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12 RANLIB |
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14 Library of Fortran Routines for Random Number Generation |
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23 Base Generator Documentation |
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32 Compiled and Written by: |
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33 |
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34 Barry W. Brown |
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35 James Lovato |
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46 Department of Biomathematics, Box 237 |
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47 The University of Texas, M.D. Anderson Cancer Center |
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48 1515 Holcombe Boulevard |
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49 Houston, TX 77030 |
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51 |
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52 This work was supported by grant CA-16672 from the National Cancer Institute. |
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53 |
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56 |
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57 Base Random Number Generator |
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58 |
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59 |
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60 |
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61 I. OVERVIEW AND DEFAULT BEHAVIOR |
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62 |
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63 This set of programs contains 32 virtual random number generators. |
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64 Each generator can provide 1,048,576 blocks of numbers, and each block |
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65 is of length 1,073,741,824. Any generator can be set to the beginning |
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66 or end of the current block or to its starting value. The methods are |
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67 from the paper cited immediately below, and most of the code is a |
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68 transliteration from the Pascal of the paper into Fortran. |
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69 |
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70 P. L'Ecuyer and S. Cote. Implementing a Random Number Package with |
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71 Splitting Facilities. ACM Transactions on Mathematical Software 17:1, |
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72 pp 98-111. |
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73 |
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74 Most users won't need the sophisticated capabilities of this package, |
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75 and will desire a single generator. This single generator (which will |
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76 have a non-repeating length of 2.3 X 10^18 numbers) is the default. |
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77 In order to accommodate this use, the concept of the current generator |
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78 is added to those of the cited paper; references to a generator are |
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79 always to the current generator. The current generator is initially |
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80 generator number 1; it can be changed by SETCGN, and the ordinal |
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81 number of the current generator can be obtained from GETCGN. |
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82 |
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83 The user of the default can set the initial values of the two integer |
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84 seeds with SETALL. If the user does not set the seeds, the random |
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85 number generation will use the default values, 1234567890 and |
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86 123456789. The values of the current seeds can be achieved by a call |
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87 to GETSD. Random number may be obtained as integers ranging from 1 to |
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88 a large integer by reference to function IGNLGI or as a floating point |
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89 number between 0 and 1 by a reference to function RANF. These are the |
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90 only routines needed by a user desiring a single stream of random |
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91 numbers. |
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92 |
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93 II. CONCEPTS |
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94 |
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95 A stream of pseudo-random numbers is a sequence, each member of which |
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96 can be obtained either as an integer in the range 1..2,147,483,563 or |
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97 as a floating point number in the range [0..1]. The user is in charge |
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98 of which representation is desired. |
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99 |
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100 The method contains an algorithm for generating a stream with a very |
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101 long period, 2.3 X 10^18. This stream in partitioned into G (=32) |
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102 virtual generators. Each virtual generator contains 2^20 (=1,048,576) |
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103 blocks of non-overlapping random numbers. Each block is 2^30 |
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104 (=1,073,741,824) in length. |
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105 |
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106 |
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107 |
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108 Base Random Number Generator Page 2 |
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109 |
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110 |
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111 The state of a generator is determined by two integers called seeds. |
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112 The seeds can be initialized by the user; the initial values of the |
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113 first must lie between 1 and 2,147,483,562, that of the second between |
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114 1 and 2,147,483,398. Each time a number is generated, the values of |
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115 the seeds change. Three values of seeds are remembered by the |
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116 generators at all times: the value with which the generator was |
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117 initialized, the value at the beginning of the current block, and the |
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118 value at the beginning of the next block. The seeds of any generator |
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119 can be set to any of these three values at any time. |
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120 |
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121 Of the 32 virtual generators, exactly one will be the current |
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122 generator, i.e., that one will be used to generate values for IGNLGI |
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123 and RANDF. Initially, the current generator is set to number one. |
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124 The current generator may be changed by calling SETCGN, and the number |
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125 of the current generator can be obtained using GETCGN. |
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126 |
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127 III. AN EXAMPLE |
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128 |
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129 An example of the need for these capabilities is as follows. Two |
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130 statistical techniques are being compared on data of different sizes. |
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131 The first technique uses bootstrapping and is thought to be as |
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132 accurate using less data than the second method which employs only |
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133 brute force. |
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134 |
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135 For the first method, a data set of size uniformly distributed between |
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136 25 and 50 will be generated. Then the data set of the specified size |
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137 will be generated and alalyzed. The second method will choose a data |
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138 set size between 100 and 200, generate the data and alalyze it. This |
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139 process will be repeated 1000 times. |
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140 |
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141 For variance reduction, we want the random numbers used in the two |
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142 methods to be the same for each of the 1000 comparisons. But method |
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143 two will use more random numbers than method one and without this |
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144 package, synchronization might be difficult. |
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145 |
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146 With the package, it is a snap. Use generator 1 to obtain the sample |
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147 size for method one and generator 2 to obtain the data. Then reset |
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148 the state to the beginning of the current block and do the same for |
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149 the second method. This assures that the initial data for method two |
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150 is that used by method one. When both have concluded, advance the |
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151 block for both generators. |
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152 |
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153 IV. THE INTERFACE |
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154 |
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155 A random number is obtained either as a random integer between 1 and |
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156 2,147,483,562 by invoking integer function IGNLGI (I GeNerate LarGe |
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157 Integer) or as a random floating point number between 0 and 1 by |
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158 invoking real function RANF. Neither function has arguments. |
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159 |
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160 The seed of the first generator can be set by invoking subroutine |
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161 SETALL; the values of the seeds of the other 31 generators are |
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162 calculated from this value. |
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163 |
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164 |
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165 |
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166 Base Random Number Generator Page 3 |
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167 |
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168 |
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169 The number of the current generator can be set by calling subroutine |
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170 SETCGN, which takes a single argument, the integer generator number in |
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171 the range 1..32. The number of the current generator can be obtained |
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172 by invoking subroutine GETCGN which returns the number in its single |
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173 integer argument. |
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174 |
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175 |
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176 V. CALLING SEQUENCES |
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177 |
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178 A. SETTING THE SEED OF ALL GENERATORS |
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179 |
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180 C********************************************************************** |
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181 C |
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182 C SUBROUTINE SETALL(ISEED1,ISEED2) |
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183 C SET ALL random number generators |
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184 C |
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185 C Sets the initial seed of generator 1 to ISEED1 and ISEED2. The |
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186 C initial seeds of the other generators are set accordingly, and |
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187 C all generators states are set to these seeds. |
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188 C |
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189 C Arguments |
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190 C |
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191 C |
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192 C ISEED1 -> First of two integer seeds |
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193 C INTEGER ISEED1 |
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194 C |
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195 C ISEED2 -> Second of two integer seeds |
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196 C INTEGER ISEED1 |
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197 C |
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198 C********************************************************************** |
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199 |
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200 |
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201 B. OBTAINING RANDOM NUMBERS |
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202 |
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203 C********************************************************************** |
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204 C |
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205 C INTEGER FUNCTION IGNLGI() |
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206 C GeNerate LarGe Integer |
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207 C |
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208 C Returns a random integer following a uniform distribution over |
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209 C (1, 2147483562) using the current generator. |
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210 C |
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211 C********************************************************************** |
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212 |
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213 C********************************************************************** |
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214 C |
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215 C REAL FUNCTION RANF() |
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216 C RANDom number generator as a Function |
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217 C |
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218 C Returns a random floating point number from a uniform distribution |
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219 C over 0 - 1 (endpoints of this interval are not returned) using the |
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220 C current generator |
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221 C |
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222 C********************************************************************** |
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223 |
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224 |
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225 |
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226 Base Random Number Generator Page 4 |
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227 |
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228 |
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229 C. SETTING AND OBTAINING THE NUMBER OF THE CURRENT GENERATOR |
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230 |
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231 C********************************************************************** |
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232 C |
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233 C SUBROUTINE SETCGN( G ) |
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234 C Set GeNerator |
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235 C |
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236 C Sets the current generator to G. All references to a generator |
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237 C are to the current generator. |
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238 C |
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239 C Arguments |
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240 C |
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241 C G --> Number of the current random number generator (1..32) |
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242 C INTEGER G |
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243 C |
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244 C********************************************************************** |
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245 |
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246 C********************************************************************** |
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247 C |
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248 C SUBROUTINE GETCGN(G) |
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249 C Get GeNerator |
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250 C |
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251 C Returns in G the number of the current random number generator |
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252 C |
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253 C Arguments |
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254 C |
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255 C G <-- Number of the current random number generator (1..32) |
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256 C INTEGER G |
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257 C |
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258 C********************************************************************** |
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259 |
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260 D. OBTAINING OR CHANGING SEEDS IN CURRENT GENERATOR |
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261 |
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262 C********************************************************************** |
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263 C |
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264 C SUBROUTINE ADVNST(K) |
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265 C ADV-a-N-ce ST-ate |
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266 C |
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267 C Advances the state of the current generator by 2^K values and |
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268 C resets the initial seed to that value. |
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269 C |
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270 C Arguments |
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271 C |
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272 C |
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273 C K -> The generator is advanced by 2^K values |
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274 C INTEGER K |
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275 C |
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276 C********************************************************************** |
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277 |
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278 |
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279 |
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280 Base Random Number Generator Page 5 |
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281 |
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282 |
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283 C********************************************************************** |
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284 C |
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285 C SUBROUTINE GETSD(ISEED1,ISEED2) |
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286 C GET SeeD |
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287 C |
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288 C Returns the value of two integer seeds of the current generator |
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289 C |
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290 C Arguments |
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291 C |
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292 C |
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293 C |
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294 C ISEED1 <- First integer seed of generator G |
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295 C INTEGER ISEED1 |
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296 C |
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297 C ISEED2 <- Second integer seed of generator G |
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298 C INTEGER ISEED1 |
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299 C |
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300 C********************************************************************** |
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301 |
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302 C********************************************************************** |
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303 C |
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304 C SUBROUTINE INITGN(ISDTYP) |
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305 C INIT-ialize current G-e-N-erator |
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306 C |
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307 C Reinitializes the state of the current generator |
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308 C |
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309 C Arguments |
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310 C |
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311 C |
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312 C ISDTYP -> The state to which the generator is to be set |
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313 C ISDTYP = -1 => sets the seeds to their initial value |
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314 C ISDTYP = 0 => sets the seeds to the first value of |
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315 C the current block |
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316 C ISDTYP = 1 => sets the seeds to the first value of |
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317 C the next block |
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318 C |
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319 C INTEGER ISDTYP |
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320 C |
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321 C********************************************************************** |
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322 |
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323 C********************************************************************** |
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324 C |
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325 C SUBROUTINE SETSD(ISEED1,ISEED2) |
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326 C SET S-ee-D of current generator |
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327 C |
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328 C Resets the initial seed of the current generator to ISEED1 and |
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329 C ISEED2. The seeds of the other generators remain unchanged. |
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330 C |
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331 C Arguments |
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332 C |
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333 C |
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334 C ISEED1 -> First integer seed |
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335 C INTEGER ISEED1 |
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336 C |
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337 C ISEED2 -> Second integer seed |
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338 C INTEGER ISEED1 |
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339 C |
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340 C********************************************************************** |
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341 |
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342 |
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343 |
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344 Base Random Number Generator Page 6 |
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345 |
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346 |
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347 E. MISCELLANY |
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348 |
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349 C********************************************************************** |
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350 C |
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351 C INTEGER FUNCTION MLTMOD(A,S,M) |
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352 C |
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353 C Returns (A*S) MOD M |
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354 C |
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355 C Arguments |
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356 C |
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357 C |
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358 C A, S, M --> |
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359 C INTEGER A,S,M |
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360 C |
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361 C********************************************************************** |
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362 |
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363 C********************************************************************** |
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364 C |
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365 C SUBROUTINE SETANT(QVALUE) |
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366 C SET ANTithetic |
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367 C |
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368 C Sets whether the current generator produces antithetic values. If |
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369 C X is the value normally returned from a uniform [0,1] random |
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370 C number generator then 1 - X is the antithetic value. If X is the |
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371 C value normally returned from a uniform [0,N] random number |
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372 C generator then N - 1 - X is the antithetic value. |
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373 C |
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374 C All generators are initialized to NOT generate antithetic values. |
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375 C |
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376 C Arguments |
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377 C |
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378 C QVALUE -> .TRUE. if generator G is to generating antithetic |
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379 C values, otherwise .FALSE. |
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380 C LOGICAL QVALUE |
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381 C |
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382 C********************************************************************** |
