174 lines
16 KiB
HTML
174 lines
16 KiB
HTML
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<title>std::expm1, std::expm1f, std::expm1l</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_expm1 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>expm1, <span style="font-size:0.7em; line-height:130%">std::</span>expm1f, <span style="font-size:0.7em; line-height:130%">std::</span>expm1l</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> expm1 <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> expm1f<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>(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> expm1 <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>(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> expm1 <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> expm1l<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>(3)</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> expm1 <span class="br0">(</span> IntegralType arg <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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <i>e</i> （欧拉数， <code>2.7182818</code> ）的给定 <code>arg</code> 次幂减 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="nu16">1.0</span></span></span> 。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-exp.html"><span class="kw1321">std::<span class="me2">exp</span></span></a><span class="br0">(</span>arg<span class="br0">)</span><span class="sy2">-</span><span class="nu16">1.0</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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<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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<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;">e<span class="t-su">arg<br /></span>-1</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 <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>若参数为 ±0 ，则返回不修改的参数</li>
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<li>若参数为 -∞ ，则返回 -1</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"><a href="cpp-numeric-math-log1p.html">std::log1p</a></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">std<span class="sy4">::</span><span class="me2">expm1</span><span class="br0">(</span>n <span class="sy2">*</span> <a href="cpp-numeric-math-log1p.html"><span class="kw1325">std::<span class="me2">log1p</span></span></a><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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<p>对于 IEEE 兼容的 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 类型，若 <span class="texhtml" style="white-space: nowrap;">709.8 < arg</span> 则保证上溢。</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 <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">#include <cfenv></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">"expm1(1) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">expm1</span><span class="br0">(</span><span class="nu0">1</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>std<span class="sy4">::</span><span class="me2">expm1</span><span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span><a href="cpp-numeric-math-log1p.html"><span class="kw1325">std::<span class="me2">log1p</span></span></a><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">"exp(1e-16)-1 = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-exp.html"><span class="kw1321">std::<span class="me2">exp</span></span></a><span class="br0">(</span><span class="nu19">1e-16</span><span class="br0">)</span><span class="sy2">-</span><span class="nu0">1</span>
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<span class="sy1"><<</span> <span class="st0">", but expm1(1e-16) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">expm1</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">"expm1(-0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">expm1</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">"expm1(-Inf) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">expm1</span><span class="br0">(</span><span class="sy2">-</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">"expm1(710) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">expm1</span><span class="br0">(</span><span class="nu0">710</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="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>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">expm1(1) = 1.71828
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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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exp(1e-16)-1 = 0 expm1(1e-16) = 1e-16
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expm1(-0) = -0
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expm1(-Inf) = -1
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expm1(710) = inf
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errno == ERANGE: Result too large
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FE_OVERFLOW raised</pre></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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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-exp.html"><span class="t-lines"><span>exp</span><span>expf</span><span>expl</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>返回 <i>e</i> 的给定次幂（ <span class="mjax" style="display:none">\({\small e^x}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">e<sup>x</sup></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-exp2.html"><span class="t-lines"><span>exp2</span><span>exp2f</span><span>exp2l</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>返回 <i>2</i> 的给定次幂（ <span class="mjax" style="display:none">\({\small 2^x}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">2<sup>x</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-log1p.html"><span class="t-lines"><span>log1p</span><span>log1pf</span><span>log1pl</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>1 加上给定数值的自然（以 <i>e</i> 为底）对数（ <span class="mjax" style="display:none">\({\small \ln{(1+x)} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">ln(1+x)</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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</body>
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