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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> |
| </div> |
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| <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
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