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color=3D#cdcd00>-32</FONT><FONT color=3D#00ffff>)));</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT>$num =3D bin2dec<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#00cd00>'0110110'</FONT><FONT color=3D#00ffff>);</FONT>  <FONT =
color=3D#bebebe># $num is 54
</FONT>$binstr =3D dec2bin<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>54</FONT><FONT color=3D#00ffff>);</FONT>      <FONT =
color=3D#bebebe># $binstr is 110110
#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN85>Operating on a Series of =
Integers</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>foreach</FONT> <FONT =
color=3D#00ffff>(</FONT>$X .. $Y<FONT color=3D#00ffff>)</FONT> <FONT =
color=3D#00ffff>{</FONT>
    <FONT color=3D#bebebe># $_ is set to every integer from X to Y, =
inclusive
</FONT><FONT color=3D#00ffff>}</FONT>

<FONT color=3D#ffa500>foreach</FONT> <FONT color=3D#9ac0cd>$i</FONT> =
<FONT color=3D#00ffff>(</FONT>$X .. $Y<FONT color=3D#00ffff>)</FONT> =
<FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#bebebe># $i is set to every integer from X to Y, =
inclusive
</FONT>    <FONT color=3D#00ffff>}</FONT>

<FONT color=3D#ffa500>for</FONT> <FONT color=3D#00ffff>(</FONT>$i =3D =
$X<FONT color=3D#00ffff>;</FONT> $i &lt;=3D $Y<FONT =
color=3D#00ffff>;</FONT> $i++<FONT color=3D#00ffff>)</FONT> <FONT =
color=3D#00ffff>{</FONT>
    <FONT color=3D#bebebe># $i is set to every integer from X to Y, =
inclusive
</FONT><FONT color=3D#00ffff>}</FONT>

<FONT color=3D#ffa500>for</FONT> <FONT color=3D#00ffff>(</FONT>$i =3D =
$X<FONT color=3D#00ffff>;</FONT> $i &lt;=3D $Y<FONT =
color=3D#00ffff>;</FONT> $i +=3D <FONT color=3D#cdcd00>7</FONT><FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#bebebe># $i is set to every integer from X to Y, =
stepsize =3D 7
</FONT><FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"Infancy =
is: "</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>foreach</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>0</FONT> .. <FONT color=3D#cdcd00>2</FONT><FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"$_ =
"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT =
color=3D#00cd00>"\n"</FONT><FONT color=3D#00ffff>;</FONT>

<FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"Toddling is: =
"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>foreach</FONT> <FONT color=3D#9ac0cd>$i</FONT> =
<FONT color=3D#00ffff>(</FONT><FONT color=3D#cdcd00>3</FONT> .. <FONT =
color=3D#cdcd00>4</FONT><FONT color=3D#00ffff>)</FONT> <FONT =
color=3D#00ffff>{</FONT>
    <FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"$i =
"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT =
color=3D#00cd00>"\n"</FONT><FONT color=3D#00ffff>;</FONT>

<FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"Childhood is: =
"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>for</FONT> <FONT color=3D#00ffff>(</FONT>$i =3D =
<FONT color=3D#cdcd00>5</FONT><FONT color=3D#00ffff>;</FONT> $i &lt;=3D =
<FONT color=3D#cdcd00>12</FONT><FONT color=3D#00ffff>;</FONT> $i++<FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"$i =
"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT =
color=3D#00cd00>"\n"</FONT><FONT color=3D#00ffff>;</FONT>

<FONT color=3D#bebebe># Infancy is: 0 1 2</FONT><FONT color=3D#43cd80> =
</FONT><FONT color=3D#bebebe>
#</FONT><FONT color=3D#43cd80> </FONT><FONT color=3D#bebebe>
# Toddling is: 3 4</FONT><FONT color=3D#43cd80> </FONT><FONT =
color=3D#bebebe>
#</FONT><FONT color=3D#43cd80> </FONT><FONT color=3D#bebebe>
# Childhood is: 5 6 7 8 9 10 11 12</FONT><FONT color=3D#43cd80> =
</FONT><FONT color=3D#bebebe>
#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN88>Working with Roman Numerals</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Roman</FONT><FONT color=3D#00ffff>;</FONT>
$roman =3D roman<FONT color=3D#00ffff>(</FONT>$arabic<FONT =
color=3D#00ffff>);</FONT>                        <FONT color=3D#bebebe># =
convert to roman numerals
</FONT>$arabic =3D arabic<FONT color=3D#00ffff>(</FONT>$roman<FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#ffa500>if</FONT> isroman<FONT =
color=3D#00ffff>(</FONT>$roman<FONT color=3D#00ffff>);</FONT>    <FONT =
color=3D#bebebe># convert from roman numerals
#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Roman</FONT><FONT color=3D#00ffff>;</FONT>
$roman_fifteen =3D roman<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>15</FONT><FONT color=3D#00ffff>);</FONT>                 =
        <FONT color=3D#bebebe># "xv"
</FONT><FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"Roman =
for fifteen is $roman_fifteen\n"</FONT><FONT color=3D#00ffff>;</FONT>
$arabic_fifteen =3D arabic<FONT =
color=3D#00ffff>(</FONT>$roman_fifteen<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"Converted =
back, $roman_fifteen is $arabic_fifteen\n"</FONT><FONT =
color=3D#00ffff>;</FONT>

Roman <FONT color=3D#ffa500>for</FONT> fifteen is xv

Converted back, xv is <FONT color=3D#cdcd00>15</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN91>Generating Random Numbers</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT>$random =3D <FONT color=3D#98fb98>int</FONT><FONT =
color=3D#00ffff>(</FONT> <FONT color=3D#98fb98>rand</FONT><FONT =
color=3D#00ffff>(</FONT> $Y-$X+<FONT color=3D#cdcd00>1</FONT> <FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>)</FONT> + $X<FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT>$random =3D <FONT color=3D#98fb98>int</FONT><FONT =
color=3D#00ffff>(</FONT> <FONT color=3D#98fb98>rand</FONT><FONT =
color=3D#00ffff>(</FONT><FONT color=3D#cdcd00>51</FONT><FONT =
color=3D#00ffff>))</FONT> + <FONT color=3D#cdcd00>25</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT =
color=3D#00cd00>"$random\n"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT>$elt =3D <FONT color=3D#cdad00>$array</FONT><FONT =
color=3D#00ffff>[</FONT> <FONT color=3D#98fb98>rand</FONT> <FONT =
color=3D#cdad00>@array</FONT> <FONT color=3D#00ffff>];</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#cdad00>@chars</FONT> =3D <FONT =
color=3D#00ffff>(</FONT> <FONT color=3D#00cd00>"A"</FONT> .. <FONT =
color=3D#00cd00>"Z"</FONT>, <FONT color=3D#00cd00>"a"</FONT> .. <FONT =
color=3D#00cd00>"z"</FONT>, <FONT color=3D#cdcd00>0</FONT> .. <FONT =
color=3D#cdcd00>9</FONT>, <FONT color=3D#ff7f50>qw</FONT><FONT =
color=3D#00ffff>(</FONT>! @ $ % ^ &amp; *<FONT color=3D#00ffff>)</FONT> =
<FONT color=3D#00ffff>);</FONT>
$password =3D <FONT color=3D#98fb98>join</FONT><FONT =
color=3D#00ffff>(</FONT><FONT color=3D#00cd00>""</FONT>, <FONT =
color=3D#cdad00>@chars</FONT><FONT color=3D#00ffff>[</FONT> <FONT =
color=3D#ff7f50>map</FONT> <FONT color=3D#00ffff>{</FONT> <FONT =
color=3D#98fb98>rand</FONT> <FONT color=3D#cdad00>@chars</FONT> <FONT =
color=3D#00ffff>}</FONT> <FONT color=3D#00ffff>(</FONT> <FONT =
color=3D#cdcd00>1</FONT> .. <FONT color=3D#cdcd00>8</FONT> <FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>]);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN94>Generating Different Random =
Numbers</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#98fb98>srand</FONT> EXPR<FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#98fb98>srand</FONT><FONT color=3D#00ffff>(</FONT> =
&lt;STDIN&gt; <FONT color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN97>Making Numbers Even More =
Random</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Math::TrulyRandom</FONT><FONT color=3D#00ffff>;</FONT>
$random =3D truly_random_value<FONT color=3D#00ffff>();</FONT>

<FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Math::Random</FONT><FONT color=3D#00ffff>;</FONT>
$random =3D random_uniform<FONT color=3D#00ffff>();</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN100>Generating Biased Random =
Numbers</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
  <TBODY>
  <TR>
    <TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>sub</FONT> gaussian_<FONT =
color=3D#98fb98>rand</FONT> <FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$u1</FONT>, <FONT color=3D#9ac0cd>$u2</FONT><FONT =
color=3D#00ffff>);</FONT>  <FONT color=3D#bebebe># uniformly distributed =
random numbers
</FONT>    <FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$w</FONT><FONT color=3D#00ffff>;</FONT>          <FONT =
color=3D#bebebe># variance, then a weight
</FONT>    <FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#00ffff>(</FONT><FONT color=3D#9ac0cd>$g1</FONT>, <FONT =
color=3D#9ac0cd>$g2</FONT><FONT color=3D#00ffff>);</FONT>  <FONT =
color=3D#bebebe># gaussian-distributed numbers
</FONT>
    <FONT color=3D#ffa500>do</FONT> <FONT color=3D#00ffff>{</FONT>
        $u1 =3D <FONT color=3D#cdcd00>2</FONT> * <FONT =
color=3D#98fb98>rand</FONT><FONT color=3D#00ffff>()</FONT> - <FONT =
color=3D#cdcd00>1</FONT><FONT color=3D#00ffff>;</FONT>
        $u2 =3D <FONT color=3D#cdcd00>2</FONT> * <FONT =
color=3D#98fb98>rand</FONT><FONT color=3D#00ffff>()</FONT> - <FONT =
color=3D#cdcd00>1</FONT><FONT color=3D#00ffff>;</FONT>
        $w =3D $u1*$u1 + $u2*$u2<FONT color=3D#00ffff>;</FONT>
    <FONT color=3D#00ffff>}</FONT> <FONT color=3D#ffa500>while</FONT> =
<FONT color=3D#00ffff>(</FONT> $w &gt;=3D <FONT color=3D#cdcd00>1</FONT> =
<FONT color=3D#00ffff>);</FONT>

    $w =3D <FONT color=3D#98fb98>sqrt</FONT><FONT =
color=3D#00ffff>(</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>-2</FONT> * <FONT color=3D#98fb98>log</FONT><FONT =
color=3D#00ffff>(</FONT>$w<FONT color=3D#00ffff>))</FONT>  / $w <FONT =
color=3D#00ffff>);</FONT>
    $g2 =3D $u1 * $w<FONT color=3D#00ffff>;</FONT>
    $g1 =3D $u2 * $w<FONT color=3D#00ffff>;</FONT>
    <FONT color=3D#bebebe># return both if wanted, else just one
</FONT>    <FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#98fb98>wantarray</FONT> ? <FONT color=3D#00ffff>(</FONT>$g1, =
$g2<FONT color=3D#00ffff>)</FONT> : $g1<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
# weight_to_dist: takes a hash mapping key to weight and returns
# a hash mapping key to probability
</FONT><FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#b2dfee>weight_to_dist</FONT> <FONT color=3D#00ffff>{</FONT>
    <FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#cdcd00>%weights</FONT> =3D <FONT color=3D#cdad00>@_</FONT><FONT =
color=3D#00ffff>;</FONT>
    <FONT color=3D#ffa500>my</FONT> <FONT color=3D#cdcd00>%dist</FONT>   =
 =3D <FONT color=3D#00ffff>();</FONT>
    <FONT color=3D#ffa500>my</FONT> <FONT color=3D#9ac0cd>$total</FONT>  =
 =3D <FONT color=3D#cdcd00>0</FONT><FONT color=3D#00ffff>;</FONT>
    <FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$key</FONT>, <FONT color=3D#9ac0cd>$weight</FONT><FONT =
color=3D#00ffff>);</FONT>

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