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| </pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/k_cos.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">C1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.16666666666666019037e-02</span>; <span class="comment">/* 0x3FA55555, 0x5555554C */</span> |
| <span class="kw">const</span> <span class="ident">C2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.38888888888741095749e-03</span>; <span class="comment">/* 0xBF56C16C, 0x16C15177 */</span> |
| <span class="kw">const</span> <span class="ident">C3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.48015872894767294178e-05</span>; <span class="comment">/* 0x3EFA01A0, 0x19CB1590 */</span> |
| <span class="kw">const</span> <span class="ident">C4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.75573143513906633035e-07</span>; <span class="comment">/* 0xBE927E4F, 0x809C52AD */</span> |
| <span class="kw">const</span> <span class="ident">C5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.08757232129817482790e-09</span>; <span class="comment">/* 0x3E21EE9E, 0xBDB4B1C4 */</span> |
| <span class="kw">const</span> <span class="ident">C6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.13596475577881948265e-11</span>; <span class="comment">/* 0xBDA8FAE9, 0xBE8838D4 */</span> |
| |
| <span class="comment">// kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164</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">//</span> |
| <span class="comment">// Algorithm</span> |
| <span class="comment">// 1. Since cos(-x) = cos(x), we need only to consider positive x.</span> |
| <span class="comment">// 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.</span> |
| <span class="comment">// 3. cos(x) is approximated by a polynomial of degree 14 on</span> |
| <span class="comment">// [0,pi/4]</span> |
| <span class="comment">// 4 14</span> |
| <span class="comment">// cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x</span> |
| <span class="comment">// where the remez error is</span> |
| <span class="comment">//</span> |
| <span class="comment">// | 2 4 6 8 10 12 14 | -58</span> |
| <span class="comment">// |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2</span> |
| <span class="comment">// | |</span> |
| <span class="comment">//</span> |
| <span class="comment">// 4 6 8 10 12 14</span> |
| <span class="comment">// 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then</span> |
| <span class="comment">// cos(x) ~ 1 - x*x/2 + r</span> |
| <span class="comment">// since cos(x+y) ~ cos(x) - sin(x)*y</span> |
| <span class="comment">// ~ cos(x) - x*y,</span> |
| <span class="comment">// a correction term is necessary in cos(x) and hence</span> |
| <span class="comment">// cos(x+y) = 1 - (x*x/2 - (r - x*y))</span> |
| <span class="comment">// For better accuracy, rearrange to</span> |
| <span class="comment">// cos(x+y) ~ w + (tmp + (r-x*y))</span> |
| <span class="comment">// where w = 1 - x*x/2 and tmp is a tiny correction term</span> |
| <span class="comment">// (1 - x*x/2 == w + tmp exactly in infinite precision).</span> |
| <span class="comment">// The exactness of w + tmp in infinite precision depends on w</span> |
| <span class="comment">// and tmp having the same precision as x. If they have extra</span> |
| <span class="comment">// precision due to compiler bugs, then the extra precision is</span> |
| <span class="comment">// only good provided it is retained in all terms of the final</span> |
| <span class="comment">// expression for cos(). Retention happens in all cases tested</span> |
| <span class="comment">// under FreeBSD, so don't pessimize things by forcibly clipping</span> |
| <span class="comment">// any extra precision in w.</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_cos</span>(<span class="ident">x</span>: <span class="ident">f64</span>, <span class="ident">y</span>: <span class="ident">f64</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">z</span> <span class="op">*</span> (<span class="ident">C1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">C2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">C3</span>)) <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">C4</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">C5</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">C6</span>)); |
| <span class="kw">let</span> <span class="ident">hz</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">z</span>; |
| <span class="kw">let</span> <span class="ident">w</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">hz</span>; |
| <span class="ident">w</span> <span class="op">+</span> (((<span class="number">1.0</span> <span class="op">-</span> <span class="ident">w</span>) <span class="op">-</span> <span class="ident">hz</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">x</span> <span class="op">*</span> <span class="ident">y</span>)) |
| } |
| </code></pre></div> |
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