diff --git a/numpy/random/_common.pyx b/numpy/random/_common.pyx
index ad43f281226a..ffc821e4485e 100644
--- a/numpy/random/_common.pyx
+++ b/numpy/random/_common.pyx
@@ -5,6 +5,7 @@ from cpython cimport PyFloat_AsDouble
 import sys
 import numpy as np
 cimport numpy as np
+cimport numpy.math as npmath
 
 from libc.stdint cimport uintptr_t
 
@@ -343,6 +344,24 @@ cdef object float_fill_from_double(void *func, bitgen_t *state, object size, obj
             out_array_data[i] = <float>random_func(state)
     return out_array
 
+cdef int _check_array_cons_bounded_0_1(np.ndarray val, object name) except -1:
+    cdef double *val_data
+    cdef np.npy_intp i
+    cdef bint err = 0
+
+    if not np.PyArray_ISONESEGMENT(val) or np.PyArray_TYPE(val) != np.NPY_DOUBLE:
+        # slow path for non-contiguous arrays or any non-double dtypes
+        err = not np.all(np.greater_equal(val, 0)) or not np.all(np.less_equal(val, 1))
+    else:
+        val_data = <double *>np.PyArray_DATA(val)
+        for i in range(np.PyArray_SIZE(val)):
+            err = (not (val_data[i] >= 0)) or (not val_data[i] <= 1)
+            if err:
+                break
+    if err:
+        raise ValueError(f"{name} < 0, {name} > 1 or {name} contains NaNs")
+
+    return 0
 
 cdef int check_array_constraint(np.ndarray val, object name, constraint_type cons) except -1:
     if cons == CONS_NON_NEGATIVE:
@@ -354,9 +373,7 @@ cdef int check_array_constraint(np.ndarray val, object name, constraint_type con
         elif np.any(np.less_equal(val, 0)):
             raise ValueError(name + " <= 0")
     elif cons == CONS_BOUNDED_0_1:
-        if not np.all(np.greater_equal(val, 0)) or \
-                not np.all(np.less_equal(val, 1)):
-            raise ValueError("{0} < 0, {0} > 1 or {0} contains NaNs".format(name))
+        return _check_array_cons_bounded_0_1(val, name)
     elif cons == CONS_BOUNDED_GT_0_1:
         if not np.all(np.greater(val, 0)) or not np.all(np.less_equal(val, 1)):
             raise ValueError("{0} <= 0, {0} > 1 or {0} contains NaNs".format(name))