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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.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">/* atan2(y,x) |
| * Method : |
| * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). |
| * 2. Reduce x to positive by (if x and y are unexceptional): |
| * ARG (x+iy) = arctan(y/x) ... if x > 0, |
| * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, |
| * |
| * Special cases: |
| * |
| * ATAN2((anything), NaN ) is NaN; |
| * ATAN2(NAN , (anything) ) is NaN; |
| * ATAN2(+-0, +(anything but NaN)) is +-0 ; |
| * ATAN2(+-0, -(anything but NaN)) is +-pi ; |
| * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; |
| * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; |
| * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; |
| * ATAN2(+-INF,+INF ) is +-pi/4 ; |
| * ATAN2(+-INF,-INF ) is +-3pi/4; |
| * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; |
| * |
| * Constants: |
| * The hexadecimal values are the intended ones for the following |
| * constants. The decimal values may be used, provided that the |
| * compiler will convert from decimal to binary accurately enough |
| * to produce the hexadecimal values shown. |
| */</span> |
| |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::atan</span>; |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::fabs</span>; |
| |
| <span class="kw">const</span> <span class="ident">PI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.1415926535897931160E+00</span>; <span class="comment">/* 0x400921FB, 0x54442D18 */</span> |
| <span class="kw">const</span> <span class="ident">PI_LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.2246467991473531772E-16</span>; <span class="comment">/* 0x3CA1A626, 0x33145C07 */</span> |
| |
| <span class="doccomment">/// Arctangent of y/x (f64)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Computes the inverse tangent (arc tangent) of `y/x`.</span> |
| <span class="doccomment">/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).</span> |
| <span class="doccomment">/// Returns a value in radians, in the range of -pi to pi.</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">fn</span> <span class="ident">atan2</span>(<span class="ident">y</span>: <span class="ident">f64</span>, <span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">if</span> <span class="ident">x</span>.<span class="ident">is_nan</span>() <span class="op">|</span><span class="op">|</span> <span class="ident">y</span>.<span class="ident">is_nan</span>() { |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">+</span> <span class="ident">y</span>; |
| } |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span> <span class="op">=</span> (<span class="ident">x</span>.<span class="ident">to_bits</span>() <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">lx</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>() <span class="kw">as</span> <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">iy</span> <span class="op">=</span> (<span class="ident">y</span>.<span class="ident">to_bits</span>() <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">ly</span> <span class="op">=</span> <span class="ident">y</span>.<span class="ident">to_bits</span>() <span class="kw">as</span> <span class="ident">u32</span>; |
| <span class="kw">if</span> ((<span class="ident">ix</span>.<span class="ident">wrapping_sub</span>(<span class="number">0x3ff00000</span>)) <span class="op">|</span> <span class="ident">lx</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* x = 1.0 */</span> |
| <span class="kw">return</span> <span class="ident">atan</span>(<span class="ident">y</span>); |
| } |
| <span class="kw">let</span> <span class="ident">m</span> <span class="op">=</span> ((<span class="ident">iy</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">&</span> <span class="number">1</span>) <span class="op">|</span> ((<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">30</span>) <span class="op">&</span> <span class="number">2</span>); <span class="comment">/* 2*sign(x)+sign(y) */</span> |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| <span class="ident">iy</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| |
| <span class="comment">/* when y = 0 */</span> |
| <span class="kw">if</span> (<span class="ident">iy</span> <span class="op">|</span> <span class="ident">ly</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="kw">match</span> <span class="ident">m</span> { |
| <span class="number">0</span> <span class="op">|</span> <span class="number">1</span> => <span class="ident">y</span>, <span class="comment">/* atan(+-0,+anything)=+-0 */</span> |
| <span class="number">2</span> => <span class="ident">PI</span>, <span class="comment">/* atan(+0,-anything) = PI */</span> |
| <span class="kw">_</span> => <span class="op">-</span><span class="ident">PI</span>, <span class="comment">/* atan(-0,-anything) =-PI */</span> |
| }; |
| } |
| <span class="comment">/* when x = 0 */</span> |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">|</span> <span class="ident">lx</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">m</span> <span class="op">&</span> <span class="number">1</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { <span class="op">-</span><span class="ident">PI</span> <span class="op">/</span> <span class="number">2.0</span> } <span class="kw">else</span> { <span class="ident">PI</span> <span class="op">/</span> <span class="number">2.0</span> }; |
| } |
| <span class="comment">/* when x is INF */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">if</span> <span class="ident">iy</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">return</span> <span class="kw">match</span> <span class="ident">m</span> { |
| <span class="number">0</span> => <span class="ident">PI</span> <span class="op">/</span> <span class="number">4.0</span>, <span class="comment">/* atan(+INF,+INF) */</span> |
| <span class="number">1</span> => <span class="op">-</span><span class="ident">PI</span> <span class="op">/</span> <span class="number">4.0</span>, <span class="comment">/* atan(-INF,+INF) */</span> |
| <span class="number">2</span> => <span class="number">3.0</span> <span class="op">*</span> <span class="ident">PI</span> <span class="op">/</span> <span class="number">4.0</span>, <span class="comment">/* atan(+INF,-INF) */</span> |
| <span class="kw">_</span> => <span class="op">-</span><span class="number">3.0</span> <span class="op">*</span> <span class="ident">PI</span> <span class="op">/</span> <span class="number">4.0</span>, <span class="comment">/* atan(-INF,-INF) */</span> |
| }; |
| } <span class="kw">else</span> { |
| <span class="kw">return</span> <span class="kw">match</span> <span class="ident">m</span> { |
| <span class="number">0</span> => <span class="number">0.0</span>, <span class="comment">/* atan(+...,+INF) */</span> |
| <span class="number">1</span> => <span class="op">-</span><span class="number">0.0</span>, <span class="comment">/* atan(-...,+INF) */</span> |
| <span class="number">2</span> => <span class="ident">PI</span>, <span class="comment">/* atan(+...,-INF) */</span> |
| <span class="kw">_</span> => <span class="op">-</span><span class="ident">PI</span>, <span class="comment">/* atan(-...,-INF) */</span> |
| }; |
| } |
| } |
| <span class="comment">/* |y/x| > 0x1p64 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span>.<span class="ident">wrapping_add</span>(<span class="number">64</span> <span class="op"><</span><span class="op"><</span> <span class="number">20</span>) <span class="op"><</span> <span class="ident">iy</span> <span class="op">|</span><span class="op">|</span> <span class="ident">iy</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">m</span> <span class="op">&</span> <span class="number">1</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { <span class="op">-</span><span class="ident">PI</span> <span class="op">/</span> <span class="number">2.0</span> } <span class="kw">else</span> { <span class="ident">PI</span> <span class="op">/</span> <span class="number">2.0</span> }; |
| } |
| |
| <span class="comment">/* z = atan(|y/x|) without spurious underflow */</span> |
| <span class="kw">let</span> <span class="ident">z</span> <span class="op">=</span> <span class="kw">if</span> (<span class="ident">m</span> <span class="op">&</span> <span class="number">2</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span>) <span class="op">&&</span> <span class="ident">iy</span>.<span class="ident">wrapping_add</span>(<span class="number">64</span> <span class="op"><</span><span class="op"><</span> <span class="number">20</span>) <span class="op"><</span> <span class="ident">ix</span> { |
| <span class="comment">/* |y/x| < 0x1p-64, x<0 */</span> |
| <span class="number">0.0</span> |
| } <span class="kw">else</span> { |
| <span class="ident">atan</span>(<span class="ident">fabs</span>(<span class="ident">y</span> <span class="op">/</span> <span class="ident">x</span>)) |
| }; |
| <span class="kw">match</span> <span class="ident">m</span> { |
| <span class="number">0</span> => <span class="ident">z</span>, <span class="comment">/* atan(+,+) */</span> |
| <span class="number">1</span> => <span class="op">-</span><span class="ident">z</span>, <span class="comment">/* atan(-,+) */</span> |
| <span class="number">2</span> => <span class="ident">PI</span> <span class="op">-</span> (<span class="ident">z</span> <span class="op">-</span> <span class="ident">PI_LO</span>), <span class="comment">/* atan(+,-) */</span> |
| <span class="kw">_</span> => (<span class="ident">z</span> <span class="op">-</span> <span class="ident">PI_LO</span>) <span class="op">-</span> <span class="ident">PI</span>, <span class="comment">/* atan(-,-) */</span> |
| } |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">sanity_check</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="number">0.0</span>, <span class="number">1.0</span>), <span class="number">0.0</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="number">0.0</span>, <span class="op">-</span><span class="number">1.0</span>), <span class="ident">PI</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="op">-</span><span class="number">0.0</span>, <span class="op">-</span><span class="number">1.0</span>), <span class="op">-</span><span class="ident">PI</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="number">3.0</span>, <span class="number">2.0</span>), <span class="ident">atan</span>(<span class="number">3.0</span> <span class="op">/</span> <span class="number">2.0</span>)); |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="number">2.0</span>, <span class="op">-</span><span class="number">1.0</span>), <span class="ident">atan</span>(<span class="number">2.0</span> <span class="op">/</span> <span class="op">-</span><span class="number">1.0</span>) <span class="op">+</span> <span class="ident">PI</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">atan2</span>(<span class="op">-</span><span class="number">2.0</span>, <span class="op">-</span><span class="number">1.0</span>), <span class="ident">atan</span>(<span class="op">-</span><span class="number">2.0</span> <span class="op">/</span> <span class="op">-</span><span class="number">1.0</span>) <span class="op">-</span> <span class="ident">PI</span>); |
| } |
| </code></pre></div> |
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