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  27 <a name="boost_multiprecision.tut.ints.egs.factorials"></a><a class="link" href="factorials.html" title="Factorials">Factorials</a>
  28 </h5></div></div></div>
  29 <p>
  30             In this simple example, we'll write a routine to print out all of the
  31             factorials which will fit into a 128-bit integer. At the end of the routine
  32             we do some fancy iostream formatting of the results:
  33           </p>
  34 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_int</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  35 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
  36 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
  37 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">vector</span><span class="special">&gt;</span>
  38
  39
  40 <span class="keyword">void</span> <span class="identifier">print_factorials</span><span class="special">()</span>
  41 <span class="special">{</span>
  42    <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_int</span><span class="special">;</span>
  43    <span class="comment">//</span>
  44    <span class="comment">// Print all the factorials that will fit inside a 128-bit integer.</span>
  45    <span class="comment">//</span>
  46    <span class="comment">// Begin by building a big table of factorials, once we know just how</span>
  47    <span class="comment">// large the largest is, we'll be able to "pretty format" the results.</span>
  48    <span class="comment">//</span>
  49    <span class="comment">// Calculate the largest number that will fit inside 128 bits, we could</span>
  50    <span class="comment">// also have used numeric_limits&lt;int128_t&gt;::max() for this value:</span>
  51    <span class="identifier">cpp_int</span> <span class="identifier">limit</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span>
  52    <span class="comment">//</span>
  53    <span class="comment">// Our table of values:</span>
  54    <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">cpp_int</span><span class="special">&gt;</span> <span class="identifier">results</span><span class="special">;</span>
  55    <span class="comment">//</span>
  56    <span class="comment">// Initial values:</span>
  57    <span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
  58    <span class="identifier">cpp_int</span> <span class="identifier">factorial</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
  59    <span class="comment">//</span>
  60    <span class="comment">// Cycle through the factorials till we reach the limit:</span>
  61    <span class="keyword">while</span><span class="special">(</span><span class="identifier">factorial</span> <span class="special">&lt;</span> <span class="identifier">limit</span><span class="special">)</span>
  62    <span class="special">{</span>
  63       <span class="identifier">results</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">factorial</span><span class="special">);</span>
  64       <span class="special">++</span><span class="identifier">i</span><span class="special">;</span>
  65       <span class="identifier">factorial</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span>
  66    <span class="special">}</span>
  67    <span class="comment">//</span>
  68    <span class="comment">// Lets see how many digits the largest factorial was:</span>
  69    <span class="keyword">unsigned</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">results</span><span class="special">.</span><span class="identifier">back</span><span class="special">().</span><span class="identifier">str</span><span class="special">().</span><span class="identifier">size</span><span class="special">();</span>
  70    <span class="comment">//</span>
  71    <span class="comment">// Now print them out, using right justification, while we're at it</span>
  72    <span class="comment">// we'll indicate the limit of each integer type, so begin by defining</span>
  73    <span class="comment">// the limits for 16, 32, 64 etc bit integers:</span>
  74    <span class="identifier">cpp_int</span> <span class="identifier">limits</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span>
  75       <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="number">16</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span>
  76       <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="number">32</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span>
  77       <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="number">64</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span>
  78       <span class="special">(</span><span class="identifier">cpp_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span>
  79    <span class="special">};</span>
  80    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">bit_counts</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="string">"16"</span><span class="special">,</span> <span class="string">"32"</span><span class="special">,</span> <span class="string">"64"</span><span class="special">,</span> <span class="string">"128"</span> <span class="special">};</span>
  81    <span class="keyword">unsigned</span> <span class="identifier">current_limit</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
  82    <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">j</span> <span class="special">&lt;</span> <span class="identifier">results</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">j</span><span class="special">)</span>
  83    <span class="special">{</span>
  84       <span class="keyword">if</span><span class="special">(</span><span class="identifier">limits</span><span class="special">[</span><span class="identifier">current_limit</span><span class="special">]</span> <span class="special">&lt;</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">])</span>
  85       <span class="special">{</span>
  86          <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Limit of "</span> <span class="special">+</span> <span class="identifier">bit_counts</span><span class="special">[</span><span class="identifier">current_limit</span><span class="special">]</span> <span class="special">+</span> <span class="string">" bit integers"</span><span class="special">;</span>
  87          <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setfill</span><span class="special">(</span><span class="char">'.'</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">digits</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">message</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setfill</span><span class="special">(</span><span class="char">' '</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
  88          <span class="special">++</span><span class="identifier">current_limit</span><span class="special">;</span>
  89       <span class="special">}</span>
  90       <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="identifier">digits</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">]</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
  91    <span class="special">}</span>
  92 <span class="special">}</span>
  93 </pre>
  94 <p>
  95             The output from this routine is:
  96           </p>
  97 <pre class="programlisting">                                       1
  98                                        2
  99                                        6
 100                                       24
 101                                      120
 102                                      720
 103                                     5040
 104                                    40320
 105 ................Limit of 16 bit integers
 106                                   362880
 107                                  3628800
 108                                 39916800
 109                                479001600
 110 ................Limit of 32 bit integers
 111                               6227020800
 112                              87178291200
 113                            1307674368000
 114                           20922789888000
 115                          355687428096000
 116                         6402373705728000
 117                       121645100408832000
 118                      2432902008176640000
 119 ................Limit of 64 bit integers
 120                     51090942171709440000
 121                   1124000727777607680000
 122                  25852016738884976640000
 123                 620448401733239439360000
 124               15511210043330985984000000
 125              403291461126605635584000000
 126            10888869450418352160768000000
 127           304888344611713860501504000000
 128          8841761993739701954543616000000
 129        265252859812191058636308480000000
 130       8222838654177922817725562880000000
 131     263130836933693530167218012160000000
 132    8683317618811886495518194401280000000
 133  295232799039604140847618609643520000000
 134 </pre>
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