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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */</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="comment">/* double log1p(double x) |
| * Return the natural logarithm of 1+x. |
| * |
| * Method : |
| * 1. Argument Reduction: find k and f such that |
| * 1+x = 2^k * (1+f), |
| * where sqrt(2)/2 < 1+f < sqrt(2) . |
| * |
| * Note. If k=0, then f=x is exact. However, if k!=0, then f |
| * may not be representable exactly. In that case, a correction |
| * term is need. Let u=1+x rounded. Let c = (1+x)-u, then |
| * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), |
| * and add back the correction term c/u. |
| * (Note: when x > 2**53, one can simply return log(x)) |
| * |
| * 2. Approximation of log(1+f): See log.c |
| * |
| * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c |
| * |
| * Special cases: |
| * log1p(x) is NaN with signal if x < -1 (including -INF) ; |
| * log1p(+INF) is +INF; log1p(-1) is -INF with signal; |
| * log1p(NaN) is that NaN with no signal. |
| * |
| * Accuracy: |
| * according to an error analysis, the error is always less than |
| * 1 ulp (unit in the last place). |
| * |
| * Constants: |
| * The hexadecimal values are the intended ones for the following |
| * constants. The decimal values may be used, provided that the |
| * compiler will convert from decimal to binary accurately enough |
| * to produce the hexadecimal values shown. |
| * |
| * Note: Assuming log() return accurate answer, the following |
| * algorithm can be used to compute log1p(x) to within a few ULP: |
| * |
| * u = 1+x; |
| * if(u==1.0) return x ; else |
| * return log(u)*(x/(u-1.0)); |
| * |
| * See HP-15C Advanced Functions Handbook, p.193. |
| */</span> |
| |
| <span class="kw">use</span> <span class="ident">core::f64</span>; |
| |
| <span class="kw">const</span> <span class="ident">LN2_HI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 3fe62e42 fee00000 */</span> |
| <span class="kw">const</span> <span class="ident">LN2_LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.90821492927058770002e-10</span>; <span class="comment">/* 3dea39ef 35793c76 */</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">log1p</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</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="kw-2">mut</span> <span class="ident">f</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">0.</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">c</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">0.</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="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">hx</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hu</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">></span><span class="op">></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">1</span>; |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0x3fda827a</span> <span class="op">|</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="number">0</span> { |
| <span class="comment">/* 1+x < sqrt(2)+ */</span> |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span><span class="op">=</span> <span class="number">0xbff00000</span> { |
| <span class="comment">/* x <= -1.0 */</span> |
| <span class="kw">if</span> <span class="ident">x</span> <span class="op">==</span> <span class="op">-</span><span class="number">1.</span> { |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">/</span> <span class="number">0.0</span>; <span class="comment">/* log1p(-1) = -inf */</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">/* log1p(x<-1) = NaN */</span> |
| } |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span><span class="op"><</span> <span class="number">1</span> <span class="op"><</span> <span class="number">0x3ca00000</span> <span class="op"><</span><span class="op"><</span> <span class="number">1</span> { |
| <span class="comment">/* |x| < 2**-53 */</span> |
| <span class="comment">/* underflow if subnormal */</span> |
| <span class="kw">if</span> (<span class="ident">hx</span> <span class="op">&</span> <span class="number">0x7ff00000</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="macro">force_eval!</span>(<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</span>); |
| } |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span><span class="op">=</span> <span class="number">0xbfd2bec4</span> { |
| <span class="comment">/* sqrt(2)/2- <= 1+x < sqrt(2)+ */</span> |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="ident">c</span> <span class="op">=</span> <span class="number">0.</span>; |
| <span class="ident">f</span> <span class="op">=</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="op">=</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="ident">ui</span> <span class="op">=</span> (<span class="number">1.</span> <span class="op">+</span> <span class="ident">x</span>).<span class="ident">to_bits</span>(); |
| <span class="ident">hu</span> <span class="op">=</span> (<span class="ident">ui</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">hu</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="ident">hu</span> <span class="op">></span><span class="op">></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="comment">/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */</span> |
| <span class="kw">if</span> <span class="ident">k</span> <span class="op"><</span> <span class="number">54</span> { |
| <span class="ident">c</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">k</span> <span class="op">></span><span class="op">=</span> <span class="number">2</span> { |
| <span class="number">1.</span> <span class="op">-</span> (<span class="ident">f64::from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="ident">x</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">x</span> <span class="op">-</span> (<span class="ident">f64::from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="number">1.</span>) |
| }; |
| <span class="ident">c</span> <span class="op">/</span><span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">ui</span>); |
| } <span class="kw">else</span> { |
| <span class="ident">c</span> <span class="op">=</span> <span class="number">0.</span>; |
| } |
| <span class="comment">/* reduce u into [sqrt(2)/2, sqrt(2)] */</span> |
| <span class="ident">hu</span> <span class="op">=</span> (<span class="ident">hu</span> <span class="op">&</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">hu</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op"><</span><span class="op"><</span> <span class="number">32</span> <span class="op">|</span> (<span class="ident">ui</span> <span class="op">&</span> <span class="number">0xffffffff</span>); |
| <span class="ident">f</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="number">1.</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="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">s</span> <span class="op">*</span> (<span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">r</span>) <span class="op">+</span> (<span class="ident">dk</span> <span class="op">*</span> <span class="ident">LN2_LO</span> <span class="op">+</span> <span class="ident">c</span>) <span class="op">-</span> <span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">f</span> <span class="op">+</span> <span class="ident">dk</span> <span class="op">*</span> <span class="ident">LN2_HI</span> |
| } |
| </code></pre></div> |
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