mirror of https://gitlab.com/rnger/amath
350 lines
37 KiB
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350 lines
37 KiB
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<h3>Bug Summary</h3>
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<table class="simpletable">
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<tr><td class="rowname">File:</td><td>real/expm1.c</td></tr>
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<tr><td class="rowname">Location:</td><td><a href="#EndPath">line 166, column 16</a></td></tr>
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<tr><td class="rowname">Description:</td><td>Value stored to 'y' is never read</td></tr>
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<h3>Annotated Source Code</h3>
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<table class="code">
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<tr><td class="num" id="LN1">1</td><td class="line"><span class='comment'>/* @(#)s_expm1.c 1.5 04/04/22 */</span></td></tr>
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<tr><td class="num" id="LN2">2</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN3">3</td><td class="line"><span class='comment'>/*</span></td></tr>
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<tr><td class="num" id="LN4">4</td><td class="line"> <span class='comment'>* Copyright (c) 2015-2017 Carsten Sonne Larsen <cs@innolan.dk></span></td></tr>
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<tr><td class="num" id="LN5">5</td><td class="line"> <span class='comment'>* All rights reserved.</span></td></tr>
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<tr><td class="num" id="LN6">6</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN7">7</td><td class="line"> <span class='comment'>* Redistribution and use in source and binary forms, with or without</span></td></tr>
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<tr><td class="num" id="LN8">8</td><td class="line"> <span class='comment'>* modification, are permitted provided that the following conditions</span></td></tr>
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<tr><td class="num" id="LN9">9</td><td class="line"> <span class='comment'>* are met:</span></td></tr>
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<tr><td class="num" id="LN10">10</td><td class="line"> <span class='comment'>* 1. Redistributions of source code must retain the above copyright</span></td></tr>
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<tr><td class="num" id="LN11">11</td><td class="line"> <span class='comment'>* notice, this list of conditions and the following disclaimer.</span></td></tr>
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<tr><td class="num" id="LN12">12</td><td class="line"> <span class='comment'>* 2. Redistributions in binary form must reproduce the above copyright</span></td></tr>
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<tr><td class="num" id="LN13">13</td><td class="line"> <span class='comment'>* notice, this list of conditions and the following disclaimer in the</span></td></tr>
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<tr><td class="num" id="LN14">14</td><td class="line"> <span class='comment'>* documentation and/or other materials provided with the distribution.</span></td></tr>
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<tr><td class="num" id="LN15">15</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN16">16</td><td class="line"> <span class='comment'>* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR</span></td></tr>
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<tr><td class="num" id="LN17">17</td><td class="line"> <span class='comment'>* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES</span></td></tr>
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<tr><td class="num" id="LN18">18</td><td class="line"> <span class='comment'>* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.</span></td></tr>
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<tr><td class="num" id="LN19">19</td><td class="line"> <span class='comment'>* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,</span></td></tr>
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<tr><td class="num" id="LN20">20</td><td class="line"> <span class='comment'>* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT</span></td></tr>
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<tr><td class="num" id="LN21">21</td><td class="line"> <span class='comment'>* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,</span></td></tr>
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<tr><td class="num" id="LN22">22</td><td class="line"> <span class='comment'>* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY</span></td></tr>
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<tr><td class="num" id="LN23">23</td><td class="line"> <span class='comment'>* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span></td></tr>
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<tr><td class="num" id="LN24">24</td><td class="line"> <span class='comment'>* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF</span></td></tr>
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<tr><td class="num" id="LN25">25</td><td class="line"> <span class='comment'>* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></td></tr>
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<tr><td class="num" id="LN26">26</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN27">27</td><td class="line"> <span class='comment'>* The origin source code can be obtained from:</span></td></tr>
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<tr><td class="num" id="LN28">28</td><td class="line"> <span class='comment'>* http://www.netlib.org/fdlibm/s_expm1.c</span></td></tr>
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<tr><td class="num" id="LN29">29</td><td class="line"> <span class='comment'>*</span> </td></tr>
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<tr><td class="num" id="LN30">30</td><td class="line"> <span class='comment'>*/</span></td></tr>
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<tr><td class="num" id="LN31">31</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN32">32</td><td class="line"><span class='comment'>/*</span></td></tr>
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<tr><td class="num" id="LN33">33</td><td class="line"> <span class='comment'>* ====================================================</span></td></tr>
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<tr><td class="num" id="LN34">34</td><td class="line"> <span class='comment'>* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.</span></td></tr>
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<tr><td class="num" id="LN35">35</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN36">36</td><td class="line"> <span class='comment'>* Permission to use, copy, modify, and distribute this</span></td></tr>
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<tr><td class="num" id="LN37">37</td><td class="line"> <span class='comment'>* software is freely granted, provided that this notice</span></td></tr>
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<tr><td class="num" id="LN38">38</td><td class="line"> <span class='comment'>* is preserved.</span></td></tr>
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<tr><td class="num" id="LN39">39</td><td class="line"> <span class='comment'>* ====================================================</span></td></tr>
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<tr><td class="num" id="LN40">40</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN41">41</td><td class="line"> <span class='comment'>*/</span></td></tr>
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<tr><td class="num" id="LN42">42</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN43">43</td><td class="line"><span class='directive'>#include "prim.h"</span></td></tr>
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<tr><td class="num" id="LN44">44</td><td class="line"><span class='directive'>#include "math.h"</span></td></tr>
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<tr><td class="num" id="LN45">45</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN46">46</td><td class="line"><span class='comment'>/* expm1(x)</span></td></tr>
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<tr><td class="num" id="LN47">47</td><td class="line"> <span class='comment'>* Returns exp(x)-1, the exponential of x minus 1.</span></td></tr>
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<tr><td class="num" id="LN48">48</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN49">49</td><td class="line"> <span class='comment'>* Method</span></td></tr>
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<tr><td class="num" id="LN50">50</td><td class="line"> <span class='comment'>* 1. Argument reduction:</span></td></tr>
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<tr><td class="num" id="LN51">51</td><td class="line"> <span class='comment'>* Given x, find r and integer k such that</span></td></tr>
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<tr><td class="num" id="LN52">52</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN53">53</td><td class="line"> <span class='comment'>* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658</span></td></tr>
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<tr><td class="num" id="LN54">54</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN55">55</td><td class="line"> <span class='comment'>* Here a correction term c will be computed to compensate</span></td></tr>
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<tr><td class="num" id="LN56">56</td><td class="line"> <span class='comment'>* the error in r when rounded to a floating-point number.</span></td></tr>
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<tr><td class="num" id="LN57">57</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN58">58</td><td class="line"> <span class='comment'>* 2. Approximating expm1(r) by a special rational function on</span></td></tr>
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<tr><td class="num" id="LN59">59</td><td class="line"> <span class='comment'>* the interval [0,0.34658]:</span></td></tr>
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<tr><td class="num" id="LN60">60</td><td class="line"> <span class='comment'>* Since</span></td></tr>
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<tr><td class="num" id="LN61">61</td><td class="line"> <span class='comment'>* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...</span></td></tr>
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<tr><td class="num" id="LN62">62</td><td class="line"> <span class='comment'>* we define R1(r*r) by</span></td></tr>
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<tr><td class="num" id="LN63">63</td><td class="line"> <span class='comment'>* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)</span></td></tr>
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<tr><td class="num" id="LN64">64</td><td class="line"> <span class='comment'>* That is,</span></td></tr>
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<tr><td class="num" id="LN65">65</td><td class="line"> <span class='comment'>* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)</span></td></tr>
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<tr><td class="num" id="LN66">66</td><td class="line"> <span class='comment'>* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))</span></td></tr>
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<tr><td class="num" id="LN67">67</td><td class="line"> <span class='comment'>* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...</span></td></tr>
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<tr><td class="num" id="LN68">68</td><td class="line"> <span class='comment'>* We use a special Remes algorithm on [0,0.347] to generate</span></td></tr>
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<tr><td class="num" id="LN69">69</td><td class="line"> <span class='comment'>* a polynomial of degree 5 in r*r to approximate R1. The</span></td></tr>
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<tr><td class="num" id="LN70">70</td><td class="line"> <span class='comment'>* maximum error of this polynomial approximation is bounded</span></td></tr>
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<tr><td class="num" id="LN71">71</td><td class="line"> <span class='comment'>* by 2**-61. In other words,</span></td></tr>
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<tr><td class="num" id="LN72">72</td><td class="line"> <span class='comment'>* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5</span></td></tr>
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<tr><td class="num" id="LN73">73</td><td class="line"> <span class='comment'>* where Q1 = -1.6666666666666567384E-2,</span></td></tr>
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<tr><td class="num" id="LN74">74</td><td class="line"> <span class='comment'>* Q2 = 3.9682539681370365873E-4,</span></td></tr>
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<tr><td class="num" id="LN75">75</td><td class="line"> <span class='comment'>* Q3 = -9.9206344733435987357E-6,</span></td></tr>
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<tr><td class="num" id="LN76">76</td><td class="line"> <span class='comment'>* Q4 = 2.5051361420808517002E-7,</span></td></tr>
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<tr><td class="num" id="LN77">77</td><td class="line"> <span class='comment'>* Q5 = -6.2843505682382617102E-9;</span></td></tr>
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<tr><td class="num" id="LN78">78</td><td class="line"> <span class='comment'>* (where z=r*r, and the values of Q1 to Q5 are listed below)</span></td></tr>
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<tr><td class="num" id="LN79">79</td><td class="line"> <span class='comment'>* with error bounded by</span></td></tr>
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<tr><td class="num" id="LN80">80</td><td class="line"> <span class='comment'>* | 5 | -61</span></td></tr>
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<tr><td class="num" id="LN81">81</td><td class="line"> <span class='comment'>* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2</span></td></tr>
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<tr><td class="num" id="LN82">82</td><td class="line"> <span class='comment'>* | |</span></td></tr>
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<tr><td class="num" id="LN83">83</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN84">84</td><td class="line"> <span class='comment'>* expm1(r) = exp(r)-1 is then computed by the following</span></td></tr>
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<tr><td class="num" id="LN85">85</td><td class="line"> <span class='comment'>* specific way which minimize the accumulation rounding error:</span></td></tr>
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<tr><td class="num" id="LN86">86</td><td class="line"> <span class='comment'>* 2 3</span></td></tr>
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<tr><td class="num" id="LN87">87</td><td class="line"> <span class='comment'>* r r [ 3 - (R1 + R1*r/2) ]</span></td></tr>
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<tr><td class="num" id="LN88">88</td><td class="line"> <span class='comment'>* expm1(r) = r + --- + --- * [--------------------]</span></td></tr>
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<tr><td class="num" id="LN89">89</td><td class="line"> <span class='comment'>* 2 2 [ 6 - r*(3 - R1*r/2) ]</span></td></tr>
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<tr><td class="num" id="LN90">90</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN91">91</td><td class="line"> <span class='comment'>* To compensate the error in the argument reduction, we use</span></td></tr>
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<tr><td class="num" id="LN92">92</td><td class="line"> <span class='comment'>* expm1(r+c) = expm1(r) + c + expm1(r)*c</span></td></tr>
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<tr><td class="num" id="LN93">93</td><td class="line"> <span class='comment'>* ~ expm1(r) + c + r*c</span></td></tr>
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<tr><td class="num" id="LN94">94</td><td class="line"> <span class='comment'>* Thus c+r*c will be added in as the correction terms for</span></td></tr>
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<tr><td class="num" id="LN95">95</td><td class="line"> <span class='comment'>* expm1(r+c). Now rearrange the term to avoid optimization</span></td></tr>
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<tr><td class="num" id="LN96">96</td><td class="line"> <span class='comment'>* screw up:</span></td></tr>
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<tr><td class="num" id="LN97">97</td><td class="line"> <span class='comment'>* ( 2 2 )</span></td></tr>
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<tr><td class="num" id="LN98">98</td><td class="line"> <span class='comment'>* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )</span></td></tr>
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<tr><td class="num" id="LN99">99</td><td class="line"> <span class='comment'>* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )</span></td></tr>
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<tr><td class="num" id="LN100">100</td><td class="line"> <span class='comment'>* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )</span></td></tr>
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<tr><td class="num" id="LN101">101</td><td class="line"> <span class='comment'>* ( )</span></td></tr>
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<tr><td class="num" id="LN102">102</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN103">103</td><td class="line"> <span class='comment'>* = r - E</span></td></tr>
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<tr><td class="num" id="LN104">104</td><td class="line"> <span class='comment'>* 3. Scale back to obtain expm1(x):</span></td></tr>
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<tr><td class="num" id="LN105">105</td><td class="line"> <span class='comment'>* From step 1, we have</span></td></tr>
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<tr><td class="num" id="LN106">106</td><td class="line"> <span class='comment'>* expm1(x) = either 2^k*[expm1(r)+1] - 1</span></td></tr>
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<tr><td class="num" id="LN107">107</td><td class="line"> <span class='comment'>* = or 2^k*[expm1(r) + (1-2^-k)]</span></td></tr>
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<tr><td class="num" id="LN108">108</td><td class="line"> <span class='comment'>* 4. Implementation notes:</span></td></tr>
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<tr><td class="num" id="LN109">109</td><td class="line"> <span class='comment'>* (A). To save one multiplication, we scale the coefficient Qi</span></td></tr>
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<tr><td class="num" id="LN110">110</td><td class="line"> <span class='comment'>* to Qi*2^i, and replace z by (x^2)/2.</span></td></tr>
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<tr><td class="num" id="LN111">111</td><td class="line"> <span class='comment'>* (B). To achieve maximum accuracy, we compute expm1(x) by</span></td></tr>
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<tr><td class="num" id="LN112">112</td><td class="line"> <span class='comment'>* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)</span></td></tr>
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<tr><td class="num" id="LN113">113</td><td class="line"> <span class='comment'>* (ii) if k=0, return r-E</span></td></tr>
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<tr><td class="num" id="LN114">114</td><td class="line"> <span class='comment'>* (iii) if k=-1, return 0.5*(r-E)-0.5</span></td></tr>
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<tr><td class="num" id="LN115">115</td><td class="line"> <span class='comment'>* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)</span></td></tr>
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<tr><td class="num" id="LN116">116</td><td class="line"> <span class='comment'>* else return 1.0+2.0*(r-E);</span></td></tr>
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<tr><td class="num" id="LN117">117</td><td class="line"> <span class='comment'>* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)</span></td></tr>
|
|
<tr><td class="num" id="LN118">118</td><td class="line"> <span class='comment'>* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else</span></td></tr>
|
|
<tr><td class="num" id="LN119">119</td><td class="line"> <span class='comment'>* (vii) return 2^k(1-((E+2^-k)-r))</span></td></tr>
|
|
<tr><td class="num" id="LN120">120</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN121">121</td><td class="line"> <span class='comment'>* Special cases:</span></td></tr>
|
|
<tr><td class="num" id="LN122">122</td><td class="line"> <span class='comment'>* expm1(INF) is INF, expm1(NaN) is NaN;</span></td></tr>
|
|
<tr><td class="num" id="LN123">123</td><td class="line"> <span class='comment'>* expm1(-INF) is -1, and</span></td></tr>
|
|
<tr><td class="num" id="LN124">124</td><td class="line"> <span class='comment'>* for finite argument, only expm1(0)=0 is exact.</span></td></tr>
|
|
<tr><td class="num" id="LN125">125</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN126">126</td><td class="line"> <span class='comment'>* Accuracy:</span></td></tr>
|
|
<tr><td class="num" id="LN127">127</td><td class="line"> <span class='comment'>* according to an error analysis, the error is always less than</span></td></tr>
|
|
<tr><td class="num" id="LN128">128</td><td class="line"> <span class='comment'>* 1 ulp (unit in the last place).</span></td></tr>
|
|
<tr><td class="num" id="LN129">129</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN130">130</td><td class="line"> <span class='comment'>* Misc. info.</span></td></tr>
|
|
<tr><td class="num" id="LN131">131</td><td class="line"> <span class='comment'>* For IEEE double</span></td></tr>
|
|
<tr><td class="num" id="LN132">132</td><td class="line"> <span class='comment'>* if x > 7.09782712893383973096e+02 then expm1(x) overflow</span></td></tr>
|
|
<tr><td class="num" id="LN133">133</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN134">134</td><td class="line"> <span class='comment'>* Constants:</span></td></tr>
|
|
<tr><td class="num" id="LN135">135</td><td class="line"> <span class='comment'>* The hexadecimal values are the intended ones for the following</span></td></tr>
|
|
<tr><td class="num" id="LN136">136</td><td class="line"> <span class='comment'>* constants. The decimal values may be used, provided that the</span></td></tr>
|
|
<tr><td class="num" id="LN137">137</td><td class="line"> <span class='comment'>* compiler will convert from decimal to binary accurately enough</span></td></tr>
|
|
<tr><td class="num" id="LN138">138</td><td class="line"> <span class='comment'>* to produce the hexadecimal values shown.</span></td></tr>
|
|
<tr><td class="num" id="LN139">139</td><td class="line"> <span class='comment'>*/</span></td></tr>
|
|
<tr><td class="num" id="LN140">140</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN141">141</td><td class="line"><span class='keyword'>static</span> <span class='keyword'>const</span> <span class='keyword'>double</span></td></tr>
|
|
<tr><td class="num" id="LN142">142</td><td class="line">one = 1.0,</td></tr>
|
|
<tr><td class="num" id="LN143">143</td><td class="line">huge = 1.0e+300,</td></tr>
|
|
<tr><td class="num" id="LN144">144</td><td class="line">tiny = 1.0e-300,</td></tr>
|
|
<tr><td class="num" id="LN145">145</td><td class="line">o_threshold = 7.09782712893383973096e+02,<span class='comment'>/* 0x40862E42, 0xFEFA39EF */</span></td></tr>
|
|
<tr><td class="num" id="LN146">146</td><td class="line">ln2_hi = 6.93147180369123816490e-01,<span class='comment'>/* 0x3fe62e42, 0xfee00000 */</span></td></tr>
|
|
<tr><td class="num" id="LN147">147</td><td class="line">ln2_lo = 1.90821492927058770002e-10,<span class='comment'>/* 0x3dea39ef, 0x35793c76 */</span></td></tr>
|
|
<tr><td class="num" id="LN148">148</td><td class="line">invln2 = 1.44269504088896338700e+00,<span class='comment'>/* 0x3ff71547, 0x652b82fe */</span></td></tr>
|
|
<tr><td class="num" id="LN149">149</td><td class="line"> <span class='comment'>/* scaled coefficients related to expm1 */</span></td></tr>
|
|
<tr><td class="num" id="LN150">150</td><td class="line">Q1 = -3.33333333333331316428e-02, <span class='comment'>/* BFA11111 111110F4 */</span></td></tr>
|
|
<tr><td class="num" id="LN151">151</td><td class="line">Q2 = 1.58730158725481460165e-03, <span class='comment'>/* 3F5A01A0 19FE5585 */</span></td></tr>
|
|
<tr><td class="num" id="LN152">152</td><td class="line">Q3 = -7.93650757867487942473e-05, <span class='comment'>/* BF14CE19 9EAADBB7 */</span></td></tr>
|
|
<tr><td class="num" id="LN153">153</td><td class="line">Q4 = 4.00821782732936239552e-06, <span class='comment'>/* 3ED0CFCA 86E65239 */</span></td></tr>
|
|
<tr><td class="num" id="LN154">154</td><td class="line">Q5 = -2.01099218183624371326e-07; <span class='comment'>/* BE8AFDB7 6E09C32D */</span></td></tr>
|
|
<tr><td class="num" id="LN155">155</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN156">156</td><td class="line"><span class='keyword'>double</span> expm1(<span class='keyword'>double</span> x)</td></tr>
|
|
<tr><td class="num" id="LN157">157</td><td class="line">{</td></tr>
|
|
<tr><td class="num" id="LN158">158</td><td class="line"> <span class='keyword'>double</span> y,hi,lo,c,t,e,hxs,hfx,r1;</td></tr>
|
|
<tr><td class="num" id="LN159">159</td><td class="line"> sword k,xsb;</td></tr>
|
|
<tr><td class="num" id="LN160">160</td><td class="line"> uword hx;</td></tr>
|
|
<tr><td class="num" id="LN161">161</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN162">162</td><td class="line"> c = 0.0;</td></tr>
|
|
<tr><td class="num" id="LN163">163</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN164">164</td><td class="line"> <span class='macro'>GET_HIGH_WORD(hx,x)<span class='expansion'>do { ieee_double_shape_type gh_u; gh_u.value = (x); (hx) = gh_u<br>.parts.msw; } while (0)</span></span>; <span class='comment'>/* high word of x */</span></td></tr>
|
|
<tr><td class="num" id="LN165">165</td><td class="line"> xsb = hx&0x80000000; <span class='comment'>/* sign bit of x */</span></td></tr>
|
|
<tr><td class="num" id="LN166">166</td><td class="line"> <span class='keyword'>if</span>(xsb==0) y=<span class="mrange">x</span>;</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="EndPath" class="msg msgEvent" style="margin-left:16ex">Value stored to 'y' is never read</div></td></tr>
|
|
<tr><td class="num" id="LN167">167</td><td class="line"> <span class='keyword'>else</span> y= -x; <span class='comment'>/* y = |x| */</span></td></tr>
|
|
<tr><td class="num" id="LN168">168</td><td class="line"> hx &= 0x7fffffff; <span class='comment'>/* high word of |x| */</span></td></tr>
|
|
<tr><td class="num" id="LN169">169</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN170">170</td><td class="line"> <span class='comment'>/* filter out huge and non-finite argument */</span></td></tr>
|
|
<tr><td class="num" id="LN171">171</td><td class="line"> <span class='keyword'>if</span>(hx >= 0x4043687A) { <span class='comment'>/* if |x|>=56*ln2 */</span></td></tr>
|
|
<tr><td class="num" id="LN172">172</td><td class="line"> <span class='keyword'>if</span>(hx >= 0x40862E42) { <span class='comment'>/* if |x|>=709.78... */</span></td></tr>
|
|
<tr><td class="num" id="LN173">173</td><td class="line"> <span class='keyword'>if</span>(hx>=0x7ff00000) {</td></tr>
|
|
<tr><td class="num" id="LN174">174</td><td class="line"> uword low;</td></tr>
|
|
<tr><td class="num" id="LN175">175</td><td class="line"> <span class='macro'>GET_LOW_WORD(low,x)<span class='expansion'>do { ieee_double_shape_type gl_u; gl_u.value = (x); (low) = gl_u<br>.parts.lsw; } while (0)</span></span>;</td></tr>
|
|
<tr><td class="num" id="LN176">176</td><td class="line"> <span class='keyword'>if</span>(((hx&0xfffff)|low)!=0)</td></tr>
|
|
<tr><td class="num" id="LN177">177</td><td class="line"> <span class='keyword'>return</span> x+x; <span class='comment'>/* NaN */</span></td></tr>
|
|
<tr><td class="num" id="LN178">178</td><td class="line"> <span class='keyword'>else</span> <span class='keyword'>return</span> (xsb==0)? x:-1.0;<span class='comment'>/* exp(+-inf)={inf,-1} */</span></td></tr>
|
|
<tr><td class="num" id="LN179">179</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN180">180</td><td class="line"> <span class='keyword'>if</span>(x > o_threshold) <span class='keyword'>return</span> huge*huge; <span class='comment'>/* overflow */</span></td></tr>
|
|
<tr><td class="num" id="LN181">181</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN182">182</td><td class="line"> <span class='keyword'>if</span>(xsb!=0) { <span class='comment'>/* x < -56*ln2, return -1.0 with inexact */</span></td></tr>
|
|
<tr><td class="num" id="LN183">183</td><td class="line"> <span class='keyword'>if</span>(x+tiny<0.0) <span class='comment'>/* raise inexact */</span></td></tr>
|
|
<tr><td class="num" id="LN184">184</td><td class="line"> <span class='keyword'>return</span> tiny-one; <span class='comment'>/* return -1 */</span></td></tr>
|
|
<tr><td class="num" id="LN185">185</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN186">186</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN187">187</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN188">188</td><td class="line"> <span class='comment'>/* argument reduction */</span></td></tr>
|
|
<tr><td class="num" id="LN189">189</td><td class="line"> <span class='keyword'>if</span>(hx > 0x3fd62e42) { <span class='comment'>/* if |x| > 0.5 ln2 */</span></td></tr>
|
|
<tr><td class="num" id="LN190">190</td><td class="line"> <span class='keyword'>if</span>(hx < 0x3FF0A2B2) { <span class='comment'>/* and |x| < 1.5 ln2 */</span></td></tr>
|
|
<tr><td class="num" id="LN191">191</td><td class="line"> <span class='keyword'>if</span>(xsb==0)</td></tr>
|
|
<tr><td class="num" id="LN192">192</td><td class="line"> {</td></tr>
|
|
<tr><td class="num" id="LN193">193</td><td class="line"> hi = x - ln2_hi;</td></tr>
|
|
<tr><td class="num" id="LN194">194</td><td class="line"> lo = ln2_lo;</td></tr>
|
|
<tr><td class="num" id="LN195">195</td><td class="line"> k = 1;</td></tr>
|
|
<tr><td class="num" id="LN196">196</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN197">197</td><td class="line"> <span class='keyword'>else</span></td></tr>
|
|
<tr><td class="num" id="LN198">198</td><td class="line"> {</td></tr>
|
|
<tr><td class="num" id="LN199">199</td><td class="line"> hi = x + ln2_hi;</td></tr>
|
|
<tr><td class="num" id="LN200">200</td><td class="line"> lo = -ln2_lo;</td></tr>
|
|
<tr><td class="num" id="LN201">201</td><td class="line"> k = -1;</td></tr>
|
|
<tr><td class="num" id="LN202">202</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN203">203</td><td class="line"> } <span class='keyword'>else</span> {</td></tr>
|
|
<tr><td class="num" id="LN204">204</td><td class="line"> k = (sword)(invln2*x+((xsb==0)?0.5:-0.5));</td></tr>
|
|
<tr><td class="num" id="LN205">205</td><td class="line"> t = k;</td></tr>
|
|
<tr><td class="num" id="LN206">206</td><td class="line"> hi = x - t*ln2_hi; <span class='comment'>/* t*ln2_hi is exact here */</span></td></tr>
|
|
<tr><td class="num" id="LN207">207</td><td class="line"> lo = t*ln2_lo;</td></tr>
|
|
<tr><td class="num" id="LN208">208</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN209">209</td><td class="line"> x = hi - lo;</td></tr>
|
|
<tr><td class="num" id="LN210">210</td><td class="line"> c = (hi-x)-lo;</td></tr>
|
|
<tr><td class="num" id="LN211">211</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN212">212</td><td class="line"> <span class='keyword'>else</span> <span class='keyword'>if</span>(hx < 0x3c900000) { <span class='comment'>/* when |x|<2**-54, return x */</span></td></tr>
|
|
<tr><td class="num" id="LN213">213</td><td class="line"> t = huge+x; <span class='comment'>/* return x with inexact flags when x!=0 */</span></td></tr>
|
|
<tr><td class="num" id="LN214">214</td><td class="line"> <span class='keyword'>return</span> x - (t-(huge+x));</td></tr>
|
|
<tr><td class="num" id="LN215">215</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN216">216</td><td class="line"> <span class='keyword'>else</span> k = 0;</td></tr>
|
|
<tr><td class="num" id="LN217">217</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN218">218</td><td class="line"> <span class='comment'>/* x is now in primary range */</span></td></tr>
|
|
<tr><td class="num" id="LN219">219</td><td class="line"> hfx = 0.5*x;</td></tr>
|
|
<tr><td class="num" id="LN220">220</td><td class="line"> hxs = x*hfx;</td></tr>
|
|
<tr><td class="num" id="LN221">221</td><td class="line"> r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));</td></tr>
|
|
<tr><td class="num" id="LN222">222</td><td class="line"> t = 3.0-r1*hfx;</td></tr>
|
|
<tr><td class="num" id="LN223">223</td><td class="line"> e = hxs*((r1-t)/(6.0 - x*t));</td></tr>
|
|
<tr><td class="num" id="LN224">224</td><td class="line"> <span class='keyword'>if</span>(k==0) <span class='keyword'>return</span> x - (x*e-hxs); <span class='comment'>/* c is 0 */</span></td></tr>
|
|
<tr><td class="num" id="LN225">225</td><td class="line"> <span class='keyword'>else</span> {</td></tr>
|
|
<tr><td class="num" id="LN226">226</td><td class="line"> e = (x*(e-c)-c);</td></tr>
|
|
<tr><td class="num" id="LN227">227</td><td class="line"> e -= hxs;</td></tr>
|
|
<tr><td class="num" id="LN228">228</td><td class="line"> <span class='keyword'>if</span>(k== -1) <span class='keyword'>return</span> 0.5*(x-e)-0.5;</td></tr>
|
|
<tr><td class="num" id="LN229">229</td><td class="line"> <span class='keyword'>if</span>(k==1) {</td></tr>
|
|
<tr><td class="num" id="LN230">230</td><td class="line"> <span class='keyword'>if</span>(x < -0.25) <span class='keyword'>return</span> -2.0*(e-(x+0.5));</td></tr>
|
|
<tr><td class="num" id="LN231">231</td><td class="line"> <span class='keyword'>else</span> <span class='keyword'>return</span> one+2.0*(x-e);</td></tr>
|
|
<tr><td class="num" id="LN232">232</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN233">233</td><td class="line"> <span class='keyword'>if</span> (k <= -2 || k>56) { <span class='comment'>/* suffice to return exp(x)-1 */</span></td></tr>
|
|
<tr><td class="num" id="LN234">234</td><td class="line"> uword hy;</td></tr>
|
|
<tr><td class="num" id="LN235">235</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN236">236</td><td class="line"> y = one-(e-x);</td></tr>
|
|
<tr><td class="num" id="LN237">237</td><td class="line"> <span class='macro'>GET_HIGH_WORD(hy,y)<span class='expansion'>do { ieee_double_shape_type gh_u; gh_u.value = (y); (hy) = gh_u<br>.parts.msw; } while (0)</span></span>;</td></tr>
|
|
<tr><td class="num" id="LN238">238</td><td class="line"> <span class='macro'>SET_HIGH_WORD(y, hy + (k<<20))<span class='expansion'>do { ieee_double_shape_type sh_u; sh_u.value = (y); sh_u.parts<br>.msw = (hy + (k<<20)); (y) = sh_u.value; } while (0)</span></span>; <span class='comment'>/* add k to y's exponent */</span></td></tr>
|
|
<tr><td class="num" id="LN239">239</td><td class="line"> <span class='keyword'>return</span> y-one;</td></tr>
|
|
<tr><td class="num" id="LN240">240</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN241">241</td><td class="line"> t = one;</td></tr>
|
|
<tr><td class="num" id="LN242">242</td><td class="line"> <span class='keyword'>if</span>(k<20) {</td></tr>
|
|
<tr><td class="num" id="LN243">243</td><td class="line"> uword hy;</td></tr>
|
|
<tr><td class="num" id="LN244">244</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN245">245</td><td class="line"> <span class='macro'>SET_HIGH_WORD(t, 0x3ff00000 - (0x200000>>k))<span class='expansion'>do { ieee_double_shape_type sh_u; sh_u.value = (t); sh_u.parts<br>.msw = (0x3ff00000 - (0x200000>>k)); (t) = sh_u.value; }<br> while (0)</span></span>; <span class='comment'>/* t=1-2^-k */</span></td></tr>
|
|
<tr><td class="num" id="LN246">246</td><td class="line"> y = t-(e-x);</td></tr>
|
|
<tr><td class="num" id="LN247">247</td><td class="line"> <span class='macro'>GET_HIGH_WORD(hy, y)<span class='expansion'>do { ieee_double_shape_type gh_u; gh_u.value = (y); (hy) = gh_u<br>.parts.msw; } while (0)</span></span>;</td></tr>
|
|
<tr><td class="num" id="LN248">248</td><td class="line"> <span class='macro'>SET_HIGH_WORD(y, hy + (k<<20))<span class='expansion'>do { ieee_double_shape_type sh_u; sh_u.value = (y); sh_u.parts<br>.msw = (hy + (k<<20)); (y) = sh_u.value; } while (0)</span></span>; <span class='comment'>/* add k to y's exponent */</span></td></tr>
|
|
<tr><td class="num" id="LN249">249</td><td class="line"> } <span class='keyword'>else</span> {</td></tr>
|
|
<tr><td class="num" id="LN250">250</td><td class="line"> uword hy;</td></tr>
|
|
<tr><td class="num" id="LN251">251</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN252">252</td><td class="line"> <span class='macro'>SET_HIGH_WORD(t, (0x3ff-k)<<20)<span class='expansion'>do { ieee_double_shape_type sh_u; sh_u.value = (t); sh_u.parts<br>.msw = ((0x3ff-k)<<20); (t) = sh_u.value; } while (0)</span></span>; <span class='comment'>/* 2^-k */</span></td></tr>
|
|
<tr><td class="num" id="LN253">253</td><td class="line"> y = x-(e+t);</td></tr>
|
|
<tr><td class="num" id="LN254">254</td><td class="line"> y += one;</td></tr>
|
|
<tr><td class="num" id="LN255">255</td><td class="line"> <span class='macro'>GET_HIGH_WORD(hy, y)<span class='expansion'>do { ieee_double_shape_type gh_u; gh_u.value = (y); (hy) = gh_u<br>.parts.msw; } while (0)</span></span>;</td></tr>
|
|
<tr><td class="num" id="LN256">256</td><td class="line"> <span class='macro'>SET_HIGH_WORD(y, hy + (k<<20))<span class='expansion'>do { ieee_double_shape_type sh_u; sh_u.value = (y); sh_u.parts<br>.msw = (hy + (k<<20)); (y) = sh_u.value; } while (0)</span></span>; <span class='comment'>/* add k to y's exponent */</span></td></tr>
|
|
<tr><td class="num" id="LN257">257</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN258">258</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN259">259</td><td class="line"> <span class='keyword'>return</span> y;</td></tr>
|
|
<tr><td class="num" id="LN260">260</td><td class="line">}</td></tr>
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</table></body></html>
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