200 lines
25 KiB
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200 lines
25 KiB
HTML
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<title>std::nextafter, std::nextafterf, std::nextafterl, std::nexttoward, std::nexttowardf, std::nexttowardl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_nextafter skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>nextafter, <span style="font-size:0.7em; line-height:130%">std::</span>nextafterf, <span style="font-size:0.7em; line-height:130%">std::</span>nextafterl, <span style="font-size:0.7em; line-height:130%">std::</span>nexttoward, <span style="font-size:0.7em; line-height:130%">std::</span>nexttowardf, <span style="font-size:0.7em; line-height:130%">std::</span>nexttowardl</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-math.html">math</a></span></div>
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<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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<table class="t-dcl-begin">
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<div>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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</td>
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<td></td>
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<td></td>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> nextafter <span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">float</span> to <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> nextafterf<span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">float</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> nextafter <span class="br0">(</span> <span class="kw4">double</span> from, <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> nextafter <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> nextafterl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp">Promoted nextafter <span class="br0">(</span> Arithmetic1 from, Arithmetic2 to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> nexttoward <span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> nexttowardf<span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(5)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> nexttoward <span class="br0">(</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(6)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> nexttoward <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> nexttowardl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(7)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> nexttoward <span class="br0">(</span> IntegralType from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(8)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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</tr>
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</tbody>
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<p>返回 <code>from</code> 于 <code>to</code> 方向的下个可表示值。</p>
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<div class="t-li1"><span class="t-li">1-3)</span> 若 <code>from</code> 等于 <code>to</code> ，则返回 <code>to</code> 。</div>
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<div class="t-li1"><span class="t-li">5-7)</span> 若 <code>from</code> 等于 <code>to</code> ，则返回从 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 转换到函数返回类型的 <code>to</code> ，而不带范围或精度的损失。</div>
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<div class="t-li1"><span class="t-li">4)</span> 所有 <span class="t-v">(1-3)</span> 所不覆盖的算术类型参数的重载集或函数模板。若任何参数拥有<a href="cpp-types-is_integral.html">整数类型</a>，则将它转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。若任何参数为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> ，则返回类型 <code>Promoted</code> 亦为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> ，否则返回类型始终为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。</div>
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<div class="t-li1"><span class="t-li">8)</span> 接受任何<a href="cpp-types-is_integral.html">整数类型</a> <code>from</code> 参数的重载集或函数模板。等价于 <span class="t-v">(6)</span> （将参数转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> ）。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<tr class="t-par">
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<td>from, to</td>
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<td>-</td>
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<td>浮点值</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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<p>若不出现错误，则返回 <code>from</code> 于 <code>to</code> 的方向的下个可表示值。若 <code>from</code> 等于 <code>to</code> ，则返回 <code>to</code> ，转换到函数的类型。</p>
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<p>若出现上溢所致的值域错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> （所带符号同 <code>from</code> ）。</p>
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<p>若出现下溢所致的值域错误，则返回正确结果。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>报告 <span class="t-lc"><a href="cpp-numeric-math-math_errhandling.html">math_errhandling</a></span> 中指定的错误。</p>
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<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
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<ul>
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<li>若 <code>from</code> 有限，但期待的结果无限，则引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INEXACT</a></span> 和 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_OVERFLOW</a></span> 。</li>
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<li>若 <code>from</code> 不等于 <code>to</code> 且结果为非正规或零，则引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INEXACT</a></span> 和 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_UNDERFLOW</a></span> 。</li>
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<li>任何情况下，返回值独立于当前舍入模式。</li>
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<li>若 <code>from</code> 或 <code>to</code> 为 NaN ，则返回 NaN</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/nextafter.html">POSIX 指定</a>上溢和下溢条件是值域错误（可以设置 errno ）。</p>
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<p>IEC 60559 推荐凡在 <code>from==to</code> 时返回 <code>from</code> 。这些函数替而返回 <code>to</code> ，这使得围绕零的行为一致： <code>std::nextafter(-0.0, +0.0)</code> 返回 <code>+0.0</code> 而 <code>std::nextafter(+0.0, -0.0)</code> 返回 <code>-0.0</code> 。</p>
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<p><code>nextafter</code> 常通过操纵 IEEE 表示实现（ <a rel="nofollow" class="external text" href="https://github.com/bminor/glibc/blob/master/math/s_nextafter.c">glibc</a> ）（ <a rel="nofollow" class="external text" href="https://github.com/ifduyue/musl/blob/master/src/math/nextafter.c">musl</a> ）。</p>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <cmath></span>
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<span class="co2">#include <iomanip></span>
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<span class="co2">#include <iostream></span>
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<span class="co2">#include <cfloat></span>
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<span class="co2">#include <cfenv></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">float</span> from1 <span class="sy1">=</span> <span class="nu0">0</span>, to1 <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span>from1, <span class="nu0">1</span>.<span class="me1">f</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"The next representable float after "</span> <span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1794">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">20</span><span class="br0">)</span> <span class="sy1"><<</span> from1
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<span class="sy1"><<</span> <span class="st0">" is "</span> <span class="sy1"><<</span> to1
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> to1 <span class="sy1"><<</span> <span class="st0">")<span class="es1">\n</span>"</span> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a><span class="sy4">;</span>
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<span class="kw4">float</span> from2 <span class="sy1">=</span> <span class="nu0">1</span>, to2 <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span>from2, <span class="nu0">2</span>.<span class="me1">f</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"The next representable float after "</span> <span class="sy1"><<</span> from2 <span class="sy1"><<</span> <span class="st0">" is "</span> <span class="sy1"><<</span> to2
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> to2 <span class="sy1"><<</span> <span class="st0">")<span class="es1">\n</span>"</span> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a><span class="sy4">;</span>
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<span class="kw4">double</span> from3 <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span><span class="nu16">0.1</span>, <span class="nu0">0</span><span class="br0">)</span>, to3 <span class="sy1">=</span> <span class="nu16">0.1</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"The number 0.1 lies between two valid doubles:<span class="es1">\n</span>"</span>
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<span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1794">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">56</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">" "</span> <span class="sy1"><<</span> from3
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> from3 <span class="sy1"><<</span> <span class="st0">')'</span> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a>
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<span class="sy1"><<</span> <span class="st0">"<span class="es1">\n</span>and "</span> <span class="sy1"><<</span> to3 <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> to3 <span class="sy1"><<</span> <span class="st0">")<span class="es1">\n</span>"</span>
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1794">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">20</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// nextafter 和 nexttoward 间的差异：</span>
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<span class="kw4">long</span> <span class="kw4">double</span> dir <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span>from1, 1.0L<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 首个非正规 long double</span>
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<span class="kw4">float</span> x <span class="sy1">=</span> nextafter<span class="br0">(</span>from1, dir<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 首先转换 dir 为 float ，给出 0</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"With nextafter, next float after "</span> <span class="sy1"><<</span> from1 <span class="sy1"><<</span> <span class="st0">" is "</span> <span class="sy1"><<</span> x <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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x <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nexttoward</span><span class="br0">(</span>from1, dir<span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"With nexttoward, next float after "</span> <span class="sy1"><<</span> from1 <span class="sy1"><<</span> <span class="st0">" is "</span> <span class="sy1"><<</span> x <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<span class="br0">{</span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</span>
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<a href="cpp-numeric-fenv-feclearexcept.html"><span class="kw1448">std::<span class="me2">feclearexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1459">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">double</span> from4 <span class="sy1">=</span> <a href="cpp-types-climits.html"><span class="kw418">DBL_MAX</span></a>, to4 <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span>from4, <a href="cpp-numeric-math-INFINITY.html"><span class="kw1375">INFINITY</span></a><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"The next representable double after "</span> <span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1794">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">6</span><span class="br0">)</span>
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<span class="sy1"><<</span> from4 <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> from4 <span class="sy1"><<</span> <span class="st0">')'</span>
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" is "</span> <span class="sy1"><<</span> to4
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">hexfloat</span></span></a> <span class="sy1"><<</span> <span class="st0">" ("</span> <span class="sy1"><<</span> to4 <span class="sy1"><<</span> <span class="st0">")<span class="es1">\n</span>"</span> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1785">std::<span class="me2">defaultfloat</span></span></a><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="cpp-numeric-fenv-fetestexcept.html"><span class="kw1449">std::<span class="me2">fetestexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1463">FE_OVERFLOW</span></a><span class="br0">)</span><span class="br0">)</span> <a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" raised FE_OVERFLOW<span class="es1">\n</span>"</span><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="cpp-numeric-fenv-fetestexcept.html"><span class="kw1449">std::<span class="me2">fetestexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1461">FE_INEXACT</span></a><span class="br0">)</span><span class="br0">)</span> <a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" raised FE_INEXACT<span class="es1">\n</span>"</span><span class="sy4">;</span>
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<span class="br0">}</span> <span class="co1">// 结束 FENV_ACCESS 块</span>
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<span class="kw4">float</span> from5 <span class="sy1">=</span> <span class="nu16">0.0</span>, to5 <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">nextafter</span><span class="br0">(</span>from5, <span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1756">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"std::nextafter(+0.0, -0.0) gives "</span> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1782">std::<span class="me2">fixed</span></span></a> <span class="sy1"><<</span> to5 <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">The next representable float after 0 is 1.4012984643248170709e-45 (0x1p-149)
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The next representable float after 1 is 1.0000001192092895508 (0x1.000002p+0)
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The number 0.1 lies between two valid doubles:
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0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
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and 0.1000000000000000055511151231257827021181583404541015625 (0x1.999999999999ap-4)
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With nextafter, next float after 0 is 0
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With nexttoward, next float after 0 is 1.4012984643248170709e-45
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The next representable double after 1.79769e+308 (0x1.fffffffffffffp+1023) is inf (inf)
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raised FE_OVERFLOW
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raised FE_INEXACT
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std::nextafter(+0.0, -0.0) gives -0.000000</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin"></table>
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</div>
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<div class="visualClear"></div>
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</div>
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</div>
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</div>
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</body>
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</html>
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