multibody_dynamics 0.4.0

Multibody dynamics algorithms in Rust
Documentation
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</pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/* acos(x)
 * Method :
 *      acos(x)  = pi/2 - asin(x)
 *      acos(-x) = pi/2 + asin(x)
 * For |x|&lt;=0.5
 *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
 * For x&gt;0.5
 *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
 *              = 2asin(sqrt((1-x)/2))
 *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
 *              = 2f + (2c + 2s*z*R(z))
 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
 *     for f so that f+c ~ sqrt(z).
 * For x&lt;-0.5
 *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
 *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
 *
 * Special cases:
 *      if x is NaN, return x itself;
 *      if |x|&gt;1, return NaN with invalid signal.
 *
 * Function needed: sqrt
 */

</span><span class="kw">use </span><span class="kw">super</span>::sqrt;

<span class="kw">const </span>PIO2_HI: f64 = <span class="number">1.57079632679489655800e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54442D18 */
</span><span class="kw">const </span>PIO2_LO: f64 = <span class="number">6.12323399573676603587e-17</span>; <span class="comment">/* 0x3C91A626, 0x33145C07 */
</span><span class="kw">const </span>PS0: f64 = <span class="number">1.66666666666666657415e-01</span>; <span class="comment">/* 0x3FC55555, 0x55555555 */
</span><span class="kw">const </span>PS1: f64 = -<span class="number">3.25565818622400915405e-01</span>; <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */
</span><span class="kw">const </span>PS2: f64 = <span class="number">2.01212532134862925881e-01</span>; <span class="comment">/* 0x3FC9C155, 0x0E884455 */
</span><span class="kw">const </span>PS3: f64 = -<span class="number">4.00555345006794114027e-02</span>; <span class="comment">/* 0xBFA48228, 0xB5688F3B */
</span><span class="kw">const </span>PS4: f64 = <span class="number">7.91534994289814532176e-04</span>; <span class="comment">/* 0x3F49EFE0, 0x7501B288 */
</span><span class="kw">const </span>PS5: f64 = <span class="number">3.47933107596021167570e-05</span>; <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */
</span><span class="kw">const </span>QS1: f64 = -<span class="number">2.40339491173441421878e+00</span>; <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */
</span><span class="kw">const </span>QS2: f64 = <span class="number">2.02094576023350569471e+00</span>; <span class="comment">/* 0x40002AE5, 0x9C598AC8 */
</span><span class="kw">const </span>QS3: f64 = -<span class="number">6.88283971605453293030e-01</span>; <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */
</span><span class="kw">const </span>QS4: f64 = <span class="number">7.70381505559019352791e-02</span>; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */

</span><span class="kw">fn </span>r(z: f64) -&gt; f64 {
    <span class="kw">let </span>p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
    <span class="kw">let </span>q: f64 = <span class="number">1.0 </span>+ z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
    p / q
}

<span class="doccomment">/// Arccosine (f64)
///
/// Computes the inverse cosine (arc cosine) of the input value.
/// Arguments must be in the range -1 to 1.
/// Returns values in radians, in the range of 0 to pi.
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>acos(x: f64) -&gt; f64 {
    <span class="kw">let </span>x1p_120f = f64::from_bits(<span class="number">0x3870000000000000</span>); <span class="comment">// 0x1p-120 === 2 ^ -120
    </span><span class="kw">let </span>z: f64;
    <span class="kw">let </span>w: f64;
    <span class="kw">let </span>s: f64;
    <span class="kw">let </span>c: f64;
    <span class="kw">let </span>df: f64;
    <span class="kw">let </span>hx: u32;
    <span class="kw">let </span>ix: u32;

    hx = (x.to_bits() &gt;&gt; <span class="number">32</span>) <span class="kw">as </span>u32;
    ix = hx &amp; <span class="number">0x7fffffff</span>;
    <span class="comment">/* |x| &gt;= 1 or nan */
    </span><span class="kw">if </span>ix &gt;= <span class="number">0x3ff00000 </span>{
        <span class="kw">let </span>lx: u32 = x.to_bits() <span class="kw">as </span>u32;

        <span class="kw">if </span>((ix - <span class="number">0x3ff00000</span>) | lx) == <span class="number">0 </span>{
            <span class="comment">/* acos(1)=0, acos(-1)=pi */
            </span><span class="kw">if </span>(hx &gt;&gt; <span class="number">31</span>) != <span class="number">0 </span>{
                <span class="kw">return </span><span class="number">2. </span>* PIO2_HI + x1p_120f;
            }
            <span class="kw">return </span><span class="number">0.</span>;
        }
        <span class="kw">return </span><span class="number">0. </span>/ (x - x);
    }
    <span class="comment">/* |x| &lt; 0.5 */
    </span><span class="kw">if </span>ix &lt; <span class="number">0x3fe00000 </span>{
        <span class="kw">if </span>ix &lt;= <span class="number">0x3c600000 </span>{
            <span class="comment">/* |x| &lt; 2**-57 */
            </span><span class="kw">return </span>PIO2_HI + x1p_120f;
        }
        <span class="kw">return </span>PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
    }
    <span class="comment">/* x &lt; -0.5 */
    </span><span class="kw">if </span>(hx &gt;&gt; <span class="number">31</span>) != <span class="number">0 </span>{
        z = (<span class="number">1.0 </span>+ x) * <span class="number">0.5</span>;
        s = sqrt(z);
        w = r(z) * s - PIO2_LO;
        <span class="kw">return </span><span class="number">2. </span>* (PIO2_HI - (s + w));
    }
    <span class="comment">/* x &gt; 0.5 */
    </span>z = (<span class="number">1.0 </span>- x) * <span class="number">0.5</span>;
    s = sqrt(z);
    <span class="comment">// Set the low 4 bytes to zero
    </span>df = f64::from_bits(s.to_bits() &amp; <span class="number">0xff_ff_ff_ff_00_00_00_00</span>);

    c = (z - df * df) / (s + df);
    w = r(z) * s + c;
    <span class="number">2. </span>* (df + w)
}
</code></pre></div>
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