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1 package MathUtil;
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2 #
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3 # $RCSfile: MathUtil.pm,v $
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4 # $Date: 2015/02/28 20:47:17 $
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5 # $Revision: 1.28 $
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6 #
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7 # Author: Manish Sud <msud@san.rr.com>
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8 #
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9 # Copyright (C) 2015 Manish Sud. All rights reserved.
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10 #
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11 # This file is part of MayaChemTools.
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12 #
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13 # MayaChemTools is free software; you can redistribute it and/or modify it under
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14 # the terms of the GNU Lesser General Public License as published by the Free
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15 # Software Foundation; either version 3 of the License, or (at your option) any
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16 # later version.
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17 #
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18 # MayaChemTools is distributed in the hope that it will be useful, but without
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19 # any warranty; without even the implied warranty of merchantability of fitness
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20 # for a particular purpose. See the GNU Lesser General Public License for more
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21 # details.
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22 #
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23 # You should have received a copy of the GNU Lesser General Public License
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24 # along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or
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25 # write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,
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26 # Boston, MA, 02111-1307, USA.
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27 #
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28
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29 use strict;
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30 use Exporter;
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31 use Constants;
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32 use Math::Trig ();
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33 use POSIX ();
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34
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35 use vars qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS);
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36
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37 @ISA = qw(Exporter);
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38 @EXPORT = qw(acos asin atan tan ceil floor log10 min max srandom random round GeneratePrimeNumbersUpToLimit GeneratePrimeNumbersUpToCount);
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39 @EXPORT_OK = qw();
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40
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41 %EXPORT_TAGS = (all => [@EXPORT, @EXPORT_OK]
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42 );
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43
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44
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45 # Return next largest integer...
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46 sub ceil ($) {
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47 my($Value) = @_;
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48
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49 return POSIX::ceil($Value);
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50 }
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51
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52 # Return previous smallest integer...
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53 sub floor ($) {
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54 my($Value) = @_;
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55
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56 return POSIX::floor($Value);
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57 }
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58
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59 # Calculate log value using base 10...
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60 sub log10 ($) {
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61 my($Value) = @_;
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62
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63 return CORE::log($Value)/CORE::log(10);
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64 }
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65
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66 # Return the smaller of two numbers...
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67 sub min ($$) {
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68 my($Value1, $Value2) = @_;
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69
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70 return ($Value1 <= $Value2) ? $Value1 : $Value2;
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71 }
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72
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73 # Return the larger of two numbers...
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74 sub max ($$) {
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75 my($Value1, $Value2) = @_;
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76
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77 return ($Value1 >= $Value2) ? $Value1 : $Value2;
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78 }
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79
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80 # The random number generator implemented in MayaChemTools is a variant of linear
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81 # congruential generator (LCG) as described by Miller et al. [ Ref 120 ]. It is
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82 # also referred to as Lehmer random number generator or Park-Miller random number
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83 # generator.
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84 #
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85 # Unlike Perl's core random number generator function rand, the random number
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86 # generator implemented in MayaChemTools generates consistent random values
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87 # across different platforms - Windows, CygWin, Linux, Unix - for a specific random
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88 # seed.
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89 #
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90
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91 # $RandomModulus = 2**31 - 1;
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92 # $RandomMultiplier = 16807;
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93 # $RandomQuotient = $RandomModulus / $RandomMultiplier;
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94 # $RandomRemainder = $RandomModulus % $RandomMultiplier
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95 #
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96 # $MaxRandomSeed = 2*31 -2
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97 #
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98 my($MaxRandomSeed, $RandomSeed, $RandomModulus, $RandomMultiplier, $RandomQuotient, $RandomRemainder);
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99
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100 $MaxRandomSeed = 2147483646;
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101 $RandomSeed = 123456789;
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102
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103 $RandomModulus = 2147483647;
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104 $RandomMultiplier = 16807;
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105 $RandomQuotient = 127773;
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106 $RandomRemainder = 2836;
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107
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108 # Set random number seed...
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109 #
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110 # The intial value of random number seed is recommeded to be an integer between 1
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111 # and 2**31 - 2 [Ref 120] which translates to be 1 and 2147483646
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112 #
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113 sub srandom ($) {
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114 my($Seed) = @_;
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115
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116 if ($Seed <= 0 ) {
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117 die "Error: srandom: Specified seed value must be greater than 0...";
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118 }
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119
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120 $RandomSeed = ($Seed > $MaxRandomSeed) ? ($Seed % $MaxRandomSeed) : $Seed;
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121
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122 return $RandomSeed;
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123 }
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124
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125 # Retrun a random number between 0 and less than 1 or specified size...
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126 #
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127 sub random (;$) {
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128 my($Size) = @_;
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129 my($Value, $LowValue, $HighValue);
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130
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131 $Size = defined $Size ? $Size : 1.0;
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132
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133 $HighValue = $RandomSeed / $RandomQuotient;
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134 $LowValue = $RandomSeed % $RandomQuotient;
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135
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136 $Value = $RandomMultiplier * $LowValue - $RandomRemainder * $HighValue;
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137
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138 $RandomSeed = ($Value > 0) ? $Value : ($Value + $RandomModulus);
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139
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140 return ($RandomSeed / $RandomModulus) * $Size;
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141 }
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142
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143 # Round a integer/real number to:
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144 # . A nearest integer
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145 # . Specified number of decimal places
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146 #
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147 sub round ($;$) {
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148 my($Value, $DecimalPlaces) = @_;
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149 my($RoundedValue);
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150
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151 if (defined($DecimalPlaces) && $DecimalPlaces > 0) {
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152 $RoundedValue = sprintf "%.${DecimalPlaces}f", $Value;
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153 }
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154 else {
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155 if ($Value < 0) {
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156 $RoundedValue = int($Value - 0.5);
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157 }
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158 else {
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159 $RoundedValue = int($Value + 0.5);
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160 }
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161 }
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162 return $RoundedValue;
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163 }
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164
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165 # Return tangent of an angle expressed in radians.
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166 sub tan {
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167 my($Value) = @_;
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168
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169 return (CORE::sin($Value)/CORE::cos($Value));
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170 }
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171
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172 # Return inverse sine of an angle expressed in radians.
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173 #
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174 # For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies
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175 # X**2 + Y**2 = 1 and sin value corresponds to Y. So asin is equivalent to atan2(Y, sqrt(1-Y**2)).
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176 # However, taking sqrt of negative numbers is problematic; Math::Trig::asin handles it using complex
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177 # numbers.
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178 #
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179 sub asin ($) {
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180 my($Value) = @_;
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181
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182 return Math::Trig::asin($Value);
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183 }
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184
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185 # Return inverse cosine of an angle expressed in radians.
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186 #
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187 # For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies
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188 # X**2 + Y**2 = 1 and cos value corresponds to X. So asin is equivalent to atan2(sqrt(1-X**2), X)
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189 # However, taking sqrt of negative numbers is problematic; Math::Trig::acos handles it using complex
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190 # numbers.
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191 #
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192 sub acos ($) {
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193 my($Value) = @_;
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194
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195 return Math::Trig::acos($Value);
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196 }
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197
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198 # Generate prime numbers up to a specified limit and return a reference to an
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199 # array containing the prime numbers.
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200 #
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201 # By default, the first 1000 prime numbers are generated. The 1000th prime
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202 # number is 7919 and that's why default limit is set to 7920.
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203 #
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204 sub GeneratePrimeNumbersUpToLimit (;$) {
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205 my($Limit) = @_;
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206
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207 $Limit = defined $Limit ? $Limit : 7920;
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208
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209 return _GeneratePrimeNumbers('ByLimit', $Limit)
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210 }
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211
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212 # Generate prime numbers up to specified count of prime numbers and return a
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213 # reference to an array containing the prime numbers.
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214 #
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215 # By default, the first 1000 prime numbers are generated. The 1000th prime
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216 # number is 7919.
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217 #
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218 sub GeneratePrimeNumbersUpToCount (;$) {
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219 my($Count) = @_;
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220
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221 $Count = defined $Count ? $Count : 1000;
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222
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223 return _GeneratePrimeNumbers('ByCount', $Count)
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224 }
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225
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226 # Generate prime numbers up to specified limit or count and return a reference
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227 # to an array containing the prime numbers.
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228 #
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229 # The algorithm to generate prime numbers is a modification of Sieve of Erastothenes
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230 # prime number generator.
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231 #
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232 sub _GeneratePrimeNumbers {
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233 my($Mode, $Value) = @_;
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234 my($ByLimit, $PrimeNumber, $Number, $SqrtOfNumber, $NumberIsPrime, @PrimeNumbers);
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235
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236 $ByLimit = ($Mode =~ /^ByLimit$/i) ? 1 : 0;
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237
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238 @PrimeNumbers = (2, 3);
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239 $Number = 3;
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240
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241 # while ($Number <= $Limit) {
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242 while ($ByLimit ? ($Number < $Value) : (@PrimeNumbers < $Value)) {
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243 $Number += 2;
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244 $SqrtOfNumber = sqrt $Number;
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245
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246 $NumberIsPrime = 1;
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247 PRIMENUMBER: for $PrimeNumber (@PrimeNumbers) {
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248 if ($PrimeNumber > $SqrtOfNumber) {
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249 last PRIMENUMBER;
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250 }
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251 if (!($Number % $PrimeNumber)) {
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252 $NumberIsPrime = 0;
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253 last PRIMENUMBER;
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254 }
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255 }
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256 if ($NumberIsPrime) {
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257 push @PrimeNumbers, $Number;
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258 }
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259 }
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260 return \@PrimeNumbers;
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261 }
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262
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263 1;
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264
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265 __END__
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266
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267 =head1 NAME
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268
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269 MathUtil
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270
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271 =head1 SYNOPSIS
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272
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273 use MathUtil;
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274
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275 use MathUtil qw(:all);
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276
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277 =head1 DESCRIPTION
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278
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279 B<MathUtil> module provides a variety of common math functions not available in core
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280 Perl package or some other useful math utilities. In order to be consistent with other
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281 Perl functions, name of all the functions in this package are in lowercase which differs
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282 from MayaChemTools naming convention for function names.
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283
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284 B<MathUtil> module provides the following functions:
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285
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286 GeneratePrimeNumbersUpToCount, GeneratePrimeNumbersUpToLimit, acos, asin, ceil,
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287 floor, log10, max, min, random, round, srandom, tan
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288
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289 =head2 FUNCTIONS
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290
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291 =over 4
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292
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293 =item B<GeneratePrimeNumbersUpToCount>
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294
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295 $PrimesRef = GeneratePrimeNumbersUpToCount();
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296 $PrimesRef = GeneratePrimeNumbersUpToCount($Count);
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297
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298 Generate prime numbers up to specified I<Count> of prime numbers and return a
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299 reference to an array containing the prime numbers.
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300
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301 By default, the first 1000 prime numbers are generated. The 1000th prime
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302 number is 7919.
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303
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304 The algorithm to generate prime numbers is a modification of Sieve of Erastothenes
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305 prime number generator.
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306
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307 =item B<GeneratePrimeNumbersUpToLimit>
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308
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309 $PrimesRef = GeneratePrimeNumbersUpToLimit();
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310 $PrimesRef = GeneratePrimeNumbersUpToLimit($Limit);
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311
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312 Generate prime numbers up to a specified I<Limit> and return a reference to an
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313 array containing the prime numbers.
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314
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315 By default, the first 1000 prime numbers are generated. The 1000th prime
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316 number is 7919 and that's why default limit is set to 7920.
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317
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318 The algorithm to generate prime numbers is a modification of Sieve of Erastothenes
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319 prime number generator.
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320
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321 =item B<acos>
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322
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323 $Value = acos($AngleInRadians);
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324
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325 Returns the nverse cosine of an angle expressed in I<Radians> using Math::Trig::acos
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326 function.
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327
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328 =item B<asin>
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329
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330 $Value = asin($AngleInRadians);
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331
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332 Returns the inverse sine of an angle expressed in I<Radians> using Math::Trig::asin
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333 function.
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334
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335 =item B<ceil>
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336
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337 $IntegerValue = ceil($Value);
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338
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339 Returns the next largest integer for I<Value> using POSIX::ceil function.
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340
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341 =item B<floor>
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342
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343 $IntegerValue = floor($Value);
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344
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345 Returns the previous smallest integer for I<Value> using POSIX::floor function.
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346
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347 =item B<log10>
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348
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349 $Log10Value = log10($Value);
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350
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351 Returns the log of I<Value> using base 10.
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352
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353 =item B<max>
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354
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355 $Number = max($Number1, $Number2);
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356
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357 Returns a B<Number> corresponding to the maximum of I<Number1> and I<Number2>.
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358
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359 =item B<min>
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360
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361 $Number = min($Number1, $Number2);
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362
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363 Returns a B<Number> corresponding to the minimum of I<Number1> and I<Number2>.
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364
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365 =item B<round>
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366
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367 $RoundedValue = round($Number);
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368 $RoundedValue = round($Number, $DecimalPlaces);
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369
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370 Returns a value corresponding to a nearst ingeter for I<Number> or formatted to I<DecimalPlaces>.
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371
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372 =item B<random>
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373
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374 $RandomNumber = random();
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375 $RandomNumber = random($Size);
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376
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377 Returns a random number between 0 and less than 1 or specified size.
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378
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379 The random number generator implemented in MayaChemTools is a variant of linear
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380 congruential generator (LCG) as described by Miller et al. [ Ref 120 ]. It is
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381 also referred to as Lehmer random number generator or Park-Miller random number
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382 generator.
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383
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384 Unlike Perl's core random number generator function rand, the random number
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385 generator implemented in MayaChemTools generates consistent random values
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386 across different platforms - Windows, CygWin, Linux, Unix - for a specific random
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387 seed.
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388
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389 =item B<srandom>
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390
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391 $Seed = srandom($Seed);
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392
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393 Sets random number seed to be used by <random> function and returns seed value.
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394
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395 The random number seed is recommeded to be an integer between 1 and 2**31 - 2
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396 [Ref 120] which translates to be 1 and 2147483646.
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397
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398 The default seed is set to 123456789.
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399
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400 =item B<tan>
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401
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402 $Value = tan($AngleInRadians);
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403
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404 Returns the tangent of an angle expressed in I<Radians>.
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405
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406 =back
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407
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408 =head1 AUTHOR
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409
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410 Manish Sud <msud@san.rr.com>
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411
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412 =head1 SEE ALSO
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413
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414 Constants.pm, ConversionsUtil.pm
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415
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416 =head1 COPYRIGHT
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417
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418 Copyright (C) 2015 Manish Sud. All rights reserved.
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419
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420 This file is part of MayaChemTools.
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421
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422 MayaChemTools is free software; you can redistribute it and/or modify it under
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423 the terms of the GNU Lesser General Public License as published by the Free
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424 Software Foundation; either version 3 of the License, or (at your option)
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425 any later version.
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426
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427 =cut
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