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 <span id="projectnumber">1.6.2</span>
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<a href="asin_8c.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* @(#)e_asin.c 1.3 95/01/18 */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">/*</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * Copyright (c) 2015-2017 Carsten Sonne Larsen <cs@innolan.dk></span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * All rights reserved.</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> *</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * Redistribution and use in source and binary forms, with or without</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * modification, are permitted provided that the following conditions</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * are met:</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * 1. Redistributions of source code must retain the above copyright</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * notice, this list of conditions and the following disclaimer.</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * 2. Redistributions in binary form must reproduce the above copyright</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * notice, this list of conditions and the following disclaimer in the</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * documentation and/or other materials provided with the distribution.</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> *</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> *</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> * The origin source code can be obtained from:</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> * http://www.netlib.org/fdlibm/e_asin.c</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> * </span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> */</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">/*</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> * ====================================================</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> *</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> * Developed at SunSoft, a Sun Microsystems, Inc. business.</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> * Permission to use, copy, modify, and distribute this</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> * software is freely granted, provided that this notice</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> * is preserved.</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> * ====================================================</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> *</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> */</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#</span><span class="preprocessor">include</span> <a class="code" href="real_2prim_8h.html">"prim.h"</a></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#</span><span class="preprocessor">include</span> <a class="code" href="math_8h.html" title="Functions in math library for handling real numbers. ">"math.h"</a></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b"> 48</a></span> <a class="code" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a> = 1.00000000000000000000e+00, <span class="comment">/* 0x3FF00000, 0x00000000 */</span></div><div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="asin_8c.html#acbd466133274923cc0785707fbdeea9a"> 49</a></span> <a class="code" href="asin_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a> = 1.000e+300,</div><div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="asin_8c.html#afb7fbaa5c31ee6a1e6a06cfafc7b4722"> 50</a></span> <a class="code" href="asin_8c.html#afb7fbaa5c31ee6a1e6a06cfafc7b4722">pio2_hi</a> = 1.57079632679489655800e+00, <span class="comment">/* 0x3FF921FB, 0x54442D18 */</span></div><div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653"> 51</a></span> <a class="code" href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653">pio2_lo</a> = 6.12323399573676603587e-17, <span class="comment">/* 0x3C91A626, 0x33145C07 */</span></div><div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="asin_8c.html#a5528ffbaf3180832340ec41a3affb60b"> 52</a></span> <a class="code" href="asin_8c.html#a5528ffbaf3180832340ec41a3affb60b">pio4_hi</a> = 7.85398163397448278999e-01, <span class="comment">/* 0x3FE921FB, 0x54442D18 */</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">/* coefficient for R(x^2) */</span></div><div class="line"><a name="l00054"></a><span class="lineno"><a class="line" href="asin_8c.html#a598e19e166b484e6636a5d2af921178e"> 54</a></span> <a class="code" href="asin_8c.html#a598e19e166b484e6636a5d2af921178e">pS0</a> = 1.66666666666666657415e-01, <span class="comment">/* 0x3FC55555, 0x55555555 */</span></div><div class="line"><a name="l00055"></a><span class="lineno"><a class="line" href="asin_8c.html#acabe4dc2fe4ed1ed9dd22dbfcc2a4a55"> 55</a></span> <a class="code" href="asin_8c.html#acabe4dc2fe4ed1ed9dd22dbfcc2a4a55">pS1</a> = -3.25565818622400915405e-01, <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */</span></div><div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="asin_8c.html#a06b3d163437b4041ac67f2cda1cc445d"> 56</a></span> <a class="code" href="asin_8c.html#a06b3d163437b4041ac67f2cda1cc445d">pS2</a> = 2.01212532134862925881e-01, <span class="comment">/* 0x3FC9C155, 0x0E884455 */</span></div><div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="asin_8c.html#aaa40612ec8cdb54cc05424e143875d6c"> 57</a></span> <a class="code" href="asin_8c.html#aaa40612ec8cdb54cc05424e143875d6c">pS3</a> = -4.00555345006794114027e-02, <span class="comment">/* 0xBFA48228, 0xB5688F3B */</span></div><div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="asin_8c.html#a4579924a5221b8718a2d834daea875c1"> 58</a></span> <a class="code" href="asin_8c.html#a4579924a5221b8718a2d834daea875c1">pS4</a> = 7.91534994289814532176e-04, <span class="comment">/* 0x3F49EFE0, 0x7501B288 */</span></div><div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="asin_8c.html#a6fe8ee6da9411328a5a01cc83cb5cafe"> 59</a></span> <a class="code" href="asin_8c.html#a6fe8ee6da9411328a5a01cc83cb5cafe">pS5</a> = 3.47933107596021167570e-05, <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */</span></div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="asin_8c.html#afb566f87cc1d33877c7a4a30d0abc813"> 60</a></span> <a class="code" href="asin_8c.html#afb566f87cc1d33877c7a4a30d0abc813">qS1</a> = -2.40339491173441421878e+00, <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */</span></div><div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="asin_8c.html#aed4dd3ffd10de8fb416b8066211fc27d"> 61</a></span> <a class="code" href="asin_8c.html#aed4dd3ffd10de8fb416b8066211fc27d">qS2</a> = 2.02094576023350569471e+00, <span class="comment">/* 0x40002AE5, 0x9C598AC8 */</span></div><div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="asin_8c.html#abb1b119c3d6cf33d182bd48155186510"> 62</a></span> <a class="code" href="asin_8c.html#abb1b119c3d6cf33d182bd48155186510">qS3</a> = -6.88283971605453293030e-01, <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */</span></div><div class="line"><a name="l00063"></a><span class="lineno"><a class="line" href="asin_8c.html#ae6b27b738027128ae51618db2d6e4c81"> 63</a></span> <a class="code" href="asin_8c.html#ae6b27b738027128ae51618db2d6e4c81">qS4</a> = 7.70381505559019352791e-02; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">/**</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> * @brief Inverse trigonometric sine function.</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> * @version 1.3</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> * @date 95/01/18</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> * @details</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> * <pre></span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> * Method :</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> * we approximate asin(x) on [0,0.5] by</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> * asin(x) = x + x*x^2*R(x^2)</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> * where</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> * R(x^2) is a rational approximation of (asin(x)-x)/x^3</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> * and its remez error is bounded by</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> *</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> * For x in [0.5,1]</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> * asin(x) = pi/2-2*asin(sqrt((1-x)/2))</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> * then for x>0.98</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> * asin(x) = pi/2 - 2*(s+s*z*R(z))</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> * For x<=0.98, let pio4_hi = pio2_hi/2, then</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> * f = hi part of s;</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> * and</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> * asin(x) = pi/2 - 2*(s+s*z*R(z))</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> *</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> * Special cases:</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> * if x is NaN, return x itself;</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> * if |x|>1, return NaN with invalid signal.</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> *</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> * </pre></span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> * @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> * @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> * to use, copy, modify, and distribute this software is freely granted,</span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> * provided that this notice is preserved.</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> */</span></div><div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="asin_8c.html#aa9528d92a3ae44ad6484da0774604454"> 104</a></span> <span class="keywordtype">double</span> <a class="code" href="asin_8c.html#aa9528d92a3ae44ad6484da0774604454">asin</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> {</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordtype">double</span> t,w,p,q,c,r,s;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <a class="code" href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a> hx,ix;</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <a class="code" href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a>(hx,x);</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  ix = hx&0x7fffffff;</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">if</span>(ix>= 0x3ff00000) { <span class="comment">/* |x|>= 1 */</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="code" href="real_2prim_8h.html#a6e60fe0e0f9f8801507e15fe2d893751">uword</a> lx;</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a>(lx,x);</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">if</span>(((ix-0x3ff00000)|lx)==0)</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">/* asin(1)=+-pi/2 with inexact */</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">return</span> x*<a class="code" href="asin_8c.html#afb7fbaa5c31ee6a1e6a06cfafc7b4722">pio2_hi</a>+x*<a class="code" href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653">pio2_lo</a>;</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">return</span> (x-x)/(x-x); <span class="comment">/* asin(|x|>1) is NaN */</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (ix<0x3fe00000) { <span class="comment">/* |x|<0.5 */</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">if</span>(ix<0x3e400000) { <span class="comment">/* if |x| < 2**-27 */</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">if</span>(<a class="code" href="asin_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a>+x><a class="code" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>) {</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">return</span> x;<span class="comment">/* return x with inexact if x!=0*/</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  t = 0;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  t = x*x;</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  p = t*(<a class="code" href="asin_8c.html#a598e19e166b484e6636a5d2af921178e">pS0</a>+t*(<a class="code" href="asin_8c.html#acabe4dc2fe4ed1ed9dd22dbfcc2a4a55">pS1</a>+t*(<a class="code" href="asin_8c.html#a06b3d163437b4041ac67f2cda1cc445d">pS2</a>+t*(<a class="code" href="asin_8c.html#aaa40612ec8cdb54cc05424e143875d6c">pS3</a>+t*(<a class="code" href="asin_8c.html#a4579924a5221b8718a2d834daea875c1">pS4</a>+t*<a class="code" href="asin_8c.html#a6fe8ee6da9411328a5a01cc83cb5cafe">pS5</a>)))));</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  q = <a class="code" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>+t*(<a class="code" href="asin_8c.html#afb566f87cc1d33877c7a4a30d0abc813">qS1</a>+t*(<a class="code" href="asin_8c.html#aed4dd3ffd10de8fb416b8066211fc27d">qS2</a>+t*(<a class="code" href="asin_8c.html#abb1b119c3d6cf33d182bd48155186510">qS3</a>+t*<a class="code" href="asin_8c.html#ae6b27b738027128ae51618db2d6e4c81">qS4</a>)));</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  w = p/q;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">return</span> x+x*w;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  }</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">/* 1> |x|>= 0.5 */</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  w = <a class="code" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>-fabs(x);</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  t = w*0.5;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  p = t*(<a class="code" href="asin_8c.html#a598e19e166b484e6636a5d2af921178e">pS0</a>+t*(<a class="code" href="asin_8c.html#acabe4dc2fe4ed1ed9dd22dbfcc2a4a55">pS1</a>+t*(<a class="code" href="asin_8c.html#a06b3d163437b4041ac67f2cda1cc445d">pS2</a>+t*(<a class="code" href="asin_8c.html#aaa40612ec8cdb54cc05424e143875d6c">pS3</a>+t*(<a class="code" href="asin_8c.html#a4579924a5221b8718a2d834daea875c1">pS4</a>+t*<a class="code" href="asin_8c.html#a6fe8ee6da9411328a5a01cc83cb5cafe">pS5</a>)))));</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  q = <a class="code" href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a>+t*(<a class="code" href="asin_8c.html#afb566f87cc1d33877c7a4a30d0abc813">qS1</a>+t*(<a class="code" href="asin_8c.html#aed4dd3ffd10de8fb416b8066211fc27d">qS2</a>+t*(<a class="code" href="asin_8c.html#abb1b119c3d6cf33d182bd48155186510">qS3</a>+t*<a class="code" href="asin_8c.html#ae6b27b738027128ae51618db2d6e4c81">qS4</a>)));</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  s = <a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">sqrt</a><a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">(</a>t<a class="code" href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">)</a>;</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">if</span>(ix>=0x3FEF3333) { <span class="comment">/* if |x| > 0.975 */</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  w = p/q;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  t = <a class="code" href="asin_8c.html#afb7fbaa5c31ee6a1e6a06cfafc7b4722">pio2_hi</a>-(2.0*(s+s*w)-<a class="code" href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653">pio2_lo</a>);</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  w = s;</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <a class="code" href="real_2prim_8h.html#af4776e0b45c17da39fce08bc7b211a03">SET_LOW_WORD</a>(w,0);</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  c = (t-w*w)/(s+w);</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  r = p/q;</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  p = 2.0*s*r-(<a class="code" href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653">pio2_lo</a>-2.0*c);</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  q = <a class="code" href="asin_8c.html#a5528ffbaf3180832340ec41a3affb60b">pio4_hi</a>-2.0*w;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  t = <a class="code" href="asin_8c.html#a5528ffbaf3180832340ec41a3affb60b">pio4_hi</a>-(p-q);</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">if</span>(hx>0) <span class="keywordflow">return</span> t;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> -t;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> }</div><div class="ttc" id="asin_8c_html_acabe4dc2fe4ed1ed9dd22dbfcc2a4a55"><div class="ttname"><a href="asin_8c.html#acabe4dc2fe4ed1ed9dd22dbfcc2a4a55">pS1</a></div><div class="ttdeci">static const double pS1</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00055">asin.c:55</a></div></div>
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<div class="ttc" id="sqrt_8c_html_ab87521a75ef827a85807f89a6c10629a"><div class="ttname"><a href="sqrt_8c.html#ab87521a75ef827a85807f89a6c10629a">sqrt</a></div><div class="ttdeci">double sqrt(double x)</div><div class="ttdoc">Square root function. </div><div class="ttdef"><b>Definition:</b> <a href="sqrt_8c_source.html#l00127">sqrt.c:127</a></div></div>
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<div class="ttc" id="asin_8c_html_aa9528d92a3ae44ad6484da0774604454"><div class="ttname"><a href="asin_8c.html#aa9528d92a3ae44ad6484da0774604454">asin</a></div><div class="ttdeci">double asin(double x)</div><div class="ttdoc">Inverse trigonometric sine function. </div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00104">asin.c:104</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae62ee08d06ab4cc06d61dc1246b73195"><div class="ttname"><a href="real_2prim_8h.html#ae62ee08d06ab4cc06d61dc1246b73195">GET_HIGH_WORD</a></div><div class="ttdeci">#define GET_HIGH_WORD(i, d)</div><div class="ttdoc">Get the more significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00165">prim.h:165</a></div></div>
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<div class="ttc" id="asin_8c_html_acbd466133274923cc0785707fbdeea9a"><div class="ttname"><a href="asin_8c.html#acbd466133274923cc0785707fbdeea9a">huge</a></div><div class="ttdeci">static const double huge</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00049">asin.c:49</a></div></div>
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<div class="ttc" id="asin_8c_html_a4579924a5221b8718a2d834daea875c1"><div class="ttname"><a href="asin_8c.html#a4579924a5221b8718a2d834daea875c1">pS4</a></div><div class="ttdeci">static const double pS4</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00058">asin.c:58</a></div></div>
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<div class="ttc" id="asin_8c_html_a6fe8ee6da9411328a5a01cc83cb5cafe"><div class="ttname"><a href="asin_8c.html#a6fe8ee6da9411328a5a01cc83cb5cafe">pS5</a></div><div class="ttdeci">static const double pS5</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00059">asin.c:59</a></div></div>
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<div class="ttc" id="asin_8c_html_afb7fbaa5c31ee6a1e6a06cfafc7b4722"><div class="ttname"><a href="asin_8c.html#afb7fbaa5c31ee6a1e6a06cfafc7b4722">pio2_hi</a></div><div class="ttdeci">static const double pio2_hi</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00050">asin.c:50</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_adee023704c856ea8f310e8e3fd765a22"><div class="ttname"><a href="real_2prim_8h.html#adee023704c856ea8f310e8e3fd765a22">GET_LOW_WORD</a></div><div class="ttdeci">#define GET_LOW_WORD(i, d)</div><div class="ttdoc">Get the less significant 32 bit int from a double. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00176">prim.h:176</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_ae91287c8a5f73a8a22a100f50dc4de77"><div class="ttname"><a href="real_2prim_8h.html#ae91287c8a5f73a8a22a100f50dc4de77">sword</a></div><div class="ttdeci">signed int sword</div><div class="ttdoc">32 bit signed integer. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00107">prim.h:107</a></div></div>
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<div class="ttc" id="asin_8c_html_afb566f87cc1d33877c7a4a30d0abc813"><div class="ttname"><a href="asin_8c.html#afb566f87cc1d33877c7a4a30d0abc813">qS1</a></div><div class="ttdeci">static const double qS1</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00060">asin.c:60</a></div></div>
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<div class="ttc" id="asin_8c_html_a5528ffbaf3180832340ec41a3affb60b"><div class="ttname"><a href="asin_8c.html#a5528ffbaf3180832340ec41a3affb60b">pio4_hi</a></div><div class="ttdeci">static const double pio4_hi</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00052">asin.c:52</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_a6e60fe0e0f9f8801507e15fe2d893751"><div class="ttname"><a href="real_2prim_8h.html#a6e60fe0e0f9f8801507e15fe2d893751">uword</a></div><div class="ttdeci">unsigned int uword</div><div class="ttdoc">32 bit unsigned integer. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00101">prim.h:101</a></div></div>
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<div class="ttc" id="asin_8c_html_a598e19e166b484e6636a5d2af921178e"><div class="ttname"><a href="asin_8c.html#a598e19e166b484e6636a5d2af921178e">pS0</a></div><div class="ttdeci">static const double pS0</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00054">asin.c:54</a></div></div>
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<div class="ttc" id="asin_8c_html_a06b3d163437b4041ac67f2cda1cc445d"><div class="ttname"><a href="asin_8c.html#a06b3d163437b4041ac67f2cda1cc445d">pS2</a></div><div class="ttdeci">static const double pS2</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00056">asin.c:56</a></div></div>
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<div class="ttc" id="asin_8c_html_ae6b27b738027128ae51618db2d6e4c81"><div class="ttname"><a href="asin_8c.html#ae6b27b738027128ae51618db2d6e4c81">qS4</a></div><div class="ttdeci">static const double qS4</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00063">asin.c:63</a></div></div>
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<div class="ttc" id="asin_8c_html_ada85e349d35971b32c8ea4238881ff8b"><div class="ttname"><a href="asin_8c.html#ada85e349d35971b32c8ea4238881ff8b">one</a></div><div class="ttdeci">static const double one</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00048">asin.c:48</a></div></div>
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<div class="ttc" id="asin_8c_html_aaa40612ec8cdb54cc05424e143875d6c"><div class="ttname"><a href="asin_8c.html#aaa40612ec8cdb54cc05424e143875d6c">pS3</a></div><div class="ttdeci">static const double pS3</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00057">asin.c:57</a></div></div>
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<div class="ttc" id="asin_8c_html_a4c04e4a8938bd8c06dbcc267cf2d1653"><div class="ttname"><a href="asin_8c.html#a4c04e4a8938bd8c06dbcc267cf2d1653">pio2_lo</a></div><div class="ttdeci">static const double pio2_lo</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00051">asin.c:51</a></div></div>
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<div class="ttc" id="real_2prim_8h_html_af4776e0b45c17da39fce08bc7b211a03"><div class="ttname"><a href="real_2prim_8h.html#af4776e0b45c17da39fce08bc7b211a03">SET_LOW_WORD</a></div><div class="ttdeci">#define SET_LOW_WORD(d, v)</div><div class="ttdoc">Set the less significant 32 bits of a double from an int. </div><div class="ttdef"><b>Definition:</b> <a href="real_2prim_8h_source.html#l00211">prim.h:211</a></div></div>
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<div class="ttc" id="asin_8c_html_aed4dd3ffd10de8fb416b8066211fc27d"><div class="ttname"><a href="asin_8c.html#aed4dd3ffd10de8fb416b8066211fc27d">qS2</a></div><div class="ttdeci">static const double qS2</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00061">asin.c:61</a></div></div>
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<div class="ttc" id="asin_8c_html_abb1b119c3d6cf33d182bd48155186510"><div class="ttname"><a href="asin_8c.html#abb1b119c3d6cf33d182bd48155186510">qS3</a></div><div class="ttdeci">static const double qS3</div><div class="ttdef"><b>Definition:</b> <a href="asin_8c_source.html#l00062">asin.c:62</a></div></div>
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