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| </pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c</span> |
| <span class="comment">//-</span> |
| <span class="comment">// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG></span> |
| <span class="comment">// All rights reserved.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Redistribution and use in source and binary forms, with or without</span> |
| <span class="comment">// modification, are permitted provided that the following conditions</span> |
| <span class="comment">// are met:</span> |
| <span class="comment">// 1. Redistributions of source code must retain the above copyright</span> |
| <span class="comment">// notice, this list of conditions and the following disclaimer.</span> |
| <span class="comment">// 2. Redistributions in binary form must reproduce the above copyright</span> |
| <span class="comment">// notice, this list of conditions and the following disclaimer in the</span> |
| <span class="comment">// documentation and/or other materials provided with the distribution.</span> |
| <span class="comment">//</span> |
| <span class="comment">// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND</span> |
| <span class="comment">// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span> |
| <span class="comment">// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE</span> |
| <span class="comment">// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE</span> |
| <span class="comment">// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL</span> |
| <span class="comment">// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS</span> |
| <span class="comment">// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)</span> |
| <span class="comment">// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT</span> |
| <span class="comment">// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY</span> |
| <span class="comment">// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF</span> |
| <span class="comment">// SUCH DAMAGE.</span> |
| |
| <span class="kw">const</span> <span class="ident">TBLSIZE</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">16</span>; |
| |
| <span class="kw">static</span> <span class="ident">EXP2FT</span>: [<span class="ident">u64</span>; <span class="ident">TBLSIZE</span>] <span class="op">=</span> [ |
| <span class="number">0x3fe6a09e667f3bcd</span>, |
| <span class="number">0x3fe7a11473eb0187</span>, |
| <span class="number">0x3fe8ace5422aa0db</span>, |
| <span class="number">0x3fe9c49182a3f090</span>, |
| <span class="number">0x3feae89f995ad3ad</span>, |
| <span class="number">0x3fec199bdd85529c</span>, |
| <span class="number">0x3fed5818dcfba487</span>, |
| <span class="number">0x3feea4afa2a490da</span>, |
| <span class="number">0x3ff0000000000000</span>, |
| <span class="number">0x3ff0b5586cf9890f</span>, |
| <span class="number">0x3ff172b83c7d517b</span>, |
| <span class="number">0x3ff2387a6e756238</span>, |
| <span class="number">0x3ff306fe0a31b715</span>, |
| <span class="number">0x3ff3dea64c123422</span>, |
| <span class="number">0x3ff4bfdad5362a27</span>, |
| <span class="number">0x3ff5ab07dd485429</span>, |
| ]; |
| |
| <span class="comment">// exp2f(x): compute the base 2 exponential of x</span> |
| <span class="comment">//</span> |
| <span class="comment">// Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Method: (equally-spaced tables)</span> |
| <span class="comment">//</span> |
| <span class="comment">// Reduce x:</span> |
| <span class="comment">// x = k + y, for integer k and |y| <= 1/2.</span> |
| <span class="comment">// Thus we have exp2f(x) = 2**k * exp2(y).</span> |
| <span class="comment">//</span> |
| <span class="comment">// Reduce y:</span> |
| <span class="comment">// y = i/TBLSIZE + z for integer i near y * TBLSIZE.</span> |
| <span class="comment">// Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),</span> |
| <span class="comment">// with |z| <= 2**-(TBLSIZE+1).</span> |
| <span class="comment">//</span> |
| <span class="comment">// We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a</span> |
| <span class="comment">// degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.</span> |
| <span class="comment">// Using double precision for everything except the reduction makes</span> |
| <span class="comment">// roundoff error insignificant and simplifies the scaling step.</span> |
| <span class="comment">//</span> |
| <span class="comment">// This method is due to Tang, but I do not use his suggested parameters:</span> |
| <span class="comment">//</span> |
| <span class="comment">// Tang, P. Table-driven Implementation of the Exponential Function</span> |
| <span class="comment">// in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).</span> |
| |
| <span class="doccomment">/// Exponential, base 2 (f32)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Calculate `2^x`, that is, 2 raised to the power `x`.</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">exp2f</span>(<span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="ident">redux</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x4b400000</span>) <span class="op">/</span> <span class="ident">TBLSIZE</span> <span class="kw">as</span> <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">p1</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x3f317218</span>); |
| <span class="kw">let</span> <span class="ident">p2</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x3e75fdf0</span>); |
| <span class="kw">let</span> <span class="ident">p3</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x3d6359a4</span>); |
| <span class="kw">let</span> <span class="ident">p4</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x3c1d964e</span>); |
| |
| <span class="comment">// double_t t, r, z;</span> |
| <span class="comment">// uint32_t ix, i0, k;</span> |
| |
| <span class="kw">let</span> <span class="ident">x1p127</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x7f000000</span>); |
| |
| <span class="comment">/* Filter out exceptional cases. */</span> |
| <span class="kw">let</span> <span class="ident">ui</span> <span class="op">=</span> <span class="ident">f32::to_bits</span>(<span class="ident">x</span>); |
| <span class="kw">let</span> <span class="ident">ix</span> <span class="op">=</span> <span class="ident">ui</span> <span class="op">&</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span> <span class="number">0x42fc0000</span> { |
| <span class="comment">/* |x| > 126 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span> <span class="number">0x7f800000</span> { |
| <span class="comment">/* NaN */</span> |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ui</span> <span class="op">></span><span class="op">=</span> <span class="number">0x43000000</span> <span class="op">&&</span> <span class="ident">ui</span> <span class="op"><</span> <span class="number">0x80000000</span> { |
| <span class="comment">/* x >= 128 */</span> |
| <span class="ident">x</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">x1p127</span>; |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ui</span> <span class="op">></span><span class="op">=</span> <span class="number">0x80000000</span> { |
| <span class="comment">/* x < -126 */</span> |
| <span class="kw">if</span> <span class="ident">ui</span> <span class="op">></span><span class="op">=</span> <span class="number">0xc3160000</span> <span class="op">|</span><span class="op">|</span> (<span class="ident">ui</span> <span class="op">&</span> <span class="number">0x0000ffff</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span>) { |
| <span class="macro">force_eval!</span>(<span class="ident">f32::from_bits</span>(<span class="number">0x80000001</span>) <span class="op">/</span> <span class="ident">x</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ui</span> <span class="op">></span><span class="op">=</span> <span class="number">0xc3160000</span> { |
| <span class="comment">/* x <= -150 */</span> |
| <span class="kw">return</span> <span class="number">0.0</span>; |
| } |
| } |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span><span class="op">=</span> <span class="number">0x33000000</span> { |
| <span class="comment">/* |x| <= 0x1p-25 */</span> |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">x</span>; |
| } |
| |
| <span class="comment">/* Reduce x, computing z, i0, and k. */</span> |
| <span class="kw">let</span> <span class="ident">ui</span> <span class="op">=</span> <span class="ident">f32::to_bits</span>(<span class="ident">x</span> <span class="op">+</span> <span class="ident">redux</span>); |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i0</span> <span class="op">=</span> <span class="ident">ui</span>; |
| <span class="ident">i0</span> <span class="op">+</span><span class="op">=</span> <span class="ident">TBLSIZE</span> <span class="kw">as</span> <span class="ident">u32</span> <span class="op">/</span> <span class="number">2</span>; |
| <span class="kw">let</span> <span class="ident">k</span> <span class="op">=</span> <span class="ident">i0</span> <span class="op">/</span> <span class="ident">TBLSIZE</span> <span class="kw">as</span> <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">ukf</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(((<span class="number">0x3ff</span> <span class="op">+</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">u64</span>) <span class="op"><</span><span class="op"><</span> <span class="number">52</span>); |
| <span class="ident">i0</span> <span class="op">&=</span> <span class="ident">TBLSIZE</span> <span class="kw">as</span> <span class="ident">u32</span> <span class="op">-</span> <span class="number">1</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">uf</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="ident">ui</span>); |
| <span class="ident">uf</span> <span class="op">-</span><span class="op">=</span> <span class="ident">redux</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span> <span class="op">=</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">uf</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="comment">/* Compute r = exp2(y) = exp2ft[i0] * p(z). */</span> |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">EXP2FT</span>[<span class="ident">i0</span> <span class="kw">as</span> <span class="ident">usize</span>]); |
| <span class="kw">let</span> <span class="ident">t</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">r</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">z</span>; |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">r</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">p1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p2</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span>) <span class="op">*</span> (<span class="ident">p3</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p4</span> <span class="kw">as</span> <span class="ident">f64</span>); |
| |
| <span class="comment">/* Scale by 2**k */</span> |
| (<span class="ident">r</span> <span class="op">*</span> <span class="ident">ukf</span>) <span class="kw">as</span> <span class="ident">f32</span> |
| } |
| </code></pre></div> |
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