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| </pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/k_sin.c</span> |
| <span class="comment">//</span> |
| <span class="comment">// ====================================================</span> |
| <span class="comment">// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Developed at SunSoft, a Sun Microsystems, Inc. business.</span> |
| <span class="comment">// Permission to use, copy, modify, and distribute this</span> |
| <span class="comment">// software is freely granted, provided that this notice</span> |
| <span class="comment">// is preserved.</span> |
| <span class="comment">// ====================================================</span> |
| |
| <span class="kw">const</span> <span class="ident">S1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.66666666666666324348e-01</span>; <span class="comment">/* 0xBFC55555, 0x55555549 */</span> |
| <span class="kw">const</span> <span class="ident">S2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.33333333332248946124e-03</span>; <span class="comment">/* 0x3F811111, 0x1110F8A6 */</span> |
| <span class="kw">const</span> <span class="ident">S3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.98412698298579493134e-04</span>; <span class="comment">/* 0xBF2A01A0, 0x19C161D5 */</span> |
| <span class="kw">const</span> <span class="ident">S4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.75573137070700676789e-06</span>; <span class="comment">/* 0x3EC71DE3, 0x57B1FE7D */</span> |
| <span class="kw">const</span> <span class="ident">S5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.50507602534068634195e-08</span>; <span class="comment">/* 0xBE5AE5E6, 0x8A2B9CEB */</span> |
| <span class="kw">const</span> <span class="ident">S6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.58969099521155010221e-10</span>; <span class="comment">/* 0x3DE5D93A, 0x5ACFD57C */</span> |
| |
| <span class="comment">// kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854</span> |
| <span class="comment">// Input x is assumed to be bounded by ~pi/4 in magnitude.</span> |
| <span class="comment">// Input y is the tail of x.</span> |
| <span class="comment">// Input iy indicates whether y is 0. (if iy=0, y assume to be 0).</span> |
| <span class="comment">//</span> |
| <span class="comment">// Algorithm</span> |
| <span class="comment">// 1. Since sin(-x) = -sin(x), we need only to consider positive x.</span> |
| <span class="comment">// 2. Callers must return sin(-0) = -0 without calling here since our</span> |
| <span class="comment">// odd polynomial is not evaluated in a way that preserves -0.</span> |
| <span class="comment">// Callers may do the optimization sin(x) ~ x for tiny x.</span> |
| <span class="comment">// 3. sin(x) is approximated by a polynomial of degree 13 on</span> |
| <span class="comment">// [0,pi/4]</span> |
| <span class="comment">// 3 13</span> |
| <span class="comment">// sin(x) ~ x + S1*x + ... + S6*x</span> |
| <span class="comment">// where</span> |
| <span class="comment">//</span> |
| <span class="comment">// |sin(x) 2 4 6 8 10 12 | -58</span> |
| <span class="comment">// |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2</span> |
| <span class="comment">// | x |</span> |
| <span class="comment">//</span> |
| <span class="comment">// 4. sin(x+y) = sin(x) + sin'(x')*y</span> |
| <span class="comment">// ~ sin(x) + (1-x*x/2)*y</span> |
| <span class="comment">// For better accuracy, let</span> |
| <span class="comment">// 3 2 2 2 2</span> |
| <span class="comment">// r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))</span> |
| <span class="comment">// then 3 2</span> |
| <span class="comment">// sin(x) = x + (S1*x + (x *(r-y/2)+y))</span> |
| <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">all</span>(<span class="ident">test</span>, <span class="ident">assert_no_panic</span>), <span class="ident">no_panic::no_panic</span>)]</span> |
| <span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn</span> <span class="ident">k_sin</span>(<span class="ident">x</span>: <span class="ident">f64</span>, <span class="ident">y</span>: <span class="ident">f64</span>, <span class="ident">iy</span>: <span class="ident">i32</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</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="kw">let</span> <span class="ident">w</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span>; |
| <span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">S2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">S4</span>) <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">S5</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">S6</span>); |
| <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">x</span> <span class="op">+</span> <span class="ident">v</span> <span class="op">*</span> (<span class="ident">S1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">r</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">x</span> <span class="op">-</span> ((<span class="ident">z</span> <span class="op">*</span> (<span class="number">0.5</span> <span class="op">*</span> <span class="ident">y</span> <span class="op">-</span> <span class="ident">v</span> <span class="op">*</span> <span class="ident">r</span>) <span class="op">-</span> <span class="ident">y</span>) <span class="op">-</span> <span class="ident">v</span> <span class="op">*</span> <span class="ident">S1</span>) |
| } |
| } |
| </code></pre></div> |
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