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