     Py_ssize_t len;
     PyObject *v;
-    PY_UINT32_T *out;
+    uint32_t *out;
 #if PY_LITTLE_ENDIAN
     int native_ordering = byteorder <= 0;
 #else
@@ -5361,7 +5361,7 @@
 
     /* output buffer is 4-bytes aligned */
     assert(_Py_IS_ALIGNED(PyBytes_AS_STRING(v), 4));
-    out = (PY_UINT32_T *)PyBytes_AS_STRING(v);
+    out = (uint32_t *)PyBytes_AS_STRING(v);
     if (byteorder == 0)
         *out++ = 0xFEFF;
     if (len == 0)
@@ -5427,7 +5427,7 @@
 
         /* four bytes are reserved for each surrogate */
         if (moreunits > 1) {
-            Py_ssize_t outpos = out - (PY_UINT32_T*) PyBytes_AS_STRING(v);
+            Py_ssize_t outpos = out - (uint32_t*) PyBytes_AS_STRING(v);
             Py_ssize_t morebytes = 4 * (moreunits - 1);
             if (PyBytes_GET_SIZE(v) > PY_SSIZE_T_MAX - morebytes) {
                 /* integer overflow */
@@ -5436,7 +5436,7 @@
             }
             if (_PyBytes_Resize(&v, PyBytes_GET_SIZE(v) + morebytes) < 0)
                 goto error;
-            out = (PY_UINT32_T*) PyBytes_AS_STRING(v) + outpos;
+            out = (uint32_t*) PyBytes_AS_STRING(v) + outpos;
         }
 
         if (PyBytes_Check(rep)) {
diff --git a/Python/pyhash.c b/Python/pyhash.c
index 97cb547..9080d25 100644
--- a/Python/pyhash.c
+++ b/Python/pyhash.c
@@ -318,40 +318,37 @@
 
  Modified for Python by Christian Heimes:
     - C89 / MSVC compatibility
-    - PY_UINT64_T, PY_UINT32_T and PY_UINT8_T
     - _rotl64() on Windows
     - letoh64() fallback
 */
 
-typedef unsigned char PY_UINT8_T;
-
 /* byte swap little endian to host endian
  * Endian conversion not only ensures that the hash function returns the same
  * value on all platforms. It is also required to for a good dispersion of
  * the hash values' least significant bits.
  */
 #if PY_LITTLE_ENDIAN
-#  define _le64toh(x) ((PY_UINT64_T)(x))
+#  define _le64toh(x) ((uint64_t)(x))
 #elif defined(__APPLE__)
 #  define _le64toh(x) OSSwapLittleToHostInt64(x)
 #elif defined(HAVE_LETOH64)
 #  define _le64toh(x) le64toh(x)
 #else
-#  define _le64toh(x) (((PY_UINT64_T)(x) << 56) | \
-                      (((PY_UINT64_T)(x) << 40) & 0xff000000000000ULL) | \
-                      (((PY_UINT64_T)(x) << 24) & 0xff0000000000ULL) | \
-                      (((PY_UINT64_T)(x) << 8)  & 0xff00000000ULL) | \
-                      (((PY_UINT64_T)(x) >> 8)  & 0xff000000ULL) | \
-                      (((PY_UINT64_T)(x) >> 24) & 0xff0000ULL) | \
-                      (((PY_UINT64_T)(x) >> 40) & 0xff00ULL) | \
-                      ((PY_UINT64_T)(x)  >> 56))
+#  define _le64toh(x) (((uint64_t)(x) << 56) | \
+                      (((uint64_t)(x) << 40) & 0xff000000000000ULL) | \
+                      (((uint64_t)(x) << 24) & 0xff0000000000ULL) | \
+                      (((uint64_t)(x) << 8)  & 0xff00000000ULL) | \
+                      (((uint64_t)(x) >> 8)  & 0xff000000ULL) | \
+                      (((uint64_t)(x) >> 24) & 0xff0000ULL) | \
+                      (((uint64_t)(x) >> 40) & 0xff00ULL) | \
+                      ((uint64_t)(x)  >> 56))
 #endif
 
 
 #ifdef _MSC_VER
 #  define ROTATE(x, b)  _rotl64(x, b)
 #else
-#  define ROTATE(x, b) (PY_UINT64_T)( ((x) << (b)) | ( (x) >> (64 - (b))) )
+#  define ROTATE(x, b) (uint64_t)( ((x) << (b)) | ( (x) >> (64 - (b))) )
 #endif
 
 #define HALF_ROUND(a,b,c,d,s,t)         \
@@ -369,22 +366,22 @@
 
 static Py_hash_t
 siphash24(const void *src, Py_ssize_t src_sz) {
-    PY_UINT64_T k0 = _le64toh(_Py_HashSecret.siphash.k0);
-    PY_UINT64_T k1 = _le64toh(_Py_HashSecret.siphash.k1);
-    PY_UINT64_T b = (PY_UINT64_T)src_sz << 56;
-    const PY_UINT64_T *in = (PY_UINT64_T*)src;
+    uint64_t k0 = _le64toh(_Py_HashSecret.siphash.k0);
+    uint64_t k1 = _le64toh(_Py_HashSecret.siphash.k1);
+    uint64_t b = (uint64_t)src_sz << 56;
+    const uint64_t *in = (uint64_t*)src;
 
-    PY_UINT64_T v0 = k0 ^ 0x736f6d6570736575ULL;
-    PY_UINT64_T v1 = k1 ^ 0x646f72616e646f6dULL;
-    PY_UINT64_T v2 = k0 ^ 0x6c7967656e657261ULL;
-    PY_UINT64_T v3 = k1 ^ 0x7465646279746573ULL;
+    uint64_t v0 = k0 ^ 0x736f6d6570736575ULL;
+    uint64_t v1 = k1 ^ 0x646f72616e646f6dULL;
+    uint64_t v2 = k0 ^ 0x6c7967656e657261ULL;
+    uint64_t v3 = k1 ^ 0x7465646279746573ULL;
 
-    PY_UINT64_T t;
-    PY_UINT8_T *pt;
-    PY_UINT8_T *m;
+    uint64_t t;
+    uint8_t *pt;
+    uint8_t *m;
 
     while (src_sz >= 8) {
-        PY_UINT64_T mi = _le64toh(*in);
+        uint64_t mi = _le64toh(*in);
         in += 1;
         src_sz -= 8;
         v3 ^= mi;
@@ -393,13 +390,13 @@
     }
 
     t = 0;
-    pt = (PY_UINT8_T *)&t;
-    m = (PY_UINT8_T *)in;
+    pt = (uint8_t *)&t;
+    m = (uint8_t *)in;
     switch (src_sz) {
         case 7: pt[6] = m[6];
         case 6: pt[5] = m[5];
         case 5: pt[4] = m[4];
-        case 4: Py_MEMCPY(pt, m, sizeof(PY_UINT32_T)); break;
+        case 4: Py_MEMCPY(pt, m, sizeof(uint32_t)); break;
         case 3: pt[2] = m[2];
         case 2: pt[1] = m[1];
         case 1: pt[0] = m[0];