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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.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">/* acos(x) |
| * Method : |
| * acos(x) = pi/2 - asin(x) |
| * acos(-x) = pi/2 + asin(x) |
| * For |x|<=0.5 |
| * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
| * For x>0.5 |
| * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
| * = 2asin(sqrt((1-x)/2)) |
| * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
| * = 2f + (2c + 2s*z*R(z)) |
| * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
| * for f so that f+c ~ sqrt(z). |
| * For x<-0.5 |
| * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
| * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
| * |
| * Special cases: |
| * if x is NaN, return x itself; |
| * if |x|>1, return NaN with invalid signal. |
| * |
| * Function needed: sqrt |
| */</span> |
| |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::sqrt</span>; |
| |
| <span class="kw">const</span> <span class="ident">PIO2_HI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.57079632679489655800e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54442D18 */</span> |
| <span class="kw">const</span> <span class="ident">PIO2_LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.12323399573676603587e-17</span>; <span class="comment">/* 0x3C91A626, 0x33145C07 */</span> |
| <span class="kw">const</span> <span class="ident">PS0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.66666666666666657415e-01</span>; <span class="comment">/* 0x3FC55555, 0x55555555 */</span> |
| <span class="kw">const</span> <span class="ident">PS1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.25565818622400915405e-01</span>; <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */</span> |
| <span class="kw">const</span> <span class="ident">PS2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.01212532134862925881e-01</span>; <span class="comment">/* 0x3FC9C155, 0x0E884455 */</span> |
| <span class="kw">const</span> <span class="ident">PS3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">4.00555345006794114027e-02</span>; <span class="comment">/* 0xBFA48228, 0xB5688F3B */</span> |
| <span class="kw">const</span> <span class="ident">PS4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.91534994289814532176e-04</span>; <span class="comment">/* 0x3F49EFE0, 0x7501B288 */</span> |
| <span class="kw">const</span> <span class="ident">PS5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.47933107596021167570e-05</span>; <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */</span> |
| <span class="kw">const</span> <span class="ident">QS1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.40339491173441421878e+00</span>; <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */</span> |
| <span class="kw">const</span> <span class="ident">QS2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.02094576023350569471e+00</span>; <span class="comment">/* 0x40002AE5, 0x9C598AC8 */</span> |
| <span class="kw">const</span> <span class="ident">QS3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.88283971605453293030e-01</span>; <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */</span> |
| <span class="kw">const</span> <span class="ident">QS4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.70381505559019352791e-02</span>; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */</span> |
| |
| <span class="kw">fn</span> <span class="ident">r</span>(<span class="ident">z</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">p</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PS0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PS1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PS2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PS3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PS4</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">PS5</span>))))); |
| <span class="kw">let</span> <span class="ident">q</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QS1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QS2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QS3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">QS4</span>))); |
| <span class="ident">p</span> <span class="op">/</span> <span class="ident">q</span> |
| } |
| |
| <span class="doccomment">/// Arccosine (f64)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Computes the inverse cosine (arc cosine) of the input value.</span> |
| <span class="doccomment">/// Arguments must be in the range -1 to 1.</span> |
| <span class="doccomment">/// Returns values in radians, in the range of 0 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">acos</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">x1p_120f</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x3870000000000000</span>); <span class="comment">// 0x1p-120 === 2 ^ -120</span> |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">w</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">c</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">df</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">hx</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| |
| <span class="ident">hx</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="ident">ix</span> <span class="op">=</span> <span class="ident">hx</span> <span class="op">&</span> <span class="number">0x7fffffff</span>; |
| <span class="comment">/* |x| >= 1 or nan */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3ff00000</span> { |
| <span class="kw">let</span> <span class="ident">lx</span>: <span class="ident">u32</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">if</span> ((<span class="ident">ix</span> <span class="op">-</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">/* acos(1)=0, acos(-1)=pi */</span> |
| <span class="kw">if</span> (<span class="ident">hx</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="number">2.</span> <span class="op">*</span> <span class="ident">PIO2_HI</span> <span class="op">+</span> <span class="ident">x1p_120f</span>; |
| } |
| <span class="kw">return</span> <span class="number">0.</span>; |
| } |
| <span class="kw">return</span> <span class="number">0.</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">x</span>); |
| } |
| <span class="comment">/* |x| < 0.5 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3fe00000</span> { |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span><span class="op">=</span> <span class="number">0x3c600000</span> { |
| <span class="comment">/* |x| < 2**-57 */</span> |
| <span class="kw">return</span> <span class="ident">PIO2_HI</span> <span class="op">+</span> <span class="ident">x1p_120f</span>; |
| } |
| <span class="kw">return</span> <span class="ident">PIO2_HI</span> <span class="op">-</span> (<span class="ident">x</span> <span class="op">-</span> (<span class="ident">PIO2_LO</span> <span class="op">-</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">r</span>(<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>))); |
| } |
| <span class="comment">/* x < -0.5 */</span> |
| <span class="kw">if</span> (<span class="ident">hx</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">z</span> <span class="op">=</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">x</span>) <span class="op">*</span> <span class="number">0.5</span>; |
| <span class="ident">s</span> <span class="op">=</span> <span class="ident">sqrt</span>(<span class="ident">z</span>); |
| <span class="ident">w</span> <span class="op">=</span> <span class="ident">r</span>(<span class="ident">z</span>) <span class="op">*</span> <span class="ident">s</span> <span class="op">-</span> <span class="ident">PIO2_LO</span>; |
| <span class="kw">return</span> <span class="number">2.</span> <span class="op">*</span> (<span class="ident">PIO2_HI</span> <span class="op">-</span> (<span class="ident">s</span> <span class="op">+</span> <span class="ident">w</span>)); |
| } |
| <span class="comment">/* x > 0.5 */</span> |
| <span class="ident">z</span> <span class="op">=</span> (<span class="number">1.0</span> <span class="op">-</span> <span class="ident">x</span>) <span class="op">*</span> <span class="number">0.5</span>; |
| <span class="ident">s</span> <span class="op">=</span> <span class="ident">sqrt</span>(<span class="ident">z</span>); |
| <span class="comment">// Set the low 4 bytes to zero</span> |
| <span class="ident">df</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">s</span>.<span class="ident">to_bits</span>() <span class="op">&</span> <span class="number">0xff_ff_ff_ff_00_00_00_00</span>); |
| |
| <span class="ident">c</span> <span class="op">=</span> (<span class="ident">z</span> <span class="op">-</span> <span class="ident">df</span> <span class="op">*</span> <span class="ident">df</span>) <span class="op">/</span> (<span class="ident">s</span> <span class="op">+</span> <span class="ident">df</span>); |
| <span class="ident">w</span> <span class="op">=</span> <span class="ident">r</span>(<span class="ident">z</span>) <span class="op">*</span> <span class="ident">s</span> <span class="op">+</span> <span class="ident">c</span>; |
| <span class="number">2.</span> <span class="op">*</span> (<span class="ident">df</span> <span class="op">+</span> <span class="ident">w</span>) |
| } |
| </code></pre></div> |
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