239 lines
17 KiB
HTML
239 lines
17 KiB
HTML
<!DOCTYPE html>
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<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
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<title>hypot, hypotf, hypotl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_math_hypot skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<h1 id="firstHeading" class="firstHeading">hypot, hypotf, hypotl</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="c.html">c</a>‎ | <a href="c-numeric.html">numeric</a>‎ | <a href="c-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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<div>定义于头文件 <code><math.h></code></div>
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</td>
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<td></td>
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<td></td>
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<div><span class="mw-geshi c source-c"><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-c99">(C99 起)</span></td>
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<div><span class="mw-geshi c source-c"><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>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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<div><span class="mw-geshi c source-c"><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-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><tgmath.h></code></div>
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</td>
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<td></td>
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<td></td>
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<div><span class="mw-geshi c source-c"><span class="co2">#define hypot( x, y )</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-c99">(C99 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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</table>
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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> 泛型宏：若任何参数拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 类型，则调用函数的 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 版本。否则，若任何参数拥有整数类型或 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，则调用函数的 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 版本。否则，调用函数的 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span></span></span> 版本。</div>
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<p>此函数计算的值是直角边长度为 <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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<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</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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<tr class="t-par">
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<td>y</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> 。</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> 。</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 <a href="c-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 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 c source-c">hypot<span class="br0">(</span>x, y<span class="br0">)</span></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">hypot<span class="br0">(</span>y, x<span class="br0">)</span></span></span> 及 <span class="t-c"><span class="mw-geshi c source-c">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 c source-c"><a href="c-numeric-math-fabs.html"><span class="kw644">fabs</span></a></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 c source-c">hypot<span class="br0">(</span>x, y<span class="br0">)</span></span></span> 等价于 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-complex-cabs.html"><span class="kw765">cabs</span></a><span class="br0">(</span>x <span class="sy2">+</span> I<span class="sy2">*</span>y<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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<p><span class="t-c"><span class="mw-geshi c source-c">hypot<span class="br0">(</span>INFINITY, NAN<span class="br0">)</span></span></span> 返回 +∞ ，但 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-sqrt.html"><span class="kw665">sqrt</span></a><span class="br0">(</span>INFINITY<span class="sy2">*</span>INFINITY<span class="sy2">+</span>NAN<span class="sy2">*</span>NAN<span class="br0">)</span></span></span> 返回 NaN 。</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="c source-c">
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<pre class="de1"><span class="co2">#include <stdio.h></span>
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<span class="co2">#include <math.h></span>
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<span class="co2">#include <errno.h></span>
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<span class="co2">#include <fenv.h></span>
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<span class="co2">#include <float.h></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="kw4">void</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="co1">// 典型用法</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"(1,1) cartesian is (%f,%f) polar<span class="es1">\n</span>"</span>, hypot<span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span>, <a href="c-numeric-math-atan2.html"><span class="kw674">atan2</span></a><span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"hypot(NAN,INFINITY) = %f<span class="es1">\n</span>"</span>, hypot<span class="br0">(</span>NAN,INFINITY<span class="br0">)</span><span class="br0">)</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> <a href="c-numeric-fenv-feclearexcept.html"><span class="kw717">feclearexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw728">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"hypot(DBL_MAX,DBL_MAX) = %f<span class="es1">\n</span>"</span>, hypot<span class="br0">(</span><a href="c-types-limits.html"><span class="kw378">DBL_MAX</span></a>,<a href="c-types-limits.html"><span class="kw378">DBL_MAX</span></a><span class="br0">)</span><span class="br0">)</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="c-error-errno_macros.html"><span class="kw478">ERANGE</span></a><span class="br0">)</span> <a href="c-io-perror.html"><span class="kw878">perror</span></a><span class="br0">(</span><span class="st0">" errno == ERANGE"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw718">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw732">FE_OVERFLOW</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw835">puts</span></a><span class="br0">(</span><span class="st0">" FE_OVERFLOW raised"</span><span class="br0">)</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>可能的输出：</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 (1.414214,0.785398) 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.BC.95.E7.94.A8">引用</span></h3>
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<div class="t-ref-std-11">
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<ul>
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<li>C11 标准（ISO/IEC 9899:2011）：</li>
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</ul>
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<dl>
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<dd>
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<ul>
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<li>7.12.7.3 The hypot functions (p: 248)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.25 Type-generic math <tgmath.h> (p: 373-375)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>F.10.4.3 The hypot functions (p: 524)</li>
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</ul>
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</dd>
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</dl>
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<div class="t-ref-std-c99">
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<ul>
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<li>C99 标准（ISO/IEC 9899:1999）：</li>
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</ul>
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<dl>
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<dd>
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<ul>
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<li>7.12.7.3 The hypot functions (p: 229)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.22 Type-generic math <tgmath.h> (p: 335-337)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>F.9.4.3 The hypot functions (p: 461)</li>
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</ul>
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</dd>
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</dl>
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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="c-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-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算一个数的给定次幂（ <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="c-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-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</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="c-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-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</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>
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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="c-numeric-complex-cabs.html"><span class="t-lines"><span>cabs</span><span>cabsf</span><span>cabsl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的模（绝对值）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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</table>
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</div>
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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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