Merge pull request #16153 from bashtage/fix-mt19937-jump

BUG: Correct loop order in MT19937 jump

6 files changed, 210 insertions, 329 deletions

diff --git a/numpy/random/_mt19937.pyx b/numpy/random/_mt19937.pyx
index 919a96a4c..16a377cc6 100644
--- a/numpy/random/_mt19937.pyx
+++ b/numpy/random/_mt19937.pyx
@@ -226,6 +226,23 @@ cdef class MT19937(BitGenerator):
         -------
         bit_generator : MT19937
             New instance of generator jumped iter times
+
+        Notes
+        -----
+        The jump step is computed using a modified version of Matsumoto's
+        implementation of Horner's method. The step polynomial is precomputed
+        to perform 2**128 steps. The jumped state has been verified to match
+        the state produced using Matsumoto's original code.
+
+        References
+        ----------
+        .. [1] Matsumoto, M, Generating multiple disjoint streams of
+           pseudorandom number sequences.  Accessed on: May 6, 2020.
+           http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/JUMP/
+        .. [2] Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, François
+           Panneton, Pierre L\'Ecuyer, "Efficient Jump Ahead for F2-Linear
+           Random Number Generators", INFORMS JOURNAL ON COMPUTING, Vol. 20,
+           No. 3, Summer 2008, pp. 385-390.
         """
         cdef MT19937 bit_generator
 
diff --git a/numpy/random/src/mt19937/mt19937-jump.c b/numpy/random/src/mt19937/mt19937-jump.c
index 46b28cf96..1a83a4c2e 100644
--- a/numpy/random/src/mt19937/mt19937-jump.c
+++ b/numpy/random/src/mt19937/mt19937-jump.c
@@ -10,28 +10,6 @@ unsigned long get_coef(unsigned long *pf, unsigned int deg) {
     return (0);
 }
 
-/* 32-bit function */
-/* set the coefficient of the polynomial pf with v */
-void set_coef(unsigned long *pf, unsigned int deg, unsigned long v) {
-  if (v != 0)
-    pf[deg >> 5] ^= (LSB << (deg & 0x1ful));
-  else
-    ;
-}
-
-void gray_code(unsigned long *h) {
-  unsigned int i, j = 1, l = 1, term = LL;
-
-  h[0] = 0;
-
-  for (i = 1; i <= QQ; i++) {
-    l = (l << 1);
-    term = (term >> 1);
-    for (; j < l; j++)
-      h[j] = h[l - j - 1] ^ term;
-  }
-}
-
 void copy_state(mt19937_state *target_state, mt19937_state *state) {
   int i;
 
@@ -83,69 +61,6 @@ void add_state(mt19937_state *state1, mt19937_state *state2) {
   }
 }
 
-/*
-void gen_vec_h(mt19937_state *state, mt19937_state *vec_h,
-               unsigned long *h) {
-  int i;
-  unsigned long k, g;
-  mt19937_state v;
-
-  gray_code(h);
-
-  copy_state(&vec_h[0], state);
-
-  for (i = 0; i < QQ; i++)
-    gen_next(&vec_h[0]);
-
-  for (i = 1; i < LL; i++) {
-    copy_state(&v, state);
-    g = h[i] ^ h[i - 1];
-    for (k = 1; k < g; k = (k << 1))
-      gen_next(&v);
-    copy_state(&vec_h[h[i]], &vec_h[h[i - 1]]);
-    add_state(&vec_h[h[i]], &v);
-  }
-}
-*/
-
-/* compute pf(ss) using Sliding window algorithm */
-/*
-void calc_state(unsigned long *pf, mt19937_state *state,
-                mt19937_state *vec_h) {
-  mt19937_state *temp1;
-  int i = MEXP - 1, j, digit, skip = 0;
-
-  temp1 = (mt19937_state *)calloc(1, sizeof(mt19937_state));
-
-  while (get_coef(pf, i) == 0)
-    i--;
-
-  for (; i >= QQ; i--) {
-    if (get_coef(pf, i) != 0) {
-      for (j = 0; j < QQ + 1; j++)
-        gen_next(temp1);
-      digit = 0;
-      for (j = 0; j < QQ; j++)
-        digit = (digit << 1) ^ get_coef(pf, i - j - 1);
-      add_state(temp1, &vec_h[digit]);
-      i -= QQ;
-    } else
-      gen_next(temp1);
-  }
-
-  for (; i > -1; i--) {
-    gen_next(temp1);
-    if (get_coef(pf, i) == 1)
-      add_state(temp1, state);
-    else
-      ;
-  }
-
-  copy_state(state, temp1);
-  free(temp1);
-}
-*/
-
 /* compute pf(ss) using standard Horner method */
 void horner1(unsigned long *pf, mt19937_state *state) {
   int i = MEXP - 1;
@@ -180,18 +95,15 @@ void horner1(unsigned long *pf, mt19937_state *state) {
   free(temp);
 }
 
-void mt19937_jump_state(mt19937_state *state, const char *jump_str) {
+void mt19937_jump_state(mt19937_state *state) {
   unsigned long *pf;
   int i;
 
   pf = (unsigned long *)calloc(P_SIZE, sizeof(unsigned long));
-
-  for (i = MEXP - 1; i > -1; i--) {
-    if (jump_str[i] == '1')
-      set_coef(pf, i, 1);
+  for (i = 0; i<P_SIZE; i++) {
+    pf[i] = poly_coef[i];
   }
-  /* TODO: Should generate the next set and start from 0, but doesn't matter ??
-   */
+
   if (state->pos >= N) {
     state->pos = 0;
   }
@@ -200,25 +112,3 @@ void mt19937_jump_state(mt19937_state *state, const char *jump_str) {
 
   free(pf);
 }
-/*
-void mt19937_jump(mt19937_state *state, const char *jump_str)
-{
-    unsigned long h[LL];
-    mt19937_state vec_h[LL];
-    unsigned long *pf;
-    int i;
-
-    pf = (unsigned long *)calloc(P_SIZE, sizeof(unsigned long));
-
-    for (i = MEXP - 1; i > -1; i--)
-    {
-        if (jump_str[i] == '1')
-            set_coef(pf, i, 1);
-    }
-
-    gen_vec_h(state, &vec_h, &h);
-    calc_state(pf, state, &vec_h);
-
-    free(pf);
-}
-*/
\ No newline at end of file
diff --git a/numpy/random/src/mt19937/mt19937-jump.h b/numpy/random/src/mt19937/mt19937-jump.h
index 394c150a0..8371cbd5f 100644
--- a/numpy/random/src/mt19937/mt19937-jump.h
+++ b/numpy/random/src/mt19937/mt19937-jump.h
@@ -10,6 +10,142 @@
 #define QQ 7
 #define LL 128 /* LL = 2^(QQ) */
 
-void mt19937_jump_state(mt19937_state *state, const char *jump_str);
+void mt19937_jump_state(mt19937_state *state);
 
-void set_coef(unsigned long *pf, unsigned int deg, unsigned long v);
\ No newline at end of file
+void set_coef(unsigned long *pf, unsigned int deg, unsigned long v);
+
+/*
+ * 2**128 step polynomial produced using the file mt19937-generate-jump-poly.c
+ * (randomgen) which is a modified version of minipoly_mt19937.c as distributed
+ * in
+ * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/JUMP/jump_ahead_1.02.tar.gz
+ *
+ * These files are not part of NumPy.
+ */
+
+static const unsigned long poly_coef[624] = {
+    1927166307UL, 3044056772UL, 2284297142UL, 2820929765UL, 651705945UL,
+    69149273UL,   3892165397UL, 2337412983UL, 1219880790UL, 3207074517UL,
+    3836784057UL, 189286826UL,  1049791363UL, 3916249550UL, 2942382547UL,
+    166392552UL,  861176918UL,  3246476411UL, 2302311555UL, 4273801148UL,
+    29196903UL,   1363664063UL, 3802562022UL, 2600400244UL, 3090369801UL,
+    4040416970UL, 1432485208UL, 3632558139UL, 4015816763UL, 3013316418UL,
+    551532385UL,  3592224467UL, 3479125595UL, 1195467127UL, 2391032553UL,
+    2393493419UL, 1482493632UL, 1625159565UL, 748389672UL,  4042774030UL,
+    2998615036UL, 3393119101UL, 2177492569UL, 2265897321UL, 2507383006UL,
+    3461498961UL, 2003319700UL, 1942857197UL, 1455226044UL, 4097545580UL,
+    529653268UL,  3204756480UL, 2486748289UL, 495294513UL,  3396001954UL,
+    2643963605UL, 2655404568UL, 3881604377UL, 624710790UL,  3443737948UL,
+    1941294296UL, 2139259604UL, 3368734020UL, 422436761UL,  3602810182UL,
+    1384691081UL, 3035786407UL, 2551797119UL, 537227499UL,  65486120UL,
+    642436100UL,  2023822537UL, 2515598203UL, 1122953367UL, 2882306242UL,
+    1743213032UL, 321965189UL,  336496623UL,  2436602518UL, 3556266590UL,
+    1055117829UL, 463541647UL,  743234441UL,  527083645UL,  2606668346UL,
+    2274046499UL, 2761475053UL, 2760669048UL, 2538258534UL, 487125077UL,
+    3365962306UL, 3604906217UL, 2714700608UL, 680709708UL,  2217161159UL,
+    1614899374UL, 3710119533UL, 3201300658UL, 3752620679UL, 2755041105UL,
+    3129723037UL, 1247297753UL, 2812642690UL, 4114340845UL, 3485092247UL,
+    2752814364UL, 3586551747UL, 4073138437UL, 3462966585UL, 2924318358UL,
+    4061374901UL, 3314086806UL, 2640385723UL, 744590670UL,  3007586513UL,
+    3959120371UL, 997207767UL,  3420235506UL, 2092400998UL, 3190305685UL,
+    60965738UL,   549507222UL,  3784354415UL, 3209279509UL, 1238863299UL,
+    2605037827UL, 178570440UL,  1743491299UL, 4079686640UL, 2136795825UL,
+    3435430548UL, 1679732443UL, 1835708342UL, 2159367000UL, 1924487218UL,
+    4059723674UL, 996192116UL,  2308091645UL, 1336281586UL, 674600050UL,
+    1642572529UL, 1383973289UL, 2202960007UL, 3165481279UL, 3385474038UL,
+    2501318550UL, 2671842890UL, 3084085109UL, 3475033915UL, 1551329147UL,
+    4101397249UL, 1205851807UL, 3641536021UL, 3607635071UL, 1609126163UL,
+    2910426664UL, 3324508658UL, 4244311266UL, 254034382UL,  1258304384UL,
+    1914048768UL, 1358592011UL, 527610138UL,  3072108727UL, 4289413885UL,
+    1417001678UL, 2445445945UL, 896462712UL,  339855811UL,  3699378285UL,
+    2529457297UL, 3049459401UL, 2723472429UL, 2838633181UL, 2520397330UL,
+    3272339035UL, 1667003847UL, 3742634787UL, 942706520UL,  2301027215UL,
+    1907791250UL, 2306299096UL, 1021173342UL, 1539334516UL, 2907834628UL,
+    3199959207UL, 1556251860UL, 3642580275UL, 2355865416UL, 285806145UL,
+    867932457UL,  1177354172UL, 3291107470UL, 4022765061UL, 1613380116UL,
+    588147929UL,  650574324UL,  1236855601UL, 1371354511UL, 2085218212UL,
+    1203081931UL, 420526905UL,  1022192219UL, 2903287064UL, 2470845899UL,
+    3649873273UL, 2502333582UL, 3972385637UL, 4246356763UL, 199084157UL,
+    1567178788UL, 2107121836UL, 4293612856UL, 1902910177UL, 332397359UL,
+    83422598UL,   3614961721UL, 456321943UL,  2277615967UL, 2302518510UL,
+    3258315116UL, 2521897172UL, 3900282042UL, 4186973154UL, 3146532165UL,
+    2299685029UL, 3889120948UL, 1293301857UL, 187455105UL,  3395849230UL,
+    913321567UL,  3093513909UL, 1440944571UL, 1923481911UL, 338680924UL,
+    1204882963UL, 2739724491UL, 2886241328UL, 2408907774UL, 1299817192UL,
+    2474012871UL, 45400213UL,   553186784UL,  134558656UL,  2180943666UL,
+    2870807589UL, 76511085UL,   3053566760UL, 2516601415UL, 4172865902UL,
+    1751297915UL, 1251975234UL, 2964780642UL, 1412975316UL, 2739978478UL,
+    2171013719UL, 637935041UL,  975972384UL,  3044407449UL, 3111425639UL,
+    1938684970UL, 2860857400UL, 13419586UL,   2772079268UL, 3484375614UL,
+    3184054178UL, 159924837UL,  1386213021UL, 2765617231UL, 2523689118UL,
+    1283505218UL, 3510789588UL, 4125878259UL, 2990287597UL, 2152014833UL,
+    3084155970UL, 2815101609UL, 1932985704UL, 114887365UL,  1712687646UL,
+    2550515629UL, 3299051916UL, 2022747614UL, 2143630992UL, 2244188960UL,
+    3309469192UL, 3234358520UL, 800720365UL,  3278176634UL, 554357439UL,
+    2415629802UL, 1620877315UL, 2389462898UL, 2229691332UL, 1007748450UL,
+    1966873768UL, 2264971043UL, 1214524156UL, 346854700UL,  3471905342UL,
+    3984889660UL, 4034246840UL, 216712649UL,  4027196762UL, 3754772604UL,
+    2121785562UL, 2347070732UL, 7457687UL,    1443375102UL, 683948143UL,
+    2940226032UL, 3211475670UL, 2836507357UL, 774899409UL,  1588968308UL,
+    780438009UL,  3278878781UL, 2217181540UL, 2184194887UL, 1642129086UL,
+    69346830UL,   297114710UL,  3841068188UL, 2631265450UL, 4167492314UL,
+    2613519651UL, 1388582503UL, 2171556668UL, 1201873758UL, 2698772382UL,
+    207791958UL,  3936134563UL, 3725025702UL, 3306317801UL, 1055730422UL,
+    4069230694UL, 1767821343UL, 4252407395UL, 2422583118UL, 3158834399UL,
+    3754582617UL, 1112422556UL, 376187931UL,  3137549150UL, 712221089UL,
+    3300799453UL, 3868250200UL, 1165257666UL, 2494837767UL, 131304831UL,
+    1619349427UL, 1958236644UL, 3678218946UL, 3651007751UL, 2261987899UL,
+    1567368524UL, 2193599522UL, 3034394674UL, 2994602555UL, 3072727647UL,
+    889094521UL,  1089692095UL, 1822324824UL, 3876999182UL, 1703361286UL,
+    902229515UL,  4213728487UL, 3838170364UL, 672727494UL,  2240733828UL,
+    3858539469UL, 1149254245UL, 4166055926UL, 4193525313UL, 1709921593UL,
+    2278290377UL, 3190784116UL, 2919588882UL, 1012709717UL, 3640562031UL,
+    2931984863UL, 3515665246UL, 250577343UL,  1147230194UL, 1183856202UL,
+    3734511989UL, 3243867808UL, 3499383067UL, 2985115159UL, 2036821626UL,
+    3298159553UL, 2726542838UL, 1686910320UL, 1778823772UL, 965412224UL,
+    233509772UL,  3843098861UL, 1312622954UL, 500855830UL,  2950562091UL,
+    1915683607UL, 3405781138UL, 596073719UL,  2195150546UL, 3381728478UL,
+    546426436UL,  3527890868UL, 2324975353UL, 2241074266UL, 3992514859UL,
+    2576108287UL, 4077653225UL, 2632319392UL, 3127212632UL, 917000669UL,
+    2498161805UL, 3980835128UL, 2259526768UL, 1083920509UL, 1187452089UL,
+    97018536UL,   3056075838UL, 2059706760UL, 2373335692UL, 182196406UL,
+    2136713111UL, 1762080153UL, 1572125803UL, 1145919955UL, 1023966754UL,
+    3921694345UL, 1632005969UL, 1418372326UL, 354407429UL,  2438288265UL,
+    1620072033UL, 1586320921UL, 1044153697UL, 969324572UL,  613487980UL,
+    4230993062UL, 397726764UL,  2194259193UL, 735511759UL,  2066049260UL,
+    88093248UL,   1562536153UL, 2114157419UL, 3630951546UL, 589238503UL,
+    3120654384UL, 2521793793UL, 2746692127UL, 2557723425UL, 889897693UL,
+    2778878177UL, 643269509UL,  3342389831UL, 19218890UL,   3442706236UL,
+    3314581273UL, 3503147052UL, 1546343434UL, 1448529060UL, 529038801UL,
+    2748942264UL, 2213019208UL, 111314040UL,  2488697563UL, 1180642808UL,
+    2605272289UL, 4207476668UL, 1502558669UL, 2972370981UL, 4204339995UL,
+    1046225278UL, 992840610UL,  3847290298UL, 2387673094UL, 2221565747UL,
+    1045901716UL, 3997739302UL, 1556952765UL, 1103336648UL, 279418400UL,
+    2711316466UL, 2336215718UL, 2317900806UL, 974624729UL,  909575434UL,
+    1675610631UL, 1922393214UL, 2054896570UL, 3197007361UL, 3932554569UL,
+    1008619802UL, 3349254938UL, 113511461UL,  932630384UL,  2098759268UL,
+    3436837432UL, 3119972401UL, 1612590197UL, 2281609013UL, 4174211248UL,
+    4016332246UL, 2097525539UL, 1398632760UL, 1543697535UL, 2419227174UL,
+    1676465074UL, 2882923045UL, 23216933UL,   808195649UL,  3690720147UL,
+    484419260UL,  2254772642UL, 2975434733UL, 288528113UL,  204598404UL,
+    589968818UL,  3021152400UL, 2463155141UL, 1397846755UL, 157285579UL,
+    4230258857UL, 2469135246UL, 625357422UL,  3435224647UL, 465239124UL,
+    1022535736UL, 2823317040UL, 274194469UL,  2214966446UL, 3661001613UL,
+    518802547UL,  2293436304UL, 1335881988UL, 2247010176UL, 1856732584UL,
+    1088028094UL, 1877563709UL, 1015352636UL, 1700817932UL, 2960695857UL,
+    1882229300UL, 1666906557UL, 1838841022UL, 3983797810UL, 1667630361UL,
+    385998221UL,  241341791UL,  403550441UL,  2629200403UL, 3552759102UL,
+    2029750442UL, 2247999048UL, 2726665298UL, 2507798776UL, 2419064129UL,
+    1266444923UL, 526255242UL,  2384866697UL, 1886200981UL, 3954956408UL,
+    2171436866UL, 2295200753UL, 1047315850UL, 1967809707UL, 2860382973UL,
+    3918334466UL, 3057439479UL, 952682588UL,  1925559679UL, 3112119050UL,
+    3833190964UL, 1430139895UL, 2089165610UL, 3009202424UL, 3989186157UL,
+    3395807230UL, 347600520UL,  120428923UL,  3017004655UL, 1384933954UL,
+    303039929UL,  234010146UL,  2278760249UL, 315514836UL,  3987659575UL,
+    1239335668UL, 2387869477UL, 3885908826UL, 1983922602UL, 698609264UL,
+    3009002846UL, 1520611399UL, 809159940UL,  3089771783UL, 374838722UL,
+    2789914419UL, 2500831937UL, 3751970335UL, 4279852547UL, 2362894437UL,
+    1588814060UL, 1671213155UL, 434218829UL,  2126587176UL, 2002526422UL,
+    2756464095UL, 141700479UL,  2965974322UL, 2211530172UL, 992085992UL,
+    1943691492UL, 2705131817UL, 2519208889UL, 1938768395UL, 3949294294UL,
+    354046666UL,  2158272751UL, 602858583UL,  0UL};
diff --git a/numpy/random/src/mt19937/mt19937-poly.h b/numpy/random/src/mt19937/mt19937-poly.h
deleted file mode 100644
index b03747881..000000000
--- a/numpy/random/src/mt19937/mt19937-poly.h
+++ /dev/null
@@ -1,207 +0,0 @@
-static const char * poly =
-"0001000111110111011100100010101111000000010100100101000001110111100010101000110100101001011001010"
-"1110101101100101011100101101011001110011100011110100001000001011100101100010100000010011101110011"
-"0100001001111010000100100101001011100111101101001100000111001000011101100100010000001111110100010"
-"0000111101000101000101101111001011000011001001001011010011001000001000011100100010110101111111101"
-"0010001001100010011011101111101110111010111000010000011010110011111101100000100100101001010000001"
-"1001111000011010011101001101011000111001110010110000011000110101111010110011011000001110110010001"
-"1001101011011101000011001011111111100011001010111100000001111011111101000101000011000011111100101"
-"0100001111101010101100000110100110010010101011011100110011000101100101011110010101110000101011100"
-"0001010100010110100000111001100000011101011001101000001000101101010100010101100000100011110110011"
-"0101100110111101010111100010100110100011111011100111000001110110010000000100000110101010111001111"
-"0011110010000110101101010001110010100111111111100100101010010011101111011000010111101001110110110"
-"1011101101101100110111000100101100111001011111110101001000011111010011000111110011100100001101111"
-"1001010110110001000100001001000010000000001011011100101010010100011000110101001000010101100111101"
-"0011110101100110111100000111001011011001100101111011000101001011011111110110100010001100101001100"
-"1111110011111111110111011011100011000100110011011011011001101011100110010001111100001111100100001"
-"1000100011001010100101010100111110001100111111011111100100011110011101101000110100101110010111111"
-"1001010110000101001110010110001011011010101111111001110001100100011001000010111001011011000111100"
-"1101001011110111111010011000110100001010000000101010101001111101111110101111110101110101010010100"
-"1100100101010110011111001101100110001011000101010001000110011011111101111110001100000010110110101"
-"1111110100001011101011101110111101100001111000011100000110110100100100100101011000111000100110001"
-"0110110001001000111110101111000000100100010100100101101111100011010100111101110010000001011111111"
-"1101010000011001010101111001111110001111100010100010100001011001110001010010100001011111110110111"
-"1100100100001111000111110111000100010101010110100111100001011001101001111101001110010110110011010"
-"1000010011000110000000110110110000111010010000111001100010100101010101111100010111000000011101110"
-"1100011010110001101100110000001010001100111101101011100111110111000110010011011011001101001111100"
-"1011111001100011010110101111100110111101011100000011000010001010001101001011000001111000101000100"
-"0110001011001010110000001101100000011000011110010000101000011010011110001101111111010010101100100"
-"1111010100000011011001111111011011111001101110101010110111110110101000100001011110111010100111100"
-"0000001001111100111111111000100000100100010001011001100001111100100000001111011101100010011000111"
-"0011110110100011011001110011100011011000010000000101101101001010111000010000010101111110000000100"
-"1011010100001001000011001100011000000111100111100101010100000111000000110111011101011111100010101"
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diff --git a/numpy/random/src/mt19937/mt19937.c b/numpy/random/src/mt19937/mt19937.c
index e5ca9e0cf..bec518af8 100644
--- a/numpy/random/src/mt19937/mt19937.c
+++ b/numpy/random/src/mt19937/mt19937.c
@@ -1,6 +1,5 @@
 #include "mt19937.h"
 #include "mt19937-jump.h"
-#include "mt19937-poly.h"
 
 void mt19937_seed(mt19937_state *state, uint32_t seed) {
   int pos;
@@ -104,4 +103,4 @@ extern inline uint32_t mt19937_next32(mt19937_state *state);
 
 extern inline double mt19937_next_double(mt19937_state *state);
 
-void mt19937_jump(mt19937_state *state) { mt19937_jump_state(state, poly); }
+void mt19937_jump(mt19937_state *state) { mt19937_jump_state(state); }
diff --git a/numpy/random/tests/test_generator_mt19937.py b/numpy/random/tests/test_generator_mt19937.py
index a28b7ca11..f72b748ba 100644
--- a/numpy/random/tests/test_generator_mt19937.py
+++ b/numpy/random/tests/test_generator_mt19937.py
@@ -1,4 +1,5 @@
 import sys
+import hashlib
 
 import pytest
 
@@ -13,6 +14,26 @@ from numpy.random import Generator, MT19937, SeedSequence
 
 random = Generator(MT19937())
 
+JUMP_TEST_DATA = [
+    {
+        "seed": 0,
+        "steps": 10,
+        "initial": {"key_md5": "64eaf265d2203179fb5ffb73380cd589", "pos": 9},
+        "jumped": {"key_md5": "8cb7b061136efceef5217a9ce2cc9a5a", "pos": 598},
+    },
+    {
+        "seed":384908324,
+        "steps":312,
+        "initial": {"key_md5": "e99708a47b82ff51a2c7b0625b81afb5", "pos": 311},
+        "jumped": {"key_md5": "2ecdbfc47a895b253e6e19ccb2e74b90", "pos": 276},
+    },
+    {
+        "seed": [839438204, 980239840, 859048019, 821],
+        "steps": 511,
+        "initial": {"key_md5": "9fcd6280df9199785e17e93162ce283c", "pos": 510},
+        "jumped": {"key_md5": "433b85229f2ed853cde06cd872818305", "pos": 475},
+    },
+]
 
 @pytest.fixture(scope='module', params=[True, False])
 def endpoint(request):
@@ -462,7 +483,6 @@ class TestIntegers:
             assert_array_equal(scalar, array)
 
     def test_repeatability(self, endpoint):
-        import hashlib
         # We use a md5 hash of generated sequences of 1000 samples
         # in the range [0, 6) for all but bool, where the range
         # is [0, 2). Hashes are for little endian numbers.
@@ -487,7 +507,7 @@ class TestIntegers:
                 val = random.integers(0, 6 - endpoint, size=1000, endpoint=endpoint,
                                  dtype=dt).byteswap()
 
-            res = hashlib.md5(val.view(np.int8)).hexdigest()
+            res = hashlib.md5(val).hexdigest()
             assert_(tgt[np.dtype(dt).name] == res)
 
         # bools do not depend on endianness
@@ -885,8 +905,6 @@ class TestRandomDist:
         assert actual.dtype == np.int64
 
     def test_choice_large_sample(self):
-        import hashlib
-
         choice_hash = 'd44962a0b1e92f4a3373c23222244e21'
         random = Generator(MT19937(self.seed))
         actual = random.choice(10000, 5000, replace=False)
@@ -2351,3 +2369,31 @@ class TestSingleEltArrayInput:
 
             out = func(self.argOne, self.argTwo[0], self.argThree)
             assert_equal(out.shape, self.tgtShape)
+
+
+@pytest.mark.parametrize("config", JUMP_TEST_DATA)
+def test_jumped(config):
+    # Each config contains the initial seed, a number of raw steps
+    # the md5 hashes of the initial and the final states' keys and
+    # the position of of the initial and the final state.
+    # These were produced using the original C implementation.
+    seed = config["seed"]
+    steps = config["steps"]
+
+    mt19937 = MT19937(seed)
+    # Burn step
+    mt19937.random_raw(steps)
+    key = mt19937.state["state"]["key"]
+    if sys.byteorder == 'big':
+        key = key.byteswap()
+    md5 = hashlib.md5(key)
+    assert mt19937.state["state"]["pos"] == config["initial"]["pos"]
+    assert md5.hexdigest() == config["initial"]["key_md5"]
+
+    jumped = mt19937.jumped()
+    key = jumped.state["state"]["key"]
+    if sys.byteorder == 'big':
+        key = key.byteswap()
+    md5 = hashlib.md5(key)
+    assert jumped.state["state"]["pos"] == config["jumped"]["pos"]
+    assert md5.hexdigest() == config["jumped"]["key_md5"]