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<div id="projectname">amath
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 <span id="projectnumber">1.6.2</span>
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<div id="projectbrief">Simple command line calculator</div>
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<a href="acosh_8c.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* @(#)e_acosh.c 1.3 95/01/18 */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">/*</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * Copyright (c) 2015-2017 Carsten Sonne Larsen <cs@innolan.dk></span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * All rights reserved.</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> *</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * Redistribution and use in source and binary forms, with or without</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * modification, are permitted provided that the following conditions</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * are met:</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * 1. Redistributions of source code must retain the above copyright</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * notice, this list of conditions and the following disclaimer.</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * 2. Redistributions in binary form must reproduce the above copyright</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * notice, this list of conditions and the following disclaimer in the</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * documentation and/or other materials provided with the distribution.</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> *</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> *</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> * The origin source code can be obtained from:</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> * http://www.netlib.org/fdlibm/e_acosh.c</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> * </span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> */</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">/*</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> * ====================================================</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> *</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> * Developed at SunSoft, a Sun Microsystems, Inc. business.</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> * Permission to use, copy, modify, and distribute this</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> * software is freely granted, provided that this notice</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> * is preserved.</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> * ====================================================</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> *</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> */</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#</span><span class="preprocessor">include</span> <a class="code" href="real_2prim_8h.html">"prim.h"</a></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#</span><span class="preprocessor">include</span> <a class="code" href="math_8h.html" title="Functions in math library for handling real numbers. ">"math.h"</a></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b"> 48</a></span> <a class="code" href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a> = 1.0,</div><div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d"> 49</a></span> <a class="code" href="acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d">ln2</a> = 6.93147180559945286227e-01; <span class="comment">/* 0x3FE62E42, 0xFEFA39EF */</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> </div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">/**</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"> * @brief Inverse hyperbolic cosine function.</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> * @version 1.3</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> * @date 95/01/18</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> * @details</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"> * <pre></span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> * Method :</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> * Based on</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> * acosh(x) = log [ x + sqrt(x*x-1) ]</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> * we have</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> * acosh(x) := log(x)+ln2, if x is large; else</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"> * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> *</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> * Special cases:</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> * acosh(x) is NaN with signal if x<1.</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> * acosh(NaN) is NaN without signal.</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> * </pre></span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> * @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> * @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> * to use, copy, modify, and distribute this software is freely granted,</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> * provided that this notice is preserved.</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> */</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div><div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="acosh_8c.html#ac862445bcb46911b1782c284829d5e46"> 75</a></span> <span class="keywordtype">double</span> <a class="code" href="acosh_8c.html#ac862445bcb46911b1782c284829d5e46">acosh</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> {</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordtype">double</span> t;</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <a class="code" href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a> hx, lx;</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(hx,x);</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <a class="code" href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a>(lx,x);</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">if</span>(hx<0x3ff00000) { <span class="comment">/* x < 1 */</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> (x-x)/(x-x);</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(hx >=0x41b00000) { <span class="comment">/* x > 2**28 */</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span>(hx >=0x7ff00000) { <span class="comment">/* x is inf of NaN */</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> x+x;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  } <span class="keywordflow">else</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">return</span> log(x)+<a class="code" href="acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d">ln2</a>; <span class="comment">/* acosh(huge)=log(2x) */</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(((hx-0x3ff00000)|lx)==0) {</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">return</span> 0.0; <span class="comment">/* acosh(1) = 0 */</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (hx > 0x40000000) { <span class="comment">/* 2**28 > x > 2 */</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  t=x*x;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span> log(2.0*x-<a class="code" href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>/(x+<a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">sqrt</a><a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">(</a>t-<a class="code" href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a><a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">)</a>));</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  } <span class="keywordflow">else</span> { <span class="comment">/* 1<x<2 */</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  t = x-<a class="code" href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>;</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">return</span> <a class="code" href="log1p_8c.html#ac2aac20ab1347498e6e4f209148fea84">log1p</a><a class="code" href="log1p_8c.html#ac2aac20ab1347498e6e4f209148fea84">(</a>t+<a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">sqrt</a><a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">(</a>2.0*t+t*t<a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">)</a><a class="code" href="log1p_8c.html#ac2aac20ab1347498e6e4f209148fea84">)</a>;</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  }</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> }</div><div class="ttc" id="sqrt_8c_html_ab87521a75ef827a85807f89a6c10629a"><div class="ttname"><a href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">sqrt</a></div><div class="ttdeci">double sqrt(double x)</div><div class="ttdoc">Square root function. </div><div class="ttdef"><b>Definition:</b> <a href="sqrt_8c_source.html#l00127">sqrt.c:127</a></div></div>
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<div class="ttc" id="acosh_8c_html_ada85e349d35971b32c8ea4238881ff8b"><div class="ttname"><a href="acosh_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a></div><div class="ttdeci">static const double one</div><div class="ttdef"><b>Definition:</b> <a href="acosh_8c_source.html#l00048">acosh.c:48</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae62ee08d06ab4cc06d61dc1246b73195"><div class="ttname"><a href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a></div><div class="ttdeci">#define GET_HIGH_WORD(i, d)</div><div class="ttdoc">Get the more significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00165">prim.h:165</a></div></div>
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<div class="ttc" id="log1p_8c_html_ac2aac20ab1347498e6e4f209148fea84"><div class="ttname"><a href="log1p_8c.html#ac2aac20ab1347498e6e4f209148fea84">log1p</a></div><div class="ttdeci">double log1p(double x)</div><div class="ttdef"><b>Definition:</b> <a href="log1p_8c_source.html#l00125">log1p.c:125</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_adee023704c856ea8f310e8e3fd765a22"><div class="ttname"><a href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a></div><div class="ttdeci">#define GET_LOW_WORD(i, d)</div><div class="ttdoc">Get the less significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00176">prim.h:176</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae91287c8a5f73a8a22a100f50dc4de77"><div class="ttname"><a href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a></div><div class="ttdeci">signed int sword</div><div class="ttdoc">32 bit signed integer. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00107">prim.h:107</a></div></div>
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<div class="ttc" id="acosh_8c_html_ac862445bcb46911b1782c284829d5e46"><div class="ttname"><a href="acosh_8c.html#ac862445bcb46911b1782c284829d5e46">acosh</a></div><div class="ttdeci">double acosh(double x)</div><div class="ttdoc">Inverse hyperbolic cosine function. </div><div class="ttdef"><b>Definition:</b> <a href="acosh_8c_source.html#l00075">acosh.c:75</a></div></div>
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<div class="ttc" id="acosh_8c_html_a703f4fc93e5a57058ce6ba2ba196918d"><div class="ttname"><a href="acosh_8c.html#a703f4fc93e5a57058ce6ba2ba196918d">ln2</a></div><div class="ttdeci">static const double ln2</div><div class="ttdef"><b>Definition:</b> <a href="acosh_8c_source.html#l00049">acosh.c:49</a></div></div>
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