<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/powf.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>powf.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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</pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* 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">use super</span>::{fabsf, scalbnf, sqrtf};
<span class="kw">const </span>BP: [f32; <span class="number">2</span>] = [<span class="number">1.0</span>, <span class="number">1.5</span>];
<span class="kw">const </span>DP_H: [f32; <span class="number">2</span>] = [<span class="number">0.0</span>, <span class="number">5.84960938e-01</span>]; <span class="comment">/* 0x3f15c000 */
</span><span class="kw">const </span>DP_L: [f32; <span class="number">2</span>] = [<span class="number">0.0</span>, <span class="number">1.56322085e-06</span>]; <span class="comment">/* 0x35d1cfdc */
</span><span class="kw">const </span>TWO24: f32 = <span class="number">16777216.0</span>; <span class="comment">/* 0x4b800000 */
</span><span class="kw">const </span>HUGE: f32 = <span class="number">1.0e30</span>;
<span class="kw">const </span>TINY: f32 = <span class="number">1.0e-30</span>;
<span class="kw">const </span>L1: f32 = <span class="number">6.0000002384e-01</span>; <span class="comment">/* 0x3f19999a */
</span><span class="kw">const </span>L2: f32 = <span class="number">4.2857143283e-01</span>; <span class="comment">/* 0x3edb6db7 */
</span><span class="kw">const </span>L3: f32 = <span class="number">3.3333334327e-01</span>; <span class="comment">/* 0x3eaaaaab */
</span><span class="kw">const </span>L4: f32 = <span class="number">2.7272811532e-01</span>; <span class="comment">/* 0x3e8ba305 */
</span><span class="kw">const </span>L5: f32 = <span class="number">2.3066075146e-01</span>; <span class="comment">/* 0x3e6c3255 */
</span><span class="kw">const </span>L6: f32 = <span class="number">2.0697501302e-01</span>; <span class="comment">/* 0x3e53f142 */
</span><span class="kw">const </span>P1: f32 = <span class="number">1.6666667163e-01</span>; <span class="comment">/* 0x3e2aaaab */
</span><span class="kw">const </span>P2: f32 = -<span class="number">2.7777778450e-03</span>; <span class="comment">/* 0xbb360b61 */
</span><span class="kw">const </span>P3: f32 = <span class="number">6.6137559770e-05</span>; <span class="comment">/* 0x388ab355 */
</span><span class="kw">const </span>P4: f32 = -<span class="number">1.6533901999e-06</span>; <span class="comment">/* 0xb5ddea0e */
</span><span class="kw">const </span>P5: f32 = <span class="number">4.1381369442e-08</span>; <span class="comment">/* 0x3331bb4c */
</span><span class="kw">const </span>LG2: f32 = <span class="number">6.9314718246e-01</span>; <span class="comment">/* 0x3f317218 */
</span><span class="kw">const </span>LG2_H: f32 = <span class="number">6.93145752e-01</span>; <span class="comment">/* 0x3f317200 */
</span><span class="kw">const </span>LG2_L: f32 = <span class="number">1.42860654e-06</span>; <span class="comment">/* 0x35bfbe8c */
</span><span class="kw">const </span>OVT: f32 = <span class="number">4.2995665694e-08</span>; <span class="comment">/* -(128-log2(ovfl+.5ulp)) */
</span><span class="kw">const </span>CP: f32 = <span class="number">9.6179670095e-01</span>; <span class="comment">/* 0x3f76384f =2/(3ln2) */
</span><span class="kw">const </span>CP_H: f32 = <span class="number">9.6191406250e-01</span>; <span class="comment">/* 0x3f764000 =12b cp */
</span><span class="kw">const </span>CP_L: f32 = -<span class="number">1.1736857402e-04</span>; <span class="comment">/* 0xb8f623c6 =tail of cp_h */
</span><span class="kw">const </span>IVLN2: f32 = <span class="number">1.4426950216e+00</span>;
<span class="kw">const </span>IVLN2_H: f32 = <span class="number">1.4426879883e+00</span>;
<span class="kw">const </span>IVLN2_L: f32 = <span class="number">7.0526075433e-06</span>;
<span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>powf(x: f32, y: f32) -> f32 {
<span class="kw">let </span><span class="kw-2">mut </span>z: f32;
<span class="kw">let </span><span class="kw-2">mut </span>ax: f32;
<span class="kw">let </span>z_h: f32;
<span class="kw">let </span>z_l: f32;
<span class="kw">let </span><span class="kw-2">mut </span>p_h: f32;
<span class="kw">let </span><span class="kw-2">mut </span>p_l: f32;
<span class="kw">let </span>y1: f32;
<span class="kw">let </span><span class="kw-2">mut </span>t1: f32;
<span class="kw">let </span>t2: f32;
<span class="kw">let </span><span class="kw-2">mut </span>r: f32;
<span class="kw">let </span>s: f32;
<span class="kw">let </span><span class="kw-2">mut </span>sn: f32;
<span class="kw">let </span><span class="kw-2">mut </span>t: f32;
<span class="kw">let </span><span class="kw-2">mut </span>u: f32;
<span class="kw">let </span><span class="kw-2">mut </span>v: f32;
<span class="kw">let </span><span class="kw-2">mut </span>w: f32;
<span class="kw">let </span>i: i32;
<span class="kw">let </span><span class="kw-2">mut </span>j: i32;
<span class="kw">let </span><span class="kw-2">mut </span>k: i32;
<span class="kw">let </span><span class="kw-2">mut </span>yisint: i32;
<span class="kw">let </span><span class="kw-2">mut </span>n: i32;
<span class="kw">let </span>hx: i32;
<span class="kw">let </span>hy: i32;
<span class="kw">let </span><span class="kw-2">mut </span>ix: i32;
<span class="kw">let </span>iy: i32;
<span class="kw">let </span><span class="kw-2">mut </span>is: i32;
hx = x.to_bits() <span class="kw">as </span>i32;
hy = y.to_bits() <span class="kw">as </span>i32;
ix = hx & <span class="number">0x7fffffff</span>;
iy = hy & <span class="number">0x7fffffff</span>;
<span class="comment">/* x**0 = 1, even if x is NaN */
</span><span class="kw">if </span>iy == <span class="number">0 </span>{
<span class="kw">return </span><span class="number">1.0</span>;
}
<span class="comment">/* 1**y = 1, even if y is NaN */
</span><span class="kw">if </span>hx == <span class="number">0x3f800000 </span>{
<span class="kw">return </span><span class="number">1.0</span>;
}
<span class="comment">/* NaN if either arg is NaN */
</span><span class="kw">if </span>ix > <span class="number">0x7f800000 </span>|| iy > <span class="number">0x7f800000 </span>{
<span class="kw">return </span>x + y;
}
<span class="comment">/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
</span>yisint = <span class="number">0</span>;
<span class="kw">if </span>hx < <span class="number">0 </span>{
<span class="kw">if </span>iy >= <span class="number">0x4b800000 </span>{
yisint = <span class="number">2</span>; <span class="comment">/* even integer y */
</span>} <span class="kw">else if </span>iy >= <span class="number">0x3f800000 </span>{
k = (iy >> <span class="number">23</span>) - <span class="number">0x7f</span>; <span class="comment">/* exponent */
</span>j = iy >> (<span class="number">23 </span>- k);
<span class="kw">if </span>(j << (<span class="number">23 </span>- k)) == iy {
yisint = <span class="number">2 </span>- (j & <span class="number">1</span>);
}
}
}
<span class="comment">/* special value of y */
</span><span class="kw">if </span>iy == <span class="number">0x7f800000 </span>{
<span class="comment">/* y is +-inf */
</span><span class="kw">if </span>ix == <span class="number">0x3f800000 </span>{
<span class="comment">/* (-1)**+-inf is 1 */
</span><span class="kw">return </span><span class="number">1.0</span>;
} <span class="kw">else if </span>ix > <span class="number">0x3f800000 </span>{
<span class="comment">/* (|x|>1)**+-inf = inf,0 */
</span><span class="kw">return if </span>hy >= <span class="number">0 </span>{ y } <span class="kw">else </span>{ <span class="number">0.0 </span>};
} <span class="kw">else </span>{
<span class="comment">/* (|x|<1)**+-inf = 0,inf */
</span><span class="kw">return if </span>hy >= <span class="number">0 </span>{ <span class="number">0.0 </span>} <span class="kw">else </span>{ -y };
}
}
<span class="kw">if </span>iy == <span class="number">0x3f800000 </span>{
<span class="comment">/* y is +-1 */
</span><span class="kw">return if </span>hy >= <span class="number">0 </span>{ x } <span class="kw">else </span>{ <span class="number">1.0 </span>/ x };
}
<span class="kw">if </span>hy == <span class="number">0x40000000 </span>{
<span class="comment">/* y is 2 */
</span><span class="kw">return </span>x * x;
}
<span class="kw">if </span>hy == <span class="number">0x3f000000
</span><span class="comment">/* y is 0.5 */
</span>&& hx >= <span class="number">0
</span>{
<span class="comment">/* x >= +0 */
</span><span class="kw">return </span>sqrtf(x);
}
ax = fabsf(x);
<span class="comment">/* special value of x */
</span><span class="kw">if </span>ix == <span class="number">0x7f800000 </span>|| ix == <span class="number">0 </span>|| ix == <span class="number">0x3f800000 </span>{
<span class="comment">/* x is +-0,+-inf,+-1 */
</span>z = ax;
<span class="kw">if </span>hy < <span class="number">0 </span>{
<span class="comment">/* z = (1/|x|) */
</span>z = <span class="number">1.0 </span>/ z;
}
<span class="kw">if </span>hx < <span class="number">0 </span>{
<span class="kw">if </span>((ix - <span class="number">0x3f800000</span>) | yisint) == <span class="number">0 </span>{
z = (z - z) / (z - z); <span class="comment">/* (-1)**non-int is NaN */
</span>} <span class="kw">else if </span>yisint == <span class="number">1 </span>{
z = -z; <span class="comment">/* (x<0)**odd = -(|x|**odd) */
</span>}
}
<span class="kw">return </span>z;
}
sn = <span class="number">1.0</span>; <span class="comment">/* sign of result */
</span><span class="kw">if </span>hx < <span class="number">0 </span>{
<span class="kw">if </span>yisint == <span class="number">0 </span>{
<span class="comment">/* (x<0)**(non-int) is NaN */
</span><span class="kw">return </span>(x - x) / (x - x);
}
<span class="kw">if </span>yisint == <span class="number">1 </span>{
<span class="comment">/* (x<0)**(odd int) */
</span>sn = -<span class="number">1.0</span>;
}
}
<span class="comment">/* |y| is HUGE */
</span><span class="kw">if </span>iy > <span class="number">0x4d000000 </span>{
<span class="comment">/* if |y| > 2**27 */
/* over/underflow if x is not close to one */
</span><span class="kw">if </span>ix < <span class="number">0x3f7ffff8 </span>{
<span class="kw">return if </span>hy < <span class="number">0 </span>{
sn * HUGE * HUGE
} <span class="kw">else </span>{
sn * TINY * TINY
};
}
<span class="kw">if </span>ix > <span class="number">0x3f800007 </span>{
<span class="kw">return if </span>hy > <span class="number">0 </span>{
sn * HUGE * HUGE
} <span class="kw">else </span>{
sn * TINY * TINY
};
}
<span class="comment">/* now |1-x| is TINY <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
</span>t = ax - <span class="number">1.</span>; <span class="comment">/* t has 20 trailing zeros */
</span>w = (t * t) * (<span class="number">0.5 </span>- t * (<span class="number">0.333333333333 </span>- t * <span class="number">0.25</span>));
u = IVLN2_H * t; <span class="comment">/* IVLN2_H has 16 sig. bits */
</span>v = t * IVLN2_L - w * IVLN2;
t1 = u + v;
is = t1.to_bits() <span class="kw">as </span>i32;
t1 = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
t2 = v - (t1 - u);
} <span class="kw">else </span>{
<span class="kw">let </span><span class="kw-2">mut </span>s2: f32;
<span class="kw">let </span><span class="kw-2">mut </span>s_h: f32;
<span class="kw">let </span>s_l: f32;
<span class="kw">let </span><span class="kw-2">mut </span>t_h: f32;
<span class="kw">let </span><span class="kw-2">mut </span>t_l: f32;
n = <span class="number">0</span>;
<span class="comment">/* take care subnormal number */
</span><span class="kw">if </span>ix < <span class="number">0x00800000 </span>{
ax <span class="kw-2">*</span>= TWO24;
n -= <span class="number">24</span>;
ix = ax.to_bits() <span class="kw">as </span>i32;
}
n += ((ix) >> <span class="number">23</span>) - <span class="number">0x7f</span>;
j = ix & <span class="number">0x007fffff</span>;
<span class="comment">/* determine interval */
</span>ix = j | <span class="number">0x3f800000</span>; <span class="comment">/* normalize ix */
</span><span class="kw">if </span>j <= <span class="number">0x1cc471 </span>{
<span class="comment">/* |x|<sqrt(3/2) */
</span>k = <span class="number">0</span>;
} <span class="kw">else if </span>j < <span class="number">0x5db3d7 </span>{
<span class="comment">/* |x|<sqrt(3) */
</span>k = <span class="number">1</span>;
} <span class="kw">else </span>{
k = <span class="number">0</span>;
n += <span class="number">1</span>;
ix -= <span class="number">0x00800000</span>;
}
ax = f32::from_bits(ix <span class="kw">as </span>u32);
<span class="comment">/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
</span>u = ax - <span class="macro">i!</span>(BP, k <span class="kw">as </span>usize); <span class="comment">/* bp[0]=1.0, bp[1]=1.5 */
</span>v = <span class="number">1.0 </span>/ (ax + <span class="macro">i!</span>(BP, k <span class="kw">as </span>usize));
s = u * v;
s_h = s;
is = s_h.to_bits() <span class="kw">as </span>i32;
s_h = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
<span class="comment">/* t_h=ax+bp[k] High */
</span>is = (((ix <span class="kw">as </span>u32 >> <span class="number">1</span>) & <span class="number">0xfffff000</span>) | <span class="number">0x20000000</span>) <span class="kw">as </span>i32;
t_h = f32::from_bits(is <span class="kw">as </span>u32 + <span class="number">0x00400000 </span>+ ((k <span class="kw">as </span>u32) << <span class="number">21</span>));
t_l = ax - (t_h - <span class="macro">i!</span>(BP, k <span class="kw">as </span>usize));
s_l = v * ((u - s_h * t_h) - s_h * t_l);
<span class="comment">/* compute log(ax) */
</span>s2 = s * s;
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + s);
s2 = s_h * s_h;
t_h = <span class="number">3.0 </span>+ s2 + r;
is = t_h.to_bits() <span class="kw">as </span>i32;
t_h = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
t_l = r - ((t_h - <span class="number">3.0</span>) - s2);
<span class="comment">/* u+v = s*(1+...) */
</span>u = s_h * t_h;
v = s_l * t_h + t_l * s;
<span class="comment">/* 2/(3log2)*(s+...) */
</span>p_h = u + v;
is = p_h.to_bits() <span class="kw">as </span>i32;
p_h = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
p_l = v - (p_h - u);
z_h = CP_H * p_h; <span class="comment">/* cp_h+cp_l = 2/(3*log2) */
</span>z_l = CP_L * p_h + p_l * CP + <span class="macro">i!</span>(DP_L, k <span class="kw">as </span>usize);
<span class="comment">/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
</span>t = n <span class="kw">as </span>f32;
t1 = ((z_h + z_l) + <span class="macro">i!</span>(DP_H, k <span class="kw">as </span>usize)) + t;
is = t1.to_bits() <span class="kw">as </span>i32;
t1 = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
t2 = z_l - (((t1 - t) - <span class="macro">i!</span>(DP_H, k <span class="kw">as </span>usize)) - z_h);
};
<span class="comment">/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
</span>is = y.to_bits() <span class="kw">as </span>i32;
y1 = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xfffff000</span>);
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
j = z.to_bits() <span class="kw">as </span>i32;
<span class="kw">if </span>j > <span class="number">0x43000000 </span>{
<span class="comment">/* if z > 128 */
</span><span class="kw">return </span>sn * HUGE * HUGE; <span class="comment">/* overflow */
</span>} <span class="kw">else if </span>j == <span class="number">0x43000000 </span>{
<span class="comment">/* if z == 128 */
</span><span class="kw">if </span>p_l + OVT > z - p_h {
<span class="kw">return </span>sn * HUGE * HUGE; <span class="comment">/* overflow */
</span>}
} <span class="kw">else if </span>(j & <span class="number">0x7fffffff</span>) > <span class="number">0x43160000 </span>{
<span class="comment">/* z < -150 */
// FIXME: check should be (uint32_t)j > 0xc3160000
</span><span class="kw">return </span>sn * TINY * TINY; <span class="comment">/* underflow */
</span>} <span class="kw">else if </span>j <span class="kw">as </span>u32 == <span class="number">0xc3160000
</span><span class="comment">/* z == -150 */
</span>&& p_l <= z - p_h
{
<span class="kw">return </span>sn * TINY * TINY; <span class="comment">/* underflow */
</span>}
<span class="comment">/*
* compute 2**(p_h+p_l)
*/
</span>i = j & <span class="number">0x7fffffff</span>;
k = (i >> <span class="number">23</span>) - <span class="number">0x7f</span>;
n = <span class="number">0</span>;
<span class="kw">if </span>i > <span class="number">0x3f000000 </span>{
<span class="comment">/* if |z| > 0.5, set n = [z+0.5] */
</span>n = j + (<span class="number">0x00800000 </span>>> (k + <span class="number">1</span>));
k = ((n & <span class="number">0x7fffffff</span>) >> <span class="number">23</span>) - <span class="number">0x7f</span>; <span class="comment">/* new k for n */
</span>t = f32::from_bits(n <span class="kw">as </span>u32 & !(<span class="number">0x007fffff </span>>> k));
n = ((n & <span class="number">0x007fffff</span>) | <span class="number">0x00800000</span>) >> (<span class="number">23 </span>- k);
<span class="kw">if </span>j < <span class="number">0 </span>{
n = -n;
}
p_h -= t;
}
t = p_l + p_h;
is = t.to_bits() <span class="kw">as </span>i32;
t = f32::from_bits(is <span class="kw">as </span>u32 & <span class="number">0xffff8000</span>);
u = t * LG2_H;
v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
r = (z * t1) / (t1 - <span class="number">2.0</span>) - (w + z * w);
z = <span class="number">1.0 </span>- (r - z);
j = z.to_bits() <span class="kw">as </span>i32;
j += n << <span class="number">23</span>;
<span class="kw">if </span>(j >> <span class="number">23</span>) <= <span class="number">0 </span>{
<span class="comment">/* subnormal output */
</span>z = scalbnf(z, n);
} <span class="kw">else </span>{
z = f32::from_bits(j <span class="kw">as </span>u32);
}
sn * z
}
</code></pre></div>
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