219 lines
22 KiB
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219 lines
22 KiB
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<title>std::hypot, std::hypotf, std::hypotl</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>hypot, <span style="font-size:0.7em; line-height:130%">std::</span>hypotf, <span style="font-size:0.7em; line-height:130%">std::</span>hypotl</h1>
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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>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> hypot <span class="br0">(</span> <span class="kw4">float</span> x, <span class="kw4">float</span> y <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> hypotf<span class="br0">(</span> <span class="kw4">float</span> x, <span class="kw4">float</span> y <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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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> hypot <span class="br0">(</span> <span class="kw4">double</span> x, <span class="kw4">double</span> y <span class="br0">)</span><span class="sy4">;</span></span></div>
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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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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> hypot <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> x, <span class="kw4">long</span> <span class="kw4">double</span> y <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> hypotl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> x, <span class="kw4">long</span> <span class="kw4">double</span> y <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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<div><span class="mw-geshi cpp source-cpp">Promoted hypot <span class="br0">(</span> Arithmetic1 x, Arithmetic2 y <span class="br0">)</span><span class="sy4">;</span></span></div>
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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-cxx17">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> hypot <span class="br0">(</span> <span class="kw4">float</span> x, <span class="kw4">float</span> y, <span class="kw4">float</span> z <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-cxx17">(C++17 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> hypot <span class="br0">(</span> <span class="kw4">double</span> x, <span class="kw4">double</span> y, <span class="kw4">double</span> z <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-cxx17">(C++17 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx17">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> hypot <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> x, <span class="kw4">long</span> <span class="kw4">double</span> y, <span class="kw4">long</span> <span class="kw4">double</span> z <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-cxx17">(C++17 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-cxx17">
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<div><span class="mw-geshi cpp source-cpp">Promoted hypot <span class="br0">(</span> Arithmetic1 x, Arithmetic2 y, Arithmetic3 z <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(8)</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>x</code> 与 <code>y</code> 平方和的平方根，而不会在计算的中间阶段有过度的上溢或下溢。</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组合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>，则它被转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。若任何其他参数为 <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">5-7)</span> 计算 <code>x</code> 、 <code>y</code> 和 <code>z</code> 平方和的平方根，而不会在计算的中间阶段有过度的上溢或下溢。</div>
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<div class="t-li1"><span class="t-li">8)</span> 所有 <span class="t-v">(5-7)</span> 所不覆盖的算术类型参数组合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>，则它被转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。若任何其他参数为 <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> ，否则为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。</div>
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<p>此函数的双参数版本所计算的是直角边长度为 <code>x</code> 和 <code>y</code> 的直角三角形的斜边长，或点 <code>(x,y)</code> 距原点 <code>(0,0)</code> 的距离，或复数 <code>x+<i>i</i>y</code> 的绝对值。</p>
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<p>此函数的三参数版本所计算的值是点 <code>(x,y,z)</code> 到原点 <code>(0,0,0)</code> 的距离。</p>
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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>x, y, z</td>
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<td>-</td>
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<td>浮点或<a href="cpp-types-is_integral.html">整数类型</a>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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<div class="t-li1"><span class="t-li">1-4)</span> 若不出现错误，则返回直角三角形的斜边， <span class="mjax" style="display:none">\(\scriptsize{\sqrt{x^2+y^2} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>√</span><span>x<span class="t-su">2<br /></span>+y<span class="t-su">2<br /></span></span></span></span> 。</div>
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<div class="t-li1"><span class="t-li">5-8)</span> 若不出现错误，则返回三维空间中到原点的距离， <span class="mjax" style="display:none">\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>√</span><span>x<span class="t-su">2<br /></span>+y<span class="t-su">2<br /></span>+z<span class="t-su">2<br /></span></span></span></span> 。</div>
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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> 。</p>
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<p>若出现下溢所致的值域错误，则返回（舍入后的）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><span class="t-c"><span class="mw-geshi cpp source-cpp">hypot<span class="br0">(</span>x, y<span class="br0">)</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">hypot<span class="br0">(</span>y, x<span class="br0">)</span></span></span> 及 <span class="t-c"><span class="mw-geshi cpp source-cpp">hypot<span class="br0">(</span>x, <span class="sy2">-</span>y<span class="br0">)</span></span></span> 等价</li>
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<li>若参数之一为 ±0 ，则 <code>hypot</code> 等价于以非零参数调用 <span class="t-c"><span class="mw-geshi cpp source-cpp">fabs</span></span></li>
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<li>若参数之一为 ±∞ ，则 <code>hypot</code> 返回 +∞ ，即使另一参数为 NaN</li>
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<li>否则，若任何参数为 NaN ，则返回 NaN</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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<p>实现通常保证小于 1 ulp （最后位置单位）的精度： <a rel="nofollow" class="external text" href="http://sourceware.org/git/?p=glibc.git;a=blob_plain;f=sysdeps/ieee754/dbl-64/e_hypot.c">GNU</a> 、 <a rel="nofollow" class="external text" href="http://www.freebsd.org/cgi/cvsweb.cgi/src/lib/msun/src/e_hypot.c?rev=1.13.4.2;content-type=text%2Fplain">BSD</a> 、 <a rel="nofollow" class="external text" href="http://www.open64.net/doc/d5/d3f/hypot_8c-source.html">Open64</a> 。</p>
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<p><span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">hypot</span><span class="br0">(</span>x, y<span class="br0">)</span></span></span> 等价于 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">abs</span><span class="br0">(</span><a href="cpp-numeric-complex.html"><span class="kw1471">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="br0">(</span>x,y<span class="br0">)</span><span class="br0">)</span></span></span> 。</p>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/hypot.html">POSIX 指定</a>仅若二个参数均为非正规且正确结果亦为非正规才可以出现下溢（这禁止朴素实现）。</p>
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<table class="t-rev-begin">
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<tr class="t-rev t-since-cxx17">
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<td>
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<p>能以 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">hypot</span><span class="br0">(</span>x2<span class="sy2">-</span>x1, y2<span class="sy2">-</span>y1, z2<span class="sy2">-</span>z1<span class="br0">)</span></span></span> 计算二个点 <code>(x1,y1,z1)</code> 和 <code>(x2,y2,z2)</code> 在三维空间中的距离。</p>
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</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 起)</span></td>
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</tr>
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</table>
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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 <iostream></span>
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<span class="co2">#include <cmath></span>
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<span class="co2">#include <cerrno></span>
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<span class="co2">#include <cfenv></span>
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<span class="co2">#include <cfloat></span>
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<span class="co2">#include <cstring></span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</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="co1">// 通常用法</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"(1,1) cartesian is ("</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">hypot</span><span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">','</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-atan2.html"><span class="kw1338">std::<span class="me2">atan2</span></span></a><span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">") polar<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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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"hypot(NAN,INFINITY) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">hypot</span><span class="br0">(</span><a href="cpp-numeric-math-NAN.html"><span class="kw1377">NAN</span></a>,<a href="cpp-numeric-math-INFINITY.html"><span class="kw1376">INFINITY</span></a><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="co1">// 错误处理</span>
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<span class="kw2">errno</span> <span class="sy1">=</span> <span class="nu0">0</span><span class="sy4">;</span>
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<a href="cpp-numeric-fenv-feclearexcept.html"><span class="kw1449">std::<span class="me2">feclearexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1460">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"hypot(DBL_MAX,DBL_MAX) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">hypot</span><span class="br0">(</span><a href="cpp-types-climits.html"><span class="kw418">DBL_MAX</span></a>,<a href="cpp-types-climits.html"><span class="kw418">DBL_MAX</span></a><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="kw1">if</span> <span class="br0">(</span><span class="kw2">errno</span> <span class="sy1">==</span> <a href="cpp-error-errno_macros.html"><span class="kw862">ERANGE</span></a><span class="br0">)</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" errno = ERANGE "</span> <span class="sy1"><<</span> <a href="cpp-string-byte-strerror.html"><span class="kw1161">std::<span class="me2">strerror</span></span></a><span class="br0">(</span><span class="kw2">errno</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="kw1">if</span> <span class="br0">(</span>fetestexcept<span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1464">FE_OVERFLOW</span></a><span class="br0">)</span><span class="br0">)</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" FE_OVERFLOW raised<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">(1,1) cartesian is (1.41421,0.785398) polar
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hypot(NAN,INFINITY) = inf
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hypot(DBL_MAX,DBL_MAX) = inf
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errno = ERANGE Numerical result out of range
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FE_OVERFLOW raised</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">
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-pow.html"><span class="t-lines"><span>pow</span><span>powf</span><span>powl</span></span></a></div>
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<div><span class="t-lines"><span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>求某数的给定次幂（ <span class="mjax" style="display:none">\(\small{x^y}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">x<sup>y</sup></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-sqrt.html"><span class="t-lines"><span>sqrt</span><span>sqrtf</span><span>sqrtl</span></span></a></div>
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<div><span class="t-lines"><span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>计算平方根（ <span class="mjax" style="display:none">\(\small{\sqrt{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>√</span><span>x</span></span></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-cbrt.html"><span class="t-lines"><span>cbrt</span><span>cbrtf</span><span>cbrtl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>计算立方根（ <span class="mjax" style="display:none">\(\small{\sqrt[3]{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>3</span><span>√</span><span>x</span></span></span> ）<br />
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<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
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<td>
|
|
<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-abs.html"><span class="t-lines"><span>abs<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>返回复数的模<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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</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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