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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_multiprecision.tut.conversions"></a><a class="link" href="conversions.html" title="Constructing and Interconverting Between Number Types">Constructing and |
| Interconverting Between Number Types</a> |
| </h3></div></div></div> |
| <p> |
| All of the number types that are based on <code class="computeroutput"><span class="identifier">number</span></code> |
| have certain conversion rules in common. In particular: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| <p class="simpara"> |
| Any number type can be constructed (or assigned) from any builtin arithmetic |
| type, as long as the conversion isn't lossy (for example float to int |
| conversion): |
| </p> |
| <pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span> <span class="comment">// OK construction from double</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">450</span><span class="special">);</span> <span class="comment">// OK constructs from signed int</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, lossy conversion.</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| A number can be explicitly constructed from an arithmetic type, even |
| when the conversion is lossy: |
| </p> |
| <pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK explicit conversion</span> |
| <span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="number">3.14</span><span class="special">)</span> <span class="comment">// OK explicit conversion</span> |
| <span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK, explicit assign and avoid a temporary from the cast above</span> |
| <span class="identifier">i</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit assignment operator for lossy conversion.</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit constructor for lossy conversion.</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| A <code class="computeroutput"><span class="identifier">number</span></code> can be converted |
| to any built in type, via the <code class="computeroutput"><span class="identifier">convert_to</span></code> |
| member function: |
| </p> |
| <pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">.</span><span class="keyword">template</span> <span class="identifier">convert_to</span><span class="special"><</span><span class="keyword">int</span><span class="special">>();</span> <span class="comment">// sets i to 2</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| Conversions to rational numbers from floating point ones are always allowed, |
| and are exact and implicit as long as the rational number uses an unbounded |
| integer type. Please be aware that constructing a rational number from |
| an extended precision floating point type with a large exponent range |
| can effectively run the system out of memory, as in the extreme case |
| <span class="emphasis"><em>2<sup>max_exponent</sup> / CHAR_BITS</em></span> bytes of storage may be |
| required. This does not represent a problem for built in floating point |
| types however, as the exponent range for these is rather limited. |
| </li> |
| <li class="listitem"> |
| Conversions to floating point numbers from rational ones are rounded |
| to nearest (less than 0.5ulp error) as long as the floating point number |
| is binary, and the integer type used by the rational number is unbounded. |
| </li> |
| </ul></div> |
| <p> |
| Additional conversions may be supported by particular backends. |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| <p class="simpara"> |
| A <code class="computeroutput"><span class="identifier">number</span></code> can be converted |
| to any built in type, via an explicit conversion operator: this functionality |
| is only available on compilers supporting C++11's explicit conversion |
| syntax. |
| </p> |
| <pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// Error, implicit conversion not allowed.</span> |
| <span class="keyword">int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">z</span><span class="special">);</span> <span class="comment">// OK explicit conversion.</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Any number type can be <span class="emphasis"><em>explicitly</em></span> constructed (or |
| assigned) from a <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code> |
| or a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>: |
| </p> |
| <pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> |
| <span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">);</span> |
| <span class="comment">// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="string">"0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000"</span><span class="special">);</span> |
| <span class="comment">// Invalid input always results in a std::runtime_error being thrown:</span> |
| <span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="string">"3.14"</span><span class="special">);</span> |
| <span class="comment">// implicit conversions from strings are not allowed:</span> |
| <span class="identifier">i</span> <span class="special">=</span> <span class="string">"23"</span><span class="special">;</span> <span class="comment">// Error, no assignment operator for implicit conversion from string</span> |
| <span class="comment">// assign member function, avoids having to create a temporary via a static_cast:</span> |
| <span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="string">"23"</span><span class="special">);</span> <span class="comment">// OK</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Any number type will interoperate with the builtin types in arithmetic |
| expressions as long as the conversions are not lossy: |
| </p> |
| <pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> |
| <span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> |
| <span class="comment">// Multiply by 2 - using an integer literal here is usually more efficient</span> |
| <span class="comment">// than constructing a temporary:</span> |
| <span class="identifier">df</span> <span class="special">*=</span> <span class="number">2</span><span class="special">;</span> |
| |
| <span class="comment">// You can't mix integer types with floats though:</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> |
| <span class="identifier">i</span> <span class="special">*=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no *= operator will be found.</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Any number type can be streamed to and from the C++ iostreams: |
| </p> |
| <pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> |
| <span class="comment">// Now print at full precision:</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">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> |
| <span class="special"><<</span> <span class="identifier">df</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> |
| <span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| <span class="identifier">i</span> <span class="special"><<=</span> <span class="number">256</span><span class="special">;</span> |
| <span class="comment">// Now print in hex format with prefix:</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">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">i</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Interconversions between number types of the same family are allowed |
| and are implicit conversions if no loss of precision is involved, and |
| explicit if it is: |
| </p> |
| <pre class="programlisting"><span class="identifier">int128_t</span> <span class="identifier">i128</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> |
| <span class="identifier">int266_t</span> <span class="identifier">i256</span> <span class="special">=</span> <span class="identifier">i128</span><span class="special">;</span> <span class="comment">// OK implicit widening conversion</span> |
| <span class="identifier">i128_t</span> <span class="special">=</span> <span class="identifier">i256</span><span class="special">;</span> <span class="comment">// Error, no assignment operator found, narrowing conversion is explicit</span> |
| <span class="identifier">i128_t</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">int128_t</span><span class="special">>(</span><span class="identifier">i256</span><span class="special">);</span> <span class="comment">// OK, explicit narrowing conversion</span> |
| |
| <span class="identifier">mpz_int</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> |
| <span class="identifier">mpf_float</span> <span class="identifier">f</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// OK, GMP handles this conversion natively, and it's not lossy and therefore implicit</span> |
| |
| <span class="identifier">mpf_float_50</span> <span class="identifier">f50</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> |
| <span class="identifier">f</span> <span class="special">=</span> <span class="identifier">f50</span><span class="special">;</span> <span class="comment">// OK, conversion from fixed to variable precision, f will have 50 digits precision.</span> |
| <span class="identifier">f50</span> <span class="special">=</span> <span class="identifier">f</span><span class="special">;</span> <span class="comment">// Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Some interconversions between number types are completely generic, and |
| are always available, albeit the conversions are always <span class="emphasis"><em>explicit</em></span>: |
| </p> |
| <pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">cppi</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="comment">// We can always convert between numbers of the same category -</span> |
| <span class="comment">// int to int, rational to rational, or float to float, so this is OK</span> |
| <span class="comment">// as long as we use an explicit conversion:</span> |
| <span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> |
| <span class="comment">// We can always promote from int to rational, int to float, or rational to float:</span> |
| <span class="identifier">cpp_rational</span> <span class="identifier">cppr</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to rational</span> |
| <span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to float</span> |
| <span class="identifier">df</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>(</span><span class="identifier">cppr</span><span class="special">);</span> <span class="comment">// OK, explicit rational to float conversion</span> |
| <span class="comment">// However narrowing and/or implicit conversions always fail:</span> |
| <span class="identifier">cppi</span> <span class="special">=</span> <span class="identifier">df</span><span class="special">;</span> <span class="comment">// Compiler error, conversion not allowed</span> |
| </pre> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Other interconversions may be allowed as special cases, whenever the |
| backend allows it: |
| </p> |
| <pre class="programlisting"><span class="identifier">mpf_t</span> <span class="identifier">m</span><span class="special">;</span> <span class="comment">// Native GMP type.</span> |
| <span class="identifier">mpf_init_set_ui</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="number">0</span><span class="special">);</span> <span class="comment">// set to a value;</span> |
| <span class="identifier">mpf_float</span> <span class="identifier">i</span><span class="special">(</span><span class="identifier">m</span><span class="special">);</span> <span class="comment">// copies the value of the native type.</span> |
| </pre> |
| </li> |
| </ul></div> |
| <p> |
| More information on what additional types a backend supports conversions |
| from are given in the tutorial for each backend. The converting constructor |
| will be implicit if the backend's converting constructor is also implicit, |
| and explicit if the backends converting constructor is also explicit. |
| </p> |
| </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>) |
| </p> |
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