Emulating the Python `random.random()` functionality in C

I'm trying to create the exact same Mersenne Twister (MT) in C that is used in Python.

Based on Lib/random.py as well as reading the docs, it seems like the entire MT is implemented in _random which is implemented in C:

The underlying implementation in C is both fast and threadsafe.

By googling "Python _random", I found this page on GitHub which seems to be exactly what I was looking for, although it doesn't seem to be official.

I used that source code and stripped away everything except the MT itself, the seed function, and the double creation function. I also changed some of the types so that integers would be 32 bits.

First, here is the license info (just to be safe)

/* Random objects */

/* ------------------------------------------------------------------
   The code in this module was based on a download from:
      http://ift.tt/2fbTjbF
   It was modified in 2002 by Raymond Hettinger as follows:
    * the principal computational lines untouched.
    * renamed genrand_res53() to random_random() and wrapped
      in python calling/return code.
    * genrand_int32() and the helper functions, init_genrand()
      and init_by_array(), were declared static, wrapped in
      Python calling/return code.  also, their global data
      references were replaced with structure references.
    * unused functions from the original were deleted.
      new, original C python code was added to implement the
      Random() interface.
   The following are the verbatim comments from the original code:
   A C-program for MT19937, with initialization improved 2002/1/26.
   Coded by Takuji Nishimura and Makoto Matsumoto.
   Before using, initialize the state by using init_genrand(seed)
   or init_by_array(init_key, key_length).
   Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
   All rights reserved.
   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions
   are met:
     1. Redistributions of source code must retain the above copyright
    notice, this list of conditions and the following disclaimer.
     2. Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
     3. The names of its contributors may not be used to endorse or promote
    products derived from this software without specific prior written
    permission.
   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   Any feedback is very welcome.
   http://ift.tt/2cHqyFM
   email: matumoto@math.keio.ac.jp
*/

/* ---------------------------------------------------------------*/

Here is the stripped down header file (with everything Python removed).

mt.h:

#ifndef MT_H
#define MT_H

#include <stdint.h>

#define N 624
#define M 397
#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
#define LOWER_MASK 0x7fffffffUL /* least significant r bits */

typedef struct {
        uint32_t state[N];
        uint32_t index;
} RandomObject;

static uint32_t
genrand_int32(RandomObject *self)
{
    uint32_t y;
    static uint32_t mag01[2]={0x0UL, MATRIX_A};
    /* mag01[x] = x * MATRIX_A  for x=0,1 */
    uint32_t *mt;

    mt = self->state;
    if (self->index >= N) { /* generate N words at one time */
        uint32_t kk;

        for (kk=0;kk<N-M;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        for (;kk<N-1;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
        mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

        self->index = 0;
    }

    y = mt[self->index++];
    y ^= (y >> 11);
    y ^= (y << 7) & 0x9d2c5680UL;
    y ^= (y << 15) & 0xefc60000UL;
    y ^= (y >> 18);
    return y;
}

static double 
random_random(RandomObject *self)
{
        uint32_t a=genrand_int32(self)>>5, b=genrand_int32(self)>>6;
        return (double)((a*67108864.0+b)*(1.0/9007199254740992.0));
}

static void
init_genrand(RandomObject *self, uint32_t s)
{
    uint32_t mti;
    uint32_t *mt;

    mt = self->state;
    mt[0]= s & 0xffffffffUL;
    for (mti=1; mti<N; mti++) {
        mt[mti] =
        (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
        /* In the previous versions, MSBs of the seed affect   */
        /* only MSBs of the array mt[].                                */
        /* 2002/01/09 modified by Makoto Matsumoto                     */
        mt[mti] &= 0xffffffffUL;
        /* for >32 bit machines */
    }
    self->index = mti;
    return;
}

#endif

And here is a main function which simply creates a MT object, seeds it, and then spits out a random double.

main.c

#include <stdio.h>
#include "mt.h"

int main() {
    RandomObject rand;
    init_genrand(&rand, 0x1234);
    printf("%lf\n", random_random(&rand));
    return 0;
}

The output is: 0.279194.

The idea is that, when I do the equivalent process in python, I get out the same random number:

Python 2.7.12 (default, Jul  1 2016, 15:12:24) 
[GCC 5.4.0 20160609] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import random
>>> random.seed(0x1234)
>>> random.random()
0.9281175899596723

The output is, of course, different (or I wouldn't be here asking).

My question is this: What is wrong with my procedure? Am I simply using the wrong source? Am I making flawed assumptions about what Python does with the values returned from C?

I honestly don't know all that much about Python, so I could be making a stupid mistake somewhere.