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</pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */
//
// ====================================================
// Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
//
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
// kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
// Input x is assumed to be bounded by ~pi/4 in magnitude.
// Input y is the tail of x.
// Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned.
//
// Algorithm
// 1. Since tan(-x) = -tan(x), we need only to consider positive x.
// 2. Callers must return tan(-0) = -0 without calling here since our
// odd polynomial is not evaluated in a way that preserves -0.
// Callers may do the optimization tan(x) ~ x for tiny x.
// 3. tan(x) is approximated by a odd polynomial of degree 27 on
// [0,0.67434]
// 3 27
// tan(x) ~ x + T1*x + ... + T13*x
// where
//
// |tan(x) 2 4 26 | -59.2
// |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
// | x |
//
// Note: tan(x+y) = tan(x) + tan'(x)*y
// ~ tan(x) + (1+x*x)*y
// Therefore, for better accuracy in computing tan(x+y), let
// 3 2 2 2 2
// r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
// then
// 3 2
// tan(x+y) = x + (T1*x + (x *(r+y)+y))
//
// 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
// tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
// = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
</span><span class="kw">static </span>T: [f64; <span class="number">13</span>] = [
<span class="number">3.33333333333334091986e-01</span>, <span class="comment">/* 3FD55555, 55555563 */
</span><span class="number">1.33333333333201242699e-01</span>, <span class="comment">/* 3FC11111, 1110FE7A */
</span><span class="number">5.39682539762260521377e-02</span>, <span class="comment">/* 3FABA1BA, 1BB341FE */
</span><span class="number">2.18694882948595424599e-02</span>, <span class="comment">/* 3F9664F4, 8406D637 */
</span><span class="number">8.86323982359930005737e-03</span>, <span class="comment">/* 3F8226E3, E96E8493 */
</span><span class="number">3.59207910759131235356e-03</span>, <span class="comment">/* 3F6D6D22, C9560328 */
</span><span class="number">1.45620945432529025516e-03</span>, <span class="comment">/* 3F57DBC8, FEE08315 */
</span><span class="number">5.88041240820264096874e-04</span>, <span class="comment">/* 3F4344D8, F2F26501 */
</span><span class="number">2.46463134818469906812e-04</span>, <span class="comment">/* 3F3026F7, 1A8D1068 */
</span><span class="number">7.81794442939557092300e-05</span>, <span class="comment">/* 3F147E88, A03792A6 */
</span><span class="number">7.14072491382608190305e-05</span>, <span class="comment">/* 3F12B80F, 32F0A7E9 */
</span>-<span class="number">1.85586374855275456654e-05</span>, <span class="comment">/* BEF375CB, DB605373 */
</span><span class="number">2.59073051863633712884e-05</span>, <span class="comment">/* 3EFB2A70, 74BF7AD4 */
</span>];
<span class="kw">const </span>PIO4: f64 = <span class="number">7.85398163397448278999e-01</span>; <span class="comment">/* 3FE921FB, 54442D18 */
</span><span class="kw">const </span>PIO4_LO: f64 = <span class="number">3.06161699786838301793e-17</span>; <span class="comment">/* 3C81A626, 33145C07 */
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>k_tan(<span class="kw-2">mut </span>x: f64, <span class="kw-2">mut </span>y: f64, odd: i32) -> f64 {
<span class="kw">let </span>hx = (f64::to_bits(x) >> <span class="number">32</span>) <span class="kw">as </span>u32;
<span class="kw">let </span>big = (hx & <span class="number">0x7fffffff</span>) >= <span class="number">0x3FE59428</span>; <span class="comment">/* |x| >= 0.6744 */
</span><span class="kw">if </span>big {
<span class="kw">let </span>sign = hx >> <span class="number">31</span>;
<span class="kw">if </span>sign != <span class="number">0 </span>{
x = -x;
y = -y;
}
x = (PIO4 - x) + (PIO4_LO - y);
y = <span class="number">0.0</span>;
}
<span class="kw">let </span>z = x * x;
<span class="kw">let </span>w = z * z;
<span class="comment">/*
* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
</span><span class="kw">let </span>r = T[<span class="number">1</span>] + w * (T[<span class="number">3</span>] + w * (T[<span class="number">5</span>] + w * (T[<span class="number">7</span>] + w * (T[<span class="number">9</span>] + w * T[<span class="number">11</span>]))));
<span class="kw">let </span>v = z * (T[<span class="number">2</span>] + w * (T[<span class="number">4</span>] + w * (T[<span class="number">6</span>] + w * (T[<span class="number">8</span>] + w * (T[<span class="number">10</span>] + w * T[<span class="number">12</span>])))));
<span class="kw">let </span>s = z * x;
<span class="kw">let </span>r = y + z * (s * (r + v) + y) + s * T[<span class="number">0</span>];
<span class="kw">let </span>w = x + r;
<span class="kw">if </span>big {
<span class="kw">let </span>sign = hx >> <span class="number">31</span>;
<span class="kw">let </span>s = <span class="number">1.0 </span>- <span class="number">2.0 </span>* odd <span class="kw">as </span>f64;
<span class="kw">let </span>v = s - <span class="number">2.0 </span>* (x + (r - w * w / (w + s)));
<span class="kw">return if </span>sign != <span class="number">0 </span>{ -v } <span class="kw">else </span>{ v };
}
<span class="kw">if </span>odd == <span class="number">0 </span>{
<span class="kw">return </span>w;
}
<span class="comment">/* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
</span><span class="kw">let </span>w0 = zero_low_word(w);
<span class="kw">let </span>v = r - (w0 - x); <span class="comment">/* w0+v = r+x */
</span><span class="kw">let </span>a = -<span class="number">1.0 </span>/ w;
<span class="kw">let </span>a0 = zero_low_word(a);
a0 + a * (<span class="number">1.0 </span>+ a0 * w0 + a0 * v)
}
<span class="kw">fn </span>zero_low_word(x: f64) -> f64 {
f64::from_bits(f64::to_bits(x) & <span class="number">0xFFFF_FFFF_0000_0000</span>)
}
</code></pre></div>
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