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/* Mersenne Twister pseudo-random number generator functions.
THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
FUTURE GNU MP RELEASES.
Copyright 2002, 2003 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include <stdio.h> /* for NULL */
#include "gmp.h"
#include "gmp-impl.h"
#include "randmt.h"
/* This code implements the Mersenne Twister pseudorandom number generator
by Takuji Nishimura and Makoto Matsumoto. The buffer initialization
function is different in order to permit seeds greater than 2^32-1.
This file contains a special __gmp_randinit_mt_noseed which excludes the
seeding function from the gmp_randfnptr_t routines. This is for use by
mpn_random and mpn_random2 on the global random generator. MT seeding
uses mpz functions, and we don't want mpn routines dragging mpz functions
into the link. */
/* Default seed to use when the generator is not initialized. */
#define DEFAULT_SEED 5489 /* was 4357 */
/* Tempering masks. */
#define MASK_1 0x9D2C5680
#define MASK_2 0xEFC60000
/* Initial state of buffer when initialized with default seed. */
static const gmp_uint_least32_t default_state[N] =
{
0xD247B233,0x9E5AA8F1,0x0FFA981B,0x9DCB0980,0x74200F2B,0xA576D044,
0xE9F05ADF,0x1538BFF5,0x59818BBF,0xCF9E58D8,0x09FCE032,0x6A1C663F,
0x5116E78A,0x69B3E0FA,0x6D92D665,0xD0A8BE98,0xF669B734,0x41AC1B68,
0x630423F1,0x4B8D6B8A,0xC2C46DD7,0x5680747D,0x43703E8F,0x3B6103D2,
0x49E5EB3F,0xCBDAB4C1,0x9C988E23,0x747BEE0B,0x9111E329,0x9F031B5A,
0xECCA71B9,0x2AFE4EF8,0x8421C7ED,0xAC89AFF1,0xAED90DF3,0x2DD74F01,
0x14906A13,0x75873FA9,0xFF83F877,0x5028A0C9,0x11B4C41D,0x7CAEDBC4,
0x8672D0A7,0x48A7C109,0x8320E59F,0xBC0B3D5F,0x75A30886,0xF9E0D128,
0x41AF7580,0x239BB94D,0xC67A3C81,0x74EEBD6E,0xBC02B53C,0x727EA449,
0x6B8A2806,0x5853B0DA,0xBDE032F4,0xCE234885,0x320D6145,0x48CC053F,
0x00DBC4D2,0xD55A2397,0xE1059B6F,0x1C3E05D1,0x09657C64,0xD07CB661,
0x6E982E34,0x6DD1D777,0xEDED1071,0xD79DFD65,0xF816DDCE,0xB6FAF1E4,
0x1C771074,0x311835BD,0x18F952F7,0xF8F40350,0x4ECED354,0x7C8AC12B,
0x31A9994D,0x4FD47747,0xDC227A23,0x6DFAFDDF,0x6796E748,0x0C6F634F,
0xF992FA1D,0x4CF670C9,0x067DFD31,0xA7A3E1A5,0x8CD7D9DF,0x972CCB34,
0x67C82156,0xD548F6A8,0x045CEC21,0xF3240BFB,0xDEF656A7,0x43DE08C5,
0xDAD1F92F,0x3726C56B,0x1409F19A,0x942FD147,0xB926749C,0xADDC31B8,
0x53D0D869,0xD1BA52FE,0x6722DF8C,0x22D95A74,0x7DC1B52A,0x1DEC6FD5,
0x7262874D,0x0A725DC9,0xE6A8193D,0xA052835A,0xDC9AD928,0xE59EBB90,
0x70DBA9FF,0xD612749D,0x5A5A638C,0x6086EC37,0x2A579709,0x1449EA3A,
0xBC8E3C06,0x2F900666,0xFBE74FD1,0x6B35B911,0xF8335008,0xEF1E979D,
0x738AB29D,0xA2DC0FDC,0x7696305D,0xF5429DAC,0x8C41813B,0x8073E02E,
0xBEF83CCD,0x7B50A95A,0x05EE5862,0x00829ECE,0x8CA1958C,0xBE4EA2E2,
0x4293BB73,0x656F7B23,0x417316D8,0x4467D7CF,0x2200E63B,0x109050C8,
0x814CBE47,0x36B1D4A8,0x36AF9305,0x308327B3,0xEBCD7344,0xA738DE27,
0x5A10C399,0x4142371D,0x64A18528,0x0B31E8B2,0x641057B9,0x6AFC363B,
0x108AD953,0x9D4DA234,0x0C2D9159,0x1C8A1A1F,0x310C66BA,0x87AA1070,
0xDAC832FF,0x0A433422,0x7AF15812,0x2D8D9BD0,0x995A25E9,0x25326CAC,
0xA34384DB,0x4C8421CC,0x4F0315EC,0x29E8649E,0xA7732D6F,0x2E94D3E3,
0x7D98A340,0x397C4D74,0x659DB4DE,0x747D4E9A,0xD9DB8435,0x4659DBE9,
0x313E6DC5,0x29D104DC,0x9F226CBA,0x452F18B0,0xD0BC5068,0x844CA299,
0x782B294E,0x4AE2EB7B,0xA4C475F8,0x70A81311,0x4B3E8BCC,0x7E20D4BA,
0xABCA33C9,0x57BE2960,0x44F9B419,0x2E567746,0x72EB757A,0x102CC0E8,
0xB07F32B9,0xD0DABD59,0xBA85AD6B,0xF3E20667,0x98D77D81,0x197AFA47,
0x518EE9AC,0xE10CE5A2,0x01CF2C2A,0xD3A3AF3D,0x16DDFD65,0x669232F8,
0x1C50A301,0xB93D9151,0x9354D3F4,0x847D79D0,0xD5FE2EC6,0x1F7B0610,
0xFA6B90A5,0xC5879041,0x2E7DC05E,0x423F1F32,0xEF623DDB,0x49C13280,
0x98714E92,0xC7B6E4AD,0xC4318466,0x0737F312,0x4D3C003F,0x9ACC1F1F,
0x5F1C926D,0x085FA771,0x185A83A2,0xF9AA159D,0x0B0B0132,0xF98E7A43,
0xCD9EBDBE,0x0190CB29,0x10D93FB6,0x3B8A4D97,0x66A65A41,0xE43E766F,
0x77BE3C41,0xB9686364,0xCB36994D,0x6846A287,0x567E77F7,0x36178DD8,
0xBDE6B1F2,0xB6EFDC64,0x82950324,0x42053F47,0xC09BE51C,0x0942D762,
0x35F92C7F,0x367DEC61,0x6EE3D983,0xDBAAF78A,0x265D2C47,0x8EB4BF5C,
0x33B232D7,0xB0137E77,0x373C39A7,0x8D2B2E76,0xC7510F01,0x50F9E032,
0x7B1FDDDB,0x724C2AAE,0xB10ECB31,0xCCA3D1B8,0x7F0BCF10,0x4254BBBD,
0xE3F93B97,0x2305039B,0x53120E22,0x1A2F3B9A,0x0FDDBD97,0x0118561E,
0x0A798E13,0x9E0B3ACD,0xDB6C9F15,0xF512D0A2,0x9E8C3A28,0xEE2184AE,
0x0051EC2F,0x2432F74F,0xB0AA66EA,0x55128D88,0xF7D83A38,0x4DAE8E82,
0x3FDC98D6,0x5F0BD341,0x7244BE1D,0xC7B48E78,0x2D473053,0x43892E20,
0xBA0F1F2A,0x524D4895,0x2E10BCB1,0x4C372D81,0x5C3E50CD,0xCF61CC2E,
0x931709AB,0x81B3AEFC,0x39E9405E,0x7FFE108C,0x4FBB3FF8,0x06ABE450,
0x7F5BF51E,0xA4E3CDFD,0xDB0F6C6F,0x159A1227,0x3B9FED55,0xD20B6F7F,
0xFBE9CC83,0x64856619,0xBF52B8AF,0x9D7006B0,0x71165BC6,0xAE324AEE,
0x29D27F2C,0x794C2086,0x74445CE2,0x782915CC,0xD4CE6886,0x3289AE7C,
0x53DEF297,0x4185F7ED,0x88B72400,0x3C09DC11,0xBCE3AAB6,0x6A75934A,
0xB267E399,0x000DF1BF,0x193BA5E2,0xFA3E1977,0x179E14F6,0x1EEDE298,
0x691F0B06,0xB84F78AC,0xC1C15316,0xFFFF3AD6,0x0B457383,0x518CD612,
0x05A00F3E,0xD5B7D275,0x4C5ECCD7,0xE02CD0BE,0x5558E9F2,0x0C89BBF0,
0xA3D96227,0x2832D2B2,0xF667B897,0xD4556554,0xF9D2F01F,0xFA1E3FAE,
0x52C2E1EE,0xE5451F31,0x7E849729,0xDABDB67A,0x54BF5E7E,0xF831C271,
0x5F1A17E3,0x9D140AFE,0x92741C47,0x48CFABCE,0x9CBBE477,0x9C3EE57F,
0xB07D4C39,0xCC21BCE2,0x697708B1,0x58DA2A6B,0x2370DB16,0x6E641948,
0xACC5BD52,0x868F24CC,0xCA1DB0F5,0x4CADA492,0x3F443E54,0xC4A4D5E9,
0xF00AD670,0xE93C86E0,0xFE90651A,0xDDE532A3,0xA66458DF,0xAB7D7151,
0x0E2E775F,0xC9109F99,0x8D96D59F,0x73CEF14C,0xC74E88E9,0x02712DC0,
0x04F41735,0x2E5914A2,0x59F4B2FB,0x0287FC83,0x80BC0343,0xF6B32559,
0xC74178D4,0xF1D99123,0x383CCC07,0xACC0637D,0x0863A548,0xA6FCAC85,
0x2A13EFF0,0xAF2EEDB1,0x41E72750,0xE0C6B342,0x5DA22B46,0x635559E0,
0xD2EA40AC,0x10AA98C0,0x19096497,0x112C542B,0x2C85040C,0xA868E7D0,
0x6E260188,0xF596D390,0xC3BB5D7A,0x7A2AA937,0xDFD15032,0x6780AE3B,
0xDB5F9CD8,0x8BD266B0,0x7744AF12,0xB463B1B0,0x589629C9,0xE30DBC6E,
0x880F5569,0x209E6E16,0x9DECA50C,0x02987A57,0xBED3EA57,0xD3A678AA,
0x70DD030D,0x0CFD9C5D,0x92A18E99,0xF5740619,0x7F6F0A7D,0x134CAF9A,
0x70F5BAE4,0x23DCA7B5,0x4D788FCD,0xC7F07847,0xBCF77DA1,0x9071D568,
0xFC627EA1,0xAE004B77,0x66B54BCB,0x7EF2DAAC,0xDCD5AC30,0xB9BDF730,
0x505A97A7,0x9D881FD3,0xADB796CC,0x94A1D202,0x97535D7F,0x31EC20C0,
0xB1887A98,0xC1475069,0xA6F73AF3,0x71E4E067,0x46A569DE,0xD2ADE430,
0x6F0762C7,0xF50876F4,0x53510542,0x03741C3E,0x53502224,0xD8E54D60,
0x3C44AB1A,0x34972B46,0x74BFA89D,0xD7D768E0,0x37E605DC,0xE13D1BDF,
0x5051C421,0xB9E057BE,0xB717A14C,0xA1730C43,0xB99638BE,0xB5D5F36D,
0xE960D9EA,0x6B1388D3,0xECB6D3B6,0xBDBE8B83,0x2E29AFC5,0x764D71EC,
0x4B8F4F43,0xC21DDC00,0xA63F657F,0x82678130,0xDBF535AC,0xA594FC58,
0x942686BC,0xBD9B657B,0x4A0F9B61,0x44FF184F,0x38E10A2F,0x61910626,
0x5E247636,0x7106D137,0xC62802F0,0xBD1D1F00,0x7CC0DCB2,0xED634909,
0xDC13B24E,0x9799C499,0xD77E3D6A,0x14773B68,0x967A4FB7,0x35EECFB1,
0x2A5110B8,0xE2F0AF94,0x9D09DEA5,0x20255D27,0x5771D34B,0xE1089EE4,
0x246F330B,0x8F7CAEE5,0xD3064712,0x75CAFBEE,0xB94F7028,0xED953666,
0x5D1975B4,0x5AF81271,0x13BE2025,0x85194659,0x30805331,0xEC9D46C0,
0xBC027C36,0x2AF84188,0xC2141B80,0xC02B1E4A,0x04D36177,0xFC50E9D7,
0x39CE79DA,0x917E0A00,0xEF7A0BF4,0xA98BD8D1,0x19424DD2,0x9439DF1F,
0xC42AF746,0xADDBE83E,0x85221F0D,0x45563E90,0x9095EC52,0x77887B25,
0x8AE46064,0xBD43B71A,0xBB541956,0x7366CF9D,0xEE8E1737,0xB5A727C9,
0x5076B3E7,0xFC70BACA,0xCE135B75,0xC4E91AA3,0xF0341911,0x53430C3F,
0x886B0824,0x6BB5B8B7,0x33E21254,0xF193B456,0x5B09617F,0x215FFF50,
0x48D97EF1,0x356479AB,0x6EA9DDC4,0x0D352746,0xA2F5CE43,0xB226A1B3,
0x1329EA3C,0x7A337CC2,0xB5CCE13D,0x563E3B5B,0x534E8E8F,0x561399C9,
0xE1596392,0xB0F03125,0x4586645B,0x1F371847,0x94EAABD1,0x41F97EDD,
0xE3E5A39B,0x71C774E2,0x507296F4,0x5960133B,0x7852C494,0x3F5B2691,
0xA3F87774,0x5A7AF89E,0x17DA3F28,0xE9D9516D,0xFCC1C1D5,0xE4618628,
0x04081047,0xD8E4DB5F,0xDC380416,0x8C4933E2,0x95074D53,0xB1B0032D,
0xCC8102EA,0x71641243,0x98D6EB6A,0x90FEC945,0xA0914345,0x6FAB037D,
0x70F49C4D,0x05BF5B0E,0x927AAF7F,0xA1940F61,0xFEE0756F,0xF815369F,
0x5C00253B,0xF2B9762F,0x4AEB3CCC,0x1069F386,0xFBA4E7B9,0x70332665,
0x6BCA810E,0x85AB8058,0xAE4B2B2F,0x9D120712,0xBEE8EACB,0x776A1112
};
void
__gmp_mt_recalc_buffer (gmp_uint_least32_t mt[])
{
gmp_uint_least32_t y;
int kk;
for (kk = 0; kk < N - M; kk++)
{
y = (mt[kk] & 0x80000000) | (mt[kk + 1] & 0x7FFFFFFF);
mt[kk] = mt[kk + M] ^ (y >> 1) ^ ((y & 0x01) != 0 ? MATRIX_A : 0);
}
for (; kk < N - 1; kk++)
{
y = (mt[kk] & 0x80000000) | (mt[kk + 1] & 0x7FFFFFFF);
mt[kk] = mt[kk - (N - M)] ^ (y >> 1) ^ ((y & 0x01) != 0 ? MATRIX_A : 0);
}
y = (mt[N - 1] & 0x80000000) | (mt[0] & 0x7FFFFFFF);
mt[N - 1] = mt[M - 1] ^ (y >> 1) ^ ((y & 0x01) != 0 ? MATRIX_A : 0);
}
/* Get nbits bits of output from the generator into dest.
Note that Mersenne Twister is designed to produce outputs in
32-bit words. */
void
__gmp_randget_mt (gmp_randstate_t rstate, mp_ptr dest, unsigned long int nbits)
{
gmp_uint_least32_t y;
int rbits;
mp_size_t i;
mp_size_t nlimbs;
int *pmti;
gmp_uint_least32_t *mt;
pmti = &((gmp_rand_mt_struct *) RNG_STATE (rstate))->mti;
mt = ((gmp_rand_mt_struct *) RNG_STATE (rstate))->mt;
nlimbs = nbits / GMP_NUMB_BITS;
rbits = nbits % GMP_NUMB_BITS;
#define NEXT_RANDOM \
do \
{ \
if (*pmti >= N) \
{ \
__gmp_mt_recalc_buffer (mt); \
*pmti = 0; \
} \
y = mt[(*pmti)++]; \
y ^= (y >> 11); \
y ^= (y << 7) & MASK_1; \
y ^= (y << 15) & MASK_2; \
y ^= (y >> 18); \
} \
while (0)
/* Handle the common cases of 32- or 64-bit limbs with fast,
optimized routines, and the rest of cases with a general
routine. In all cases, no more than 31 bits are rejected
for the last limb so that every version of the code is
consistent with the others. */
#if (GMP_NUMB_BITS == 32)
for (i = 0; i < nlimbs; i++)
{
NEXT_RANDOM;
dest[i] = (mp_limb_t) y;
}
if (rbits)
{
NEXT_RANDOM;
dest[nlimbs] = (mp_limb_t) (y & ~(ULONG_MAX << rbits));
}
#else /* GMP_NUMB_BITS != 32 */
#if (GMP_NUMB_BITS == 64)
for (i = 0; i < nlimbs; i++)
{
NEXT_RANDOM;
dest[i] = (mp_limb_t) y;
NEXT_RANDOM;
dest[i] |= (mp_limb_t) y << 32;
}
if (rbits)
{
if (rbits < 32)
{
NEXT_RANDOM;
dest[nlimbs] = (mp_limb_t) (y & ~(ULONG_MAX << rbits));
}
else
{
NEXT_RANDOM;
dest[nlimbs] = (mp_limb_t) y;
if (rbits > 32)
{
NEXT_RANDOM;
dest[nlimbs] |=
((mp_limb_t) (y & ~(ULONG_MAX << (rbits-32)))) << 32;
}
}
}
#else /* GMP_NUMB_BITS != 64 */
{
/* Fall back to a general algorithm. This algorithm works by
keeping a pool of up to 64 bits (2 outputs from MT) acting
as a shift register from which bits are consumed as needed.
Bits are consumed using the LSB bits of bitpool_l, and
inserted via bitpool_h and shifted to the right place. */
gmp_uint_least32_t bitpool_h = 0;
gmp_uint_least32_t bitpool_l = 0;
int bits_in_pool = 0; /* Holds number of valid bits in the pool. */
int bits_to_fill; /* Holds total number of bits to put in
destination. */
int bitidx; /* Holds the destination bit position. */
mp_size_t nlimbs2; /* Number of whole+partial limbs to fill. */
nlimbs2 = nlimbs + (rbits != 0);
for (i = 0; i < nlimbs2; i++)
{
bitidx = 0;
if (i < nlimbs)
bits_to_fill = GMP_NUMB_BITS;
else
bits_to_fill = rbits;
dest[i] = CNST_LIMB (0);
while (bits_to_fill >= 32) /* Process whole 32-bit blocks first. */
{
if (bits_in_pool < 32) /* Need more bits. */
{
/* 64-bit right shift. */
NEXT_RANDOM;
bitpool_h = y;
bitpool_l |= (bitpool_h << bits_in_pool) & 0xFFFFFFFF;
if (bits_in_pool == 0)
bitpool_h = 0;
else
bitpool_h >>= 32 - bits_in_pool;
bits_in_pool += 32; /* We've got 32 more bits. */
}
/* Fill a 32-bit chunk */
dest[i] |= ((mp_limb_t) bitpool_l) << bitidx;
bitpool_l = bitpool_h;
bits_in_pool -= 32;
bits_to_fill -= 32;
bitidx += 32;
}
/* Cover the case where GMP_NUMB_BITS is not a multiple of 32. */
if (bits_to_fill != 0)
{
if (bits_in_pool < bits_to_fill)
{
NEXT_RANDOM;
bitpool_h = y;
bitpool_l |= (bitpool_h << bits_in_pool) & 0xFFFFFFFF;
if (bits_in_pool == 0)
bitpool_h = 0;
else
bitpool_h >>= 32 - bits_in_pool;
bits_in_pool += 32;
}
dest[i] |= (((mp_limb_t) bitpool_l
& ~(~CNST_LIMB (0) << bits_to_fill))
<< bitidx);
bitpool_l = ((bitpool_l >> bits_to_fill)
| (bitpool_h << (32 - bits_to_fill))) & 0xFFFFFFFF;
bitpool_h >>= bits_to_fill;
bits_in_pool -= bits_to_fill;
}
}
}
#endif /* GMP_NUMB_BITS != 64 */
#endif /* GMP_NUMB_BITS != 32 */
}
void
__gmp_randclear_mt (gmp_randstate_t rstate)
{
(*__gmp_free_func) ((void *) RNG_STATE (rstate),
sizeof (gmp_rand_mt_struct));
}
void __gmp_randiset_mt __GMP_PROTO ((gmp_randstate_ptr dst, gmp_randstate_srcptr src));
static const gmp_randfnptr_t Mersenne_Twister_Generator_Noseed = {
NULL,
__gmp_randget_mt,
__gmp_randclear_mt,
__gmp_randiset_mt
};
void
__gmp_randiset_mt (gmp_randstate_ptr dst, gmp_randstate_srcptr src)
{
gmp_rand_mt_struct *dstp, *srcp;
int i;
srcp = (gmp_rand_mt_struct *) RNG_STATE (src);
dstp = (*__gmp_allocate_func) (sizeof (gmp_rand_mt_struct));
RNG_STATE (dst) = (void *) dstp;
RNG_FNPTR (dst) = (void *) &Mersenne_Twister_Generator_Noseed;
for (i = 0; i < N; i++)
dstp->mt[i] = srcp->mt[i];
dstp->mti = srcp->mti;
}
/* Initialize MT-specific data. */
void
__gmp_randinit_mt_noseed (gmp_randstate_t rstate)
{
int i;
gmp_rand_mt_struct *p;
/* Set the generator functions. */
RNG_FNPTR (rstate) = (void *) &Mersenne_Twister_Generator_Noseed;
/* Allocate the MT-specific state. */
p = (gmp_rand_mt_struct *)
(*__gmp_allocate_func) (sizeof (gmp_rand_mt_struct));
RNG_STATE (rstate) = (mp_ptr) p;
/* Set state for default seed. */
for (i = 0; i < N; i++)
p->mt[i] = default_state[i];
((gmp_rand_mt_struct *) RNG_STATE (rstate))->mti = WARM_UP % N;
}