Some changes suggested by reviewers

Use psuedo-random, instead of quasi-random.

Use Intel oneAPI Math Kernel Library official name, and oneMKL as official acronym.

docs/source/how_to.rst

@@ -4,11 +4,11 @@ How-to Guides
 How to save and resume long computation
 ---------------------------------------
 
-:class:`RandomState` is pickleable, and pickling allows to save and restore
-the internal state of the quasi-random number generators.
+:class:`RandomState` is pickleable. Pickling allows to save and restore
+the internal state of the pseudorandom number generators.
 
 .. code-block:: python
-    :caption: Saving state of quasi-random basic random number generators
+    :caption: Saving state of pseudorandom basic random number generators
 
         import numpy as np
         import mkl_random

docs/source/index.rst

@@ -3,7 +3,7 @@ Random sampling powered by Intel(R) Math Kernel Library
 
 :mod:`mkl_random` is Python package exposing pseudo-random and non-deterministic random 
 number generators with continuous and discrete distribution available in 
-Intel(R) Math Kernel Library (MKL).
+Intel(R) oneAPI Math Kernel Library (`oneMKL <https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl.html>`_).
 
 .. grid:: 2
     :gutter: 3

docs/source/reference/ars5.rst

@@ -3,11 +3,11 @@
 ARS5 brng
 =========
 
-The ARS5 counter-based pseudorandom number generator based on AES encryption algorithm can be 
+The ARS5 counter-based pseudo-random number generator based on AES encryption algorithm can be 
 initialized with either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for ARS5 basic random number generator with scalar seed
+    :caption: Construction for ARS5 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="ars5")
@@ -17,7 +17,7 @@ initialized with either an integral seed, a list of integral seeds, or automatic
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for ARS5 basic random number generator with vector seed
+    :caption: Construction for ARS5 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="ars5")
@@ -29,7 +29,7 @@ initialized with either an integral seed, a list of integral seeds, or automatic
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for ARS5 basic random number generator automatic seed
+    :caption: Construction for ARS5 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="ars5")

docs/source/reference/index.rst

@@ -8,17 +8,17 @@ The basic random number generator is chosen by specifying :code:`brng` keyword a
 
 The list of supported basic random number generators is as follows (also see `oneMKL Engines <oneMKLBRNG_>`_):
 
-* :code:`'MT19937'` - the Mersenne Twister pseudo-random number generator (default), :doc:`example <mt19937>`
-* :code:`'SFMT19937'` - the SIMD-oriented Mersenne Twister pseudo-random number generator, :doc:`example <sfmt19937>`
-* :code:`'MT2203'` -  the set of 6024 Mersenne Twister pseudorandom number generators, :doc:`example <mt2203>`
-* :code:`'R250'` - the 32-bit generalized feedback shift register pseudorandom number generator GFSR(250,103), :doc:`example <r250>`
-* :code:`'WH'` -  the set of 273 Wichmann-Hill’s combined multiplicative congruential generators, :doc:`example <wichmann_hill>`
-* :code:`'MCG31'` - the 31-bit multiplicative congruential pseudorandom number generator, :doc:`example <mcg31>`
-* :code:`'MCG59'` - the 59-bit multiplicative congruential pseudorandom number generator, :doc:`example <mcg59>`
-* :code:`'MRG32K3A'` - the combined multiple recursive pseudorandom number generator MRG32k3a, :doc:`example <mrg32k3a>`
-* :code:`'PHILOX4X32X10'` - the Philox4x32x10 counter-based pseudorandom number generator, :doc:`example <philox4x32x10>`
-* :code:`'NONDETERM'` - the generator with non-deterministic source of randomness (for example, a hardware device), :doc:`example <nondeterministic>`
-* :code:`'ARS5'` - the ARS5 counter-based pseudorandom number generator based on AES encryption algorithm, :doc:`example <ars5>`
+* :ref:`'MT19937' <mt19937_brng>` - the Mersenne Twister pseudo-random number generator (default)
+* :ref:`'SFMT19937' <sfmt19937_brng>` - the SIMD-oriented Mersenne Twister pseudo-random number generator
+* :ref:`'MT2203' <mt2203_brng>` -  the set of 6024 Mersenne Twister pseudo-random number generators
+* :ref:`'R250' <r250_brng>` - the 32-bit generalized feedback shift register pseudo-random number generator GFSR(250,103)
+* :ref:`'WH' <wh_brng>` -  the set of 273 Wichmann-Hill’s combined multiplicative congruential pseudo-random number generators
+* :ref:`'MCG31' <mcg31m1_brng>` - the 31-bit multiplicative congruential pseudo-random number generator
+* :ref:`'MCG59' <mcg59_brng>` - the 59-bit multiplicative congruential pseudo-random number generator
+* :ref:`'MRG32K3A' <mrg32k3a_brng>` - the combined multiple recursive pseudo-random number generator MRG32k3a
+* :ref:`'PHILOX4X32X10' <philox4x32x10_brng>` - the Philox4x32x10 counter-based pseudo-random number generator
+* :ref:`'NONDETERM' <nondeterm_brng>` - the generator with non-deterministic source of randomness (for example, a hardware device)
+* :ref:`'ARS5' <ars5_brng>` - the ARS5 counter-based pseudo-random number generator based on AES encryption algorithm
 
 .. _oneMKLBRNG: https://spec.oneapi.io/versions/1.0-rev-2/elements/oneMKL/source/domains/rng/engines-basic-random-number-generators.html
 

docs/source/reference/mcg31.rst

@@ -3,11 +3,11 @@
 MCG31 brng
 ==========
 
-The 31-bit multiplicative congruential pseudorandom number generator MCG(1132489760, 2**31 -1) can be 
+The 31-bit multiplicative congruential pseudo-random number generator :math:`mcg(1132489760, 2^{31} -1)` can be 
 initialized with  either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator with scalar seed
+    :caption: Construction for MCG31 basic random pseudo-number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="MCG31")
@@ -17,7 +17,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator with vector seed
+    :caption: Construction for MCG31 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="MCG31")
@@ -29,7 +29,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator automatic seed
+    :caption: Construction for MCG31 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="MCG31")

docs/source/reference/mcg59.rst

@@ -3,11 +3,11 @@
 MCG59 brng
 ==========
 
-The 59-bit multiplicative congruential pseudorandom number generator can be 
+The 59-bit multiplicative congruential pseudo-random number generator can be 
 initialized with  either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator with scalar seed
+    :caption: Construction for MCG31 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="MCG59")
@@ -17,7 +17,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator with vector seed
+    :caption: Construction for MCG31 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="MCG59")
@@ -29,7 +29,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for MCG31 basic random number generator automatic seed
+    :caption: Construction for MCG31 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="MCG59")

docs/source/reference/mrg32k3a.rst

@@ -3,11 +3,11 @@
 MRG32k3a brng
 =============
 
-The combined multiple recursive pseudorandom number generator MRG32k3a can be 
+The combined multiple recursive pseudo-random number generator MRG32k3a can be 
 initialized with  either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for MRG32k3a basic random number generator with scalar seed
+    :caption: Construction for MRG32k3a basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="MRG32k3a")
@@ -17,7 +17,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for MRG32k3a basic random number generator with vector seed
+    :caption: Construction for MRG32k3a basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="MRG32k3a")
@@ -29,7 +29,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for MRG32k3a basic random number generator automatic seed
+    :caption: Construction for MRG32k3a basic psuedo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="MRG32k3a")

docs/source/reference/mt19937.rst

@@ -3,11 +3,11 @@
 MT19937 brng
 ============
 
-The Mersenne Twister random number generator can be initialized with either an integral seed, 
+The Mersenne Twister pseudo-random number generator can be initialized with either an integral seed, 
 a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for MT19937 basic random number generator with scalar seed
+    :caption: Construction for MT19937 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="MT19937")
@@ -16,7 +16,7 @@ a list of integral seeds, or automatically.
         usample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for MT19937 basic random number generator with vector seed
+    :caption: Construction for MT19937 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="MT19937")
@@ -27,7 +27,7 @@ a list of integral seeds, or automatically.
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for MT19937 basic random number generator automatic seed
+    :caption: Construction for MT19937 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="MT19937")

docs/source/reference/mt2203.rst

@@ -10,7 +10,7 @@ An individual member of the set can be addressed by using a tuple to specify the
 :code:`brng=("MT2203", set_id)` where :math:`0 \leq \text{set_id} < 6024`.
 
 .. code-block:: python
-    :caption: Construction for MT2203 basic random number generator with scalar seed
+    :caption: Construction for MT2203 basic psuedo-random number generator with scalar seed
 
         import mkl_random
         seed = 777
@@ -26,7 +26,7 @@ An individual member of the set can be addressed by using a tuple to specify the
         sample = rs5.uniform(0, 1, size=1_000_000)
 
 .. code-block:: python
-    :caption: Construction for MT2203 basic random number generator with vector seed
+    :caption: Construction for MT2203 basic psuedo-random number generator with vector seed
 
         import mkl_random
         rs = mkl_random.RandomState([1234, 567, 89, 0], brng=("MT2203", 6023))
@@ -38,7 +38,7 @@ An individual member of the set can be addressed by using a tuple to specify the
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for MT2203 basic random number generator automatic seed
+    :caption: Construction for MT2203 basic psuedo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="MT2203")

docs/source/reference/nondeterministic.rst

@@ -4,7 +4,9 @@ Nondeterm brng
 ==============
 
 The generator with non-deterministic source of randomness, such as a hardware device, requires no seeding.
-This basic random number generator should not be used if reproducibility of stochastic simulation is required.
+
+.. note::
+    This basic random number generator should not be used if reproducibility of stochastic simulation is required.
 
 .. code-block:: python
     :caption: Construction for non-deterministic basic random number generator

docs/source/reference/philox4x32x10.rst

@@ -3,11 +3,11 @@
 Philox4x32x10 brng
 ==================
 
-The Philox 4x32x10 counter-based pseudorandom number generator can be 
+The Philox 4x32x10 counter-based pseudo-random number generator can be 
 initialized with  either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for Philox4x32x10 basic random number generator with scalar seed
+    :caption: Construction for Philox4x32x10 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="philox4x32x10")
@@ -17,7 +17,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for Philox4x32x10 basic random number generator with vector seed
+    :caption: Construction for Philox4x32x10 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="philox4x32x10")
@@ -29,7 +29,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for Philox4x32x10 basic random number generator automatic seed
+    :caption: Construction for Philox4x32x10 basic pseudo random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="philox4x32x10")

docs/source/reference/r250.rst

@@ -3,11 +3,11 @@
 R250 brng
 =========
 
-The 32-bit generalized feedback shift register pseudorandom number generator GFSR(250,103) can be 
+The 32-bit generalized feedback shift register pseudo-random number generator GFSR(250,103) can be 
 initialized with  either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for R250 basic random number generator with scalar seed
+    :caption: Construction for R250 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="R250")
@@ -17,7 +17,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
         esample = rs.uniform(0, 1, size=1000)
 
 .. code-block:: python
-    :caption: Construction for R250 basic random number generator with vector seed
+    :caption: Construction for R250 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="R250")
@@ -29,7 +29,7 @@ initialized with  either an integral seed, a list of integral seeds, or automati
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for R250 basic random number generator automatic seed
+    :caption: Construction for R250 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="R250")

docs/source/reference/sfmt19937.rst

@@ -3,11 +3,11 @@
 SFMT19937 brng
 ==============
 
-The SIMD-oriented Mersenne Twister random number generator can be initialized with 
+The SIMD-oriented Mersenne Twister pseudo-random number generator can be initialized with 
 either an integral seed, a list of integral seeds, or automatically.
 
 .. code-block:: python
-    :caption: Construction for SFMT19937 basic random number generator with scalar seed
+    :caption: Construction for SFMT19937 basic pseudo-random number generator with scalar seed
 
         import mkl_random
         rs = mkl_random.RandomState(1234, brng="SFMT19937")
@@ -17,7 +17,7 @@ either an integral seed, a list of integral seeds, or automatically.
         esample = rs.exponential(2.3, size=1000)
 
 .. code-block:: python
-    :caption: Construction for SFMT19937 basic random number generator with vector seed
+    :caption: Construction for SFMT19937 basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs_vec = mkl_random.RandomState([1234, 567, 89, 0], brng="SFMT19937")
@@ -29,7 +29,7 @@ either an integral seed, a list of integral seeds, or automatically.
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for SFMT19937 basic random number generator automatic seed
+    :caption: Construction for SFMT19937 basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="SFMT19937")

docs/source/reference/wichmann_hill.rst

@@ -11,7 +11,7 @@ An individual member of the set can be addressed by using a tuple to specify the
 :code:`brng=("WH", set_id)` where :math:`0 \leq \text{set_id} < 273`.
 
 .. code-block:: python
-    :caption: Construction for WH basic random number generator with scalar seed
+    :caption: Construction for WH basic psuedo-random number generator with scalar seed
 
         import mkl_random
         seed = 777
@@ -27,7 +27,7 @@ An individual member of the set can be addressed by using a tuple to specify the
         sample = rs5.uniform(0, 1, size=1_000_000)
 
 .. code-block:: python
-    :caption: Construction for WH basic random number generator with vector seed
+    :caption: Construction for WH basic pseudo-random number generator with vector seed
 
         import mkl_random
         rs = mkl_random.RandomState([1234, 567, 89, 0], brng=("WH", 200))
@@ -39,7 +39,7 @@ An individual member of the set can be addressed by using a tuple to specify the
 When seed is not specified, the generator is initialized using system clock, e.g.:
 
 .. code-block:: python
-    :caption: Construction for WH basic random number generator automatic seed
+    :caption: Construction for WH basic pseudo-random number generator with automatic seed
 
         import mkl_random
         rs_def = mkl_random.RandomState(brng="WH")