0
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1 /*
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2 * Copyright (c) 1983 Regents of the University of California.
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3 * All rights reserved.
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4 *
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5 * Redistribution and use in source and binary forms, with or without
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6 * modification, are permitted provided that the following conditions
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7 * are met:
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8 * 1. Redistributions of source code must retain the above copyright
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9 * notice, this list of conditions and the following disclaimer.
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10 * 2. Redistributions in binary form must reproduce the above copyright
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11 * notice, this list of conditions and the following disclaimer in the
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12 * documentation and/or other materials provided with the distribution.
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13 * 3. [rescinded 22 July 1999]
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14 * 4. Neither the name of the University nor the names of its contributors
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15 * may be used to endorse or promote products derived from this software
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16 * without specific prior written permission.
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17 *
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18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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28 * SUCH DAMAGE.
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29 */
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30
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31 /*
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32 * This is derived from the Berkeley source:
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33 * @(#)random.c 5.5 (Berkeley) 7/6/88
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34 * It was reworked for the GNU C Library by Roland McGrath.
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35 */
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36
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37 /*
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38
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39 @deftypefn Supplement {long int} random (void)
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40 @deftypefnx Supplement void srandom (unsigned int @var{seed})
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41 @deftypefnx Supplement void* initstate (unsigned int @var{seed}, void *@var{arg_state}, unsigned long @var{n})
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42 @deftypefnx Supplement void* setstate (void *@var{arg_state})
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43
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44 Random number functions. @code{random} returns a random number in the
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45 range 0 to @code{LONG_MAX}. @code{srandom} initializes the random
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46 number generator to some starting point determined by @var{seed}
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47 (else, the values returned by @code{random} are always the same for each
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48 run of the program). @code{initstate} and @code{setstate} allow fine-grained
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49 control over the state of the random number generator.
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50
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51 @end deftypefn
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52
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53 */
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54
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55 #include <errno.h>
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56
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57 #if 0
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58
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59 #include <ansidecl.h>
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60 #include <limits.h>
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61 #include <stddef.h>
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62 #include <stdlib.h>
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63
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64 #else
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65
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66 #define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */
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67 #define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/
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68
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69 #ifdef __STDC__
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70 # define PTR void *
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71 # ifndef NULL
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72 # define NULL (void *) 0
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73 # endif
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74 #else
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75 # define PTR char *
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76 # ifndef NULL
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77 # define NULL (void *) 0
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78 # endif
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79 #endif
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80
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81 #endif
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82
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83 long int random (void);
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84
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85 /* An improved random number generation package. In addition to the standard
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86 rand()/srand() like interface, this package also has a special state info
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87 interface. The initstate() routine is called with a seed, an array of
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88 bytes, and a count of how many bytes are being passed in; this array is
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89 then initialized to contain information for random number generation with
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90 that much state information. Good sizes for the amount of state
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91 information are 32, 64, 128, and 256 bytes. The state can be switched by
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92 calling the setstate() function with the same array as was initiallized
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93 with initstate(). By default, the package runs with 128 bytes of state
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94 information and generates far better random numbers than a linear
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95 congruential generator. If the amount of state information is less than
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96 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
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97 state information is treated as an array of longs; the zeroeth element of
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98 the array is the type of R.N.G. being used (small integer); the remainder
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99 of the array is the state information for the R.N.G. Thus, 32 bytes of
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100 state information will give 7 longs worth of state information, which will
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101 allow a degree seven polynomial. (Note: The zeroeth word of state
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102 information also has some other information stored in it; see setstate
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103 for details). The random number generation technique is a linear feedback
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104 shift register approach, employing trinomials (since there are fewer terms
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105 to sum up that way). In this approach, the least significant bit of all
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106 the numbers in the state table will act as a linear feedback shift register,
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107 and will have period 2^deg - 1 (where deg is the degree of the polynomial
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108 being used, assuming that the polynomial is irreducible and primitive).
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109 The higher order bits will have longer periods, since their values are
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110 also influenced by pseudo-random carries out of the lower bits. The
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111 total period of the generator is approximately deg*(2**deg - 1); thus
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112 doubling the amount of state information has a vast influence on the
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113 period of the generator. Note: The deg*(2**deg - 1) is an approximation
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114 only good for large deg, when the period of the shift register is the
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115 dominant factor. With deg equal to seven, the period is actually much
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116 longer than the 7*(2**7 - 1) predicted by this formula. */
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117
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118
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119
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120 /* For each of the currently supported random number generators, we have a
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121 break value on the amount of state information (you need at least thi
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122 bytes of state info to support this random number generator), a degree for
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123 the polynomial (actually a trinomial) that the R.N.G. is based on, and
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124 separation between the two lower order coefficients of the trinomial. */
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125
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126 /* Linear congruential. */
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127 #define TYPE_0 0
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128 #define BREAK_0 8
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129 #define DEG_0 0
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130 #define SEP_0 0
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131
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132 /* x**7 + x**3 + 1. */
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133 #define TYPE_1 1
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134 #define BREAK_1 32
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135 #define DEG_1 7
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136 #define SEP_1 3
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137
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138 /* x**15 + x + 1. */
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139 #define TYPE_2 2
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140 #define BREAK_2 64
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141 #define DEG_2 15
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142 #define SEP_2 1
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143
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144 /* x**31 + x**3 + 1. */
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145 #define TYPE_3 3
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146 #define BREAK_3 128
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147 #define DEG_3 31
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148 #define SEP_3 3
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149
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150 /* x**63 + x + 1. */
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151 #define TYPE_4 4
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152 #define BREAK_4 256
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153 #define DEG_4 63
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154 #define SEP_4 1
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155
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156
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157 /* Array versions of the above information to make code run faster.
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158 Relies on fact that TYPE_i == i. */
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159
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160 #define MAX_TYPES 5 /* Max number of types above. */
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161
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162 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
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163 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
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164
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165
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166
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167 /* Initially, everything is set up as if from:
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168 initstate(1, randtbl, 128);
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169 Note that this initialization takes advantage of the fact that srandom
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170 advances the front and rear pointers 10*rand_deg times, and hence the
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171 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
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172 element of the state information, which contains info about the current
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173 position of the rear pointer is just
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174 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
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175
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176 static long int randtbl[DEG_3 + 1] =
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177 { TYPE_3,
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178 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
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179 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
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180 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
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181 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
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182 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
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183 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
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184 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
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185 0xf5ad9d0e, 0x8999220b, 0x27fb47b9
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186 };
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187
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188 /* FPTR and RPTR are two pointers into the state info, a front and a rear
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189 pointer. These two pointers are always rand_sep places aparts, as they
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190 cycle through the state information. (Yes, this does mean we could get
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191 away with just one pointer, but the code for random is more efficient
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192 this way). The pointers are left positioned as they would be from the call:
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193 initstate(1, randtbl, 128);
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194 (The position of the rear pointer, rptr, is really 0 (as explained above
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195 in the initialization of randtbl) because the state table pointer is set
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196 to point to randtbl[1] (as explained below).) */
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197
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198 static long int *fptr = &randtbl[SEP_3 + 1];
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199 static long int *rptr = &randtbl[1];
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200
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201
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202
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203 /* The following things are the pointer to the state information table,
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204 the type of the current generator, the degree of the current polynomial
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205 being used, and the separation between the two pointers.
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206 Note that for efficiency of random, we remember the first location of
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207 the state information, not the zeroeth. Hence it is valid to access
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208 state[-1], which is used to store the type of the R.N.G.
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209 Also, we remember the last location, since this is more efficient than
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210 indexing every time to find the address of the last element to see if
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211 the front and rear pointers have wrapped. */
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212
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213 static long int *state = &randtbl[1];
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214
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215 static int rand_type = TYPE_3;
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216 static int rand_deg = DEG_3;
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217 static int rand_sep = SEP_3;
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218
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219 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
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220
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221 /* Initialize the random number generator based on the given seed. If the
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222 type is the trivial no-state-information type, just remember the seed.
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223 Otherwise, initializes state[] based on the given "seed" via a linear
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224 congruential generator. Then, the pointers are set to known locations
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225 that are exactly rand_sep places apart. Lastly, it cycles the state
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226 information a given number of times to get rid of any initial dependencies
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227 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
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228 for default usage relies on values produced by this routine. */
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229 void
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230 srandom (unsigned int x)
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231 {
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232 state[0] = x;
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233 if (rand_type != TYPE_0)
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234 {
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235 register long int i;
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236 for (i = 1; i < rand_deg; ++i)
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237 state[i] = (1103515145 * state[i - 1]) + 12345;
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238 fptr = &state[rand_sep];
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239 rptr = &state[0];
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240 for (i = 0; i < 10 * rand_deg; ++i)
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241 random();
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242 }
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243 }
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244
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245 /* Initialize the state information in the given array of N bytes for
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246 future random number generation. Based on the number of bytes we
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247 are given, and the break values for the different R.N.G.'s, we choose
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248 the best (largest) one we can and set things up for it. srandom is
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249 then called to initialize the state information. Note that on return
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250 from srandom, we set state[-1] to be the type multiplexed with the current
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251 value of the rear pointer; this is so successive calls to initstate won't
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252 lose this information and will be able to restart with setstate.
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253 Note: The first thing we do is save the current state, if any, just like
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254 setstate so that it doesn't matter when initstate is called.
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255 Returns a pointer to the old state. */
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256 PTR
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257 initstate (unsigned int seed, PTR arg_state, unsigned long n)
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258 {
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259 PTR ostate = (PTR) &state[-1];
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260
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261 if (rand_type == TYPE_0)
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262 state[-1] = rand_type;
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263 else
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264 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
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265 if (n < BREAK_1)
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266 {
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267 if (n < BREAK_0)
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268 {
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269 errno = EINVAL;
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270 return NULL;
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271 }
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272 rand_type = TYPE_0;
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273 rand_deg = DEG_0;
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274 rand_sep = SEP_0;
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275 }
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276 else if (n < BREAK_2)
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277 {
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278 rand_type = TYPE_1;
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279 rand_deg = DEG_1;
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280 rand_sep = SEP_1;
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281 }
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282 else if (n < BREAK_3)
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283 {
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284 rand_type = TYPE_2;
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285 rand_deg = DEG_2;
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286 rand_sep = SEP_2;
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287 }
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288 else if (n < BREAK_4)
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289 {
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290 rand_type = TYPE_3;
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291 rand_deg = DEG_3;
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292 rand_sep = SEP_3;
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293 }
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294 else
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295 {
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296 rand_type = TYPE_4;
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297 rand_deg = DEG_4;
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298 rand_sep = SEP_4;
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299 }
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300
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301 state = &((long int *) arg_state)[1]; /* First location. */
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302 /* Must set END_PTR before srandom. */
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303 end_ptr = &state[rand_deg];
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304 srandom(seed);
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305 if (rand_type == TYPE_0)
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306 state[-1] = rand_type;
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307 else
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308 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
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309
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310 return ostate;
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311 }
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312
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313 /* Restore the state from the given state array.
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314 Note: It is important that we also remember the locations of the pointers
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315 in the current state information, and restore the locations of the pointers
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316 from the old state information. This is done by multiplexing the pointer
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317 location into the zeroeth word of the state information. Note that due
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318 to the order in which things are done, it is OK to call setstate with the
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319 same state as the current state
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320 Returns a pointer to the old state information. */
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321
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322 PTR
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323 setstate (PTR arg_state)
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324 {
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325 register long int *new_state = (long int *) arg_state;
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326 register int type = new_state[0] % MAX_TYPES;
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327 register int rear = new_state[0] / MAX_TYPES;
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328 PTR ostate = (PTR) &state[-1];
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329
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330 if (rand_type == TYPE_0)
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331 state[-1] = rand_type;
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332 else
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333 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
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334
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335 switch (type)
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336 {
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337 case TYPE_0:
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338 case TYPE_1:
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339 case TYPE_2:
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340 case TYPE_3:
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341 case TYPE_4:
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342 rand_type = type;
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343 rand_deg = degrees[type];
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344 rand_sep = seps[type];
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345 break;
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346 default:
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347 /* State info munged. */
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348 errno = EINVAL;
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349 return NULL;
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350 }
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351
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352 state = &new_state[1];
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353 if (rand_type != TYPE_0)
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354 {
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355 rptr = &state[rear];
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356 fptr = &state[(rear + rand_sep) % rand_deg];
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357 }
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358 /* Set end_ptr too. */
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359 end_ptr = &state[rand_deg];
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360
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361 return ostate;
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362 }
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363
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364 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
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365 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
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366 same in all ther other cases due to all the global variables that have been
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367 set up. The basic operation is to add the number at the rear pointer into
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368 the one at the front pointer. Then both pointers are advanced to the next
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369 location cyclically in the table. The value returned is the sum generated,
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370 reduced to 31 bits by throwing away the "least random" low bit.
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371 Note: The code takes advantage of the fact that both the front and
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372 rear pointers can't wrap on the same call by not testing the rear
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373 pointer if the front one has wrapped. Returns a 31-bit random number. */
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374
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375 long int
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376 random (void)
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377 {
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378 if (rand_type == TYPE_0)
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379 {
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380 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
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381 return state[0];
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382 }
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383 else
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384 {
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385 long int i;
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386 *fptr += *rptr;
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387 /* Chucking least random bit. */
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388 i = (*fptr >> 1) & LONG_MAX;
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389 ++fptr;
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390 if (fptr >= end_ptr)
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391 {
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392 fptr = state;
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393 ++rptr;
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394 }
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395 else
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396 {
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397 ++rptr;
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398 if (rptr >= end_ptr)
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399 rptr = state;
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400 }
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401 return i;
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402 }
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403 }
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