<!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/pow.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>pow.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_pow.c */
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
// pow(x,y) return x**y
//
// n
// Method: Let x = 2 * (1+f)
// 1. Compute and return log2(x) in two pieces:
// log2(x) = w1 + w2,
// where w1 has 53-24 = 29 bit trailing zeros.
// 2. Perform y*log2(x) = n+y' by simulating muti-precision
// arithmetic, where |y'|<=0.5.
// 3. Return x**y = 2**n*exp(y'*log2)
//
// Special cases:
// 1. (anything) ** 0 is 1
// 2. 1 ** (anything) is 1
// 3. (anything except 1) ** NAN is NAN
// 4. NAN ** (anything except 0) is NAN
// 5. +-(|x| > 1) ** +INF is +INF
// 6. +-(|x| > 1) ** -INF is +0
// 7. +-(|x| < 1) ** +INF is +0
// 8. +-(|x| < 1) ** -INF is +INF
// 9. -1 ** +-INF is 1
// 10. +0 ** (+anything except 0, NAN) is +0
// 11. -0 ** (+anything except 0, NAN, odd integer) is +0
// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
// 14. -0 ** (+odd integer) is -0
// 15. -0 ** (-odd integer) is -INF, raise divbyzero
// 16. +INF ** (+anything except 0,NAN) is +INF
// 17. +INF ** (-anything except 0,NAN) is +0
// 18. -INF ** (+odd integer) is -INF
// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
// 20. (anything) ** 1 is (anything)
// 21. (anything) ** -1 is 1/(anything)
// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
// 23. (-anything except 0 and inf) ** (non-integer) is NAN
//
// Accuracy:
// pow(x,y) returns x**y nearly rounded. In particular
// pow(integer,integer)
// always returns the correct integer provided it is
// representable.
//
// 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.
//
</span><span class="kw">use super</span>::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word};
<span class="kw">const </span>BP: [f64; <span class="number">2</span>] = [<span class="number">1.0</span>, <span class="number">1.5</span>];
<span class="kw">const </span>DP_H: [f64; <span class="number">2</span>] = [<span class="number">0.0</span>, <span class="number">5.84962487220764160156e-01</span>]; <span class="comment">/* 0x3fe2b803_40000000 */
</span><span class="kw">const </span>DP_L: [f64; <span class="number">2</span>] = [<span class="number">0.0</span>, <span class="number">1.35003920212974897128e-08</span>]; <span class="comment">/* 0x3E4CFDEB, 0x43CFD006 */
</span><span class="kw">const </span>TWO53: f64 = <span class="number">9007199254740992.0</span>; <span class="comment">/* 0x43400000_00000000 */
</span><span class="kw">const </span>HUGE: f64 = <span class="number">1.0e300</span>;
<span class="kw">const </span>TINY: f64 = <span class="number">1.0e-300</span>;
<span class="comment">// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
</span><span class="kw">const </span>L1: f64 = <span class="number">5.99999999999994648725e-01</span>; <span class="comment">/* 0x3fe33333_33333303 */
</span><span class="kw">const </span>L2: f64 = <span class="number">4.28571428578550184252e-01</span>; <span class="comment">/* 0x3fdb6db6_db6fabff */
</span><span class="kw">const </span>L3: f64 = <span class="number">3.33333329818377432918e-01</span>; <span class="comment">/* 0x3fd55555_518f264d */
</span><span class="kw">const </span>L4: f64 = <span class="number">2.72728123808534006489e-01</span>; <span class="comment">/* 0x3fd17460_a91d4101 */
</span><span class="kw">const </span>L5: f64 = <span class="number">2.30660745775561754067e-01</span>; <span class="comment">/* 0x3fcd864a_93c9db65 */
</span><span class="kw">const </span>L6: f64 = <span class="number">2.06975017800338417784e-01</span>; <span class="comment">/* 0x3fca7e28_4a454eef */
</span><span class="kw">const </span>P1: f64 = <span class="number">1.66666666666666019037e-01</span>; <span class="comment">/* 0x3fc55555_5555553e */
</span><span class="kw">const </span>P2: f64 = -<span class="number">2.77777777770155933842e-03</span>; <span class="comment">/* 0xbf66c16c_16bebd93 */
</span><span class="kw">const </span>P3: f64 = <span class="number">6.61375632143793436117e-05</span>; <span class="comment">/* 0x3f11566a_af25de2c */
</span><span class="kw">const </span>P4: f64 = -<span class="number">1.65339022054652515390e-06</span>; <span class="comment">/* 0xbebbbd41_c5d26bf1 */
</span><span class="kw">const </span>P5: f64 = <span class="number">4.13813679705723846039e-08</span>; <span class="comment">/* 0x3e663769_72bea4d0 */
</span><span class="kw">const </span>LG2: f64 = <span class="number">6.93147180559945286227e-01</span>; <span class="comment">/* 0x3fe62e42_fefa39ef */
</span><span class="kw">const </span>LG2_H: f64 = <span class="number">6.93147182464599609375e-01</span>; <span class="comment">/* 0x3fe62e43_00000000 */
</span><span class="kw">const </span>LG2_L: f64 = -<span class="number">1.90465429995776804525e-09</span>; <span class="comment">/* 0xbe205c61_0ca86c39 */
</span><span class="kw">const </span>OVT: f64 = <span class="number">8.0085662595372944372e-017</span>; <span class="comment">/* -(1024-log2(ovfl+.5ulp)) */
</span><span class="kw">const </span>CP: f64 = <span class="number">9.61796693925975554329e-01</span>; <span class="comment">/* 0x3feec709_dc3a03fd =2/(3ln2) */
</span><span class="kw">const </span>CP_H: f64 = <span class="number">9.61796700954437255859e-01</span>; <span class="comment">/* 0x3feec709_e0000000 =(float)cp */
</span><span class="kw">const </span>CP_L: f64 = -<span class="number">7.02846165095275826516e-09</span>; <span class="comment">/* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
</span><span class="kw">const </span>IVLN2: f64 = <span class="number">1.44269504088896338700e+00</span>; <span class="comment">/* 0x3ff71547_652b82fe =1/ln2 */
</span><span class="kw">const </span>IVLN2_H: f64 = <span class="number">1.44269502162933349609e+00</span>; <span class="comment">/* 0x3ff71547_60000000 =24b 1/ln2*/
</span><span class="kw">const </span>IVLN2_L: f64 = <span class="number">1.92596299112661746887e-08</span>; <span class="comment">/* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>pow(x: f64, y: f64) -> f64 {
<span class="kw">let </span>t1: f64;
<span class="kw">let </span>t2: f64;
<span class="kw">let </span>(hx, lx): (i32, u32) = ((x.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>i32, x.to_bits() <span class="kw">as </span>u32);
<span class="kw">let </span>(hy, ly): (i32, u32) = ((y.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>i32, y.to_bits() <span class="kw">as </span>u32);
<span class="kw">let </span><span class="kw-2">mut </span>ix: i32 = (hx & <span class="number">0x7fffffff</span>) <span class="kw">as </span>i32;
<span class="kw">let </span>iy: i32 = (hy & <span class="number">0x7fffffff</span>) <span class="kw">as </span>i32;
<span class="comment">/* x**0 = 1, even if x is NaN */
</span><span class="kw">if </span>((iy <span class="kw">as </span>u32) | ly) == <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">0x3ff00000 </span>&& lx == <span class="number">0 </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">0x7ff00000
</span>|| (ix == <span class="number">0x7ff00000 </span>&& lx != <span class="number">0</span>)
|| iy > <span class="number">0x7ff00000
</span>|| (iy == <span class="number">0x7ff00000 </span>&& ly != <span class="number">0</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><span class="kw">let </span><span class="kw-2">mut </span>yisint: i32 = <span class="number">0</span>;
<span class="kw">let </span><span class="kw-2">mut </span>k: i32;
<span class="kw">let </span><span class="kw-2">mut </span>j: i32;
<span class="kw">if </span>hx < <span class="number">0 </span>{
<span class="kw">if </span>iy >= <span class="number">0x43400000 </span>{
yisint = <span class="number">2</span>; <span class="comment">/* even integer y */
</span>} <span class="kw">else if </span>iy >= <span class="number">0x3ff00000 </span>{
k = (iy >> <span class="number">20</span>) - <span class="number">0x3ff</span>; <span class="comment">/* exponent */
</span><span class="kw">if </span>k > <span class="number">20 </span>{
j = (ly >> (<span class="number">52 </span>- k)) <span class="kw">as </span>i32;
<span class="kw">if </span>(j << (<span class="number">52 </span>- k)) == (ly <span class="kw">as </span>i32) {
yisint = <span class="number">2 </span>- (j & <span class="number">1</span>);
}
} <span class="kw">else if </span>ly == <span class="number">0 </span>{
j = iy >> (<span class="number">20 </span>- k);
<span class="kw">if </span>(j << (<span class="number">20 </span>- k)) == iy {
yisint = <span class="number">2 </span>- (j & <span class="number">1</span>);
}
}
}
}
<span class="kw">if </span>ly == <span class="number">0 </span>{
<span class="comment">/* special value of y */
</span><span class="kw">if </span>iy == <span class="number">0x7ff00000 </span>{
<span class="comment">/* y is +-inf */
</span><span class="kw">return if </span>((ix - <span class="number">0x3ff00000</span>) | (lx <span class="kw">as </span>i32)) == <span class="number">0 </span>{
<span class="comment">/* (-1)**+-inf is 1 */
</span><span class="number">1.0
</span>} <span class="kw">else if </span>ix >= <span class="number">0x3ff00000 </span>{
<span class="comment">/* (|x|>1)**+-inf = inf,0 */
</span><span class="kw">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">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">0x3ff00000 </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">0x3fe00000 </span>{
<span class="comment">/* y is 0.5 */
</span><span class="kw">if </span>hx >= <span class="number">0 </span>{
<span class="comment">/* x >= +0 */
</span><span class="kw">return </span>sqrt(x);
}
}
}
<span class="kw">let </span><span class="kw-2">mut </span>ax: f64 = fabs(x);
<span class="kw">if </span>lx == <span class="number">0 </span>{
<span class="comment">/* special value of x */
</span><span class="kw">if </span>ix == <span class="number">0x7ff00000 </span>|| ix == <span class="number">0 </span>|| ix == <span class="number">0x3ff00000 </span>{
<span class="comment">/* x is +-0,+-inf,+-1 */
</span><span class="kw">let </span><span class="kw-2">mut </span>z: f64 = 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">0x3ff00000</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;
}
}
<span class="kw">let </span><span class="kw-2">mut </span>s: f64 = <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>s = -<span class="number">1.0</span>;
}
}
<span class="comment">/* |y| is HUGE */
</span><span class="kw">if </span>iy > <span class="number">0x41e00000 </span>{
<span class="comment">/* if |y| > 2**31 */
</span><span class="kw">if </span>iy > <span class="number">0x43f00000 </span>{
<span class="comment">/* if |y| > 2**64, must o/uflow */
</span><span class="kw">if </span>ix <= <span class="number">0x3fefffff </span>{
<span class="kw">return if </span>hy < <span class="number">0 </span>{ HUGE * HUGE } <span class="kw">else </span>{ TINY * TINY };
}
<span class="kw">if </span>ix >= <span class="number">0x3ff00000 </span>{
<span class="kw">return if </span>hy > <span class="number">0 </span>{ HUGE * HUGE } <span class="kw">else </span>{ TINY * TINY };
}
}
<span class="comment">/* over/underflow if x is not close to one */
</span><span class="kw">if </span>ix < <span class="number">0x3fefffff </span>{
<span class="kw">return if </span>hy < <span class="number">0 </span>{
s * HUGE * HUGE
} <span class="kw">else </span>{
s * TINY * TINY
};
}
<span class="kw">if </span>ix > <span class="number">0x3ff00000 </span>{
<span class="kw">return if </span>hy > <span class="number">0 </span>{
s * HUGE * HUGE
} <span class="kw">else </span>{
s * 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><span class="kw">let </span>t: f64 = ax - <span class="number">1.0</span>; <span class="comment">/* t has 20 trailing zeros */
</span><span class="kw">let </span>w: f64 = (t * t) * (<span class="number">0.5 </span>- t * (<span class="number">0.3333333333333333333333 </span>- t * <span class="number">0.25</span>));
<span class="kw">let </span>u: f64 = IVLN2_H * t; <span class="comment">/* ivln2_h has 21 sig. bits */
</span><span class="kw">let </span>v: f64 = t * IVLN2_L - w * IVLN2;
t1 = with_set_low_word(u + v, <span class="number">0</span>);
t2 = v - (t1 - u);
} <span class="kw">else </span>{
<span class="comment">// double ss,s2,s_h,s_l,t_h,t_l;
</span><span class="kw">let </span><span class="kw-2">mut </span>n: i32 = <span class="number">0</span>;
<span class="kw">if </span>ix < <span class="number">0x00100000 </span>{
<span class="comment">/* take care subnormal number */
</span>ax <span class="kw-2">*</span>= TWO53;
n -= <span class="number">53</span>;
ix = get_high_word(ax) <span class="kw">as </span>i32;
}
n += (ix >> <span class="number">20</span>) - <span class="number">0x3ff</span>;
j = ix & <span class="number">0x000fffff</span>;
<span class="comment">/* determine interval */
</span><span class="kw">let </span>k: i32;
ix = j | <span class="number">0x3ff00000</span>; <span class="comment">/* normalize ix */
</span><span class="kw">if </span>j <= <span class="number">0x3988E </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">0xBB67A </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">0x00100000</span>;
}
ax = with_set_high_word(ax, ix <span class="kw">as </span>u32);
<span class="comment">/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
</span><span class="kw">let </span>u: f64 = 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><span class="kw">let </span>v: f64 = <span class="number">1.0 </span>/ (ax + <span class="macro">i!</span>(BP, k <span class="kw">as </span>usize));
<span class="kw">let </span>ss: f64 = u * v;
<span class="kw">let </span>s_h = with_set_low_word(ss, <span class="number">0</span>);
<span class="comment">/* t_h=ax+bp[k] High */
</span><span class="kw">let </span>t_h: f64 = with_set_high_word(
<span class="number">0.0</span>,
((ix <span class="kw">as </span>u32 >> <span class="number">1</span>) | <span class="number">0x20000000</span>) + <span class="number">0x00080000 </span>+ ((k <span class="kw">as </span>u32) << <span class="number">18</span>),
);
<span class="kw">let </span>t_l: f64 = ax - (t_h - <span class="macro">i!</span>(BP, k <span class="kw">as </span>usize));
<span class="kw">let </span>s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
<span class="comment">/* compute log(ax) */
</span><span class="kw">let </span>s2: f64 = ss * ss;
<span class="kw">let </span><span class="kw-2">mut </span>r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + ss);
<span class="kw">let </span>s2: f64 = s_h * s_h;
<span class="kw">let </span>t_h: f64 = with_set_low_word(<span class="number">3.0 </span>+ s2 + r, <span class="number">0</span>);
<span class="kw">let </span>t_l: f64 = r - ((t_h - <span class="number">3.0</span>) - s2);
<span class="comment">/* u+v = ss*(1+...) */
</span><span class="kw">let </span>u: f64 = s_h * t_h;
<span class="kw">let </span>v: f64 = s_l * t_h + t_l * ss;
<span class="comment">/* 2/(3log2)*(ss+...) */
</span><span class="kw">let </span>p_h: f64 = with_set_low_word(u + v, <span class="number">0</span>);
<span class="kw">let </span>p_l = v - (p_h - u);
<span class="kw">let </span>z_h: f64 = CP_H * p_h; <span class="comment">/* cp_h+cp_l = 2/(3*log2) */
</span><span class="kw">let </span>z_l: f64 = 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) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
</span><span class="kw">let </span>t: f64 = n <span class="kw">as </span>f64;
t1 = with_set_low_word(((z_h + z_l) + <span class="macro">i!</span>(DP_H, k <span class="kw">as </span>usize)) + t, <span class="number">0</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><span class="kw">let </span>y1: f64 = with_set_low_word(y, <span class="number">0</span>);
<span class="kw">let </span>p_l: f64 = (y - y1) * t1 + y * t2;
<span class="kw">let </span><span class="kw-2">mut </span>p_h: f64 = y1 * t1;
<span class="kw">let </span>z: f64 = p_l + p_h;
<span class="kw">let </span><span class="kw-2">mut </span>j: i32 = (z.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>i32;
<span class="kw">let </span>i: i32 = z.to_bits() <span class="kw">as </span>i32;
<span class="comment">// let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
</span><span class="kw">if </span>j >= <span class="number">0x40900000 </span>{
<span class="comment">/* z >= 1024 */
</span><span class="kw">if </span>(j - <span class="number">0x40900000</span>) | i != <span class="number">0 </span>{
<span class="comment">/* if z > 1024 */
</span><span class="kw">return </span>s * HUGE * HUGE; <span class="comment">/* overflow */
</span>}
<span class="kw">if </span>p_l + OVT > z - p_h {
<span class="kw">return </span>s * HUGE * HUGE; <span class="comment">/* overflow */
</span>}
} <span class="kw">else if </span>(j & <span class="number">0x7fffffff</span>) >= <span class="number">0x4090cc00 </span>{
<span class="comment">/* z <= -1075 */
// FIXME: instead of abs(j) use unsigned j
</span><span class="kw">if </span>(((j <span class="kw">as </span>u32) - <span class="number">0xc090cc00</span>) | (i <span class="kw">as </span>u32)) != <span class="number">0 </span>{
<span class="comment">/* z < -1075 */
</span><span class="kw">return </span>s * TINY * TINY; <span class="comment">/* underflow */
</span>}
<span class="kw">if </span>p_l <= z - p_h {
<span class="kw">return </span>s * TINY * TINY; <span class="comment">/* underflow */
</span>}
}
<span class="comment">/* compute 2**(p_h+p_l) */
</span><span class="kw">let </span>i: i32 = j & (<span class="number">0x7fffffff </span><span class="kw">as </span>i32);
k = (i >> <span class="number">20</span>) - <span class="number">0x3ff</span>;
<span class="kw">let </span><span class="kw-2">mut </span>n: i32 = <span class="number">0</span>;
<span class="kw">if </span>i > <span class="number">0x3fe00000 </span>{
<span class="comment">/* if |z| > 0.5, set n = [z+0.5] */
</span>n = j + (<span class="number">0x00100000 </span>>> (k + <span class="number">1</span>));
k = ((n & <span class="number">0x7fffffff</span>) >> <span class="number">20</span>) - <span class="number">0x3ff</span>; <span class="comment">/* new k for n */
</span><span class="kw">let </span>t: f64 = with_set_high_word(<span class="number">0.0</span>, (n & !(<span class="number">0x000fffff </span>>> k)) <span class="kw">as </span>u32);
n = ((n & <span class="number">0x000fffff</span>) | <span class="number">0x00100000</span>) >> (<span class="number">20 </span>- k);
<span class="kw">if </span>j < <span class="number">0 </span>{
n = -n;
}
p_h -= t;
}
<span class="kw">let </span>t: f64 = with_set_low_word(p_l + p_h, <span class="number">0</span>);
<span class="kw">let </span>u: f64 = t * LG2_H;
<span class="kw">let </span>v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
<span class="kw">let </span><span class="kw-2">mut </span>z: f64 = u + v;
<span class="kw">let </span>w: f64 = v - (z - u);
<span class="kw">let </span>t: f64 = z * z;
<span class="kw">let </span>t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
<span class="kw">let </span>r: f64 = (z * t1) / (t1 - <span class="number">2.0</span>) - (w + z * w);
z = <span class="number">1.0 </span>- (r - z);
j = get_high_word(z) <span class="kw">as </span>i32;
j += n << <span class="number">20</span>;
<span class="kw">if </span>(j >> <span class="number">20</span>) <= <span class="number">0 </span>{
<span class="comment">/* subnormal output */
</span>z = scalbn(z, n);
} <span class="kw">else </span>{
z = with_set_high_word(z, j <span class="kw">as </span>u32);
}
s * z
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">extern crate </span>core;
<span class="kw">use </span><span class="self">self</span>::core::f64::consts::{E, PI};
<span class="kw">use </span><span class="self">self</span>::core::f64::{EPSILON, INFINITY, MAX, MIN, MIN_POSITIVE, NAN, NEG_INFINITY};
<span class="kw">use </span><span class="kw">super</span>::pow;
<span class="kw">const </span>POS_ZERO: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[<span class="number">0.0</span>];
<span class="kw">const </span>NEG_ZERO: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[-<span class="number">0.0</span>];
<span class="kw">const </span>POS_ONE: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[<span class="number">1.0</span>];
<span class="kw">const </span>NEG_ONE: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[-<span class="number">1.0</span>];
<span class="kw">const </span>POS_FLOATS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[<span class="number">99.0 </span>/ <span class="number">70.0</span>, E, PI];
<span class="kw">const </span>NEG_FLOATS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[-<span class="number">99.0 </span>/ <span class="number">70.0</span>, -E, -PI];
<span class="kw">const </span>POS_SMALL_FLOATS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[(<span class="number">1.0 </span>/ <span class="number">2.0</span>), MIN_POSITIVE, EPSILON];
<span class="kw">const </span>NEG_SMALL_FLOATS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[-(<span class="number">1.0 </span>/ <span class="number">2.0</span>), -MIN_POSITIVE, -EPSILON];
<span class="kw">const </span>POS_EVENS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[<span class="number">2.0</span>, <span class="number">6.0</span>, <span class="number">8.0</span>, <span class="number">10.0</span>, <span class="number">22.0</span>, <span class="number">100.0</span>, MAX];
<span class="kw">const </span>NEG_EVENS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[MIN, -<span class="number">100.0</span>, -<span class="number">22.0</span>, -<span class="number">10.0</span>, -<span class="number">8.0</span>, -<span class="number">6.0</span>, -<span class="number">2.0</span>];
<span class="kw">const </span>POS_ODDS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[<span class="number">3.0</span>, <span class="number">7.0</span>];
<span class="kw">const </span>NEG_ODDS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[-<span class="number">7.0</span>, -<span class="number">3.0</span>];
<span class="kw">const </span>NANS: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[NAN];
<span class="kw">const </span>POS_INF: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[INFINITY];
<span class="kw">const </span>NEG_INF: <span class="kw-2">&</span>[f64] = <span class="kw-2">&</span>[NEG_INFINITY];
<span class="kw">const </span>ALL: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]] = <span class="kw-2">&</span>[
POS_ZERO,
NEG_ZERO,
NANS,
NEG_SMALL_FLOATS,
POS_SMALL_FLOATS,
NEG_FLOATS,
POS_FLOATS,
NEG_EVENS,
POS_EVENS,
NEG_ODDS,
POS_ODDS,
NEG_INF,
POS_INF,
NEG_ONE,
POS_ONE,
];
<span class="kw">const </span>POS: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]] = <span class="kw-2">&</span>[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
<span class="kw">const </span>NEG: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]] = <span class="kw-2">&</span>[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];
<span class="kw">fn </span>pow_test(base: f64, exponent: f64, expected: f64) {
<span class="kw">let </span>res = pow(base, exponent);
<span class="macro">assert!</span>(
<span class="kw">if </span>expected.is_nan() {
res.is_nan()
} <span class="kw">else </span>{
pow(base, exponent) == expected
},
<span class="string">"{} ** {} was {} instead of {}"</span>,
base,
exponent,
res,
expected
);
}
<span class="kw">fn </span>test_sets_as_base(sets: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]], exponent: f64, expected: f64) {
sets.iter()
.for_each(|s| s.iter().for_each(|val| pow_test(<span class="kw-2">*</span>val, exponent, expected)));
}
<span class="kw">fn </span>test_sets_as_exponent(base: f64, sets: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]], expected: f64) {
sets.iter()
.for_each(|s| s.iter().for_each(|val| pow_test(base, <span class="kw-2">*</span>val, expected)));
}
<span class="kw">fn </span>test_sets(sets: <span class="kw-2">&</span>[<span class="kw-2">&</span>[f64]], computed: <span class="kw-2">&</span><span class="kw">dyn </span>Fn(f64) -> f64, expected: <span class="kw-2">&</span><span class="kw">dyn </span>Fn(f64) -> f64) {
sets.iter().for_each(|s| {
s.iter().for_each(|val| {
<span class="kw">let </span>exp = expected(<span class="kw-2">*</span>val);
<span class="kw">let </span>res = computed(<span class="kw-2">*</span>val);
<span class="attr">#[cfg(all(target_arch = <span class="string">"x86"</span>, not(target_feature = <span class="string">"sse2"</span>)))]
</span><span class="kw">let </span>exp = <span class="macro">force_eval!</span>(exp);
<span class="attr">#[cfg(all(target_arch = <span class="string">"x86"</span>, not(target_feature = <span class="string">"sse2"</span>)))]
</span><span class="kw">let </span>res = <span class="macro">force_eval!</span>(res);
<span class="macro">assert!</span>(
<span class="kw">if </span>exp.is_nan() {
res.is_nan()
} <span class="kw">else </span>{
exp == res
},
<span class="string">"test for {} was {} instead of {}"</span>,
val,
res,
exp
);
})
});
}
<span class="attr">#[test]
</span><span class="kw">fn </span>zero_as_exponent() {
test_sets_as_base(ALL, <span class="number">0.0</span>, <span class="number">1.0</span>);
test_sets_as_base(ALL, -<span class="number">0.0</span>, <span class="number">1.0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>one_as_base() {
test_sets_as_exponent(<span class="number">1.0</span>, ALL, <span class="number">1.0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>nan_inputs() {
<span class="comment">// NAN as the base:
// (NAN ^ anything *but 0* should be NAN)
</span>test_sets_as_exponent(NAN, <span class="kw-2">&</span>ALL[<span class="number">2</span>..], NAN);
<span class="comment">// NAN as the exponent:
// (anything *but 1* ^ NAN should be NAN)
</span>test_sets_as_base(<span class="kw-2">&</span>ALL[..(ALL.len() - <span class="number">2</span>)], NAN, NAN);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>infinity_as_base() {
<span class="comment">// Positive Infinity as the base:
// (+Infinity ^ positive anything but 0 and NAN should be +Infinity)
</span>test_sets_as_exponent(INFINITY, <span class="kw-2">&</span>POS[<span class="number">1</span>..], INFINITY);
<span class="comment">// (+Infinity ^ negative anything except 0 and NAN should be 0.0)
</span>test_sets_as_exponent(INFINITY, <span class="kw-2">&</span>NEG[<span class="number">1</span>..], <span class="number">0.0</span>);
<span class="comment">// Negative Infinity as the base:
// (-Infinity ^ positive odd ints should be -Infinity)
</span>test_sets_as_exponent(NEG_INFINITY, <span class="kw-2">&</span>[POS_ODDS], NEG_INFINITY);
<span class="comment">// (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
// We can lump in pos/neg odd ints here because they don't seem to
// cause panics (div by zero) in release mode (I think).
</span>test_sets(ALL, <span class="kw-2">&</span>|v: f64| pow(NEG_INFINITY, v), <span class="kw-2">&</span>|v: f64| pow(-<span class="number">0.0</span>, -v));
}
<span class="attr">#[test]
</span><span class="kw">fn </span>infinity_as_exponent() {
<span class="comment">// Positive/Negative base greater than 1:
// (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base)
</span>test_sets_as_base(<span class="kw-2">&</span>ALL[<span class="number">5</span>..(ALL.len() - <span class="number">2</span>)], INFINITY, INFINITY);
<span class="comment">// (pos/neg > 1 ^ -Infinity should be 0.0)
</span>test_sets_as_base(<span class="kw-2">&</span>ALL[<span class="number">5</span>..ALL.len() - <span class="number">2</span>], NEG_INFINITY, <span class="number">0.0</span>);
<span class="comment">// Positive/Negative base less than 1:
</span><span class="kw">let </span>base_below_one = <span class="kw-2">&</span>[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];
<span class="comment">// (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base)
</span>test_sets_as_base(base_below_one, INFINITY, <span class="number">0.0</span>);
<span class="comment">// (pos/neg < 1 ^ -Infinity should be Infinity)
</span>test_sets_as_base(base_below_one, NEG_INFINITY, INFINITY);
<span class="comment">// Positive/Negative 1 as the base:
// (pos/neg 1 ^ Infinity should be 1)
</span>test_sets_as_base(<span class="kw-2">&</span>[NEG_ONE, POS_ONE], INFINITY, <span class="number">1.0</span>);
<span class="comment">// (pos/neg 1 ^ -Infinity should be 1)
</span>test_sets_as_base(<span class="kw-2">&</span>[NEG_ONE, POS_ONE], NEG_INFINITY, <span class="number">1.0</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>zero_as_base() {
<span class="comment">// Positive Zero as the base:
// (+0 ^ anything positive but 0 and NAN should be +0)
</span>test_sets_as_exponent(<span class="number">0.0</span>, <span class="kw-2">&</span>POS[<span class="number">1</span>..], <span class="number">0.0</span>);
<span class="comment">// (+0 ^ anything negative but 0 and NAN should be Infinity)
// (this should panic because we're dividing by zero)
</span>test_sets_as_exponent(<span class="number">0.0</span>, <span class="kw-2">&</span>NEG[<span class="number">1</span>..], INFINITY);
<span class="comment">// Negative Zero as the base:
// (-0 ^ anything positive but 0, NAN, and odd ints should be +0)
</span>test_sets_as_exponent(-<span class="number">0.0</span>, <span class="kw-2">&</span>POS[<span class="number">3</span>..], <span class="number">0.0</span>);
<span class="comment">// (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity)
// (should panic because of divide by zero)
</span>test_sets_as_exponent(-<span class="number">0.0</span>, <span class="kw-2">&</span>NEG[<span class="number">3</span>..], INFINITY);
<span class="comment">// (-0 ^ positive odd ints should be -0)
</span>test_sets_as_exponent(-<span class="number">0.0</span>, <span class="kw-2">&</span>[POS_ODDS], -<span class="number">0.0</span>);
<span class="comment">// (-0 ^ negative odd ints should be -Infinity)
// (should panic because of divide by zero)
</span>test_sets_as_exponent(-<span class="number">0.0</span>, <span class="kw-2">&</span>[NEG_ODDS], NEG_INFINITY);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>special_cases() {
<span class="comment">// One as the exponent:
// (anything ^ 1 should be anything - i.e. the base)
</span>test_sets(ALL, <span class="kw-2">&</span>|v: f64| pow(v, <span class="number">1.0</span>), <span class="kw-2">&</span>|v: f64| v);
<span class="comment">// Negative One as the exponent:
// (anything ^ -1 should be 1/anything)
</span>test_sets(ALL, <span class="kw-2">&</span>|v: f64| pow(v, -<span class="number">1.0</span>), <span class="kw-2">&</span>|v: f64| <span class="number">1.0 </span>/ v);
<span class="comment">// Factoring -1 out:
// (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
</span>(<span class="kw-2">&</span>[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS])
.iter()
.for_each(|int_set| {
int_set.iter().for_each(|int| {
test_sets(ALL, <span class="kw-2">&</span>|v: f64| pow(-v, <span class="kw-2">*</span>int), <span class="kw-2">&</span>|v: f64| {
pow(-<span class="number">1.0</span>, <span class="kw-2">*</span>int) * pow(v, <span class="kw-2">*</span>int)
});
})
});
<span class="comment">// Negative base (imaginary results):
// (-anything except 0 and Infinity ^ non-integer should be NAN)
</span>(<span class="kw-2">&</span>NEG[<span class="number">1</span>..(NEG.len() - <span class="number">1</span>)]).iter().for_each(|set| {
set.iter().for_each(|val| {
test_sets(<span class="kw-2">&</span>ALL[<span class="number">3</span>..<span class="number">7</span>], <span class="kw-2">&</span>|v: f64| pow(<span class="kw-2">*</span>val, v), <span class="kw-2">&</span>|<span class="kw">_</span>| NAN);
})
});
}
<span class="attr">#[test]
</span><span class="kw">fn </span>normal_cases() {
<span class="macro">assert_eq!</span>(pow(<span class="number">2.0</span>, <span class="number">20.0</span>), (<span class="number">1 </span><< <span class="number">20</span>) <span class="kw">as </span>f64);
<span class="macro">assert_eq!</span>(pow(-<span class="number">1.0</span>, <span class="number">9.0</span>), -<span class="number">1.0</span>);
<span class="macro">assert!</span>(pow(-<span class="number">1.0</span>, <span class="number">2.2</span>).is_nan());
<span class="macro">assert!</span>(pow(-<span class="number">1.0</span>, -<span class="number">1.14</span>).is_nan());
}
}
</code></pre></div>
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