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</pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* 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>core::f64;
<span class="kw">const </span>LN2_HI: f64 = <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 3fe62e42 fee00000 */
</span><span class="kw">const </span>LN2_LO: f64 = <span class="number">1.90821492927058770002e-10</span>; <span class="comment">/* 3dea39ef 35793c76 */
</span><span class="kw">const </span>LG1: f64 = <span class="number">6.666666666666735130e-01</span>; <span class="comment">/* 3FE55555 55555593 */
</span><span class="kw">const </span>LG2: f64 = <span class="number">3.999999999940941908e-01</span>; <span class="comment">/* 3FD99999 9997FA04 */
</span><span class="kw">const </span>LG3: f64 = <span class="number">2.857142874366239149e-01</span>; <span class="comment">/* 3FD24924 94229359 */
</span><span class="kw">const </span>LG4: f64 = <span class="number">2.222219843214978396e-01</span>; <span class="comment">/* 3FCC71C5 1D8E78AF */
</span><span class="kw">const </span>LG5: f64 = <span class="number">1.818357216161805012e-01</span>; <span class="comment">/* 3FC74664 96CB03DE */
</span><span class="kw">const </span>LG6: f64 = <span class="number">1.531383769920937332e-01</span>; <span class="comment">/* 3FC39A09 D078C69F */
</span><span class="kw">const </span>LG7: f64 = <span class="number">1.479819860511658591e-01</span>; <span class="comment">/* 3FC2F112 DF3E5244 */
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>log1p(x: f64) -> f64 {
<span class="kw">let </span><span class="kw-2">mut </span>ui: u64 = x.to_bits();
<span class="kw">let </span>hfsq: f64;
<span class="kw">let </span><span class="kw-2">mut </span>f: f64 = <span class="number">0.</span>;
<span class="kw">let </span><span class="kw-2">mut </span>c: f64 = <span class="number">0.</span>;
<span class="kw">let </span>s: f64;
<span class="kw">let </span>z: f64;
<span class="kw">let </span>r: f64;
<span class="kw">let </span>w: f64;
<span class="kw">let </span>t1: f64;
<span class="kw">let </span>t2: f64;
<span class="kw">let </span>dk: f64;
<span class="kw">let </span>hx: u32;
<span class="kw">let </span><span class="kw-2">mut </span>hu: u32;
<span class="kw">let </span><span class="kw-2">mut </span>k: i32;
hx = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32;
k = <span class="number">1</span>;
<span class="kw">if </span>hx < <span class="number">0x3fda827a </span>|| (hx >> <span class="number">31</span>) > <span class="number">0 </span>{
<span class="comment">/* 1+x < sqrt(2)+ */
</span><span class="kw">if </span>hx >= <span class="number">0xbff00000 </span>{
<span class="comment">/* x <= -1.0 */
</span><span class="kw">if </span>x == -<span class="number">1. </span>{
<span class="kw">return </span>x / <span class="number">0.0</span>; <span class="comment">/* log1p(-1) = -inf */
</span>}
<span class="kw">return </span>(x - x) / <span class="number">0.0</span>; <span class="comment">/* log1p(x<-1) = NaN */
</span>}
<span class="kw">if </span>hx << <span class="number">1 </span>< <span class="number">0x3ca00000 </span><< <span class="number">1 </span>{
<span class="comment">/* |x| < 2**-53 */
/* underflow if subnormal */
</span><span class="kw">if </span>(hx & <span class="number">0x7ff00000</span>) == <span class="number">0 </span>{
<span class="macro">force_eval!</span>(x <span class="kw">as </span>f32);
}
<span class="kw">return </span>x;
}
<span class="kw">if </span>hx <= <span class="number">0xbfd2bec4 </span>{
<span class="comment">/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
</span>k = <span class="number">0</span>;
c = <span class="number">0.</span>;
f = x;
}
} <span class="kw">else if </span>hx >= <span class="number">0x7ff00000 </span>{
<span class="kw">return </span>x;
}
<span class="kw">if </span>k > <span class="number">0 </span>{
ui = (<span class="number">1. </span>+ x).to_bits();
hu = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32;
hu += <span class="number">0x3ff00000 </span>- <span class="number">0x3fe6a09e</span>;
k = (hu >> <span class="number">20</span>) <span class="kw">as </span>i32 - <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>k < <span class="number">54 </span>{
c = <span class="kw">if </span>k >= <span class="number">2 </span>{
<span class="number">1. </span>- (f64::from_bits(ui) - x)
} <span class="kw">else </span>{
x - (f64::from_bits(ui) - <span class="number">1.</span>)
};
c /= f64::from_bits(ui);
} <span class="kw">else </span>{
c = <span class="number">0.</span>;
}
<span class="comment">/* reduce u into [sqrt(2)/2, sqrt(2)] */
</span>hu = (hu & <span class="number">0x000fffff</span>) + <span class="number">0x3fe6a09e</span>;
ui = (hu <span class="kw">as </span>u64) << <span class="number">32 </span>| (ui & <span class="number">0xffffffff</span>);
f = f64::from_bits(ui) - <span class="number">1.</span>;
}
hfsq = <span class="number">0.5 </span>* f * f;
s = f / (<span class="number">2.0 </span>+ f);
z = s * s;
w = z * z;
t1 = w * (LG2 + w * (LG4 + w * LG6));
t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
r = t2 + t1;
dk = k <span class="kw">as </span>f64;
s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
}
</code></pre></div>
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