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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */</span> |
| <span class="comment">/* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */</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="kw">const</span> <span class="ident">O_THRESHOLD</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">8.8721679688e+01</span>; <span class="comment">/* 0x42b17180 */</span> |
| <span class="kw">const</span> <span class="ident">LN2_HI</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">6.9313812256e-01</span>; <span class="comment">/* 0x3f317180 */</span> |
| <span class="kw">const</span> <span class="ident">LN2_LO</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">9.0580006145e-06</span>; <span class="comment">/* 0x3717f7d1 */</span> |
| <span class="kw">const</span> <span class="ident">INV_LN2</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.4426950216e+00</span>; <span class="comment">/* 0x3fb8aa3b */</span> |
| <span class="comment">/* |
| * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: |
| * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 |
| * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): |
| */</span> |
| <span class="kw">const</span> <span class="ident">Q1</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.3333212137e-2</span>; <span class="comment">/* -0x888868.0p-28 */</span> |
| <span class="kw">const</span> <span class="ident">Q2</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.5807170421e-3</span>; <span class="comment">/* 0xcf3010.0p-33 */</span> |
| |
| <span class="doccomment">/// Exponential, base *e*, of x-1 (f32)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Calculates the exponential of `x` and subtract 1, that is, *e* raised</span> |
| <span class="doccomment">/// to the power `x` minus 1 (where *e* is the base of the natural</span> |
| <span class="doccomment">/// system of logarithms, approximately 2.71828).</span> |
| <span class="doccomment">/// The result is accurate even for small values of `x`,</span> |
| <span class="doccomment">/// where using `exp(x)-1` would lose many significant digits.</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">expm1f</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">x1p127</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(<span class="number">0x7f000000</span>); <span class="comment">// 0x1p127f === 2 ^ 127</span> |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hx</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>(); |
| <span class="kw">let</span> <span class="ident">sign</span> <span class="op">=</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">hx</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| |
| <span class="comment">/* filter out huge and non-finite argument */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4195b844</span> { |
| <span class="comment">/* if |x|>=27*ln2 */</span> |
| <span class="kw">if</span> <span class="ident">hx</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">sign</span> { |
| <span class="kw">return</span> <span class="op">-</span><span class="number">1.</span>; |
| } |
| <span class="kw">if</span> <span class="ident">x</span> <span class="op">></span> <span class="ident">O_THRESHOLD</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">let</span> <span class="ident">k</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="ident">hi</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">lo</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">c</span> <span class="op">=</span> <span class="number">0f32</span>; |
| <span class="comment">/* argument reduction */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span> <span class="number">0x3eb17218</span> { |
| <span class="comment">/* if |x| > 0.5 ln2 */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0x3F851592</span> { |
| <span class="comment">/* and |x| < 1.5 ln2 */</span> |
| <span class="kw">if</span> <span class="op">!</span><span class="ident">sign</span> { |
| <span class="ident">hi</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">LN2_HI</span>; |
| <span class="ident">lo</span> <span class="op">=</span> <span class="ident">LN2_LO</span>; |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">1</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">hi</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">+</span> <span class="ident">LN2_HI</span>; |
| <span class="ident">lo</span> <span class="op">=</span> <span class="op">-</span><span class="ident">LN2_LO</span>; |
| <span class="ident">k</span> <span class="op">=</span> <span class="op">-</span><span class="number">1</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="ident">k</span> <span class="op">=</span> (<span class="ident">INV_LN2</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">+</span> (<span class="kw">if</span> <span class="ident">sign</span> { <span class="op">-</span><span class="number">0.5</span> } <span class="kw">else</span> { <span class="number">0.5</span> })) <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f32</span>; |
| <span class="ident">hi</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">LN2_HI</span>; <span class="comment">/* t*ln2_hi is exact here */</span> |
| <span class="ident">lo</span> <span class="op">=</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">LN2_LO</span>; |
| } |
| <span class="ident">x</span> <span class="op">=</span> <span class="ident">hi</span> <span class="op">-</span> <span class="ident">lo</span>; |
| <span class="ident">c</span> <span class="op">=</span> (<span class="ident">hi</span> <span class="op">-</span> <span class="ident">x</span>) <span class="op">-</span> <span class="ident">lo</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0x33000000</span> { |
| <span class="comment">/* when |x|<2**-25, return x */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0x00800000</span> { |
| <span class="macro">force_eval!</span>(<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>); |
| } |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>; |
| } |
| |
| <span class="comment">/* x is now in primary range */</span> |
| <span class="kw">let</span> <span class="ident">hfx</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="kw">let</span> <span class="ident">hxs</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">hfx</span>; |
| <span class="kw">let</span> <span class="ident">r1</span> <span class="op">=</span> <span class="number">1.</span> <span class="op">+</span> <span class="ident">hxs</span> <span class="op">*</span> (<span class="ident">Q1</span> <span class="op">+</span> <span class="ident">hxs</span> <span class="op">*</span> <span class="ident">Q2</span>); |
| <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="number">3.</span> <span class="op">-</span> <span class="ident">r1</span> <span class="op">*</span> <span class="ident">hfx</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">e</span> <span class="op">=</span> <span class="ident">hxs</span> <span class="op">*</span> ((<span class="ident">r1</span> <span class="op">-</span> <span class="ident">t</span>) <span class="op">/</span> (<span class="number">6.</span> <span class="op">-</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">t</span>)); |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* c is 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">e</span> <span class="op">-</span> <span class="ident">hxs</span>); |
| } |
| <span class="ident">e</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> (<span class="ident">e</span> <span class="op">-</span> <span class="ident">c</span>) <span class="op">-</span> <span class="ident">c</span>; |
| <span class="ident">e</span> <span class="op">-</span><span class="op">=</span> <span class="ident">hxs</span>; |
| <span class="comment">/* exp(x) ~ 2^k (x_reduced - e + 1) */</span> |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="op">-</span><span class="number">1</span> { |
| <span class="kw">return</span> <span class="number">0.5</span> <span class="op">*</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">e</span>) <span class="op">-</span> <span class="number">0.5</span>; |
| } |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="number">1</span> { |
| <span class="kw">if</span> <span class="ident">x</span> <span class="op"><</span> <span class="op">-</span><span class="number">0.25</span> { |
| <span class="kw">return</span> <span class="op">-</span><span class="number">2.</span> <span class="op">*</span> (<span class="ident">e</span> <span class="op">-</span> (<span class="ident">x</span> <span class="op">+</span> <span class="number">0.5</span>)); |
| } |
| <span class="kw">return</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="op">-</span> <span class="ident">e</span>); |
| } |
| <span class="kw">let</span> <span class="ident">twopk</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(((<span class="number">0x7f</span> <span class="op">+</span> <span class="ident">k</span>) <span class="op"><</span><span class="op"><</span> <span class="number">23</span>) <span class="kw">as</span> <span class="ident">u32</span>); <span class="comment">/* 2^k */</span> |
| <span class="kw">if</span> (<span class="ident">k</span> <span class="op"><</span> <span class="number">0</span>) <span class="op">|</span><span class="op">|</span> (<span class="ident">k</span> <span class="op">></span> <span class="number">56</span>) { |
| <span class="comment">/* suffice to return exp(x)-1 */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">y</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">e</span> <span class="op">+</span> <span class="number">1.</span>; |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="number">128</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> <span class="number">2.</span> <span class="op">*</span> <span class="ident">x1p127</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">*</span> <span class="ident">twopk</span>; |
| } |
| <span class="kw">return</span> <span class="ident">y</span> <span class="op">-</span> <span class="number">1.</span>; |
| } |
| <span class="kw">let</span> <span class="ident">uf</span> <span class="op">=</span> <span class="ident">f32::from_bits</span>(((<span class="number">0x7f</span> <span class="op">-</span> <span class="ident">k</span>) <span class="op"><</span><span class="op"><</span> <span class="number">23</span>) <span class="kw">as</span> <span class="ident">u32</span>); <span class="comment">/* 2^-k */</span> |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op"><</span> <span class="number">23</span> { |
| (<span class="ident">x</span> <span class="op">-</span> <span class="ident">e</span> <span class="op">+</span> (<span class="number">1.</span> <span class="op">-</span> <span class="ident">uf</span>)) <span class="op">*</span> <span class="ident">twopk</span> |
| } <span class="kw">else</span> { |
| (<span class="ident">x</span> <span class="op">-</span> (<span class="ident">e</span> <span class="op">+</span> <span class="ident">uf</span>) <span class="op">+</span> <span class="number">1.</span>) <span class="op">*</span> <span class="ident">twopk</span> |
| } |
| } |
| </code></pre></div> |
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