<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source to the Rust file `/home/mrh/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.1.4/src/math/j0.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>j0.rs.html -- source</title><link rel="stylesheet" type="text/css" href="../../../normalize.css"><link rel="stylesheet" type="text/css" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../../dark.css"><link rel="stylesheet" type="text/css" href="../../../light.css" id="themeStyle"><script src="../../../storage.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="shortcut icon" href="../../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../../libm/index.html'><div class='logo-container'><img src='../../../rust-logo.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../../settings.html"><img src="../../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><pre class="line-numbers"><span id="1"> 1</span>
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</pre><div class="example-wrap"><pre class="rust ">
<span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_j0.c */</span>
<span class="comment">/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/</span>
<span class="comment">/* j0(x), y0(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j0(x):
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
* 2. Reduce x to |x| since j0(x)=j0(-x), and
* for x in (0,2)
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
* for x in (2,inf)
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* as follow:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (cos(x) + sin(x))
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j0(nan)= nan
* j0(0) = 1
* j0(inf) = 0
*
* Method -- y0(x):
* 1. For x<2.
* Since
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
* We use the following function to approximate y0,
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
* where
* U(z) = u00 + u01*z + ... + u06*z^6
* V(z) = 1 + v01*z + ... + v04*z^4
* with absolute approximation error bounded by 2**-72.
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
* 2. For x>=2.
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* by the method mentioned above.
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
*/</span>
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">cos</span>, <span class="ident">fabs</span>, <span class="ident">get_high_word</span>, <span class="ident">get_low_word</span>, <span class="ident">log</span>, <span class="ident">sin</span>, <span class="ident">sqrt</span>};
<span class="kw">const</span> <span class="ident">INVSQRTPI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.64189583547756279280e-01</span>; <span class="comment">/* 0x3FE20DD7, 0x50429B6D */</span>
<span class="kw">const</span> <span class="ident">TPI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.36619772367581382433e-01</span>; <span class="comment">/* 0x3FE45F30, 0x6DC9C883 */</span>
<span class="comment">/* common method when |x|>=2 */</span>
<span class="kw">fn</span> <span class="ident">common</span>(<span class="ident">ix</span>: <span class="ident">u32</span>, <span class="ident">x</span>: <span class="ident">f64</span>, <span class="ident">y0</span>: <span class="ident">bool</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">c</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ss</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">cc</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="comment">/*
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4))
* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4))
*
* sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2)
* cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2)
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
*/</span>
<span class="ident">s</span> <span class="op">=</span> <span class="ident">sin</span>(<span class="ident">x</span>);
<span class="ident">c</span> <span class="op">=</span> <span class="ident">cos</span>(<span class="ident">x</span>);
<span class="kw">if</span> <span class="ident">y0</span> {
<span class="ident">c</span> <span class="op">=</span> <span class="op">-</span><span class="ident">c</span>;
}
<span class="ident">cc</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">+</span> <span class="ident">c</span>;
<span class="comment">/* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */</span>
<span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x7fe00000</span> {
<span class="ident">ss</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">-</span> <span class="ident">c</span>;
<span class="ident">z</span> <span class="op">=</span> <span class="op">-</span><span class="ident">cos</span>(<span class="number">2.0</span> <span class="op">*</span> <span class="ident">x</span>);
<span class="kw">if</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">c</span> <span class="op"><</span> <span class="number">0.0</span> {
<span class="ident">cc</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">/</span> <span class="ident">ss</span>;
} <span class="kw">else</span> {
<span class="ident">ss</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">/</span> <span class="ident">cc</span>;
}
<span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x48000000</span> {
<span class="kw">if</span> <span class="ident">y0</span> {
<span class="ident">ss</span> <span class="op">=</span> <span class="op">-</span><span class="ident">ss</span>;
}
<span class="ident">cc</span> <span class="op">=</span> <span class="ident">pzero</span>(<span class="ident">x</span>) <span class="op">*</span> <span class="ident">cc</span> <span class="op">-</span> <span class="ident">qzero</span>(<span class="ident">x</span>) <span class="op">*</span> <span class="ident">ss</span>;
}
}
<span class="kw">return</span> <span class="ident">INVSQRTPI</span> <span class="op">*</span> <span class="ident">cc</span> <span class="op">/</span> <span class="ident">sqrt</span>(<span class="ident">x</span>);
}
<span class="comment">/* R0/S0 on [0, 2.00] */</span>
<span class="kw">const</span> <span class="ident">R02</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.56249999999999947958e-02</span>; <span class="comment">/* 0x3F8FFFFF, 0xFFFFFFFD */</span>
<span class="kw">const</span> <span class="ident">R03</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.89979294238854721751e-04</span>; <span class="comment">/* 0xBF28E6A5, 0xB61AC6E9 */</span>
<span class="kw">const</span> <span class="ident">R04</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.82954049532700665670e-06</span>; <span class="comment">/* 0x3EBEB1D1, 0x0C503919 */</span>
<span class="kw">const</span> <span class="ident">R05</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">4.61832688532103189199e-09</span>; <span class="comment">/* 0xBE33D5E7, 0x73D63FCE */</span>
<span class="kw">const</span> <span class="ident">S01</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.56191029464890010492e-02</span>; <span class="comment">/* 0x3F8FFCE8, 0x82C8C2A4 */</span>
<span class="kw">const</span> <span class="ident">S02</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.16926784663337450260e-04</span>; <span class="comment">/* 0x3F1EA6D2, 0xDD57DBF4 */</span>
<span class="kw">const</span> <span class="ident">S03</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.13546550207318111446e-07</span>; <span class="comment">/* 0x3EA13B54, 0xCE84D5A9 */</span>
<span class="kw">const</span> <span class="ident">S04</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.16614003333790000205e-09</span>; <span class="comment">/* 0x3E1408BC, 0xF4745D8F */</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">j0</span>(<span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>;
<span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>);
<span class="ident">ix</span> <span class="kw-2">&</span><span class="op">=</span> <span class="number">0x7fffffff</span>;
<span class="comment">/* j0(+-inf)=0, j0(nan)=nan */</span>
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> {
<span class="kw">return</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>);
}
<span class="ident">x</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>);
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40000000</span> {
<span class="comment">/* |x| >= 2 */</span>
<span class="comment">/* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */</span>
<span class="kw">return</span> <span class="ident">common</span>(<span class="ident">ix</span>, <span class="ident">x</span>, <span class="bool-val">false</span>);
}
<span class="comment">/* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */</span>
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3f200000</span> {
<span class="comment">/* |x| >= 2**-13 */</span>
<span class="comment">/* up to 4ulp error close to 2 */</span>
<span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>;
<span class="ident">r</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R03</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R04</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">R05</span>)));
<span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S01</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S03</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">S04</span>)));
<span class="kw">return</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">x</span> <span class="op">/</span> <span class="number">2.0</span>) <span class="op">*</span> (<span class="number">1.0</span> <span class="op">-</span> <span class="ident">x</span> <span class="op">/</span> <span class="number">2.0</span>) <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>);
}
<span class="comment">/* 1 - x*x/4 */</span>
<span class="comment">/* prevent underflow */</span>
<span class="comment">/* inexact should be raised when x!=0, this is not done correctly */</span>
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x38000000</span> {
<span class="comment">/* |x| >= 2**-127 */</span>
<span class="ident">x</span> <span class="op">=</span> <span class="number">0.25</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>;
}
<span class="kw">return</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">x</span>;
}
<span class="kw">const</span> <span class="ident">U00</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">7.38042951086872317523e-02</span>; <span class="comment">/* 0xBFB2E4D6, 0x99CBD01F */</span>
<span class="kw">const</span> <span class="ident">U01</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.76666452509181115538e-01</span>; <span class="comment">/* 0x3FC69D01, 0x9DE9E3FC */</span>
<span class="kw">const</span> <span class="ident">U02</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.38185671945596898896e-02</span>; <span class="comment">/* 0xBF8C4CE8, 0xB16CFA97 */</span>
<span class="kw">const</span> <span class="ident">U03</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.47453432093683650238e-04</span>; <span class="comment">/* 0x3F36C54D, 0x20B29B6B */</span>
<span class="kw">const</span> <span class="ident">U04</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.81407053724364161125e-06</span>; <span class="comment">/* 0xBECFFEA7, 0x73D25CAD */</span>
<span class="kw">const</span> <span class="ident">U05</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.95590137035022920206e-08</span>; <span class="comment">/* 0x3E550057, 0x3B4EABD4 */</span>
<span class="kw">const</span> <span class="ident">U06</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.98205194132103398453e-11</span>; <span class="comment">/* 0xBDC5E43D, 0x693FB3C8 */</span>
<span class="kw">const</span> <span class="ident">V01</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.27304834834123699328e-02</span>; <span class="comment">/* 0x3F8A1270, 0x91C9C71A */</span>
<span class="kw">const</span> <span class="ident">V02</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.60068627350353253702e-05</span>; <span class="comment">/* 0x3F13ECBB, 0xF578C6C1 */</span>
<span class="kw">const</span> <span class="ident">V03</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.59150851840457805467e-07</span>; <span class="comment">/* 0x3E91642D, 0x7FF202FD */</span>
<span class="kw">const</span> <span class="ident">V04</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.41110311332675467403e-10</span>; <span class="comment">/* 0x3DFE5018, 0x3BD6D9EF */</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">y0</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">ix</span>: <span class="ident">u32</span>;
<span class="kw">let</span> <span class="ident">lx</span>: <span class="ident">u32</span>;
<span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>);
<span class="ident">lx</span> <span class="op">=</span> <span class="ident">get_low_word</span>(<span class="ident">x</span>);
<span class="comment">/* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */</span>
<span class="kw">if</span> ((<span class="ident">ix</span> <span class="op"><</span><span class="op"><</span> <span class="number">1</span>) <span class="op">|</span> <span class="ident">lx</span>) <span class="op">=</span><span class="op">=</span> <span class="number">0</span> {
<span class="kw">return</span> <span class="op">-</span><span class="number">1.0</span> <span class="op">/</span> <span class="number">0.0</span>;
}
<span class="kw">if</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> {
<span class="kw">return</span> <span class="number">0.0</span> <span class="op">/</span> <span class="number">0.0</span>;
}
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> {
<span class="kw">return</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span>;
}
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40000000</span> {
<span class="comment">/* x >= 2 */</span>
<span class="comment">/* large ulp errors near zeros: 3.958, 7.086,.. */</span>
<span class="kw">return</span> <span class="ident">common</span>(<span class="ident">ix</span>, <span class="ident">x</span>, <span class="bool-val">true</span>);
}
<span class="comment">/* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */</span>
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3e400000</span> {
<span class="comment">/* x >= 2**-27 */</span>
<span class="comment">/* large ulp error near the first zero, x ~= 0.89 */</span>
<span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>;
<span class="ident">u</span> <span class="op">=</span> <span class="ident">U00</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U01</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U03</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U04</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U05</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">U06</span>)))));
<span class="ident">v</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V01</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V03</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">V04</span>)));
<span class="kw">return</span> <span class="ident">u</span> <span class="op">/</span> <span class="ident">v</span> <span class="op">+</span> <span class="ident">TPI</span> <span class="op">*</span> (<span class="ident">j0</span>(<span class="ident">x</span>) <span class="op">*</span> <span class="ident">log</span>(<span class="ident">x</span>));
}
<span class="kw">return</span> <span class="ident">U00</span> <span class="op">+</span> <span class="ident">TPI</span> <span class="op">*</span> <span class="ident">log</span>(<span class="ident">x</span>);
}
<span class="comment">/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/</span>
<span class="kw">const</span> <span class="ident">PR8</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [inf, 8]=1/[0,0.125] */</span>
<span class="number">0.00000000000000000000e+00</span>, <span class="comment">/* 0x00000000, 0x00000000 */</span>
<span class="op">-</span><span class="number">7.03124999999900357484e-02</span>, <span class="comment">/* 0xBFB1FFFF, 0xFFFFFD32 */</span>
<span class="op">-</span><span class="number">8.08167041275349795626e+00</span>, <span class="comment">/* 0xC02029D0, 0xB44FA779 */</span>
<span class="op">-</span><span class="number">2.57063105679704847262e+02</span>, <span class="comment">/* 0xC0701102, 0x7B19E863 */</span>
<span class="op">-</span><span class="number">2.48521641009428822144e+03</span>, <span class="comment">/* 0xC0A36A6E, 0xCD4DCAFC */</span>
<span class="op">-</span><span class="number">5.25304380490729545272e+03</span>, <span class="comment">/* 0xC0B4850B, 0x36CC643D */</span>
];
<span class="kw">const</span> <span class="ident">PS8</span>: [<span class="ident">f64</span>; <span class="number">5</span>] <span class="op">=</span> [
<span class="number">1.16534364619668181717e+02</span>, <span class="comment">/* 0x405D2233, 0x07A96751 */</span>
<span class="number">3.83374475364121826715e+03</span>, <span class="comment">/* 0x40ADF37D, 0x50596938 */</span>
<span class="number">4.05978572648472545552e+04</span>, <span class="comment">/* 0x40E3D2BB, 0x6EB6B05F */</span>
<span class="number">1.16752972564375915681e+05</span>, <span class="comment">/* 0x40FC810F, 0x8F9FA9BD */</span>
<span class="number">4.76277284146730962675e+04</span>, <span class="comment">/* 0x40E74177, 0x4F2C49DC */</span>
];
<span class="kw">const</span> <span class="ident">PR5</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */</span>
<span class="op">-</span><span class="number">1.14125464691894502584e-11</span>, <span class="comment">/* 0xBDA918B1, 0x47E495CC */</span>
<span class="op">-</span><span class="number">7.03124940873599280078e-02</span>, <span class="comment">/* 0xBFB1FFFF, 0xE69AFBC6 */</span>
<span class="op">-</span><span class="number">4.15961064470587782438e+00</span>, <span class="comment">/* 0xC010A370, 0xF90C6BBF */</span>
<span class="op">-</span><span class="number">6.76747652265167261021e+01</span>, <span class="comment">/* 0xC050EB2F, 0x5A7D1783 */</span>
<span class="op">-</span><span class="number">3.31231299649172967747e+02</span>, <span class="comment">/* 0xC074B3B3, 0x6742CC63 */</span>
<span class="op">-</span><span class="number">3.46433388365604912451e+02</span>, <span class="comment">/* 0xC075A6EF, 0x28A38BD7 */</span>
];
<span class="kw">const</span> <span class="ident">PS5</span>: [<span class="ident">f64</span>; <span class="number">5</span>] <span class="op">=</span> [
<span class="number">6.07539382692300335975e+01</span>, <span class="comment">/* 0x404E6081, 0x0C98C5DE */</span>
<span class="number">1.05125230595704579173e+03</span>, <span class="comment">/* 0x40906D02, 0x5C7E2864 */</span>
<span class="number">5.97897094333855784498e+03</span>, <span class="comment">/* 0x40B75AF8, 0x8FBE1D60 */</span>
<span class="number">9.62544514357774460223e+03</span>, <span class="comment">/* 0x40C2CCB8, 0xFA76FA38 */</span>
<span class="number">2.40605815922939109441e+03</span>, <span class="comment">/* 0x40A2CC1D, 0xC70BE864 */</span>
];
<span class="kw">const</span> <span class="ident">PR3</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */</span>
<span class="op">-</span><span class="number">2.54704601771951915620e-09</span>, <span class="comment">/* 0xBE25E103, 0x6FE1AA86 */</span>
<span class="op">-</span><span class="number">7.03119616381481654654e-02</span>, <span class="comment">/* 0xBFB1FFF6, 0xF7C0E24B */</span>
<span class="op">-</span><span class="number">2.40903221549529611423e+00</span>, <span class="comment">/* 0xC00345B2, 0xAEA48074 */</span>
<span class="op">-</span><span class="number">2.19659774734883086467e+01</span>, <span class="comment">/* 0xC035F74A, 0x4CB94E14 */</span>
<span class="op">-</span><span class="number">5.80791704701737572236e+01</span>, <span class="comment">/* 0xC04D0A22, 0x420A1A45 */</span>
<span class="op">-</span><span class="number">3.14479470594888503854e+01</span>, <span class="comment">/* 0xC03F72AC, 0xA892D80F */</span>
];
<span class="kw">const</span> <span class="ident">PS3</span>: [<span class="ident">f64</span>; <span class="number">5</span>] <span class="op">=</span> [
<span class="number">3.58560338055209726349e+01</span>, <span class="comment">/* 0x4041ED92, 0x84077DD3 */</span>
<span class="number">3.61513983050303863820e+02</span>, <span class="comment">/* 0x40769839, 0x464A7C0E */</span>
<span class="number">1.19360783792111533330e+03</span>, <span class="comment">/* 0x4092A66E, 0x6D1061D6 */</span>
<span class="number">1.12799679856907414432e+03</span>, <span class="comment">/* 0x40919FFC, 0xB8C39B7E */</span>
<span class="number">1.73580930813335754692e+02</span>, <span class="comment">/* 0x4065B296, 0xFC379081 */</span>
];
<span class="kw">const</span> <span class="ident">PR2</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */</span>
<span class="op">-</span><span class="number">8.87534333032526411254e-08</span>, <span class="comment">/* 0xBE77D316, 0xE927026D */</span>
<span class="op">-</span><span class="number">7.03030995483624743247e-02</span>, <span class="comment">/* 0xBFB1FF62, 0x495E1E42 */</span>
<span class="op">-</span><span class="number">1.45073846780952986357e+00</span>, <span class="comment">/* 0xBFF73639, 0x8A24A843 */</span>
<span class="op">-</span><span class="number">7.63569613823527770791e+00</span>, <span class="comment">/* 0xC01E8AF3, 0xEDAFA7F3 */</span>
<span class="op">-</span><span class="number">1.11931668860356747786e+01</span>, <span class="comment">/* 0xC02662E6, 0xC5246303 */</span>
<span class="op">-</span><span class="number">3.23364579351335335033e+00</span>, <span class="comment">/* 0xC009DE81, 0xAF8FE70F */</span>
];
<span class="kw">const</span> <span class="ident">PS2</span>: [<span class="ident">f64</span>; <span class="number">5</span>] <span class="op">=</span> [
<span class="number">2.22202997532088808441e+01</span>, <span class="comment">/* 0x40363865, 0x908B5959 */</span>
<span class="number">1.36206794218215208048e+02</span>, <span class="comment">/* 0x4061069E, 0x0EE8878F */</span>
<span class="number">2.70470278658083486789e+02</span>, <span class="comment">/* 0x4070E786, 0x42EA079B */</span>
<span class="number">1.53875394208320329881e+02</span>, <span class="comment">/* 0x40633C03, 0x3AB6FAFF */</span>
<span class="number">1.46576176948256193810e+01</span>, <span class="comment">/* 0x402D50B3, 0x44391809 */</span>
];
<span class="kw">fn</span> <span class="ident">pzero</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">p</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>; <span class="number">6</span>];
<span class="kw">let</span> <span class="ident">q</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>; <span class="number">5</span>];
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>;
<span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>);
<span class="ident">ix</span> <span class="kw-2">&</span><span class="op">=</span> <span class="number">0x7fffffff</span>;
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40200000</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR8</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS8</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40122E8B</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR5</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS5</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4006DB6D</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR3</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS3</span>;
} <span class="kw">else</span>
<span class="comment">/*ix >= 0x40000000*/</span>
{
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR2</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS2</span>;
}
<span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>);
<span class="ident">r</span> <span class="op">=</span> <span class="ident">p</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p</span>[<span class="number">5</span>]))));
<span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">q</span>[<span class="number">4</span>]))));
<span class="kw">return</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>;
}
<span class="comment">/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate pzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/</span>
<span class="kw">const</span> <span class="ident">QR8</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [inf, 8]=1/[0,0.125] */</span>
<span class="number">0.00000000000000000000e+00</span>, <span class="comment">/* 0x00000000, 0x00000000 */</span>
<span class="number">7.32421874999935051953e-02</span>, <span class="comment">/* 0x3FB2BFFF, 0xFFFFFE2C */</span>
<span class="number">1.17682064682252693899e+01</span>, <span class="comment">/* 0x40278952, 0x5BB334D6 */</span>
<span class="number">5.57673380256401856059e+02</span>, <span class="comment">/* 0x40816D63, 0x15301825 */</span>
<span class="number">8.85919720756468632317e+03</span>, <span class="comment">/* 0x40C14D99, 0x3E18F46D */</span>
<span class="number">3.70146267776887834771e+04</span>, <span class="comment">/* 0x40E212D4, 0x0E901566 */</span>
];
<span class="kw">const</span> <span class="ident">QS8</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="number">1.63776026895689824414e+02</span>, <span class="comment">/* 0x406478D5, 0x365B39BC */</span>
<span class="number">8.09834494656449805916e+03</span>, <span class="comment">/* 0x40BFA258, 0x4E6B0563 */</span>
<span class="number">1.42538291419120476348e+05</span>, <span class="comment">/* 0x41016652, 0x54D38C3F */</span>
<span class="number">8.03309257119514397345e+05</span>, <span class="comment">/* 0x412883DA, 0x83A52B43 */</span>
<span class="number">8.40501579819060512818e+05</span>, <span class="comment">/* 0x4129A66B, 0x28DE0B3D */</span>
<span class="op">-</span><span class="number">3.43899293537866615225e+05</span>, <span class="comment">/* 0xC114FD6D, 0x2C9530C5 */</span>
];
<span class="kw">const</span> <span class="ident">QR5</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */</span>
<span class="number">1.84085963594515531381e-11</span>, <span class="comment">/* 0x3DB43D8F, 0x29CC8CD9 */</span>
<span class="number">7.32421766612684765896e-02</span>, <span class="comment">/* 0x3FB2BFFF, 0xD172B04C */</span>
<span class="number">5.83563508962056953777e+00</span>, <span class="comment">/* 0x401757B0, 0xB9953DD3 */</span>
<span class="number">1.35111577286449829671e+02</span>, <span class="comment">/* 0x4060E392, 0x0A8788E9 */</span>
<span class="number">1.02724376596164097464e+03</span>, <span class="comment">/* 0x40900CF9, 0x9DC8C481 */</span>
<span class="number">1.98997785864605384631e+03</span>, <span class="comment">/* 0x409F17E9, 0x53C6E3A6 */</span>
];
<span class="kw">const</span> <span class="ident">QS5</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="number">8.27766102236537761883e+01</span>, <span class="comment">/* 0x4054B1B3, 0xFB5E1543 */</span>
<span class="number">2.07781416421392987104e+03</span>, <span class="comment">/* 0x40A03BA0, 0xDA21C0CE */</span>
<span class="number">1.88472887785718085070e+04</span>, <span class="comment">/* 0x40D267D2, 0x7B591E6D */</span>
<span class="number">5.67511122894947329769e+04</span>, <span class="comment">/* 0x40EBB5E3, 0x97E02372 */</span>
<span class="number">3.59767538425114471465e+04</span>, <span class="comment">/* 0x40E19118, 0x1F7A54A0 */</span>
<span class="op">-</span><span class="number">5.35434275601944773371e+03</span>, <span class="comment">/* 0xC0B4EA57, 0xBEDBC609 */</span>
];
<span class="kw">const</span> <span class="ident">QR3</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */</span>
<span class="number">4.37741014089738620906e-09</span>, <span class="comment">/* 0x3E32CD03, 0x6ADECB82 */</span>
<span class="number">7.32411180042911447163e-02</span>, <span class="comment">/* 0x3FB2BFEE, 0x0E8D0842 */</span>
<span class="number">3.34423137516170720929e+00</span>, <span class="comment">/* 0x400AC0FC, 0x61149CF5 */</span>
<span class="number">4.26218440745412650017e+01</span>, <span class="comment">/* 0x40454F98, 0x962DAEDD */</span>
<span class="number">1.70808091340565596283e+02</span>, <span class="comment">/* 0x406559DB, 0xE25EFD1F */</span>
<span class="number">1.66733948696651168575e+02</span>, <span class="comment">/* 0x4064D77C, 0x81FA21E0 */</span>
];
<span class="kw">const</span> <span class="ident">QS3</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="number">4.87588729724587182091e+01</span>, <span class="comment">/* 0x40486122, 0xBFE343A6 */</span>
<span class="number">7.09689221056606015736e+02</span>, <span class="comment">/* 0x40862D83, 0x86544EB3 */</span>
<span class="number">3.70414822620111362994e+03</span>, <span class="comment">/* 0x40ACF04B, 0xE44DFC63 */</span>
<span class="number">6.46042516752568917582e+03</span>, <span class="comment">/* 0x40B93C6C, 0xD7C76A28 */</span>
<span class="number">2.51633368920368957333e+03</span>, <span class="comment">/* 0x40A3A8AA, 0xD94FB1C0 */</span>
<span class="op">-</span><span class="number">1.49247451836156386662e+02</span>, <span class="comment">/* 0xC062A7EB, 0x201CF40F */</span>
];
<span class="kw">const</span> <span class="ident">QR2</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */</span>
<span class="number">1.50444444886983272379e-07</span>, <span class="comment">/* 0x3E84313B, 0x54F76BDB */</span>
<span class="number">7.32234265963079278272e-02</span>, <span class="comment">/* 0x3FB2BEC5, 0x3E883E34 */</span>
<span class="number">1.99819174093815998816e+00</span>, <span class="comment">/* 0x3FFFF897, 0xE727779C */</span>
<span class="number">1.44956029347885735348e+01</span>, <span class="comment">/* 0x402CFDBF, 0xAAF96FE5 */</span>
<span class="number">3.16662317504781540833e+01</span>, <span class="comment">/* 0x403FAA8E, 0x29FBDC4A */</span>
<span class="number">1.62527075710929267416e+01</span>, <span class="comment">/* 0x403040B1, 0x71814BB4 */</span>
];
<span class="kw">const</span> <span class="ident">QS2</span>: [<span class="ident">f64</span>; <span class="number">6</span>] <span class="op">=</span> [
<span class="number">3.03655848355219184498e+01</span>, <span class="comment">/* 0x403E5D96, 0xF7C07AED */</span>
<span class="number">2.69348118608049844624e+02</span>, <span class="comment">/* 0x4070D591, 0xE4D14B40 */</span>
<span class="number">8.44783757595320139444e+02</span>, <span class="comment">/* 0x408A6645, 0x22B3BF22 */</span>
<span class="number">8.82935845112488550512e+02</span>, <span class="comment">/* 0x408B977C, 0x9C5CC214 */</span>
<span class="number">2.12666388511798828631e+02</span>, <span class="comment">/* 0x406A9553, 0x0E001365 */</span>
<span class="op">-</span><span class="number">5.31095493882666946917e+00</span>, <span class="comment">/* 0xC0153E6A, 0xF8B32931 */</span>
];
<span class="kw">fn</span> <span class="ident">qzero</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">p</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>; <span class="number">6</span>];
<span class="kw">let</span> <span class="ident">q</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>; <span class="number">6</span>];
<span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>;
<span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>);
<span class="ident">ix</span> <span class="kw-2">&</span><span class="op">=</span> <span class="number">0x7fffffff</span>;
<span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40200000</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR8</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS8</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x40122E8B</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR5</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS5</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4006DB6D</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR3</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS3</span>;
} <span class="kw">else</span>
<span class="comment">/*ix >= 0x40000000*/</span>
{
<span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR2</span>;
<span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS2</span>;
}
<span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>);
<span class="ident">r</span> <span class="op">=</span> <span class="ident">p</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p</span>[<span class="number">5</span>]))));
<span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">q</span>[<span class="number">5</span>])))));
<span class="kw">return</span> (<span class="op">-</span><span class="number">0.125</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>) <span class="op">/</span> <span class="ident">x</span>;
}
</pre></div>
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