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</pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.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">/*
* Return the base 10 logarithm of x. See log.c for most comments.
*
* Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
* as in log.c, then combine and scale in extra precision:
* log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
*/</span>
<span class="kw">use</span> <span class="ident">core::f64</span>;
<span class="kw">const</span> <span class="ident">IVLN10HI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.34294481878168880939e-01</span>; <span class="comment">/* 0x3fdbcb7b, 0x15200000 */</span>
<span class="kw">const</span> <span class="ident">IVLN10LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.50829467116452752298e-11</span>; <span class="comment">/* 0x3dbb9438, 0xca9aadd5 */</span>
<span class="kw">const</span> <span class="ident">LOG10_2HI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.01029995663611771306e-01</span>; <span class="comment">/* 0x3FD34413, 0x509F6000 */</span>
<span class="kw">const</span> <span class="ident">LOG10_2LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.69423907715893078616e-13</span>; <span class="comment">/* 0x3D59FEF3, 0x11F12B36 */</span>
<span class="kw">const</span> <span class="ident">LG1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.666666666666735130e-01</span>; <span class="comment">/* 3FE55555 55555593 */</span>
<span class="kw">const</span> <span class="ident">LG2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.999999999940941908e-01</span>; <span class="comment">/* 3FD99999 9997FA04 */</span>
<span class="kw">const</span> <span class="ident">LG3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.857142874366239149e-01</span>; <span class="comment">/* 3FD24924 94229359 */</span>
<span class="kw">const</span> <span class="ident">LG4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.222219843214978396e-01</span>; <span class="comment">/* 3FCC71C5 1D8E78AF */</span>
<span class="kw">const</span> <span class="ident">LG5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.818357216161805012e-01</span>; <span class="comment">/* 3FC74664 96CB03DE */</span>
<span class="kw">const</span> <span class="ident">LG6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.531383769920937332e-01</span>; <span class="comment">/* 3FC39A09 D078C69F */</span>
<span class="kw">const</span> <span class="ident">LG7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.479819860511658591e-01</span>; <span class="comment">/* 3FC2F112 DF3E5244 */</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">log10</span>(<span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) -&gt; <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">x1p54</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x4350000000000000</span>); <span class="comment">// 0x1p54 === 2 ^ 54</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ui</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>();
<span class="kw">let</span> <span class="ident">hfsq</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">f</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">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">w</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">t1</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">t2</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">dk</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">y</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hi</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">lo</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">val_hi</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">val_lo</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hx</span>: <span class="ident">u32</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span>: <span class="ident">i32</span>;
<span class="ident">hx</span> <span class="op">=</span> (<span class="ident">ui</span> <span class="op">&gt;</span><span class="op">&gt;</span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>;
<span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">if</span> <span class="ident">hx</span> <span class="op">&lt;</span> <span class="number">0x00100000</span> <span class="op">|</span><span class="op">|</span> (<span class="ident">hx</span> <span class="op">&gt;</span><span class="op">&gt;</span> <span class="number">31</span>) <span class="op">&gt;</span> <span class="number">0</span> {
<span class="kw">if</span> <span class="ident">ui</span> <span class="op">&lt;</span><span class="op">&lt;</span> <span class="number">1</span> <span class="op">==</span> <span class="number">0</span> {
<span class="kw">return</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="ident">x</span>); <span class="comment">/* log(+-0)=-inf */</span>
}
<span class="kw">if</span> (<span class="ident">hx</span> <span class="op">&gt;</span><span class="op">&gt;</span> <span class="number">31</span>) <span class="op">&gt;</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="number">0.0</span>; <span class="comment">/* log(-#) = NaN */</span>
}
<span class="comment">/* subnormal number, scale x up */</span>
<span class="ident">k</span> <span class="op">-</span><span class="op">=</span> <span class="number">54</span>;
<span class="ident">x</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">x1p54</span>;
<span class="ident">ui</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>();
<span class="ident">hx</span> <span class="op">=</span> (<span class="ident">ui</span> <span class="op">&gt;</span><span class="op">&gt;</span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">hx</span> <span class="op">&gt;</span><span class="op">=</span> <span class="number">0x7ff00000</span> {
<span class="kw">return</span> <span class="ident">x</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">hx</span> <span class="op">==</span> <span class="number">0x3ff00000</span> <span class="op">&amp;&amp;</span> <span class="ident">ui</span> <span class="op">&lt;</span><span class="op">&lt;</span> <span class="number">32</span> <span class="op">==</span> <span class="number">0</span> {
<span class="kw">return</span> <span class="number">0.</span>;
}
<span class="comment">/* reduce x into [sqrt(2)/2, sqrt(2)] */</span>
<span class="ident">hx</span> <span class="op">+</span><span class="op">=</span> <span class="number">0x3ff00000</span> <span class="op">-</span> <span class="number">0x3fe6a09e</span>;
<span class="ident">k</span> <span class="op">+</span><span class="op">=</span> (<span class="ident">hx</span> <span class="op">&gt;</span><span class="op">&gt;</span> <span class="number">20</span>) <span class="kw">as</span> <span class="ident">i32</span> <span class="op">-</span> <span class="number">0x3ff</span>;
<span class="ident">hx</span> <span class="op">=</span> (<span class="ident">hx</span> <span class="op">&amp;</span> <span class="number">0x000fffff</span>) <span class="op">+</span> <span class="number">0x3fe6a09e</span>;
<span class="ident">ui</span> <span class="op">=</span> (<span class="ident">hx</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op">&lt;</span><span class="op">&lt;</span> <span class="number">32</span> <span class="op">|</span> (<span class="ident">ui</span> <span class="op">&amp;</span> <span class="number">0xffffffff</span>);
<span class="ident">x</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">ui</span>);
<span class="ident">f</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1.0</span>;
<span class="ident">hfsq</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">f</span> <span class="op">*</span> <span class="ident">f</span>;
<span class="ident">s</span> <span class="op">=</span> <span class="ident">f</span> <span class="op">/</span> (<span class="number">2.0</span> <span class="op">+</span> <span class="ident">f</span>);
<span class="ident">z</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">s</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="ident">t1</span> <span class="op">=</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG2</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG4</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">LG6</span>));
<span class="ident">t2</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">LG1</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG3</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG5</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">LG7</span>)));
<span class="ident">r</span> <span class="op">=</span> <span class="ident">t2</span> <span class="op">+</span> <span class="ident">t1</span>;
<span class="comment">/* See log2.c for details. */</span>
<span class="comment">/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */</span>
<span class="ident">hi</span> <span class="op">=</span> <span class="ident">f</span> <span class="op">-</span> <span class="ident">hfsq</span>;
<span class="ident">ui</span> <span class="op">=</span> <span class="ident">hi</span>.<span class="ident">to_bits</span>();
<span class="ident">ui</span> <span class="op">&amp;=</span> (<span class="op">-</span><span class="number">1i64</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op">&lt;</span><span class="op">&lt;</span> <span class="number">32</span>;
<span class="ident">hi</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">ui</span>);
<span class="ident">lo</span> <span class="op">=</span> <span class="ident">f</span> <span class="op">-</span> <span class="ident">hi</span> <span class="op">-</span> <span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">r</span>);
<span class="comment">/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */</span>
<span class="ident">val_hi</span> <span class="op">=</span> <span class="ident">hi</span> <span class="op">*</span> <span class="ident">IVLN10HI</span>;
<span class="ident">dk</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span>;
<span class="ident">y</span> <span class="op">=</span> <span class="ident">dk</span> <span class="op">*</span> <span class="ident">LOG10_2HI</span>;
<span class="ident">val_lo</span> <span class="op">=</span> <span class="ident">dk</span> <span class="op">*</span> <span class="ident">LOG10_2LO</span> <span class="op">+</span> (<span class="ident">lo</span> <span class="op">+</span> <span class="ident">hi</span>) <span class="op">*</span> <span class="ident">IVLN10LO</span> <span class="op">+</span> <span class="ident">lo</span> <span class="op">*</span> <span class="ident">IVLN10HI</span>;
<span class="comment">/*
* Extra precision in for adding y is not strictly needed
* since there is no very large cancellation near x = sqrt(2) or
* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
* with some parallelism and it reduces the error for many args.
*/</span>
<span class="ident">w</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="ident">val_hi</span>;
<span class="ident">val_lo</span> <span class="op">+</span><span class="op">=</span> (<span class="ident">y</span> <span class="op">-</span> <span class="ident">w</span>) <span class="op">+</span> <span class="ident">val_hi</span>;
<span class="ident">val_hi</span> <span class="op">=</span> <span class="ident">w</span>;
<span class="ident">val_lo</span> <span class="op">+</span> <span class="ident">val_hi</span>
}
</code></pre></div>
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