diff --git a/numpy/random/randomgen/generator.pyx b/numpy/random/randomgen/generator.pyx
index 0ca02e9127fe..b05f490334fe 100644
--- a/numpy/random/randomgen/generator.pyx
+++ b/numpy/random/randomgen/generator.pyx
@@ -2557,8 +2557,8 @@ cdef class RandomGenerator:
 
         >>> def logist(x, loc, scale):
         ...     return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)
-        >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\
-        ...          logist(bins, loc, scale).max())
+        >>> lgst_val = logist(bins, loc, scale)
+        >>> plt.plot(bins, lgst_val * count.max() / lgst_val.max())
         >>> plt.show()
 
         """
diff --git a/numpy/random/randomgen/mtrand.pyx b/numpy/random/randomgen/mtrand.pyx
index 4f81f92d1077..2f89f5eb0cd7 100644
--- a/numpy/random/randomgen/mtrand.pyx
+++ b/numpy/random/randomgen/mtrand.pyx
@@ -2573,8 +2573,8 @@ cdef class RandomState:
 
         >>> def logist(x, loc, scale):
         ...     return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)
-        >>> plt.plot(bins, logist(bins, loc, scale)*count.max(),
-        ...          logist(bins, loc, scale).max())
+        >>> lgst_val = logist(bins, loc, scale)
+        >>> plt.plot(bins, lgst_val * count.max() / lgst_val.max())
         >>> plt.show()
 
         """
diff --git a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-benchmark.c b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-benchmark.c
index 108058eeb103..9a7b52bfbf29 100644
--- a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-benchmark.c
+++ b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-benchmark.c
@@ -14,14 +14,16 @@
 
 #define N 1000000000
 
-int main() {
+int main()
+{
   uint64_t count = 0, sum = 0;
   uint64_t seed = 0xDEADBEAF;
   s[0] = splitmix64_next(&seed);
   s[1] = splitmix64_next(&seed);
   int i;
   clock_t begin = clock();
-  for (i = 0; i < N; i++) {
+  for (i = 0; i < N; i++)
+  {
     sum += next();
     count++;
   }
diff --git a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-test-data-gen.c b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-test-data-gen.c
index d95260eca176..d50e63f5e6da 100644
--- a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-test-data-gen.c
+++ b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128-test-data-gen.c
@@ -21,50 +21,61 @@
 
 #define N 1000
 
-int main() {
+int main()
+{
   uint64_t sum = 0;
   uint64_t state, seed = 0xDEADBEAF;
   state = seed;
   int i;
-  for (i = 0; i < 2; i++) {
+  for (i = 0; i < 2; i++)
+  {
     s[i] = splitmix64_next(&state);
   }
   uint64_t store[N];
-  for (i = 0; i < N; i++) {
+  for (i = 0; i < N; i++)
+  {
     store[i] = next();
   }
 
   FILE *fp;
   fp = fopen("xoroshiro128-testset-1.csv", "w");
-  if (fp == NULL) {
+  if (fp == NULL)
+  {
     printf("Couldn't open file\n");
     return -1;
   }
   fprintf(fp, "seed, 0x%" PRIx64 "\n", seed);
-  for (i = 0; i < N; i++) {
+  for (i = 0; i < N; i++)
+  {
     fprintf(fp, "%d, 0x%" PRIx64 "\n", i, store[i]);
-    if (i == 999) {
+    if (i == 999)
+    {
       printf("%d, 0x%" PRIx64 "\n", i, store[i]);
     }
   }
   fclose(fp);
 
   seed = state = 0;
-  for (i = 0; i < 2; i++) {
+  for (i = 0; i < 2; i++)
+  {
     s[i] = splitmix64_next(&state);
   }
-  for (i = 0; i < N; i++) {
+  for (i = 0; i < N; i++)
+  {
     store[i] = next();
   }
   fp = fopen("xoroshiro128-testset-2.csv", "w");
-  if (fp == NULL) {
+  if (fp == NULL)
+  {
     printf("Couldn't open file\n");
     return -1;
   }
   fprintf(fp, "seed, 0x%" PRIx64 "\n", seed);
-  for (i = 0; i < N; i++) {
+  for (i = 0; i < N; i++)
+  {
     fprintf(fp, "%d, 0x%" PRIx64 "\n", i, store[i]);
-    if (i == 999) {
+    if (i == 999)
+    {
       printf("%d, 0x%" PRIx64 "\n", i, store[i]);
     }
   }
diff --git a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.c b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.c
index 981aeab8478c..060eb8a518c1 100644
--- a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.c
+++ b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.c
@@ -1,4 +1,4 @@
-/*  Written in 2016 by David Blackman and Sebastiano Vigna (vigna@acm.org)
+/*  Written in 2016-2018 by David Blackman and Sebastiano Vigna (vigna@acm.org)
 
 To the extent possible under law, the author has dedicated all copyright
 and related and neighboring rights to this software to the public domain
@@ -6,29 +6,28 @@ worldwide. This software is distributed without any warranty.
 
 See <http://creativecommons.org/publicdomain/zero/1.0/>. */
 
-/* This is the successor to xorshift128+. It is the fastest full-period
-   generator passing BigCrush without systematic failures, but due to the
-   relatively short period it is acceptable only for applications with a
-   mild amount of parallelism; otherwise, use a xorshift1024* generator.
-
-   Beside passing BigCrush, this generator passes the PractRand test suite
-   up to (and included) 16TB, with the exception of binary rank tests, as
-   the lowest bit of this generator is an LFSR of degree 128. The next bit
-   can be described by an LFSR of degree 8256, but in the long run it will
-   fail linearity tests, too. The other bits needs a much higher degree to
-   be represented as LFSRs.
+/* This is xoroshiro128+ 1.0, our best and fastest small-state generator
+   for floating-point numbers. We suggest to use its upper bits for
+   floating-point generation, as it is slightly faster than
+   xoroshiro128**. It passes all tests we are aware of except for the four
+   lower bits, which might fail linearity tests (and just those), so if
+   low linear complexity is not considered an issue (as it is usually the
+   case) it can be used to generate 64-bit outputs, too; moreover, this
+   generator has a very mild Hamming-weight dependency making our test
+   (http://prng.di.unimi.it/hwd.php) fail after 5 TB of output; we believe
+   this slight bias cannot affect any application. If you are concerned,
+   use xoroshiro128** or xoshiro256+.
 
    We suggest to use a sign test to extract a random Boolean value, and
    right shifts to extract subsets of bits.
 
-   Note that the generator uses a simulated rotate operation, which most C
-   compilers will turn into a single instruction. In Java, you can use
-   Long.rotateLeft(). In languages that do not make low-level rotation
-   instructions accessible xorshift128+ could be faster.
-
    The state must be seeded so that it is not everywhere zero. If you have
    a 64-bit seed, we suggest to seed a splitmix64 generator and use its
-   output to fill s. */
+   output to fill s.
+
+   NOTE: the parameters (a=24, b=16, b=37) of this version give slightly
+   better results in our test than the 2016 version (a=55, b=14, c=36).
+*/
 
 #include "xoroshiro128.h"
 
@@ -36,17 +35,20 @@ extern INLINE uint64_t xoroshiro128_next64(xoroshiro128_state *state);
 
 extern INLINE uint32_t xoroshiro128_next32(xoroshiro128_state *state);
 
-void xoroshiro128_jump(xoroshiro128_state *state) {
+void xoroshiro128_jump(xoroshiro128_state *state)
+{
   int i, b;
   uint64_t s0;
   uint64_t s1;
-  static const uint64_t JUMP[] = {0xbeac0467eba5facb, 0xd86b048b86aa9922};
+  static const uint64_t JUMP[] = {0xdf900294d8f554a5, 0x170865df4b3201fc};
 
   s0 = 0;
   s1 = 0;
   for (i = 0; i < sizeof JUMP / sizeof *JUMP; i++)
-    for (b = 0; b < 64; b++) {
-      if (JUMP[i] & UINT64_C(1) << b) {
+    for (b = 0; b < 64; b++)
+    {
+      if (JUMP[i] & UINT64_C(1) << b)
+      {
         s0 ^= state->s[0];
         s1 ^= state->s[1];
       }
diff --git a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.h b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.h
index 40cb39218908..0db82b173839 100644
--- a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.h
+++ b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128.h
@@ -14,35 +14,41 @@
 #define INLINE inline
 #endif
 
-typedef struct s_xoroshiro128_state {
+typedef struct s_xoroshiro128_state
+{
   uint64_t s[2];
   int has_uint32;
   uint32_t uinteger;
 } xoroshiro128_state;
 
-static INLINE uint64_t rotl(const uint64_t x, int k) {
+static INLINE uint64_t rotl(const uint64_t x, int k)
+{
   return (x << k) | (x >> (64 - k));
 }
 
-static INLINE uint64_t xoroshiro128_next(uint64_t *s) {
+static INLINE uint64_t xoroshiro128_next(uint64_t *s)
+{
   const uint64_t s0 = s[0];
   uint64_t s1 = s[1];
   const uint64_t result = s0 + s1;
 
   s1 ^= s0;
-  s[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14); // a, b
-  s[1] = rotl(s1, 36);                   // c
+  s[0] = rotl(s0, 24) ^ s1 ^ (s1 << 16); // a, b
+  s[1] = rotl(s1, 37);                   // c
 
   return result;
 }
 
-static INLINE uint64_t xoroshiro128_next64(xoroshiro128_state *state) {
+static INLINE uint64_t xoroshiro128_next64(xoroshiro128_state *state)
+{
   return xoroshiro128_next(&state->s[0]);
 }
 
-static INLINE uint32_t xoroshiro128_next32(xoroshiro128_state *state) {
+static INLINE uint32_t xoroshiro128_next32(xoroshiro128_state *state)
+{
   uint64_t next;
-  if (state->has_uint32) {
+  if (state->has_uint32)
+  {
     state->has_uint32 = 0;
     return state->uinteger;
   }
diff --git a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128plus.orig.c b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128plus.orig.c
index c0293cc2b586..1b5f46e4bdb5 100644
--- a/numpy/random/randomgen/src/xoroshiro128/xoroshiro128plus.orig.c
+++ b/numpy/random/randomgen/src/xoroshiro128/xoroshiro128plus.orig.c
@@ -1,4 +1,4 @@
-/*  Written in 2016 by David Blackman and Sebastiano Vigna (vigna@acm.org)
+/*  Written in 2016-2018 by David Blackman and Sebastiano Vigna (vigna@acm.org)
 
 To the extent possible under law, the author has dedicated all copyright
 and related and neighboring rights to this software to the public domain
@@ -8,44 +8,45 @@ See <http://creativecommons.org/publicdomain/zero/1.0/>. */
 
 #include <stdint.h>
 
-/* This is the successor to xorshift128+. It is the fastest full-period
-   generator passing BigCrush without systematic failures, but due to the
-   relatively short period it is acceptable only for applications with a
-   mild amount of parallelism; otherwise, use a xorshift1024* generator.
-
-   Beside passing BigCrush, this generator passes the PractRand test suite
-   up to (and included) 16TB, with the exception of binary rank tests, as
-   the lowest bit of this generator is an LFSR of degree 128. The next bit
-   can be described by an LFSR of degree 8256, but in the long run it will
-   fail linearity tests, too. The other bits needs a much higher degree to
-   be represented as LFSRs.
+/* This is xoroshiro128+ 1.0, our best and fastest small-state generator
+   for floating-point numbers. We suggest to use its upper bits for
+   floating-point generation, as it is slightly faster than
+   xoroshiro128**. It passes all tests we are aware of except for the four
+   lower bits, which might fail linearity tests (and just those), so if
+   low linear complexity is not considered an issue (as it is usually the
+   case) it can be used to generate 64-bit outputs, too; moreover, this
+   generator has a very mild Hamming-weight dependency making our test
+   (http://prng.di.unimi.it/hwd.php) fail after 5 TB of output; we believe
+   this slight bias cannot affect any application. If you are concerned,
+   use xoroshiro128** or xoshiro256+.
 
    We suggest to use a sign test to extract a random Boolean value, and
    right shifts to extract subsets of bits.
 
-   Note that the generator uses a simulated rotate operation, which most C
-   compilers will turn into a single instruction. In Java, you can use
-   Long.rotateLeft(). In languages that do not make low-level rotation
-   instructions accessible xorshift128+ could be faster.
-
    The state must be seeded so that it is not everywhere zero. If you have
    a 64-bit seed, we suggest to seed a splitmix64 generator and use its
-   output to fill s. */
+   output to fill s.
+
+   NOTE: the parameters (a=24, b=16, b=37) of this version give slightly
+   better results in our test than the 2016 version (a=55, b=14, c=36).
+*/
 
 uint64_t s[2];
 
-static inline uint64_t rotl(const uint64_t x, int k) {
+static inline uint64_t rotl(const uint64_t x, int k)
+{
   return (x << k) | (x >> (64 - k));
 }
 
-uint64_t next(void) {
+uint64_t next(void)
+{
   const uint64_t s0 = s[0];
   uint64_t s1 = s[1];
   const uint64_t result = s0 + s1;
 
   s1 ^= s0;
-  s[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14); // a, b
-  s[1] = rotl(s1, 36);                   // c
+  s[0] = rotl(s0, 24) ^ s1 ^ (s1 << 16); // a, b
+  s[1] = rotl(s1, 37);                   // c
 
   return result;
 }
@@ -54,14 +55,42 @@ uint64_t next(void) {
    to 2^64 calls to next(); it can be used to generate 2^64
    non-overlapping subsequences for parallel computations. */
 
-void jump(void) {
-  static const uint64_t JUMP[] = {0xbeac0467eba5facb, 0xd86b048b86aa9922};
+void jump(void)
+{
+  static const uint64_t JUMP[] = {0xdf900294d8f554a5, 0x170865df4b3201fc};
 
   uint64_t s0 = 0;
   uint64_t s1 = 0;
   for (int i = 0; i < sizeof JUMP / sizeof *JUMP; i++)
-    for (int b = 0; b < 64; b++) {
-      if (JUMP[i] & UINT64_C(1) << b) {
+    for (int b = 0; b < 64; b++)
+    {
+      if (JUMP[i] & UINT64_C(1) << b)
+      {
+        s0 ^= s[0];
+        s1 ^= s[1];
+      }
+      next();
+    }
+  s[0] = s0;
+  s[1] = s1;
+}
+
+/* This is the long-jump function for the generator. It is equivalent to
+   2^96 calls to next(); it can be used to generate 2^32 starting points,
+   from each of which jump() will generate 2^32 non-overlapping
+   subsequences for parallel distributed computations. */
+
+void long_jump(void)
+{
+  static const uint64_t LONG_JUMP[] = {0xd2a98b26625eee7b, 0xdddf9b1090aa7ac1};
+
+  uint64_t s0 = 0;
+  uint64_t s1 = 0;
+  for (int i = 0; i < sizeof LONG_JUMP / sizeof *LONG_JUMP; i++)
+    for (int b = 0; b < 64; b++)
+    {
+      if (LONG_JUMP[i] & UINT64_C(1) << b)
+      {
         s0 ^= s[0];
         s1 ^= s[1];
       }
diff --git a/numpy/random/randomgen/src/xorshift1024/xorshift1024.orig.c b/numpy/random/randomgen/src/xorshift1024/xorshift1024.orig.c
index e4f899fb7b09..03c1c17fe800 100644
--- a/numpy/random/randomgen/src/xorshift1024/xorshift1024.orig.c
+++ b/numpy/random/randomgen/src/xorshift1024/xorshift1024.orig.c
@@ -14,7 +14,7 @@ See <http://creativecommons.org/publicdomain/zero/1.0/>. */
    linear dependencies from one of the lowest bits. The previous
    multiplier was 1181783497276652981 (M_8 in the paper). If you need to
    tell apart the two generators, you can refer to this generator as
-   xorshift1024*φ and to the previous one as xorshift1024*M_8.
+   xorshift1024φ and to the previous one as xorshift1024*M_8.
 
    This is a fast, high-quality generator. If 1024 bits of state are too
    much, try a xoroshiro128+ generator.
@@ -36,7 +36,7 @@ int p;
 uint64_t next(void) {
   const uint64_t s0 = s[p];
   uint64_t s1 = s[p = (p + 1) & 15];
-  s1 ^= s1 << 31;                           // a
+  s1 ^= s1 << 31; // a
   s[p] = s1 ^ s0 ^ (s1 >> 11) ^ (s0 >> 30); // b,c
   return s[p] * 0x9e3779b97f4a7c13;
 }
diff --git a/numpy/random/randomgen/tests/data/xoroshiro128-testset-1.csv b/numpy/random/randomgen/tests/data/xoroshiro128-testset-1.csv
index 8289ff27eb96..4ef7172e1735 100644
--- a/numpy/random/randomgen/tests/data/xoroshiro128-testset-1.csv
+++ b/numpy/random/randomgen/tests/data/xoroshiro128-testset-1.csv
@@ -1,1001 +1,1001 @@
 seed, 0xdeadbeaf
 0, 0x86f9f4feeebed928
-1, 0xcd2c9d2d1dc1c071
-2, 0x94741e0555641979
-3, 0x81eed88d38a9138e
-4, 0x54b9f49cd0035507
-5, 0x8c112b85821a173a
-6, 0x51f4c2eabf05c192
-7, 0xefa6a9ad4ca56d94
-8, 0xd3bd969b3aeb5457
-9, 0xcd4f28af5618e25a
-10, 0xa20fd197fb60aad
-11, 0x796b5146f61afc52
-12, 0xf6fe619effce6d62
-13, 0x763ed6613d00e8bd
-14, 0x333d357571b249c
-15, 0xc2a39f35ba8f4ce6
-16, 0xae35d916c6cf8a2b
-17, 0xfdfaa6b7eb9591d3
-18, 0x52668584489de943
-19, 0xca982b4b760effb8
-20, 0x32c7256797c26f09
-21, 0x3115b9539d722cc
-22, 0x5183f1d23dd2f56e
-23, 0xa0a2a2c524e6650c
-24, 0x3191f4b5260e5a2d
-25, 0x1eebe2655fb4f190
-26, 0x5781c6b75a253a88
-27, 0xae45a39543b4140d
-28, 0xfc62724b20d2df78
-29, 0x3770290ba157dc9c
-30, 0xc4731569807dbff4
-31, 0xd42ec771a7a0a08f
-32, 0x743276e0eb868d75
-33, 0x37f95d1ba1faebc6
-34, 0x3b4800b089a323cf
-35, 0x437fa9c71af61839
-36, 0x1cab936dd28c6f1c
-37, 0xe9d60347286dd9f0
-38, 0x716625cbd57bbd63
-39, 0xbd6c0f5e6aea7288
-40, 0x7c782d5b111a89f3
-41, 0xaeb1b9478b99970
-42, 0xbdffccb6a96cb533
-43, 0x9423e6ea789f29f1
-44, 0x53df9a7a0ea73fe6
-45, 0x7d9bec5c15c7e349
-46, 0xd1fc83fcf223aea5
-47, 0xd1dce35338ad3bab
-48, 0x297bd5f1cf79e758
-49, 0x19ec39a6191419da
-50, 0x45e57323ad58071b
-51, 0x395bcbebe1ddf611
-52, 0x22d9065efb013222
-53, 0x4ea2d534fd9fecb3
-54, 0x9b9779e1edeb2e27
-55, 0x1ba777ba576a236e
-56, 0x23cf95e34d62dd3f
-57, 0x6d1689730795e6bd
-58, 0x24e510f9d2f65379
-59, 0x1e12d607e78701e8
-60, 0x3347fe3ddc50a23e
-61, 0x331754f825305d97
-62, 0xf21a675c0344709c
-63, 0xcc9bd2062ae5fb39
-64, 0xd2dcd3a1ee6afe9e
-65, 0xbdb0388382c408d1
-66, 0x19476497aaef64ad
-67, 0x906dfff3b1181dd7
-68, 0x47edd3c528f4c753
-69, 0xba2a0f289279aec2
-70, 0x710bc73fd1c732a9
-71, 0xe0238b1ab604610d
-72, 0x10f68d7eb0d19e19
-73, 0xc13654f8b8f3d9b7
-74, 0x112c76bf71ad04a9
-75, 0x4b9d965062e9a0fd
-76, 0xe0b13496fec19aa8
-77, 0x999493dababe73c8
-78, 0x87104db5240f12fb
-79, 0x8fc8dff016c96a13
-80, 0x3eff4853e8b167a8
-81, 0x438b6f5c3d10b85d
-82, 0xc2f94a0707d949f5
-83, 0x87981b13beefb01f
-84, 0x1718db5072923bb2
-85, 0xbe7ae4310234b5f1
-86, 0x3ad4306f2b2b3b47
-87, 0x9de166baaf152f81
-88, 0xebca2cf057a00802
-89, 0x99bfd19b5e0a87b2
-90, 0x5ae7b3ab9d2623c0
-91, 0x8de5811587a53d2e
-92, 0x629a57a87d068ee4
-93, 0xfd80a82607740601
-94, 0x5758bfc8610d0b8b
-95, 0x8f0c00fab932c1f5
-96, 0x3d49bd296a34582d
-97, 0xc99c1bb8319ce526
-98, 0x1dd5ba47ac1443ba
-99, 0xb5a40a33c9ca1cf9
-100, 0xa1025156b711394c
-101, 0xdb3ef94ee8bc71a4
-102, 0x6d3292123ffa9bc9
-103, 0x4b9683ebf2f98d1f
-104, 0x4d1a4709b547bfe7
-105, 0x3623a9c4054355b1
-106, 0xed15f8852d329b4d
-107, 0x60ef76852f40e346
-108, 0xe64c2bfc6d0ef2dc
-109, 0xf286f874cfb68ee2
-110, 0xb1b07a7ca9268329
-111, 0xf618a9bfe00b7cdd
-112, 0x54a40c4f52cab527
-113, 0x5007a4d41eaf0af1
-114, 0x6fa7f2210a7b7f3a
-115, 0x7b448faa473ad765
-116, 0x901b6276232cb3c2
-117, 0xd69d06b85d118dfd
-118, 0xf8fb03c5dfef937a
-119, 0x5a53e96d5ebc4689
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diff --git a/numpy/random/randomgen/tests/data/xoroshiro128-testset-2.csv b/numpy/random/randomgen/tests/data/xoroshiro128-testset-2.csv
index 6c513476bbef..2de341ecda94 100644
--- a/numpy/random/randomgen/tests/data/xoroshiro128-testset-2.csv
+++ b/numpy/random/randomgen/tests/data/xoroshiro128-testset-2.csv
@@ -1,1001 +1,1001 @@
 seed, 0x0
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diff --git a/numpy/random/randomgen/tests/test_direct.py b/numpy/random/randomgen/tests/test_direct.py
index 5bfc872cb188..6e856de414cb 100644
--- a/numpy/random/randomgen/tests/test_direct.py
+++ b/numpy/random/randomgen/tests/test_direct.py
@@ -9,7 +9,7 @@
 
 from ...randomgen import RandomGenerator, MT19937, DSFMT, ThreeFry32, ThreeFry, \
     PCG32, PCG64, Philox, Xoroshiro128, Xorshift1024, Xoshiro256StarStar, \
-    Xoshiro512StarStar
+    Xoshiro512StarStar, RandomState
 from ...randomgen.common import interface
 
 try:
@@ -51,14 +51,6 @@ def uniform32_from_uint64(x):
     out = (joined >> np.uint32(9)) * (1.0 / 2 ** 23)
     return out.astype(np.float32)
 
-
-def uniform32_from_uint63(x):
-    x = np.uint64(x)
-    x = np.uint32(x >> np.uint64(32))
-    out = (x >> np.uint32(9)) * (1.0 / 2 ** 23)
-    return out.astype(np.float32)
-
-
 def uniform32_from_uint53(x):
     x = np.uint64(x) >> np.uint64(16)
     x = np.uint32(x & np.uint64(0xffffffff))
@@ -73,8 +65,6 @@ def uniform32_from_uint32(x):
 def uniform32_from_uint(x, bits):
     if bits == 64:
         return uniform32_from_uint64(x)
-    elif bits == 63:
-        return uniform32_from_uint63(x)
     elif bits == 53:
         return uniform32_from_uint53(x)
     elif bits == 32:
@@ -102,16 +92,6 @@ def uniform_from_uint32(x):
         out[i // 2] = (a * 67108864.0 + b) / 9007199254740992.0
     return out
 
-
-def uint64_from_uint63(x):
-    out = np.empty(len(x) // 2, dtype=np.uint64)
-    for i in range(0, len(x), 2):
-        a = x[i] & np.uint64(0xffffffff00000000)
-        b = x[i + 1] >> np.uint64(32)
-        out[i // 2] = a | b
-    return out
-
-
 def uniform_from_dsfmt(x):
     return x.view(np.double) - 1.0
 
@@ -185,15 +165,14 @@ def test_random_raw(self):
         uints = brng.random_raw(1000, output=False)
         assert uints is None
 
-    @pytest.mark.skip(reason='Polar transform no longer supported')
     def test_gauss_inv(self):
         n = 25
-        rs = RandomGenerator(self.brng(*self.data1['seed']))
+        rs = RandomState(self.brng(*self.data1['seed']))
         gauss = rs.standard_normal(n)
         assert_allclose(gauss,
                         gauss_from_uint(self.data1['data'], n, self.bits))
 
-        rs = RandomGenerator(self.brng(*self.data2['seed']))
+        rs = RandomState(self.brng(*self.data2['seed']))
         gauss = rs.standard_normal(25)
         assert_allclose(gauss,
                         gauss_from_uint(self.data2['data'], n, self.bits))
@@ -548,15 +527,14 @@ def test_uniform_double(self):
         assert_equal(uniform_from_dsfmt(self.data2['data']),
                      rs.random_sample(1000))
 
-    @pytest.mark.skip(reason='Polar transform no longer supported')
     def test_gauss_inv(self):
         n = 25
-        rs = RandomGenerator(self.brng(*self.data1['seed']))
+        rs = RandomState(self.brng(*self.data1['seed']))
         gauss = rs.standard_normal(n)
         assert_allclose(gauss,
                         gauss_from_uint(self.data1['data'], n, 'dsfmt'))
 
-        rs = RandomGenerator(self.brng(*self.data2['seed']))
+        rs = RandomState(self.brng(*self.data2['seed']))
         gauss = rs.standard_normal(25)
         assert_allclose(gauss,
                         gauss_from_uint(self.data2['data'], n, 'dsfmt'))
diff --git a/numpy/random/randomgen/tests/test_randomstate.py b/numpy/random/randomgen/tests/test_randomstate.py
index 371be78de5bf..167d1b0aa545 100644
--- a/numpy/random/randomgen/tests/test_randomstate.py
+++ b/numpy/random/randomgen/tests/test_randomstate.py
@@ -1,5 +1,6 @@
-import warnings
 import pickle
+import sys
+import warnings
 
 import numpy as np
 from numpy.testing import (
@@ -7,7 +8,6 @@
         assert_no_warnings, assert_array_equal, assert_array_almost_equal,
         suppress_warnings
         )
-import sys
 
 from ...randomgen import MT19937, Xoshiro256StarStar, mtrand as random