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<div class="titlepage"><div><div><h5 class="title">
<a name="boost_multiprecision.tut.ints.egs.factorials"></a><a class="link" href="factorials.html" title="Factorials">Factorials</a>
</h5></div></div></div>
<p>
In this simple example, we'll write a routine to print out all of the
factorials which will fit into a 128-bit integer. At the end of the routine
we do some fancy iostream formatting of the results:
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</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">></span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">vector</span><span class="special">></span>
<span class="keyword">void</span> <span class="identifier">print_factorials</span><span class="special">()</span>
<span class="special">{</span>
<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>
<span class="comment">//</span>
<span class="comment">// Print all the factorials that will fit inside a 128-bit integer.</span>
<span class="comment">//</span>
<span class="comment">// Begin by building a big table of factorials, once we know just how </span>
<span class="comment">// large the largest is, we'll be able to "pretty format" the results.</span>
<span class="comment">//</span>
<span class="comment">// Calculate the largest number that will fit inside 128 bits, we could</span>
<span class="comment">// also have used numeric_limits<int128_t>::max() for this value:</span>
<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"><<</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span>
<span class="comment">// </span>
<span class="comment">// Our table of values:</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">></span> <span class="identifier">results</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Initial values:</span>
<span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="identifier">cpp_int</span> <span class="identifier">factorial</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Cycle through the factorials till we reach the limit:</span>
<span class="keyword">while</span><span class="special">(</span><span class="identifier">factorial</span> <span class="special"><</span> <span class="identifier">limit</span><span class="special">)</span>
<span class="special">{</span>
<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>
<span class="special">++</span><span class="identifier">i</span><span class="special">;</span>
<span class="identifier">factorial</span> <span class="special">*=</span> <span class="identifier">i</span><span class="special">;</span>
<span class="special">}</span>
<span class="comment">//</span>
<span class="comment">// Lets see how many digits the largest factorial was:</span>
<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>
<span class="comment">//</span>
<span class="comment">// Now print them out, using right justification, while we're at it</span>
<span class="comment">// we'll indicate the limit of each integer type, so begin by defining</span>
<span class="comment">// the limits for 16, 32, 64 etc bit integers:</span>
<span class="identifier">cpp_int</span> <span class="identifier">limits</span><span class="special">[]</span> <span class="special">=</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"><<</span> <span class="number">16</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</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"><<</span> <span class="number">32</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</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"><<</span> <span class="number">64</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</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"><<</span> <span class="number">128</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">,</span>
<span class="special">};</span>
<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>
<span class="keyword">unsigned</span> <span class="identifier">current_limit</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
<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"><</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>
<span class="special">{</span>
<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"><</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">])</span>
<span class="special">{</span>
<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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</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"><<</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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">message</span> <span class="special"><<</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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">++</span><span class="identifier">current_limit</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">results</span><span class="special">[</span><span class="identifier">j</span><span class="special">]</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span>
</pre>
<p>
The output from this routine is:
</p>
<pre class="programlisting"> 1
2
6
24
120
720
5040
40320
................Limit of 16 bit integers
362880
3628800
39916800
479001600
................Limit of 32 bit integers
6227020800
87178291200
1307674368000
20922789888000
355687428096000
6402373705728000
121645100408832000
2432902008176640000
................Limit of 64 bit integers
51090942171709440000
1124000727777607680000
25852016738884976640000
620448401733239439360000
15511210043330985984000000
403291461126605635584000000
10888869450418352160768000000
304888344611713860501504000000
8841761993739701954543616000000
265252859812191058636308480000000
8222838654177922817725562880000000
263130836933693530167218012160000000
8683317618811886495518194401280000000
295232799039604140847618609643520000000
</pre>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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