mirror of https://gitlab.com/rnger/amath
468 lines
55 KiB
HTML
468 lines
55 KiB
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<!-- BUGDESC The left operand of '-' is a garbage value -->
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<!-- BUGTYPE Result of operation is garbage or undefined -->
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<!-- BUGCATEGORY Logic error -->
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<!-- BUGFILE /home/carsten/amath/lib/real/kremp2.c -->
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<!-- FILENAME kremp2.c -->
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<!-- FUNCTIONNAME __kernel_rem_pio2 -->
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<!-- ISSUEHASHCONTENTOFLINEINCONTEXT a395a6f4121103612025bf7df4711fbc -->
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<!-- BUGLINE 329 -->
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<!-- BUGCOLUMN 19 -->
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<!-- BUGPATHLENGTH 23 -->
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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/kremp2.c</td></tr>
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<tr><td class="rowname">Location:</td><td><a href="#EndPath">line 329, column 19</a></td></tr>
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<tr><td class="rowname">Description:</td><td>The left operand of '-' is a garbage value</td></tr>
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</table>
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<!-- REPORTSUMMARYEXTRA -->
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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'>/* @(#)k_rem_pio2.c 1.3 95/01/18 */</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/k_rem_pio2.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) 1993 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'>* Developed at SunSoft, a Sun Microsystems, Inc. business.</span></td></tr>
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<tr><td class="num" id="LN37">37</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="LN38">38</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="LN39">39</td><td class="line"> <span class='comment'>* is preserved.</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'>/*</span></td></tr>
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<tr><td class="num" id="LN47">47</td><td class="line"> <span class='comment'>* Constants:</span></td></tr>
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<tr><td class="num" id="LN48">48</td><td class="line"> <span class='comment'>* The hexadecimal values are the intended ones for the following</span></td></tr>
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<tr><td class="num" id="LN49">49</td><td class="line"> <span class='comment'>* constants. The decimal values may be used, provided that the</span></td></tr>
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<tr><td class="num" id="LN50">50</td><td class="line"> <span class='comment'>* compiler will convert from decimal to binary accurately enough</span></td></tr>
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<tr><td class="num" id="LN51">51</td><td class="line"> <span class='comment'>* to produce the hexadecimal values shown.</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"> </td></tr>
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<tr><td class="num" id="LN54">54</td><td class="line"><span class='keyword'>static</span> <span class='keyword'>const</span> <span class='keyword'>int</span> init_jk[] = {2,3,4,6}; <span class='comment'>/* initial value for jk */</span></td></tr>
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<tr><td class="num" id="LN55">55</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN56">56</td><td class="line"><span class='keyword'>static</span> <span class='keyword'>const</span> <span class='keyword'>double</span> PIo2[] = {</td></tr>
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<tr><td class="num" id="LN57">57</td><td class="line"> 1.57079625129699707031e+00, <span class='comment'>/* 0x3FF921FB, 0x40000000 */</span></td></tr>
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<tr><td class="num" id="LN58">58</td><td class="line"> 7.54978941586159635335e-08, <span class='comment'>/* 0x3E74442D, 0x00000000 */</span></td></tr>
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<tr><td class="num" id="LN59">59</td><td class="line"> 5.39030252995776476554e-15, <span class='comment'>/* 0x3CF84698, 0x80000000 */</span></td></tr>
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<tr><td class="num" id="LN60">60</td><td class="line"> 3.28200341580791294123e-22, <span class='comment'>/* 0x3B78CC51, 0x60000000 */</span></td></tr>
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<tr><td class="num" id="LN61">61</td><td class="line"> 1.27065575308067607349e-29, <span class='comment'>/* 0x39F01B83, 0x80000000 */</span></td></tr>
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<tr><td class="num" id="LN62">62</td><td class="line"> 1.22933308981111328932e-36, <span class='comment'>/* 0x387A2520, 0x40000000 */</span></td></tr>
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<tr><td class="num" id="LN63">63</td><td class="line"> 2.73370053816464559624e-44, <span class='comment'>/* 0x36E38222, 0x80000000 */</span></td></tr>
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<tr><td class="num" id="LN64">64</td><td class="line"> 2.16741683877804819444e-51, <span class='comment'>/* 0x3569F31D, 0x00000000 */</span></td></tr>
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<tr><td class="num" id="LN65">65</td><td class="line">};</td></tr>
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<tr><td class="num" id="LN66">66</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN67">67</td><td class="line"><span class='keyword'>static</span> <span class='keyword'>const</span> <span class='keyword'>double</span></td></tr>
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<tr><td class="num" id="LN68">68</td><td class="line">zero = 0.0,</td></tr>
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<tr><td class="num" id="LN69">69</td><td class="line">one = 1.0,</td></tr>
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<tr><td class="num" id="LN70">70</td><td class="line">two24 = 1.67772160000000000000e+07, <span class='comment'>/* 0x41700000, 0x00000000 */</span></td></tr>
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<tr><td class="num" id="LN71">71</td><td class="line">twon24 = 5.96046447753906250000e-08; <span class='comment'>/* 0x3E700000, 0x00000000 */</span></td></tr>
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<tr><td class="num" id="LN72">72</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN73">73</td><td class="line"><span class='comment'>/**</span></td></tr>
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<tr><td class="num" id="LN74">74</td><td class="line"> <span class='comment'>* @brief Kernel reduction function.</span></td></tr>
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<tr><td class="num" id="LN75">75</td><td class="line"> <span class='comment'>* @version 1.4</span></td></tr>
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<tr><td class="num" id="LN76">76</td><td class="line"> <span class='comment'>* @date 96/03/07</span></td></tr>
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<tr><td class="num" id="LN77">77</td><td class="line"> <span class='comment'>* @details</span></td></tr>
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<tr><td class="num" id="LN78">78</td><td class="line"> <span class='comment'>* <pre></span></td></tr>
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<tr><td class="num" id="LN79">79</td><td class="line"> <span class='comment'>* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)</span></td></tr>
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<tr><td class="num" id="LN80">80</td><td class="line"> <span class='comment'>* double x[],y[]; int e0,nx,prec; int ipio2[];</span></td></tr>
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<tr><td class="num" id="LN81">81</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN82">82</td><td class="line"> <span class='comment'>* __kernel_rem_pio2 return the last three digits of N with</span></td></tr>
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<tr><td class="num" id="LN83">83</td><td class="line"> <span class='comment'>* y = x - N*pi/2</span></td></tr>
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<tr><td class="num" id="LN84">84</td><td class="line"> <span class='comment'>* so that |y| < pi/2.</span></td></tr>
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<tr><td class="num" id="LN85">85</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN86">86</td><td class="line"> <span class='comment'>* The method is to compute the integer (mod 8) and fraction parts of</span></td></tr>
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<tr><td class="num" id="LN87">87</td><td class="line"> <span class='comment'>* (2/pi)*x without doing the full multiplication. In general we</span></td></tr>
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<tr><td class="num" id="LN88">88</td><td class="line"> <span class='comment'>* skip the part of the product that are known to be a huge integer (</span></td></tr>
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<tr><td class="num" id="LN89">89</td><td class="line"> <span class='comment'>* more accurately, = 0 mod 8 ). Thus the number of operations are</span></td></tr>
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<tr><td class="num" id="LN90">90</td><td class="line"> <span class='comment'>* independent of the exponent of the input.</span></td></tr>
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<tr><td class="num" id="LN91">91</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN92">92</td><td class="line"> <span class='comment'>* (2/pi) is represented by an array of 24-bit integers in ipio2[].</span></td></tr>
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<tr><td class="num" id="LN93">93</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN94">94</td><td class="line"> <span class='comment'>* Input parameters:</span></td></tr>
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<tr><td class="num" id="LN95">95</td><td class="line"> <span class='comment'>* x[] The input value (must be positive) is broken into nx</span></td></tr>
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<tr><td class="num" id="LN96">96</td><td class="line"> <span class='comment'>* pieces of 24-bit integers in double precision format.</span></td></tr>
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<tr><td class="num" id="LN97">97</td><td class="line"> <span class='comment'>* x[i] will be the i-th 24 bit of x. The scaled exponent</span></td></tr>
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<tr><td class="num" id="LN98">98</td><td class="line"> <span class='comment'>* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0</span></td></tr>
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<tr><td class="num" id="LN99">99</td><td class="line"> <span class='comment'>* match x's up to 24 bits.</span></td></tr>
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<tr><td class="num" id="LN100">100</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN101">101</td><td class="line"> <span class='comment'>* Example of breaking a double positive z into x[0]+x[1]+x[2]:</span></td></tr>
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<tr><td class="num" id="LN102">102</td><td class="line"> <span class='comment'>* e0 = ilogb(z)-23</span></td></tr>
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<tr><td class="num" id="LN103">103</td><td class="line"> <span class='comment'>* z = scalbn(z,-e0)</span></td></tr>
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<tr><td class="num" id="LN104">104</td><td class="line"> <span class='comment'>* for i = 0,1,2</span></td></tr>
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<tr><td class="num" id="LN105">105</td><td class="line"> <span class='comment'>* x[i] = floor(z)</span></td></tr>
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<tr><td class="num" id="LN106">106</td><td class="line"> <span class='comment'>* z = (z-x[i])*2**24</span></td></tr>
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<tr><td class="num" id="LN107">107</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN108">108</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN109">109</td><td class="line"> <span class='comment'>* y[] ouput result in an array of double precision numbers.</span></td></tr>
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<tr><td class="num" id="LN110">110</td><td class="line"> <span class='comment'>* The dimension of y[] is:</span></td></tr>
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<tr><td class="num" id="LN111">111</td><td class="line"> <span class='comment'>* 24-bit precision 1</span></td></tr>
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<tr><td class="num" id="LN112">112</td><td class="line"> <span class='comment'>* 53-bit precision 2</span></td></tr>
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<tr><td class="num" id="LN113">113</td><td class="line"> <span class='comment'>* 64-bit precision 2</span></td></tr>
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<tr><td class="num" id="LN114">114</td><td class="line"> <span class='comment'>* 113-bit precision 3</span></td></tr>
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<tr><td class="num" id="LN115">115</td><td class="line"> <span class='comment'>* The actual value is the sum of them. Thus for 113-bit</span></td></tr>
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<tr><td class="num" id="LN116">116</td><td class="line"> <span class='comment'>* precison, one may have to do something like:</span></td></tr>
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<tr><td class="num" id="LN117">117</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN118">118</td><td class="line"> <span class='comment'>* long double t,w,r_head, r_tail;</span></td></tr>
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<tr><td class="num" id="LN119">119</td><td class="line"> <span class='comment'>* t = (long double)y[2] + (long double)y[1];</span></td></tr>
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<tr><td class="num" id="LN120">120</td><td class="line"> <span class='comment'>* w = (long double)y[0];</span></td></tr>
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|
<tr><td class="num" id="LN121">121</td><td class="line"> <span class='comment'>* r_head = t+w;</span></td></tr>
|
|
<tr><td class="num" id="LN122">122</td><td class="line"> <span class='comment'>* r_tail = w - (r_head - t);</span></td></tr>
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|
<tr><td class="num" id="LN123">123</td><td class="line"> <span class='comment'>*</span></td></tr>
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|
<tr><td class="num" id="LN124">124</td><td class="line"> <span class='comment'>* e0 The exponent of x[0]</span></td></tr>
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|
<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'>* nx dimension of x[]</span></td></tr>
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<tr><td class="num" id="LN127">127</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN128">128</td><td class="line"> <span class='comment'>* prec an integer indicating the precision:</span></td></tr>
|
|
<tr><td class="num" id="LN129">129</td><td class="line"> <span class='comment'>* 0 24 bits (single)</span></td></tr>
|
|
<tr><td class="num" id="LN130">130</td><td class="line"> <span class='comment'>* 1 53 bits (double)</span></td></tr>
|
|
<tr><td class="num" id="LN131">131</td><td class="line"> <span class='comment'>* 2 64 bits (extended)</span></td></tr>
|
|
<tr><td class="num" id="LN132">132</td><td class="line"> <span class='comment'>* 3 113 bits (quad)</span></td></tr>
|
|
<tr><td class="num" id="LN133">133</td><td class="line"> <span class='comment'>*</span></td></tr>
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<tr><td class="num" id="LN134">134</td><td class="line"> <span class='comment'>* ipio2[]</span></td></tr>
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|
<tr><td class="num" id="LN135">135</td><td class="line"> <span class='comment'>* integer array, contains the (24*i)-th to (24*i+23)-th</span></td></tr>
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<tr><td class="num" id="LN136">136</td><td class="line"> <span class='comment'>* bit of 2/pi after binary point. The corresponding</span></td></tr>
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|
<tr><td class="num" id="LN137">137</td><td class="line"> <span class='comment'>* floating value is</span></td></tr>
|
|
<tr><td class="num" id="LN138">138</td><td class="line"> <span class='comment'>*</span></td></tr>
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|
<tr><td class="num" id="LN139">139</td><td class="line"> <span class='comment'>* ipio2[i] * 2^(-24(i+1)).</span></td></tr>
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|
<tr><td class="num" id="LN140">140</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN141">141</td><td class="line"> <span class='comment'>* External function:</span></td></tr>
|
|
<tr><td class="num" id="LN142">142</td><td class="line"> <span class='comment'>* double scalbn(), floor();</span></td></tr>
|
|
<tr><td class="num" id="LN143">143</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN144">144</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN145">145</td><td class="line"> <span class='comment'>* Here is the description of some local variables:</span></td></tr>
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|
<tr><td class="num" id="LN146">146</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN147">147</td><td class="line"> <span class='comment'>* jk jk+1 is the initial number of terms of ipio2[] needed</span></td></tr>
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<tr><td class="num" id="LN148">148</td><td class="line"> <span class='comment'>* in the computation. The recommended value is 2,3,4,</span></td></tr>
|
|
<tr><td class="num" id="LN149">149</td><td class="line"> <span class='comment'>* 6 for single, double, extended,and quad.</span></td></tr>
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|
<tr><td class="num" id="LN150">150</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN151">151</td><td class="line"> <span class='comment'>* jz local integer variable indicating the number of</span></td></tr>
|
|
<tr><td class="num" id="LN152">152</td><td class="line"> <span class='comment'>* terms of ipio2[] used.</span></td></tr>
|
|
<tr><td class="num" id="LN153">153</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN154">154</td><td class="line"> <span class='comment'>* jx nx - 1</span></td></tr>
|
|
<tr><td class="num" id="LN155">155</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN156">156</td><td class="line"> <span class='comment'>* jv index for pointing to the suitable ipio2[] for the</span></td></tr>
|
|
<tr><td class="num" id="LN157">157</td><td class="line"> <span class='comment'>* computation. In general, we want</span></td></tr>
|
|
<tr><td class="num" id="LN158">158</td><td class="line"> <span class='comment'>* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8</span></td></tr>
|
|
<tr><td class="num" id="LN159">159</td><td class="line"> <span class='comment'>* is an integer. Thus</span></td></tr>
|
|
<tr><td class="num" id="LN160">160</td><td class="line"> <span class='comment'>* e0-3-24*jv >= 0 or (e0-3)/24 >= jv</span></td></tr>
|
|
<tr><td class="num" id="LN161">161</td><td class="line"> <span class='comment'>* Hence jv = max(0,(e0-3)/24).</span></td></tr>
|
|
<tr><td class="num" id="LN162">162</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN163">163</td><td class="line"> <span class='comment'>* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.</span></td></tr>
|
|
<tr><td class="num" id="LN164">164</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN165">165</td><td class="line"> <span class='comment'>* q[] double array with integral value, representing the</span></td></tr>
|
|
<tr><td class="num" id="LN166">166</td><td class="line"> <span class='comment'>* 24-bits chunk of the product of x and 2/pi.</span></td></tr>
|
|
<tr><td class="num" id="LN167">167</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN168">168</td><td class="line"> <span class='comment'>* q0 the corresponding exponent of q[0]. Note that the</span></td></tr>
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|
<tr><td class="num" id="LN169">169</td><td class="line"> <span class='comment'>* exponent for q[i] would be q0-24*i.</span></td></tr>
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|
<tr><td class="num" id="LN170">170</td><td class="line"> <span class='comment'>*</span></td></tr>
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|
<tr><td class="num" id="LN171">171</td><td class="line"> <span class='comment'>* PIo2[] double precision array, obtained by cutting pi/2</span></td></tr>
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|
<tr><td class="num" id="LN172">172</td><td class="line"> <span class='comment'>* into 24 bits chunks.</span></td></tr>
|
|
<tr><td class="num" id="LN173">173</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN174">174</td><td class="line"> <span class='comment'>* f[] ipio2[] in floating point</span></td></tr>
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|
<tr><td class="num" id="LN175">175</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN176">176</td><td class="line"> <span class='comment'>* iq[] integer array by breaking up q[] in 24-bits chunk.</span></td></tr>
|
|
<tr><td class="num" id="LN177">177</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN178">178</td><td class="line"> <span class='comment'>* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]</span></td></tr>
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|
<tr><td class="num" id="LN179">179</td><td class="line"> <span class='comment'>*</span></td></tr>
|
|
<tr><td class="num" id="LN180">180</td><td class="line"> <span class='comment'>* ih integer. If >0 it indicates q[] is >= 0.5, hence</span></td></tr>
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<tr><td class="num" id="LN181">181</td><td class="line"> <span class='comment'>* it also indicates the *sign* of the result.</span></td></tr>
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|
<tr><td class="num" id="LN182">182</td><td class="line"> <span class='comment'>*</span></td></tr>
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|
<tr><td class="num" id="LN183">183</td><td class="line"> <span class='comment'>* </pre></span></td></tr>
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|
<tr><td class="num" id="LN184">184</td><td class="line"> <span class='comment'>* @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span></td></tr>
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<tr><td class="num" id="LN185">185</td><td class="line"> <span class='comment'>* @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission</span></td></tr>
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<tr><td class="num" id="LN186">186</td><td class="line"> <span class='comment'>* to use, copy, modify, and distribute this software is freely granted,</span></td></tr>
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<tr><td class="num" id="LN187">187</td><td class="line"> <span class='comment'>* provided that this notice is preserved.</span></td></tr>
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<tr><td class="num" id="LN188">188</td><td class="line"> <span class='comment'>*/</span></td></tr>
|
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<tr><td class="num" id="LN189">189</td><td class="line"> </td></tr>
|
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<tr><td class="num" id="LN190">190</td><td class="line"><span class='keyword'>int</span> __kernel_rem_pio2(<span class='keyword'>double</span> *x, <span class='keyword'>double</span> *y, <span class='keyword'>int</span> e0, <span class='keyword'>int</span> nx, <span class='keyword'>int</span> prec, <span class='keyword'>const</span> <span class='keyword'>int</span> *ipio2)</td></tr>
|
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<tr><td class="num" id="LN191">191</td><td class="line">{</td></tr>
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|
<tr><td class="num" id="LN192">192</td><td class="line"> <span class='keyword'>int</span> jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;</td></tr>
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<tr><td class="num" id="LN193">193</td><td class="line"> <span class='keyword'>double</span> z,fw,f[20],fq[20],q[20];</td></tr>
|
|
<tr><td class="num" id="LN194">194</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN195">195</td><td class="line"> <span class='comment'>/* initialize jk*/</span></td></tr>
|
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<tr><td class="num" id="LN196">196</td><td class="line"> jk = init_jk[prec];</td></tr>
|
|
<tr><td class="num" id="LN197">197</td><td class="line"> jp = jk;</td></tr>
|
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<tr><td class="num" id="LN198">198</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN199">199</td><td class="line"> <span class='comment'>/* determine jx,jv,q0, note that 3>q0 */</span></td></tr>
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<tr><td class="num" id="LN200">200</td><td class="line"> jx = nx-1;</td></tr>
|
|
<tr><td class="num" id="LN201">201</td><td class="line"> jv = (e0-3)/24;</td></tr>
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<tr><td class="num" id="LN202">202</td><td class="line"> <span class='keyword'>if</span>(<span class="mrange">jv<0</span>) jv=0;</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path1" class="msg msgEvent" style="margin-left:8ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">1</div></td><td>Assuming 'jv' is >= 0</td><td><div class="PathNav"><a href="#Path2" title="Next event (2)">→</a></div></td></tr></table></div></td></tr>
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|
<tr><td class="num"></td><td class="line"><div id="Path2" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">2</div></td><td><div class="PathNav"><a href="#Path1" title="Previous event (1)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path3" title="Next event (3)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN203">203</td><td class="line"> q0 = e0-24*(jv+1);</td></tr>
|
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<tr><td class="num" id="LN204">204</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN205">205</td><td class="line"> <span class='comment'>/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */</span></td></tr>
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<tr><td class="num" id="LN206">206</td><td class="line"> j = jv-jx;</td></tr>
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<tr><td class="num" id="LN207">207</td><td class="line"> m = jx+jk;</td></tr>
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<tr><td class="num" id="LN208">208</td><td class="line"> <span class='keyword'>for</span>(i=0; <span class="mrange">i<=m</span>; i++,j++) f[i] = (j<0)? zero : (<span class='keyword'>double</span>) ipio2[j];</td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path3" class="msg msgEvent" style="margin-left:14ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">3</div></td><td><div class="PathNav"><a href="#Path2" title="Previous event (2)">←</a></div></td></td><td>Assuming 'i' is > 'm'</td><td><div class="PathNav"><a href="#Path4" title="Next event (4)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path4" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">4</div></td><td><div class="PathNav"><a href="#Path3" title="Previous event (3)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 211</td><td><div class="PathNav"><a href="#Path5" title="Next event (5)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN209">209</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN210">210</td><td class="line"> <span class='comment'>/* compute q[0],q[1],...q[jk] */</span></td></tr>
|
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<tr><td class="num" id="LN211">211</td><td class="line"> <span class='keyword'>for</span> (i=0; <span class="mrange">i<=jk</span>; i++) {</td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path5" class="msg msgEvent" style="margin-left:15ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">5</div></td><td><div class="PathNav"><a href="#Path4" title="Previous event (4)">←</a></div></td></td><td>Assuming 'i' is > 'jk'</td><td><div class="PathNav"><a href="#Path6" title="Next event (6)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path6" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">6</div></td><td><div class="PathNav"><a href="#Path5" title="Previous event (5)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 216</td><td><div class="PathNav"><a href="#Path7" title="Next event (7)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN212">212</td><td class="line"> <span class='keyword'>for</span>(j=0,fw=0.0; j<=jx; j++) fw += x[j]*f[jx+i-j];</td></tr>
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<tr><td class="num" id="LN213">213</td><td class="line"> q[i] = fw;</td></tr>
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<tr><td class="num" id="LN214">214</td><td class="line"> }</td></tr>
|
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<tr><td class="num" id="LN215">215</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN216">216</td><td class="line"> jz = jk;</td></tr>
|
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<tr><td class="num" id="LN217">217</td><td class="line">recompute:</td></tr>
|
|
<tr><td class="num" id="LN218">218</td><td class="line"> <span class='comment'>/* distill q[] into iq[] reversingly */</span></td></tr>
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<tr><td class="num" id="LN219">219</td><td class="line"> <span class='keyword'>for</span>(i=0,j=jz,z=q[jz]; j>0; i++,j--) {</td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path7" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">7</div></td><td><div class="PathNav"><a href="#Path6" title="Previous event (6)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 226</td><td><div class="PathNav"><a href="#Path8" title="Next event (8)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN220">220</td><td class="line"> fw = (<span class='keyword'>double</span>)((<span class='keyword'>int</span>)(twon24* z));</td></tr>
|
|
<tr><td class="num" id="LN221">221</td><td class="line"> iq[i] = (<span class='keyword'>int</span>)(z-two24*fw);</td></tr>
|
|
<tr><td class="num" id="LN222">222</td><td class="line"> z = q[j-1]+fw;</td></tr>
|
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<tr><td class="num" id="LN223">223</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN224">224</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN225">225</td><td class="line"> <span class='comment'>/* compute n */</span></td></tr>
|
|
<tr><td class="num" id="LN226">226</td><td class="line"> z = scalbn(z,q0); <span class='comment'>/* actual value of z */</span></td></tr>
|
|
<tr><td class="num" id="LN227">227</td><td class="line"> z -= 8.0*floor(z*0.125); <span class='comment'>/* trim off integer >= 8 */</span></td></tr>
|
|
<tr><td class="num" id="LN228">228</td><td class="line"> n = (<span class='keyword'>int</span>) z;</td></tr>
|
|
<tr><td class="num" id="LN229">229</td><td class="line"> z -= (<span class='keyword'>double</span>)n;</td></tr>
|
|
<tr><td class="num" id="LN230">230</td><td class="line"> ih = 0;</td></tr>
|
|
<tr><td class="num" id="LN231">231</td><td class="line"> <span class='keyword'>if</span>(<span class="mrange">q0>0</span>) { <span class='comment'>/* need iq[jz-1] to determine n */</span></td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path8" class="msg msgEvent" style="margin-left:8ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">8</div></td><td><div class="PathNav"><a href="#Path7" title="Previous event (7)">←</a></div></td></td><td>Assuming 'q0' is <= 0</td><td><div class="PathNav"><a href="#Path9" title="Next event (9)">→</a></div></td></tr></table></div></td></tr>
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|
<tr><td class="num"></td><td class="line"><div id="Path9" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">9</div></td><td><div class="PathNav"><a href="#Path8" title="Previous event (8)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path10" title="Next event (10)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN232">232</td><td class="line"> i = (iq[jz-1]>>(24-q0));</td></tr>
|
|
<tr><td class="num" id="LN233">233</td><td class="line"> n += i;</td></tr>
|
|
<tr><td class="num" id="LN234">234</td><td class="line"> iq[jz-1] -= i<<(24-q0);</td></tr>
|
|
<tr><td class="num" id="LN235">235</td><td class="line"> ih = iq[jz-1]>>(23-q0);</td></tr>
|
|
<tr><td class="num" id="LN236">236</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN237">237</td><td class="line"> <span class='keyword'>else</span> <span class='keyword'>if</span>(<span class="mrange">q0==0</span>) ih = iq[jz-1]>>23;</td></tr>
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|
<tr><td class="num"></td><td class="line"><div id="Path10" class="msg msgEvent" style="margin-left:13ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">10</div></td><td><div class="PathNav"><a href="#Path9" title="Previous event (9)">←</a></div></td></td><td>Assuming 'q0' is not equal to 0</td><td><div class="PathNav"><a href="#Path11" title="Next event (11)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path11" class="msg msgControl" style="margin-left:10ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">11</div></td><td><div class="PathNav"><a href="#Path10" title="Previous event (10)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path12" title="Next event (12)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN238">238</td><td class="line"> <span class='keyword'>else</span> <span class='keyword'>if</span>(z>=0.5) ih=2;</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path12" class="msg msgControl" style="margin-left:10ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">12</div></td><td><div class="PathNav"><a href="#Path11" title="Previous event (11)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path13" title="Next event (13)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN239">239</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN240">240</td><td class="line"> <span class='keyword'>if</span>(ih>0) { <span class='comment'>/* q > 0.5 */</span></td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path13" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">13</div></td><td><div class="PathNav"><a href="#Path12" title="Previous event (12)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path14" title="Next event (14)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN241">241</td><td class="line"> n += 1;</td></tr>
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<tr><td class="num" id="LN242">242</td><td class="line"> carry = 0;</td></tr>
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<tr><td class="num" id="LN243">243</td><td class="line"> <span class='keyword'>for</span>(i=0; i<jz ; i++) { <span class='comment'>/* compute 1-q */</span></td></tr>
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<tr><td class="num" id="LN244">244</td><td class="line"> j = iq[i];</td></tr>
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<tr><td class="num" id="LN245">245</td><td class="line"> <span class='keyword'>if</span>(carry==0) {</td></tr>
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<tr><td class="num" id="LN246">246</td><td class="line"> <span class='keyword'>if</span>(j!=0) {</td></tr>
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<tr><td class="num" id="LN247">247</td><td class="line"> carry = 1;</td></tr>
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<tr><td class="num" id="LN248">248</td><td class="line"> iq[i] = 0x1000000- j;</td></tr>
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<tr><td class="num" id="LN249">249</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN250">250</td><td class="line"> } <span class='keyword'>else</span> iq[i] = 0xffffff - j;</td></tr>
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<tr><td class="num" id="LN251">251</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN252">252</td><td class="line"> <span class='keyword'>if</span>(q0>0) { <span class='comment'>/* rare case: chance is 1 in 12 */</span></td></tr>
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<tr><td class="num" id="LN253">253</td><td class="line"> <span class='keyword'>switch</span>(q0) {</td></tr>
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<tr><td class="num" id="LN254">254</td><td class="line"> <span class='keyword'>case</span> 1:</td></tr>
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<tr><td class="num" id="LN255">255</td><td class="line"> iq[jz-1] &= 0x7fffff;</td></tr>
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<tr><td class="num" id="LN256">256</td><td class="line"> <span class='keyword'>break</span>;</td></tr>
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<tr><td class="num" id="LN257">257</td><td class="line"> <span class='keyword'>case</span> 2:</td></tr>
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<tr><td class="num" id="LN258">258</td><td class="line"> iq[jz-1] &= 0x3fffff;</td></tr>
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<tr><td class="num" id="LN259">259</td><td class="line"> <span class='keyword'>break</span>;</td></tr>
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<tr><td class="num" id="LN260">260</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN261">261</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN262">262</td><td class="line"> <span class='keyword'>if</span>(ih==2) {</td></tr>
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<tr><td class="num" id="LN263">263</td><td class="line"> z = one - z;</td></tr>
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<tr><td class="num" id="LN264">264</td><td class="line"> <span class='keyword'>if</span>(carry!=0) z -= scalbn(one,q0);</td></tr>
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<tr><td class="num" id="LN265">265</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN266">266</td><td class="line"> }</td></tr>
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<tr><td class="num" id="LN267">267</td><td class="line"> </td></tr>
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<tr><td class="num" id="LN268">268</td><td class="line"> <span class='comment'>/* check if recomputation is needed */</span></td></tr>
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<tr><td class="num" id="LN269">269</td><td class="line"> <span class='keyword'>if</span>(z==zero) {</td></tr>
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<tr><td class="num"></td><td class="line"><div id="Path14" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">14</div></td><td><div class="PathNav"><a href="#Path13" title="Previous event (13)">←</a></div></td></td><td>Taking false branch</td><td><div class="PathNav"><a href="#Path15" title="Next event (15)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN270">270</td><td class="line"> j = 0;</td></tr>
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<tr><td class="num" id="LN271">271</td><td class="line"> <span class='keyword'>for</span> (i=jz-1; i>=jk; i--) j |= iq[i];</td></tr>
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<tr><td class="num" id="LN272">272</td><td class="line"> <span class='keyword'>if</span>(j==0) { <span class='comment'>/* need recomputation */</span></td></tr>
|
|
<tr><td class="num" id="LN273">273</td><td class="line"> <span class='keyword'>for</span>(k=1; iq[jk-k]==0; k++); <span class='comment'>/* k = no. of terms needed */</span></td></tr>
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<tr><td class="num" id="LN274">274</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN275">275</td><td class="line"> <span class='keyword'>for</span>(i=jz+1; i<=jz+k; i++) { <span class='comment'>/* add q[jz+1] to q[jz+k] */</span></td></tr>
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<tr><td class="num" id="LN276">276</td><td class="line"> f[jx+i] = (<span class='keyword'>double</span>) ipio2[jv+i];</td></tr>
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|
<tr><td class="num" id="LN277">277</td><td class="line"> <span class='keyword'>for</span>(j=0,fw=0.0; j<=jx; j++) fw += x[j]*f[jx+i-j];</td></tr>
|
|
<tr><td class="num" id="LN278">278</td><td class="line"> q[i] = fw;</td></tr>
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|
<tr><td class="num" id="LN279">279</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN280">280</td><td class="line"> jz += k;</td></tr>
|
|
<tr><td class="num" id="LN281">281</td><td class="line"> <span class='keyword'>goto</span> recompute;</td></tr>
|
|
<tr><td class="num" id="LN282">282</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN283">283</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN284">284</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN285">285</td><td class="line"> <span class='comment'>/* chop off zero terms */</span></td></tr>
|
|
<tr><td class="num" id="LN286">286</td><td class="line"> <span class='keyword'>if</span>(z==0.0) {</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path15" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">15</div></td><td><div class="PathNav"><a href="#Path14" title="Previous event (14)">←</a></div></td></td><td>Taking true branch</td><td><div class="PathNav"><a href="#Path16" title="Next event (16)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN287">287</td><td class="line"> jz -= 1;</td></tr>
|
|
<tr><td class="num" id="LN288">288</td><td class="line"> q0 -= 24;</td></tr>
|
|
<tr><td class="num" id="LN289">289</td><td class="line"> <span class='keyword'>while</span>(iq[jz]==0) {</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path16" class="msg msgControl" style="margin-left:9ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">16</div></td><td><div class="PathNav"><a href="#Path15" title="Previous event (15)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 305</td><td><div class="PathNav"><a href="#Path17" title="Next event (17)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN290">290</td><td class="line"> jz--;</td></tr>
|
|
<tr><td class="num" id="LN291">291</td><td class="line"> q0-=24;</td></tr>
|
|
<tr><td class="num" id="LN292">292</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN293">293</td><td class="line"> } <span class='keyword'>else</span> { <span class='comment'>/* break z into 24-bit if necessary */</span></td></tr>
|
|
<tr><td class="num" id="LN294">294</td><td class="line"> z = scalbn(z,-q0);</td></tr>
|
|
<tr><td class="num" id="LN295">295</td><td class="line"> <span class='keyword'>if</span>(z>=two24) {</td></tr>
|
|
<tr><td class="num" id="LN296">296</td><td class="line"> fw = (<span class='keyword'>double</span>)((<span class='keyword'>int</span>)(twon24*z));</td></tr>
|
|
<tr><td class="num" id="LN297">297</td><td class="line"> iq[jz] = (<span class='keyword'>int</span>)(z-two24*fw);</td></tr>
|
|
<tr><td class="num" id="LN298">298</td><td class="line"> jz += 1;</td></tr>
|
|
<tr><td class="num" id="LN299">299</td><td class="line"> q0 += 24;</td></tr>
|
|
<tr><td class="num" id="LN300">300</td><td class="line"> iq[jz] = (<span class='keyword'>int</span>) fw;</td></tr>
|
|
<tr><td class="num" id="LN301">301</td><td class="line"> } <span class='keyword'>else</span> iq[jz] = (<span class='keyword'>int</span>) z ;</td></tr>
|
|
<tr><td class="num" id="LN302">302</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN303">303</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN304">304</td><td class="line"> <span class='comment'>/* convert integer "bit" chunk to floating-point value */</span></td></tr>
|
|
<tr><td class="num" id="LN305">305</td><td class="line"> fw = scalbn(one,q0);</td></tr>
|
|
<tr><td class="num" id="LN306">306</td><td class="line"> <span class='keyword'>for</span>(i=jz; <span class="mrange">i>=0</span>; i--) {</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path17" class="msg msgEvent" style="margin-left:15ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">17</div></td><td><div class="PathNav"><a href="#Path16" title="Previous event (16)">←</a></div></td></td><td>Assuming 'i' is < 0</td><td><div class="PathNav"><a href="#Path18" title="Next event (18)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path18" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">18</div></td><td><div class="PathNav"><a href="#Path17" title="Previous event (17)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 312</td><td><div class="PathNav"><a href="#Path19" title="Next event (19)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN307">307</td><td class="line"> q[i] = fw*(<span class='keyword'>double</span>)iq[i];</td></tr>
|
|
<tr><td class="num" id="LN308">308</td><td class="line"> fw*=twon24;</td></tr>
|
|
<tr><td class="num" id="LN309">309</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN310">310</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN311">311</td><td class="line"> <span class='comment'>/* compute PIo2[0,...,jp]*q[jz,...,0] */</span></td></tr>
|
|
<tr><td class="num" id="LN312">312</td><td class="line"> <span class='keyword'>for</span>(i=jz; i>=0; i--) {</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path19" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">19</div></td><td><div class="PathNav"><a href="#Path18" title="Previous event (18)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 318</td><td><div class="PathNav"><a href="#Path20" title="Next event (20)">→</a></div></td></tr></table></div></td></tr>
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<tr><td class="num" id="LN313">313</td><td class="line"> <span class='keyword'>for</span>(fw=0.0,k=0; k<=jp&&k<=jz-i; k++) fw += PIo2[k]*q[i+k];</td></tr>
|
|
<tr><td class="num" id="LN314">314</td><td class="line"> fq[jz-i] = fw;</td></tr>
|
|
<tr><td class="num" id="LN315">315</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN316">316</td><td class="line"> </td></tr>
|
|
<tr><td class="num" id="LN317">317</td><td class="line"> <span class='comment'>/* compress fq[] into y[] */</span></td></tr>
|
|
<tr><td class="num" id="LN318">318</td><td class="line"> <span class='keyword'>switch</span>(prec) {</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path20" class="msg msgControl" style="margin-left:5ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">20</div></td><td><div class="PathNav"><a href="#Path19" title="Previous event (19)">←</a></div></td></td><td>Control jumps to 'case 2:' at line 325</td><td><div class="PathNav"><a href="#Path21" title="Next event (21)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN319">319</td><td class="line"> <span class='keyword'>case</span> 0:</td></tr>
|
|
<tr><td class="num" id="LN320">320</td><td class="line"> fw = 0.0;</td></tr>
|
|
<tr><td class="num" id="LN321">321</td><td class="line"> <span class='keyword'>for</span> (i=jz; i>=0; i--) fw += fq[i];</td></tr>
|
|
<tr><td class="num" id="LN322">322</td><td class="line"> y[0] = (ih==0)? fw: -fw;</td></tr>
|
|
<tr><td class="num" id="LN323">323</td><td class="line"> <span class='keyword'>break</span>;</td></tr>
|
|
<tr><td class="num" id="LN324">324</td><td class="line"> <span class='keyword'>case</span> 1:</td></tr>
|
|
<tr><td class="num" id="LN325">325</td><td class="line"> <span class='keyword'>case</span> 2:</td></tr>
|
|
<tr><td class="num" id="LN326">326</td><td class="line"> fw = 0.0;</td></tr>
|
|
<tr><td class="num" id="LN327">327</td><td class="line"> <span class='keyword'>for</span> (i=jz; i>=0; i--) fw += fq[i];</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path21" class="msg msgControl" style="margin-left:9ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">21</div></td><td><div class="PathNav"><a href="#Path20" title="Previous event (20)">←</a></div></td></td><td>Loop condition is false. Execution continues on line 328</td><td><div class="PathNav"><a href="#Path22" title="Next event (22)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN328">328</td><td class="line"> y[0] = (ih==0)? fw: -fw;</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="Path22" class="msg msgControl" style="margin-left:16ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexControl">22</div></td><td><div class="PathNav"><a href="#Path21" title="Previous event (21)">←</a></div></td></td><td>'?' condition is true</td><td><div class="PathNav"><a href="#EndPath" title="Next event (23)">→</a></div></td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN329">329</td><td class="line"> fw = <span class="mrange">fq[0]</span>-fw;</td></tr>
|
|
<tr><td class="num"></td><td class="line"><div id="EndPath" class="msg msgEvent" style="margin-left:19ex"><table class="msgT"><tr><td valign="top"><div class="PathIndex PathIndexEvent">23</div></td><td><div class="PathNav"><a href="#Path22" title="Previous event (22)">←</a></div></td></td><td>The left operand of '-' is a garbage value</td></tr></table></div></td></tr>
|
|
<tr><td class="num" id="LN330">330</td><td class="line"> <span class='keyword'>for</span> (i=1; i<=jz; i++) fw += fq[i];</td></tr>
|
|
<tr><td class="num" id="LN331">331</td><td class="line"> y[1] = (ih==0)? fw: -fw;</td></tr>
|
|
<tr><td class="num" id="LN332">332</td><td class="line"> <span class='keyword'>break</span>;</td></tr>
|
|
<tr><td class="num" id="LN333">333</td><td class="line"> <span class='keyword'>case</span> 3: <span class='comment'>/* painful */</span></td></tr>
|
|
<tr><td class="num" id="LN334">334</td><td class="line"> <span class='keyword'>for</span> (i=jz; i>0; i--) {</td></tr>
|
|
<tr><td class="num" id="LN335">335</td><td class="line"> fw = fq[i-1]+fq[i];</td></tr>
|
|
<tr><td class="num" id="LN336">336</td><td class="line"> fq[i] += fq[i-1]-fw;</td></tr>
|
|
<tr><td class="num" id="LN337">337</td><td class="line"> fq[i-1] = fw;</td></tr>
|
|
<tr><td class="num" id="LN338">338</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN339">339</td><td class="line"> <span class='keyword'>for</span> (i=jz; i>1; i--) {</td></tr>
|
|
<tr><td class="num" id="LN340">340</td><td class="line"> fw = fq[i-1]+fq[i];</td></tr>
|
|
<tr><td class="num" id="LN341">341</td><td class="line"> fq[i] += fq[i-1]-fw;</td></tr>
|
|
<tr><td class="num" id="LN342">342</td><td class="line"> fq[i-1] = fw;</td></tr>
|
|
<tr><td class="num" id="LN343">343</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN344">344</td><td class="line"> <span class='keyword'>for</span> (fw=0.0,i=jz; i>=2; i--) fw += fq[i];</td></tr>
|
|
<tr><td class="num" id="LN345">345</td><td class="line"> <span class='keyword'>if</span>(ih==0) {</td></tr>
|
|
<tr><td class="num" id="LN346">346</td><td class="line"> y[0] = fq[0];</td></tr>
|
|
<tr><td class="num" id="LN347">347</td><td class="line"> y[1] = fq[1];</td></tr>
|
|
<tr><td class="num" id="LN348">348</td><td class="line"> y[2] = fw;</td></tr>
|
|
<tr><td class="num" id="LN349">349</td><td class="line"> } <span class='keyword'>else</span> {</td></tr>
|
|
<tr><td class="num" id="LN350">350</td><td class="line"> y[0] = -fq[0];</td></tr>
|
|
<tr><td class="num" id="LN351">351</td><td class="line"> y[1] = -fq[1];</td></tr>
|
|
<tr><td class="num" id="LN352">352</td><td class="line"> y[2] = -fw;</td></tr>
|
|
<tr><td class="num" id="LN353">353</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN354">354</td><td class="line"> }</td></tr>
|
|
<tr><td class="num" id="LN355">355</td><td class="line"> <span class='keyword'>return</span> n&7;</td></tr>
|
|
<tr><td class="num" id="LN356">356</td><td class="line">}</td></tr>
|
|
</table></body></html>
|