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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, 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">/* atan(x) |
| * Method |
| * 1. Reduce x to positive by atan(x) = -atan(-x). |
| * 2. According to the integer k=4t+0.25 chopped, t=x, the argument |
| * is further reduced to one of the following intervals and the |
| * arctangent of t is evaluated by the corresponding formula: |
| * |
| * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) |
| * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) |
| * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) |
| * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) |
| * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) |
| * |
| * 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>::fabs</span>; |
| <span class="kw">use</span> <span class="ident">core::f64</span>; |
| |
| <span class="kw">const</span> <span class="ident">ATANHI</span>: [<span class="ident">f64</span>; <span class="number">4</span>] <span class="op">=</span> [ |
| <span class="number">4.63647609000806093515e-01</span>, <span class="comment">/* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */</span> |
| <span class="number">7.85398163397448278999e-01</span>, <span class="comment">/* atan(1.0)hi 0x3FE921FB, 0x54442D18 */</span> |
| <span class="number">9.82793723247329054082e-01</span>, <span class="comment">/* atan(1.5)hi 0x3FEF730B, 0xD281F69B */</span> |
| <span class="number">1.57079632679489655800e+00</span>, <span class="comment">/* atan(inf)hi 0x3FF921FB, 0x54442D18 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">ATANLO</span>: [<span class="ident">f64</span>; <span class="number">4</span>] <span class="op">=</span> [ |
| <span class="number">2.26987774529616870924e-17</span>, <span class="comment">/* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */</span> |
| <span class="number">3.06161699786838301793e-17</span>, <span class="comment">/* atan(1.0)lo 0x3C81A626, 0x33145C07 */</span> |
| <span class="number">1.39033110312309984516e-17</span>, <span class="comment">/* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */</span> |
| <span class="number">6.12323399573676603587e-17</span>, <span class="comment">/* atan(inf)lo 0x3C91A626, 0x33145C07 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">AT</span>: [<span class="ident">f64</span>; <span class="number">11</span>] <span class="op">=</span> [ |
| <span class="number">3.33333333333329318027e-01</span>, <span class="comment">/* 0x3FD55555, 0x5555550D */</span> |
| <span class="op">-</span><span class="number">1.99999999998764832476e-01</span>, <span class="comment">/* 0xBFC99999, 0x9998EBC4 */</span> |
| <span class="number">1.42857142725034663711e-01</span>, <span class="comment">/* 0x3FC24924, 0x920083FF */</span> |
| <span class="op">-</span><span class="number">1.11111104054623557880e-01</span>, <span class="comment">/* 0xBFBC71C6, 0xFE231671 */</span> |
| <span class="number">9.09088713343650656196e-02</span>, <span class="comment">/* 0x3FB745CD, 0xC54C206E */</span> |
| <span class="op">-</span><span class="number">7.69187620504482999495e-02</span>, <span class="comment">/* 0xBFB3B0F2, 0xAF749A6D */</span> |
| <span class="number">6.66107313738753120669e-02</span>, <span class="comment">/* 0x3FB10D66, 0xA0D03D51 */</span> |
| <span class="op">-</span><span class="number">5.83357013379057348645e-02</span>, <span class="comment">/* 0xBFADDE2D, 0x52DEFD9A */</span> |
| <span class="number">4.97687799461593236017e-02</span>, <span class="comment">/* 0x3FA97B4B, 0x24760DEB */</span> |
| <span class="op">-</span><span class="number">3.65315727442169155270e-02</span>, <span class="comment">/* 0xBFA2B444, 0x2C6A6C2F */</span> |
| <span class="number">1.62858201153657823623e-02</span>, <span class="comment">/* 0x3F90AD3A, 0xE322DA11 */</span> |
| ]; |
| |
| <span class="doccomment">/// Arctangent (f64)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Computes the inverse tangent (arc tangent) of the input value.</span> |
| <span class="doccomment">/// Returns a value in radians, in the range of -pi/2 to pi/2.</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">atan</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="ident">x</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">sign</span> <span class="op">=</span> <span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>; |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fff_ffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4410_0000</span> { |
| <span class="kw">if</span> <span class="ident">x</span>.<span class="ident">is_nan</span>() { |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| |
| <span class="kw">let</span> <span class="ident">z</span> <span class="op">=</span> <span class="ident">ATANHI</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">f64::from_bits</span>(<span class="number">0x0380_0000</span>); <span class="comment">// 0x1p-120f</span> |
| <span class="kw">return</span> <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { <span class="op">-</span><span class="ident">z</span> } <span class="kw">else</span> { <span class="ident">z</span> }; |
| } |
| |
| <span class="kw">let</span> <span class="ident">id</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3fdc_0000</span> { |
| <span class="comment">/* |x| < 0.4375 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3e40_0000</span> { |
| <span class="comment">/* |x| < 2^-27 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x0010_0000</span> { |
| <span class="comment">/* raise underflow for subnormal x */</span> |
| <span class="macro">force_eval!</span>(<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</span>); |
| } |
| |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| |
| <span class="op">-</span><span class="number">1</span> |
| } <span class="kw">else</span> { |
| <span class="ident">x</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3ff30000</span> { |
| <span class="comment">/* |x| < 1.1875 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3fe60000</span> { |
| <span class="comment">/* 7/16 <= |x| < 11/16 */</span> |
| <span class="ident">x</span> <span class="op">=</span> (<span class="number">2.</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1.</span>) <span class="op">/</span> (<span class="number">2.</span> <span class="op">+</span> <span class="ident">x</span>); |
| <span class="number">0</span> |
| } <span class="kw">else</span> { |
| <span class="comment">/* 11/16 <= |x| < 19/16 */</span> |
| <span class="ident">x</span> <span class="op">=</span> (<span class="ident">x</span> <span class="op">-</span> <span class="number">1.</span>) <span class="op">/</span> (<span class="ident">x</span> <span class="op">+</span> <span class="number">1.</span>); |
| <span class="number">1</span> |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x40038000</span> { |
| <span class="comment">/* |x| < 2.4375 */</span> |
| <span class="ident">x</span> <span class="op">=</span> (<span class="ident">x</span> <span class="op">-</span> <span class="number">1.5</span>) <span class="op">/</span> (<span class="number">1.</span> <span class="op">+</span> <span class="number">1.5</span> <span class="op">*</span> <span class="ident">x</span>); |
| <span class="number">2</span> |
| } <span class="kw">else</span> { |
| <span class="comment">/* 2.4375 <= |x| < 2^66 */</span> |
| <span class="ident">x</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.</span> <span class="op">/</span> <span class="ident">x</span>; |
| <span class="number">3</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="comment">/* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */</span> |
| <span class="kw">let</span> <span class="ident">s1</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">6</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">8</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">AT</span>[<span class="number">10</span>]))))); |
| <span class="kw">let</span> <span class="ident">s2</span> <span class="op">=</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">5</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">AT</span>[<span class="number">7</span>] <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">AT</span>[<span class="number">9</span>])))); |
| |
| <span class="kw">if</span> <span class="ident">id</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">x</span> <span class="op">*</span> (<span class="ident">s1</span> <span class="op">+</span> <span class="ident">s2</span>); |
| } |
| |
| <span class="kw">let</span> <span class="ident">z</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">ATANHI</span>, <span class="ident">id</span> <span class="kw">as</span> <span class="ident">usize</span>) <span class="op">-</span> (<span class="ident">x</span> <span class="op">*</span> (<span class="ident">s1</span> <span class="op">+</span> <span class="ident">s2</span>) <span class="op">-</span> <span class="macro">i!</span>(<span class="ident">ATANLO</span>, <span class="ident">id</span> <span class="kw">as</span> <span class="ident">usize</span>) <span class="op">-</span> <span class="ident">x</span>); |
| |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="op">-</span><span class="ident">z</span> |
| } <span class="kw">else</span> { |
| <span class="ident">z</span> |
| } |
| } |
| |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span> |
| <span class="kw">mod</span> <span class="ident">tests</span> { |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::atan</span>; |
| <span class="kw">use</span> <span class="ident">core::f64</span>; |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">sanity_check</span>() { |
| <span class="kw">for</span> (<span class="ident">input</span>, <span class="ident">answer</span>) <span class="kw">in</span> [ |
| (<span class="number">3.0_f64</span>.<span class="ident">sqrt</span>() <span class="op">/</span> <span class="number">3.0</span>, <span class="ident">f64::consts::FRAC_PI_6</span>), |
| (<span class="number">1.0</span>, <span class="ident">f64::consts::FRAC_PI_4</span>), |
| (<span class="number">3.0_f64</span>.<span class="ident">sqrt</span>(), <span class="ident">f64::consts::FRAC_PI_3</span>), |
| (<span class="op">-</span><span class="number">3.0_f64</span>.<span class="ident">sqrt</span>() <span class="op">/</span> <span class="number">3.0</span>, <span class="op">-</span><span class="ident">f64::consts::FRAC_PI_6</span>), |
| (<span class="op">-</span><span class="number">1.0</span>, <span class="op">-</span><span class="ident">f64::consts::FRAC_PI_4</span>), |
| (<span class="op">-</span><span class="number">3.0_f64</span>.<span class="ident">sqrt</span>(), <span class="op">-</span><span class="ident">f64::consts::FRAC_PI_3</span>), |
| ] |
| .<span class="ident">iter</span>() |
| { |
| <span class="macro">assert!</span>( |
| (<span class="ident">atan</span>(<span class="kw-2">*</span><span class="ident">input</span>) <span class="op">-</span> <span class="ident">answer</span>) <span class="op">/</span> <span class="ident">answer</span> <span class="op"><</span> <span class="number">1e-5</span>, |
| <span class="string">"\natan({:.4}/16) = {:.4}, actual: {}"</span>, |
| <span class="ident">input</span> <span class="op">*</span> <span class="number">16.0</span>, |
| <span class="ident">answer</span>, |
| <span class="ident">atan</span>(<span class="kw-2">*</span><span class="ident">input</span>) |
| ); |
| } |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">zero</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">atan</span>(<span class="number">0.0</span>), <span class="number">0.0</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">infinity</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">atan</span>(<span class="ident">f64::INFINITY</span>), <span class="ident">f64::consts::FRAC_PI_2</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">minus_infinity</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">atan</span>(<span class="ident">f64::NEG_INFINITY</span>), <span class="op">-</span><span class="ident">f64::consts::FRAC_PI_2</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">nan</span>() { |
| <span class="macro">assert!</span>(<span class="ident">atan</span>(<span class="ident">f64::NAN</span>).<span class="ident">is_nan</span>()); |
| } |
| } |
| </code></pre></div> |
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