188 lines
18 KiB
HTML
188 lines
18 KiB
HTML
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<title>std::log1p, std::log1pf, std::log1pl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_log1p 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>log1p, <span style="font-size:0.7em; line-height:130%">std::</span>log1pf, <span style="font-size:0.7em; line-height:130%">std::</span>log1pl</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>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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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> log1p <span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> log1pf<span class="br0">(</span> <span class="kw4">float</span> arg <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 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">double</span> log1p <span class="br0">(</span> <span class="kw4">double</span> arg <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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<td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> log1p <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> log1pl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <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"><span class="kw4">double</span> log1p <span class="br0">(</span> IntegralType arg <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-sep">
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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 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="nu0">1</span><span class="sy2">+</span>arg</span></span> 的自然（底 <span class="t-c"><span class="mw-geshi cpp source-cpp">e</span></span> ）对数。若 <code>arg</code> 接近零，则此函数比表达式 <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span>arg<span class="br0">)</span></span></span> 更精确。</div>
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<div class="t-li1"><span class="t-li">4)</span> 接受任何<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板，等价于 2) （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>arg</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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<p>若不出现错误则返回 <span class="texhtml" style="white-space: nowrap;">ln(1+arg)</span> 。</p>
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<p>若出现定义域错误，则返回实现定义值（受支持平台上为 NaN ）。</p>
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<p>若出现极点错误，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 <code>arg</code> 小于 <span class="texhtml" style="white-space: nowrap;">-1</span> 则出现定义域错误。</p>
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<p>若 <code>arg</code> 为 <span class="texhtml" style="white-space: nowrap;">-1</span> 则可能出现极点错误。</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>若参数为 ±0 ，则返回不修改的参数。</li>
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<li>若参数为 -1 ，则返回 -∞ 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span> 。</li>
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<li>若参数小于 -1 ，则返回 NaN 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若参数为 +∞ ，则返回 +∞ 。</li>
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<li>若参数为 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>函数 <code>std::expm1</code> 和 <span class="t-lc"><strong class="selflink">std::log1p</strong></span> 对于金融计算有用：例如在计算小的日利率时： <span class="texhtml" style="white-space: nowrap;">(1+x)<span class="t-su">n<br /></span>-1</span> 能表示为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-expm1.html"><span class="kw1323">std::<span class="me2">expm1</span></span></a><span class="br0">(</span>n <span class="sy2">*</span> std<span class="sy4">::</span><span class="me2">log1p</span><span class="br0">(</span>x<span class="br0">)</span><span class="br0">)</span></span></span> 。这些函数亦简化书写精确的反双曲函数。</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 <iostream></span>
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<span class="co2">#include <cfenv></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 <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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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"log1p(0) = "</span> <span class="sy1"><<</span> log1p<span class="br0">(</span><span class="nu0">0</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"Interest earned in 2 days on on $100, compounded daily at 1%<span class="es1">\n</span>"</span>
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<span class="sy1"><<</span> <span class="st0">" on a 30/360 calendar = "</span>
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<span class="sy1"><<</span> <span class="nu0">100</span><span class="sy2">*</span>expm1<span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>log1p<span class="br0">(</span><span class="nu16">0.01</span><span class="sy2">/</span><span class="nu0">360</span><span class="br0">)</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"log(1+1e-16) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span><span class="nu19">1e-16</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">" log1p(1e-16) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">log1p</span><span class="br0">(</span><span class="nu19">1e-16</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="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">"log1p(-0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">log1p</span><span class="br0">(</span><span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"log1p(+Inf) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">log1p</span><span class="br0">(</span><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">"log1p(-1) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">log1p</span><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</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><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><a href="cpp-numeric-fenv-fetestexcept.html"><span class="kw1450">std::<span class="me2">fetestexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1461">FE_DIVBYZERO</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_DIVBYZERO 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>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">log1p(0) = 0
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Interest earned in 2 days on on $100, compounded daily at 1%
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on a 30/360 calendar = 0.00555563
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log(1+1e-16) = 0 log1p(1e-16) = 1e-16
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log1p(-0) = -0
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log1p(+Inf) = inf
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log1p(-1) = -inf
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errno == ERANGE: Result too large
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FE_DIVBYZERO raised</pre></div>
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</div>
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</div>
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<p><br /></p>
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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-log.html"><span class="t-lines"><span>log</span><span>logf</span><span>logl</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>计算自然（以 <i>e</i> 为底）对数（ <span class="mjax" style="display:none">\({\small \ln{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">ln(x)</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-log10.html"><span class="t-lines"><span>log10</span><span>log10f</span><span>log10l</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>计算常用（以 <i>10</i> 为底）对数（ <span class="mjax" style="display:none">\({\small \log_{10}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">log<sub>10</sub>(x)</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-log2.html"><span class="t-lines"><span>log2</span><span>log2f</span><span>log2l</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>给定数值的以 2 为底的对数（ <span class="mjax" style="display:none">\({\small \log_{2}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">log<sub>2</sub>(x)</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-expm1.html"><span class="t-lines"><span>expm1</span><span>expm1f</span><span>expm1l</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>返回 <i>e</i> 的给定次幂减一（ <span class="mjax" style="display:none">\({\small e^x-1}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">e<sup>x</sup>-1</span> ）<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 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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