[16] | 1 | ! |
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| 2 | ! A Fortran90/95 module program for Multiple Stream Mersenne Twister. |
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| 3 | ! 2010/02/12, Ken-Ichi Ishikawa [ishikawa[at]theo.phys.sci.hiroshima-u.ac.jp] |
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| 4 | ! 2010/07/20, M. S. Briggs, [michael.s.briggs[at]nasa.gov], minor improvements. |
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| 5 | ! |
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| 6 | ! This module provides the Mersenne Twister pseudo random number generator |
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| 7 | ! (MT-PRNG) with multiple stream ability. |
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| 8 | ! A long period MT generaotr (backbone stream) is divided into disjoint streams, |
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| 9 | ! and the each stream has continuous stream from the backbone stream. |
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| 10 | ! The distance between each stream is chosen to have long enough length. |
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| 11 | ! The status and parameters of the each stream are encapsulated in |
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| 12 | ! the f90 type components so that we can use multiple streams simultaneously. |
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| 13 | ! The stream length is fixed to 2^nj. |
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| 14 | ! |
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| 15 | ! This code is converted from original/sample codes located at |
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| 16 | ! Mersenne Twister Home Page: |
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| 17 | ! [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/mt.html] |
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| 18 | ! |
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| 19 | ! For the Original MT PRNG, see also: |
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| 20 | ! M. Matsumoto and T. Nishimura, |
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| 21 | ! "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom |
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| 22 | ! number generator", |
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| 23 | ! ACM Trans. on Modeling and Computer Simulation Vol. 8, No. 1, |
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| 24 | ! January pp.3-30 (1998) DOI:10.1145/272991.272995. |
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| 25 | ! |
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| 26 | ! For the jump ahead mechanism, see also: |
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| 27 | ! H. Haramoto, M. Matsumoto, T. Nishimura, F. Panneton, and P. L'Ecuyer, |
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| 28 | ! "Efficient Jump Ahead for F_2-Linear Random Number Generators", |
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| 29 | ! GERAD Report G-2006-62. INFORMS Journal on Computing, 20, 3 (2008), 385-390. |
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| 30 | ! |
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| 31 | ! This routine uses; |
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| 32 | ! Fast arithmetic in GF(2)[x], [http://wwwmaths.anu.edu.au/~brent/software.html] |
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| 33 | ! NTL : A Library for doing Number Theory, [http://www.shoup.net/ntl/index.html] |
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| 34 | ! |
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| 35 | ! |
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| 36 | ! Copyright (c) 2010, Ken-Ichi Ishikawa [ishikawa[at]theo.phys.sci.hiroshima-u.ac.jp] |
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| 37 | ! All rights reserved. |
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| 38 | ! |
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| 39 | ! Redistribution and use in source and binary forms, with or without |
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| 40 | ! modification, are permitted provided that the following conditions are |
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| 41 | ! met: |
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| 42 | ! |
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| 43 | ! * Redistributions of source code must retain the above copyright |
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| 44 | ! notice, this list of conditions and the following disclaimer. |
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| 45 | ! |
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| 46 | ! * Redistributions in binary form must reproduce the above copyright |
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| 47 | ! notice, this list of conditions and the following disclaimer listed |
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| 48 | ! in this license in the documentation and/or other materials |
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| 49 | ! provided with the distribution. |
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| 50 | ! |
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| 51 | ! * Neither the name of the copyright holders nor the names of its |
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| 52 | ! contributors may be used to endorse or promote products derived from |
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| 53 | ! this software without specific prior written permission. |
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| 54 | ! |
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| 55 | ! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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| 56 | ! "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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| 57 | ! LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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| 58 | ! A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
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| 59 | ! OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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| 60 | ! SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
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| 61 | ! LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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| 62 | ! DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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| 63 | ! THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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| 64 | ! (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
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| 65 | ! OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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| 66 | ! |
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| 67 | |
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| 68 | !define _TEMPERING_ |
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| 69 | |
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| 70 | !ifdef _DEBUG_ |
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| 71 | !module mt_stream_debug |
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| 72 | !else |
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| 73 | module mt_stream |
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| 74 | !endif |
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| 75 | use mt_kind_defs |
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| 76 | implicit none |
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| 77 | private |
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| 78 | public :: MTS_SUCCESS |
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| 79 | public :: MTS_FAIL |
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| 80 | public :: mt_state |
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| 81 | public :: new,delete |
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| 82 | public :: init |
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| 83 | public :: print |
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| 84 | public :: save |
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| 85 | public :: read |
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| 86 | public :: set_mt19937 |
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| 87 | public :: create_stream |
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| 88 | public :: genrand_int32 |
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| 89 | public :: genrand_double1 |
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| 90 | public :: genrand_double2 |
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| 91 | public :: genrand_double3 |
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| 92 | public :: genrand_double4 |
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| 93 | |
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| 94 | integer(INT32), parameter :: MTS_SUCCESS = 0 |
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| 95 | integer(INT32), parameter :: MTS_FAIL = -1 |
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| 96 | !#ifdef _DEBUG_ |
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| 97 | ! integer(INT32), parameter :: MT_JUMP_DISTANCE_EXP = 16 ! test jump distance (2^16 steps) |
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| 98 | !#else |
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| 99 | integer(INT32), parameter :: MT_JUMP_DISTANCE_EXP = 256 ! default jump distance (2^256 steps) |
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| 100 | !#endif |
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| 101 | |
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| 102 | !====================================== |
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| 103 | ! MT19937 parameters |
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| 104 | !====================================== |
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| 105 | integer(INT32), parameter :: MT19937_N = 624 |
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| 106 | integer(INT32), parameter :: MT19937_M = 397 |
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| 107 | integer(INT32), parameter :: MT19937_W = 32 |
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| 108 | integer(INT32), parameter :: MT19937_R = 31 |
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| 109 | integer(INT32), parameter :: MT19937_MATA = INT (Z'9908b0df', INT32) |
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| 110 | integer(INT32), parameter :: MT19937_WMASK = INT (Z'ffffffff', INT32) |
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| 111 | integer(INT32), parameter :: MT19937_UMASK = INT (Z'80000000', INT32) |
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| 112 | integer(INT32), parameter :: MT19937_LMASK = INT (Z'7fffffff', INT32) |
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| 113 | integer(INT32), parameter :: MT19937_SHFT0 = 11 |
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| 114 | integer(INT32), parameter :: MT19937_SHFT1 = 18 |
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| 115 | integer(INT32), parameter :: MT19937_SHFTB = 7 |
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| 116 | integer(INT32), parameter :: MT19937_SHFTC = 15 |
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| 117 | integer(INT32), parameter :: MT19937_MASKB = INT (Z'9d2c5680', INT32) |
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| 118 | integer(INT32), parameter :: MT19937_MASKC = INT (Z'efc60000', INT32) |
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| 119 | |
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| 120 | !====================================== |
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| 121 | ! MT state |
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| 122 | ! Period = 2^(N*W-R)-1 |
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| 123 | !====================================== |
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| 124 | type mt_state |
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| 125 | private |
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| 126 | integer(INT32) :: i = -1 ! state vector index |
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| 127 | integer(INT32) :: stream_id = -1 ! stream ID |
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| 128 | integer(INT32) :: istatus = -1 ! initialization status |
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| 129 | integer(INT32) :: nn = -1 ! MT parameter N |
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| 130 | integer(INT32) :: mm = -1 ! MT parameter M |
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| 131 | integer(INT32) :: rr = -1 ! MT parameter R |
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| 132 | integer(INT32) :: ww = -1 ! MT parameter W (width =32) |
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| 133 | integer(INT32) :: aaa = 0 ! Companion matrix parameter |
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| 134 | integer(INT32) :: wmask = 0 ! 32-bit mask |
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| 135 | integer(INT32) :: umask = 0 ! Twist mask x(1) |
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| 136 | integer(INT32) :: lmask = 0 ! Twist mask x(0) |
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| 137 | integer(INT32) :: shift0 = 0 ! Temparing parameters ... |
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| 138 | integer(INT32) :: shift1 = 0 |
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| 139 | integer(INT32) :: maskB = 0 |
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| 140 | integer(INT32) :: maskC = 0 |
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| 141 | integer(INT32) :: shiftB = 0 |
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| 142 | integer(INT32) :: shiftC = 0 |
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| 143 | integer(INT32) :: mag(0:1) = 0 ! mag(0) = 0, mag(1) = aaa |
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| 144 | integer(INT32), pointer :: state(:) => NULL() ! state vector |
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| 145 | end type |
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| 146 | |
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| 147 | type(mt_state), save :: g_mt_master ! this keeps MT parameters |
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| 148 | integer(INT32), save :: total_stream = 0 |
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| 149 | |
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| 150 | interface new |
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| 151 | module procedure mt_new |
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| 152 | end interface |
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| 153 | |
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| 154 | interface delete |
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| 155 | module procedure mt_delete |
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| 156 | end interface |
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| 157 | |
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| 158 | interface print |
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| 159 | module procedure mt_print |
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| 160 | end interface |
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| 161 | |
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| 162 | interface read |
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| 163 | module procedure mt_read |
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| 164 | end interface |
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| 165 | |
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| 166 | interface save |
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| 167 | module procedure mt_save |
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| 168 | end interface |
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| 169 | |
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| 170 | interface set_mt19937 |
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| 171 | module procedure mt_set_mt19937 |
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| 172 | end interface |
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| 173 | |
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| 174 | interface init |
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| 175 | module procedure mt_init_by_scalar |
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| 176 | module procedure mt_init_by_array |
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| 177 | end interface |
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| 178 | |
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| 179 | interface create_stream |
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| 180 | module procedure mt_create_stream |
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| 181 | end interface |
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| 182 | |
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| 183 | interface genrand_int32 |
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| 184 | ! in [0,0xFFFFFFFF] |
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| 185 | module procedure mt_genrand_int32 |
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| 186 | end interface |
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| 187 | |
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| 188 | interface genrand_double1 |
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| 189 | ! in [0,1] (53-bit resolution) |
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| 190 | module procedure mt_genrand_double1 |
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| 191 | end interface |
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| 192 | |
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| 193 | interface genrand_double2 |
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| 194 | ! in [0,1) (53-bit resolution) |
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| 195 | module procedure mt_genrand_double2 |
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| 196 | end interface |
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| 197 | |
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| 198 | interface genrand_double3 |
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| 199 | ! in (0,1) (52-bit resolution) |
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| 200 | module procedure mt_genrand_double3 |
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| 201 | end interface |
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| 202 | |
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| 203 | interface genrand_double4 |
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| 204 | ! in (0,1] (53-bit resolution) |
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| 205 | module procedure mt_genrand_double4 |
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| 206 | end interface |
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| 207 | |
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| 208 | contains |
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| 209 | |
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| 210 | subroutine mt_new(this,ierr) |
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| 211 | ! |
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| 212 | != Allocate mt state |
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| 213 | ! |
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| 214 | implicit none |
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| 215 | type(mt_state), intent(inout) :: this |
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| 216 | integer(INT32), optional, intent(out) :: ierr |
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| 217 | character(256), parameter :: myname="mt_new" |
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| 218 | integer(INT32) :: jerr,kerr |
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| 219 | jerr = MTS_SUCCESS |
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| 220 | if (0 == g_mt_master%nn) then |
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| 221 | write(*,'(A,": MT master parameter is not initialized.")')TRIM(myname) |
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| 222 | write(*,'(A,": Stop!")')TRIM(myname) |
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| 223 | stop |
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| 224 | endif |
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| 225 | call mt_copy(g_mt_master,this) |
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| 226 | this%stream_id = total_stream |
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| 227 | total_stream = total_stream + 1 |
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| 228 | if (.not.associated(this%state)) then |
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| 229 | if (this%nn <= 0) then |
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| 230 | jerr = MTS_FAIL |
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| 231 | this%istatus = jerr |
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| 232 | goto 100 |
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| 233 | endif |
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| 234 | allocate(this%state(0:this%nn-1),STAT=kerr) |
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| 235 | if (kerr /= 0) then |
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| 236 | jerr = MTS_FAIL |
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| 237 | this%istatus = jerr |
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| 238 | goto 100 |
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| 239 | endif |
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| 240 | this%istatus = jerr |
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| 241 | goto 100 |
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| 242 | endif |
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| 243 | 100 if (present(ierr)) then |
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| 244 | ierr = jerr |
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| 245 | return |
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| 246 | else |
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| 247 | if (jerr /= MTS_SUCCESS) then |
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| 248 | write(*,'(A,": Something wrong.")')TRIM(myname) |
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| 249 | write(*,'(A,": Stop!")')TRIM(myname) |
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| 250 | stop |
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| 251 | endif |
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| 252 | endif |
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| 253 | end subroutine |
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| 254 | |
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| 255 | subroutine mt_delete(this) |
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| 256 | ! |
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| 257 | != deallocate state vector |
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| 258 | ! |
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| 259 | implicit none |
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| 260 | type(mt_state), intent(inout) :: this |
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| 261 | if (associated(this%state)) then |
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| 262 | deallocate(this%state) |
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| 263 | endif |
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| 264 | total_stream = total_stream - 1 |
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| 265 | return |
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| 266 | end subroutine |
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| 267 | |
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| 268 | subroutine mt_set_mt19937 |
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| 269 | ! |
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| 270 | != set MT19937 parameters on g_mt_master |
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| 271 | ! |
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| 272 | implicit none |
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| 273 | g_mt_master%nn = MT19937_N |
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| 274 | g_mt_master%mm = MT19937_M |
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| 275 | g_mt_master%ww = MT19937_W |
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| 276 | g_mt_master%rr = MT19937_R |
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| 277 | g_mt_master%aaa = MT19937_MATA |
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| 278 | g_mt_master%wmask = MT19937_WMASK |
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| 279 | g_mt_master%umask = MT19937_UMASK |
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| 280 | g_mt_master%lmask = MT19937_LMASK |
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| 281 | g_mt_master%shift0 = MT19937_SHFT0 |
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| 282 | g_mt_master%shift1 = MT19937_SHFT1 |
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| 283 | g_mt_master%shiftB = MT19937_SHFTB |
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| 284 | g_mt_master%shiftC = MT19937_SHFTC |
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| 285 | g_mt_master%maskB = MT19937_MASKB |
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| 286 | g_mt_master%maskC = MT19937_MASKC |
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| 287 | g_mt_master%mag(0) = 0 |
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| 288 | g_mt_master%mag(1) = g_mt_master%aaa |
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| 289 | total_stream = 0 |
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| 290 | return |
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| 291 | end subroutine |
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| 292 | |
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| 293 | subroutine mt_copy(this,that) |
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| 294 | ! |
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| 295 | != duplicate/copy MT paramters |
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| 296 | ! |
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| 297 | ! that <= this |
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| 298 | ! |
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| 299 | implicit none |
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| 300 | type(mt_state), intent(in) :: this |
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| 301 | type(mt_state), intent(out) :: that |
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| 302 | that%i = this%i |
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| 303 | that%stream_id = this%stream_id |
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| 304 | that%istatus = this%istatus |
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| 305 | that%nn = this%nn |
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| 306 | that%nn = this%nn |
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| 307 | that%mm = this%mm |
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| 308 | that%ww = this%ww |
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| 309 | that%aaa = this%aaa |
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| 310 | that%rr = this%rr |
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| 311 | that%wmask = this%wmask |
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| 312 | that%umask = this%umask |
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| 313 | that%lmask = this%lmask |
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| 314 | that%shift0 = this%shift0 |
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| 315 | that%shift1 = this%shift1 |
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| 316 | that%shiftB = this%shiftB |
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| 317 | that%shiftC = this%shiftC |
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| 318 | that%maskB = this%maskB |
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| 319 | that%maskC = this%maskC |
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| 320 | that%mag(0) = 0 |
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| 321 | that%mag(1) = that%aaa |
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| 322 | return |
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| 323 | end subroutine |
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| 324 | |
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| 325 | subroutine mt_save(this,unit) |
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| 326 | ! |
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| 327 | != save MT status to file with unit |
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| 328 | ! |
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| 329 | implicit none |
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| 330 | type(mt_state), intent(in) :: this |
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| 331 | integer(INT32), intent(in) :: unit |
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| 332 | write(unit) this%i |
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| 333 | write(unit) this%stream_id |
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| 334 | write(unit) this%istatus |
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| 335 | write(unit) this%nn |
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| 336 | write(unit) this%mm |
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| 337 | write(unit) this%ww |
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| 338 | write(unit) this%aaa |
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| 339 | write(unit) this%rr |
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| 340 | write(unit) this%wmask |
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| 341 | write(unit) this%umask |
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| 342 | write(unit) this%lmask |
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| 343 | write(unit) this%shift0 |
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| 344 | write(unit) this%shift1 |
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| 345 | write(unit) this%shiftB |
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| 346 | write(unit) this%shiftC |
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| 347 | write(unit) this%maskB |
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| 348 | write(unit) this%maskC |
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| 349 | write(unit) this%mag(:) |
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| 350 | write(unit) this%state(:) |
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| 351 | return |
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| 352 | end subroutine |
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| 353 | |
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| 354 | subroutine mt_read(this,unit) |
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| 355 | ! |
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| 356 | != read MT status from file with unit |
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| 357 | ! |
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| 358 | implicit none |
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| 359 | type(mt_state), intent(inout) :: this |
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| 360 | integer(INT32), intent(in) :: unit |
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| 361 | read(unit) this%i |
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| 362 | read(unit) this%stream_id |
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| 363 | read(unit) this%istatus |
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| 364 | read(unit) this%nn |
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| 365 | read(unit) this%mm |
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| 366 | read(unit) this%ww |
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| 367 | read(unit) this%aaa |
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| 368 | read(unit) this%rr |
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| 369 | read(unit) this%wmask |
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| 370 | read(unit) this%umask |
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| 371 | read(unit) this%lmask |
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| 372 | read(unit) this%shift0 |
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| 373 | read(unit) this%shift1 |
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| 374 | read(unit) this%shiftB |
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| 375 | read(unit) this%shiftC |
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| 376 | read(unit) this%maskB |
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| 377 | read(unit) this%maskC |
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| 378 | read(unit) this%mag(:) |
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| 379 | if (associated(this%state)) then |
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| 380 | deallocate(this%state) |
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| 381 | allocate(this%state(0:this%nn-1)) |
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| 382 | endif |
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| 383 | read(unit) this%state(:) |
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| 384 | return |
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| 385 | end subroutine |
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| 386 | |
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| 387 | subroutine mt_print(this) |
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| 388 | ! |
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| 389 | != print MT stream parameter and states |
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| 390 | ! |
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| 391 | implicit none |
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| 392 | type(mt_state), intent(in) :: this |
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| 393 | character(256) :: str |
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| 394 | write(*,'("===============================================================================")') |
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| 395 | write(*,'(" MT PARAMETERS")') |
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| 396 | write(str,*)this%stream_id |
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| 397 | write(*,'(" STREAMID= ",A)')TRIM(ADJUSTL(str)) |
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| 398 | write(str,*)this%nn*this%ww-this%rr |
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| 399 | write(*,'(" PERIOD= 2^",A," - 1")')TRIM(ADJUSTL(str)) |
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| 400 | write(*,'(" NN=",I8," MM=",I8," WW=",I3," RR=",I3)')this%nn,this%mm,this%ww,this%rr |
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| 401 | write(*,'(" AVEC= 0x",Z8.8)', advance='no' )this%aaa |
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| 402 | write(*,'(" WMASK= 0x",Z8.8)', advance='no' )this%wmask |
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| 403 | write(*,'(" UMASK= 0x",Z8.8)', advance='no' )this%umask |
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| 404 | write(*,'(" LMASK= 0x",Z8.8)') this%lmask |
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| 405 | write(*,'(" MAG= 0x",Z8.8," 0x",Z8.8)') this%mag |
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| 406 | write(*,'(" SHFT0=",I3)', advance='no' )this%shift0 |
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| 407 | write(*,'(" SHFT1=",I3)', advance='no' )this%shift1 |
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| 408 | write(*,'(" SHFTB=",I3)', advance='no' )this%shiftB |
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| 409 | write(*,'(" SHFTC=",I3)', advance='no' )this%shiftC |
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| 410 | write(*,'(" MASKB= 0x",Z8.8)', advance='no' )this%maskB |
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| 411 | write(*,'(" MASKC= 0x",Z8.8)') this%maskC |
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| 412 | write(str,*)this%i |
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| 413 | write(*,'(" POINTER= ",A)')TRIM(ADJUSTL(str)) |
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| 414 | write(*,'("===============================================================================")') |
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| 415 | return |
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| 416 | end subroutine |
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| 417 | |
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| 418 | |
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| 419 | subroutine mt_init_by_scalar(this,iseed,ierr) |
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| 420 | ! |
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| 421 | != initialize MT state by a scalar seed. |
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| 422 | ! |
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| 423 | implicit none |
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| 424 | type(mt_state), intent(inout) :: this |
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| 425 | integer(INT32), intent(in) :: iseed |
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| 426 | integer(INT32), optional, intent(out) :: ierr |
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| 427 | character(256), parameter :: myname="mt_init_by_scalar" |
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| 428 | integer(INT32) :: i,jseed,jerr |
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| 429 | if (.not.associated(this%state)) then |
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| 430 | jerr = MTS_FAIL |
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| 431 | goto 100 |
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| 432 | endif |
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| 433 | jseed = iseed |
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| 434 | do i=0,this%nn-1 |
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| 435 | this%state(i) = jseed |
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| 436 | jseed = 1812433253 * IEOR(jseed, ISHFT(jseed,-30)) + i + 1 |
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| 437 | enddo |
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| 438 | this%i = this%nn |
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| 439 | do i=0,this%nn-1 |
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| 440 | this%state(i) = IAND(this%state(i),this%wmask) |
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| 441 | enddo |
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| 442 | this%mag(0) = 0 |
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| 443 | this%mag(1) = this%aaa |
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| 444 | jerr = MTS_SUCCESS |
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| 445 | 100 if (present(ierr)) then |
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| 446 | ierr = jerr |
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| 447 | else |
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| 448 | if (jerr /= MTS_SUCCESS) then |
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| 449 | write(*,'(A,": State vector allocation fails.")')TRIM(myname) |
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| 450 | write(*,'(A,": Stop!")')TRIM(myname) |
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| 451 | stop |
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| 452 | endif |
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| 453 | endif |
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| 454 | return |
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| 455 | end subroutine |
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| 456 | |
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| 457 | subroutine mt_init_by_array(this,iseed,ierr) |
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| 458 | ! |
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| 459 | != initialize MT state by array seeds. |
---|
| 460 | ! |
---|
| 461 | implicit none |
---|
| 462 | type(mt_state), intent(inout) :: this |
---|
| 463 | integer(INT32), intent(in) :: iseed(0:) |
---|
| 464 | integer(INT32), optional, intent(out) :: ierr |
---|
| 465 | integer :: isize,i,j,k,n,jerr |
---|
| 466 | character(256), parameter :: myname="mt_init_by_array" |
---|
| 467 | integer(INT32), parameter :: ASEED = 19650218 |
---|
| 468 | |
---|
| 469 | call mt_init_by_scalar(this,ASEED,jerr) |
---|
| 470 | if (jerr /= MTS_SUCCESS) goto 100 |
---|
| 471 | |
---|
| 472 | isize = SIZE(iseed) |
---|
| 473 | n = this%nn |
---|
| 474 | i = 1 |
---|
| 475 | j = 0 |
---|
| 476 | do k = MAX(n,isize),1,-1 |
---|
| 477 | this%state(i) = IEOR(this%state(i),(IEOR(this%state(i-1),ISHFT(this%state(i-1),-30))*1664525)) + iseed(j) + j |
---|
| 478 | this%state(i) = IAND(this%state(i),this%wmask) ! for WORDSIZE > 32 machines |
---|
| 479 | i = i + 1 |
---|
| 480 | j = j + 1 |
---|
| 481 | if (i >= n) then |
---|
| 482 | this%state(0) = this%state(n-1) |
---|
| 483 | i = 1 |
---|
| 484 | endif |
---|
| 485 | if (j >= isize) j = 0 |
---|
| 486 | enddo |
---|
| 487 | do k = n-1,1,-1 |
---|
| 488 | this%state(i) = IEOR(this%state(i),(IEOR(this%state(i-1),ISHFT(this%state(i-1),-30))*1566083941)) - i |
---|
| 489 | this%state(i) = IAND(this%state(i),this%wmask) ! for WORDSIZE > 32 machines |
---|
| 490 | i = i + 1 |
---|
| 491 | if (i >= n) then |
---|
| 492 | this%state(0) = this%state(n-1) |
---|
| 493 | i = 1 |
---|
| 494 | endif |
---|
| 495 | enddo |
---|
| 496 | this%state(0) = INT (Z'80000000', INT32) ! MSB is 1; assuring non-zero initial array |
---|
| 497 | jerr = MTS_SUCCESS |
---|
| 498 | 100 if (present(ierr)) then |
---|
| 499 | ierr = jerr |
---|
| 500 | else |
---|
| 501 | if (jerr /= MTS_SUCCESS) then |
---|
| 502 | write(*,'(A,": mt_init_by_scalar fails.")')TRIM(myname) |
---|
| 503 | write(*,'(A,": Stop!")')TRIM(myname) |
---|
| 504 | stop |
---|
| 505 | endif |
---|
| 506 | endif |
---|
| 507 | return |
---|
| 508 | end subroutine |
---|
| 509 | |
---|
| 510 | function mt_genrand_int32(this) result(ir) |
---|
| 511 | ! |
---|
| 512 | != return a value in [0,0xFFFFFFFF] |
---|
| 513 | ! |
---|
| 514 | implicit none |
---|
| 515 | type(mt_state), intent(inout) :: this |
---|
| 516 | integer(INT32) :: ir |
---|
| 517 | integer(INT32) :: umask,lmask,n,m,is |
---|
| 518 | integer(INT32) :: k,nm,n1 |
---|
| 519 | if (this%i >= this%nn) then |
---|
| 520 | n = this%nn |
---|
| 521 | m = this%mm |
---|
| 522 | lmask = this%lmask |
---|
| 523 | umask = this%umask |
---|
| 524 | nm = n - m |
---|
| 525 | n1 = n - 1 |
---|
| 526 | do k=0,nm-1 |
---|
| 527 | is = IOR(IAND(this%state(k),umask),IAND(this%state(k+1),lmask)) |
---|
| 528 | this%state(k) = IEOR(IEOR(this%state(k+m),ISHFT(is,-1)),this%mag(IAND(is,1))) |
---|
| 529 | enddo |
---|
| 530 | do k=nm,n1-1 |
---|
| 531 | is = IOR(IAND(this%state(k),umask),IAND(this%state(k+1),lmask)) |
---|
| 532 | this%state(k) = IEOR(IEOR(this%state(k+m-n),ISHFT(is,-1)),this%mag(IAND(is,1))) |
---|
| 533 | enddo |
---|
| 534 | is = IOR(IAND(this%state(n-1),umask),IAND(this%state(0),lmask)) |
---|
| 535 | this%state(n-1) = IEOR(IEOR(this%state(m-1),ISHFT(is,-1)),this%mag(IAND(is,1))) |
---|
| 536 | this%i = 0 |
---|
| 537 | endif |
---|
| 538 | |
---|
| 539 | is = this%state(this%i) |
---|
| 540 | this%i = this%i + 1 |
---|
| 541 | !#ifdef _TEMPERING_ |
---|
| 542 | ! is = IEOR(is,ISHFT(is,-this%shift0)) |
---|
| 543 | ! is = IEOR(is,IAND(ISHFT(is, this%shiftB),this%maskB)) |
---|
| 544 | ! is = IEOR(is,IAND(ISHFT(is, this%shiftC),this%maskC)) |
---|
| 545 | ! is = IEOR(is,ISHFT(is,-this%shift1)) |
---|
| 546 | !#endif |
---|
| 547 | ir = is |
---|
| 548 | return |
---|
| 549 | end function |
---|
| 550 | |
---|
| 551 | subroutine mt_matvec(this,v,w) |
---|
| 552 | ! |
---|
| 553 | != Multiply transition matrix on a state vector v |
---|
| 554 | ! |
---|
| 555 | ! w = B v |
---|
| 556 | ! |
---|
| 557 | ! this : MT parameters(transition matrix) |
---|
| 558 | ! v : input vector |
---|
| 559 | ! w : output vector |
---|
| 560 | ! |
---|
| 561 | implicit none |
---|
| 562 | type(mt_state), intent(in) :: this |
---|
| 563 | integer(INT32), intent(in) :: v(0:this%nn-1) |
---|
| 564 | integer(INT32), intent(out) :: w(0:this%nn-1) |
---|
| 565 | integer(INT32) :: umask,lmask,n,m,is |
---|
| 566 | integer(INT32) :: k |
---|
| 567 | n = this%nn |
---|
| 568 | m = this%mm |
---|
| 569 | lmask = this%lmask |
---|
| 570 | umask = this%umask |
---|
| 571 | w(0) = IAND(v(1),umask) |
---|
| 572 | do k=1,n-2 |
---|
| 573 | w(k) = v(k+1) |
---|
| 574 | enddo |
---|
| 575 | is = IOR(IAND(v(0),umask),IAND(v(1),lmask)) |
---|
| 576 | w(n-1) = IEOR(IEOR(v(m),ISHFT(is,-1)),this%mag(IAND(is,1))) |
---|
| 577 | return |
---|
| 578 | end subroutine |
---|
| 579 | |
---|
| 580 | subroutine mt_create_stream(this,that,id) |
---|
| 581 | ! |
---|
| 582 | != Create New stream (that) with distance id*2^(jp) from (this) |
---|
| 583 | ! |
---|
| 584 | implicit none |
---|
| 585 | type(mt_state), intent(inout) :: this ! input state |
---|
| 586 | type(mt_state), intent(inout) :: that ! output state |
---|
| 587 | integer(INT32), intent(in) :: id |
---|
| 588 | character(256), parameter :: myname="mt_create_stream" |
---|
| 589 | integer(INT32), parameter :: jp = MT_JUMP_DISTANCE_EXP |
---|
| 590 | if (id < 0) then |
---|
| 591 | write(*,'(A,": Positive ID is requried.")')TRIM(myname) |
---|
| 592 | write(*,'(A,": Stop!")')TRIM(myname) |
---|
| 593 | stop |
---|
| 594 | endif |
---|
| 595 | call mt_jumpahead(this,that,jp,id) |
---|
| 596 | that%stream_id = id |
---|
| 597 | total_stream = total_stream + 1 |
---|
| 598 | this%i = this%nn |
---|
| 599 | return |
---|
| 600 | end subroutine |
---|
| 601 | |
---|
| 602 | subroutine mt_jumpahead(this,that,jp,id) |
---|
| 603 | ! |
---|
| 604 | != Jump ahead by (id+1) * 2^jp steps. |
---|
| 605 | ! |
---|
| 606 | ! this : input state |
---|
| 607 | ! that : output state, proceeds by id*2^jp steps. |
---|
| 608 | ! |
---|
| 609 | implicit none |
---|
| 610 | type(mt_state), intent(inout) :: this ! input state |
---|
| 611 | type(mt_state), intent(inout) :: that ! output state |
---|
| 612 | integer(INT32), intent(in) :: jp ! exponent (jump step = id*2^jp) |
---|
| 613 | integer(INT32), intent(in) :: id ! id (jump step = id*2^jp) |
---|
| 614 | integer(INT32) :: v(0:this%nn-1) |
---|
| 615 | integer(INT32) :: w(0:this%nn-1) |
---|
| 616 | integer(INT32) :: s(0:this%nn-1) |
---|
| 617 | integer(INT32) :: i,iwp,ibp |
---|
| 618 | character(256) :: str,str2 |
---|
| 619 | integer(INT32) :: p(0:this%nn-1) |
---|
| 620 | integer(INT32) :: np |
---|
| 621 | ! |
---|
| 622 | ! external routine in |
---|
| 623 | ! jump_ahead_coeff/get_coeff.cxx |
---|
| 624 | ! written in C++ with NTL and gf2x libraries. |
---|
| 625 | ! |
---|
| 626 | !#ifdef _NTL_ |
---|
| 627 | ! interface get_coeff_interface |
---|
| 628 | ! subroutine get_coeff(nn,mm,rr,ww,avec,nj,id,pp,np) bind (C, name="get_coeff") |
---|
| 629 | ! use, intrinsic :: iso_c_binding, only: c_int |
---|
| 630 | ! integer (c_int), intent(in) :: nn,mm,rr,ww,avec,nj,id |
---|
| 631 | ! integer (c_int), intent(inout) :: pp(0:nn-1),np |
---|
| 632 | ! end subroutine get_coeff |
---|
| 633 | ! end interface get_coeff_interface |
---|
| 634 | !#else |
---|
| 635 | interface f_get_coeff_interface |
---|
| 636 | subroutine f_get_coeff(nn,mm,rr,ww,avec,nj,id,pp,np) |
---|
| 637 | integer, intent(in) :: nn,mm,rr,ww,avec,nj,id |
---|
| 638 | integer, intent(inout) :: pp(0:nn-1),np |
---|
| 639 | end subroutine f_get_coeff |
---|
| 640 | end interface f_get_coeff_interface |
---|
| 641 | !#endif |
---|
| 642 | |
---|
| 643 | !================================== |
---|
| 644 | ! state copy: this => that |
---|
| 645 | !================================== |
---|
| 646 | call mt_copy(this,that) |
---|
| 647 | |
---|
| 648 | write(str,'(I12)')id |
---|
| 649 | write(str2,'(I12)')jp |
---|
| 650 | write(*,'("# ID ",I12)')id |
---|
| 651 | write(*,'("# Jump Ahead by (",A,")*2^",A)')TRIM(ADJUSTL(str)),TRIM(ADJUSTL(str2)) |
---|
| 652 | if ( this%i /= this%nn) then |
---|
| 653 | write(*,'("Error in jumpahead: input state pointer should point nn.")') |
---|
| 654 | write(*,'("this%i = ",I12)')this%i |
---|
| 655 | write(*,'("this%nn = ",I12)')this%nn |
---|
| 656 | write(str,*)this%i |
---|
| 657 | write(str2,*)this%nn-1 |
---|
| 658 | write(*,'(A,"-",A," random numbers are dropped.")') & |
---|
| 659 | & TRIM(ADJUSTL(str)),TRIM(ADJUSTL(str2)) |
---|
| 660 | write(*,'("forced to point nn")') |
---|
| 661 | this%i = this%nn |
---|
| 662 | endif |
---|
| 663 | |
---|
| 664 | !================================== |
---|
| 665 | ! compute jump ahead polynomial |
---|
| 666 | ! p(x) coefficients |
---|
| 667 | ! for this MT parameter |
---|
| 668 | !================================== |
---|
| 669 | !#ifdef _NTL_ |
---|
| 670 | ! call get_coeff(this%nn,this%mm,this%rr,this%ww,this%aaa,jp,id,p,np) |
---|
| 671 | !#else |
---|
| 672 | call f_get_coeff(this%nn,this%mm,this%rr,this%ww,this%aaa,jp,id,p,np) |
---|
| 673 | !#endif |
---|
| 674 | |
---|
| 675 | !================================== |
---|
| 676 | ! multiply p(B) on a state vector v |
---|
| 677 | ! p(x) : jump ahead polynomial |
---|
| 678 | ! B : transition matrix |
---|
| 679 | ! with simple Horner's method |
---|
| 680 | ! w = p(B) v = B^(2^jp) v |
---|
| 681 | !================================== |
---|
| 682 | v(:) = this%state(:) |
---|
| 683 | iwp = (np-1)/32 |
---|
| 684 | ibp = mod(np-1,32) |
---|
| 685 | if (BTEST(p(iwp),ibp)) then |
---|
| 686 | w(:) = v(:) |
---|
| 687 | endif |
---|
| 688 | do i=np-2,0,-1 |
---|
| 689 | iwp = i/32 |
---|
| 690 | ibp = mod(i,32) |
---|
| 691 | call mt_matvec(this,w,s) ! s = B w |
---|
| 692 | if (BTEST(p(iwp),ibp)) then |
---|
| 693 | w(:) = IEOR(v(:),s(:)) ! w = 1 v + s |
---|
| 694 | else |
---|
| 695 | w(:) = s(:) ! w = 0 v + s |
---|
| 696 | endif |
---|
| 697 | enddo |
---|
| 698 | |
---|
| 699 | if (.not. associated(that%state)) then |
---|
| 700 | allocate(that%state(0:that%nn-1)) |
---|
| 701 | endif |
---|
| 702 | that%state(:) = w(:) |
---|
| 703 | that%i = this%nn |
---|
| 704 | |
---|
| 705 | return |
---|
| 706 | end subroutine |
---|
| 707 | |
---|
| 708 | function mt_genrand_double1(this) result(r) |
---|
| 709 | ! |
---|
| 710 | ! r in [0,1] (53-bit resolution) |
---|
| 711 | ! |
---|
| 712 | implicit none |
---|
| 713 | type(mt_state), intent(inout) :: this |
---|
| 714 | real(REAL64) :: r |
---|
| 715 | real(REAL64) :: a,b |
---|
| 716 | integer(INT32) :: ia,ib |
---|
| 717 | ia = mt_genrand_int32(this) ! ia in [0,0xFFFFFFFF] |
---|
| 718 | ib = mt_genrand_int32(this) ! ib in [0,0xFFFFFFFF] |
---|
| 719 | ia = ISHFT(ia,-5) ! ia in [0,2^27-1] |
---|
| 720 | ib = ISHFT(ib,-6) ! ib in [0,2^26-1] |
---|
| 721 | a = REAL(ia,kind=KIND(r)) |
---|
| 722 | b = REAL(ib,kind=KIND(r)) |
---|
| 723 | !=============================== |
---|
| 724 | ! ( a*2^26 + b ) in [0,2^53-1] |
---|
| 725 | ! r = ( a*2^26 + b )/(2^53-1) |
---|
| 726 | !=============================== |
---|
| 727 | r = (a*67108864.0_REAL64 + b)*(1.0_REAL64/9007199254740991.0_REAL64) |
---|
| 728 | return |
---|
| 729 | end function |
---|
| 730 | |
---|
| 731 | function mt_genrand_double2(this) result(r) |
---|
| 732 | ! |
---|
| 733 | ! r in [0,1) (53-bit resolution) |
---|
| 734 | ! |
---|
| 735 | implicit none |
---|
| 736 | type(mt_state), intent(inout) :: this |
---|
| 737 | real(REAL64) :: r |
---|
| 738 | real(REAL64) :: a,b |
---|
| 739 | integer(INT32) :: ia,ib |
---|
| 740 | ia = mt_genrand_int32(this) ! ia in [0,0xFFFFFFFF] |
---|
| 741 | ib = mt_genrand_int32(this) ! ib in [0,0xFFFFFFFF] |
---|
| 742 | ia = ISHFT(ia,-5) ! ia in [0,2^27-1] |
---|
| 743 | ib = ISHFT(ib,-6) ! ib in [0,2^26-1] |
---|
| 744 | a = REAL(ia,kind=KIND(r)) |
---|
| 745 | b = REAL(ib,kind=KIND(r)) |
---|
| 746 | !=============================== |
---|
| 747 | ! ( a*2^26 + b ) in [0,2^53-1] |
---|
| 748 | ! r = ( a*2^26 + b )/(2^53) |
---|
| 749 | !=============================== |
---|
| 750 | r = (a*67108864.0_REAL64 + b)*(1.0_REAL64/9007199254740992.0_REAL64) |
---|
| 751 | return |
---|
| 752 | end function |
---|
| 753 | |
---|
| 754 | function mt_genrand_double3(this) result(r) |
---|
| 755 | ! |
---|
| 756 | ! r in (0,1) (52-bit resolution) |
---|
| 757 | ! |
---|
| 758 | implicit none |
---|
| 759 | type(mt_state), intent(inout) :: this |
---|
| 760 | real(REAL64) :: r |
---|
| 761 | real(REAL64) :: a,b |
---|
| 762 | integer(INT32) :: ia,ib |
---|
| 763 | ia = mt_genrand_int32(this) ! ia in [0,0xFFFFFFFF] |
---|
| 764 | ib = mt_genrand_int32(this) ! ib in [0,0xFFFFFFFF] |
---|
| 765 | ia = ISHFT(ia,-6) ! ia in [0,2^26-1] |
---|
| 766 | ib = ISHFT(ib,-6) ! ib in [0,2^26-1] |
---|
| 767 | a = REAL(ia,kind=KIND(r)) |
---|
| 768 | b = REAL(ib,kind=KIND(r)) |
---|
| 769 | !=============================== |
---|
| 770 | ! ( a*2^26 + b ) in [0,2^52-1] |
---|
| 771 | ! r = ( a*2^26 + b + 1/2 )/(2^52) |
---|
| 772 | !=============================== |
---|
| 773 | r = (a*67108864.0_REAL64 + b + 0.5_REAL64)*(1.0_REAL64/4503599627370496.0_REAL64) |
---|
| 774 | return |
---|
| 775 | end function |
---|
| 776 | |
---|
| 777 | function mt_genrand_double4(this) result(r) |
---|
| 778 | ! |
---|
| 779 | ! r in (0,1] (53-bit resolution) |
---|
| 780 | ! |
---|
| 781 | implicit none |
---|
| 782 | type(mt_state), intent(inout) :: this |
---|
| 783 | real(REAL64) :: r |
---|
| 784 | r = 1.0_REAL64 - mt_genrand_double2(this) |
---|
| 785 | return |
---|
| 786 | end function |
---|
| 787 | |
---|
| 788 | end module |
---|