<!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/jnf.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>jnf.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_jnf.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, j0f, j1f, logf, y0f, y1f};
<span class="kw">pub fn </span>jnf(n: i32, <span class="kw-2">mut </span>x: f32) -> f32 {
<span class="kw">let </span><span class="kw-2">mut </span>ix: u32;
<span class="kw">let </span><span class="kw-2">mut </span>nm1: i32;
<span class="kw">let </span><span class="kw-2">mut </span>sign: bool;
<span class="kw">let </span><span class="kw-2">mut </span>i: i32;
<span class="kw">let </span><span class="kw-2">mut </span>a: f32;
<span class="kw">let </span><span class="kw-2">mut </span>b: f32;
<span class="kw">let </span><span class="kw-2">mut </span>temp: f32;
ix = x.to_bits();
sign = (ix >> <span class="number">31</span>) != <span class="number">0</span>;
ix &= <span class="number">0x7fffffff</span>;
<span class="kw">if </span>ix > <span class="number">0x7f800000 </span>{
<span class="comment">/* nan */
</span><span class="kw">return </span>x;
}
<span class="comment">/* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
</span><span class="kw">if </span>n == <span class="number">0 </span>{
<span class="kw">return </span>j0f(x);
}
<span class="kw">if </span>n < <span class="number">0 </span>{
nm1 = -(n + <span class="number">1</span>);
x = -x;
sign = !sign;
} <span class="kw">else </span>{
nm1 = n - <span class="number">1</span>;
}
<span class="kw">if </span>nm1 == <span class="number">0 </span>{
<span class="kw">return </span>j1f(x);
}
sign &= (n & <span class="number">1</span>) != <span class="number">0</span>; <span class="comment">/* even n: 0, odd n: signbit(x) */
</span>x = fabsf(x);
<span class="kw">if </span>ix == <span class="number">0 </span>|| ix == <span class="number">0x7f800000 </span>{
<span class="comment">/* if x is 0 or inf */
</span>b = <span class="number">0.0</span>;
} <span class="kw">else if </span>(nm1 <span class="kw">as </span>f32) < x {
<span class="comment">/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
</span>a = j0f(x);
b = j1f(x);
i = <span class="number">0</span>;
<span class="kw">while </span>i < nm1 {
i += <span class="number">1</span>;
temp = b;
b = b * (<span class="number">2.0 </span>* (i <span class="kw">as </span>f32) / x) - a;
a = temp;
}
} <span class="kw">else </span>{
<span class="kw">if </span>ix < <span class="number">0x35800000 </span>{
<span class="comment">/* x < 2**-20 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
</span><span class="kw">if </span>nm1 > <span class="number">8 </span>{
<span class="comment">/* underflow */
</span>nm1 = <span class="number">8</span>;
}
temp = <span class="number">0.5 </span>* x;
b = temp;
a = <span class="number">1.0</span>;
i = <span class="number">2</span>;
<span class="kw">while </span>i <= nm1 + <span class="number">1 </span>{
a <span class="kw-2">*</span>= i <span class="kw">as </span>f32; <span class="comment">/* a = n! */
</span>b <span class="kw-2">*</span>= temp; <span class="comment">/* b = (x/2)^n */
</span>i += <span class="number">1</span>;
}
b = b / a;
} <span class="kw">else </span>{
<span class="comment">/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
</span><span class="kw">let </span><span class="kw-2">mut </span>t: f32;
<span class="kw">let </span><span class="kw-2">mut </span>q0: f32;
<span class="kw">let </span><span class="kw-2">mut </span>q1: f32;
<span class="kw">let </span><span class="kw-2">mut </span>w: f32;
<span class="kw">let </span>h: 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>tmp: f32;
<span class="kw">let </span>nf: f32;
<span class="kw">let </span><span class="kw-2">mut </span>k: i32;
nf = (nm1 <span class="kw">as </span>f32) + <span class="number">1.0</span>;
w = <span class="number">2.0 </span>* (nf <span class="kw">as </span>f32) / x;
h = <span class="number">2.0 </span>/ x;
z = w + h;
q0 = w;
q1 = w * z - <span class="number">1.0</span>;
k = <span class="number">1</span>;
<span class="kw">while </span>q1 < <span class="number">1.0e4 </span>{
k += <span class="number">1</span>;
z += h;
tmp = z * q1 - q0;
q0 = q1;
q1 = tmp;
}
t = <span class="number">0.0</span>;
i = k;
<span class="kw">while </span>i >= <span class="number">0 </span>{
t = <span class="number">1.0 </span>/ (<span class="number">2.0 </span>* ((i <span class="kw">as </span>f32) + nf) / x - t);
i -= <span class="number">1</span>;
}
a = t;
b = <span class="number">1.0</span>;
<span class="comment">/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
</span>tmp = nf * logf(fabsf(w));
<span class="kw">if </span>tmp < <span class="number">88.721679688 </span>{
i = nm1;
<span class="kw">while </span>i > <span class="number">0 </span>{
temp = b;
b = <span class="number">2.0 </span>* (i <span class="kw">as </span>f32) * b / x - a;
a = temp;
i -= <span class="number">1</span>;
}
} <span class="kw">else </span>{
i = nm1;
<span class="kw">while </span>i > <span class="number">0 </span>{
temp = b;
b = <span class="number">2.0 </span>* (i <span class="kw">as </span>f32) * b / x - a;
a = temp;
<span class="comment">/* scale b to avoid spurious overflow */
</span><span class="kw">let </span>x1p60 = f32::from_bits(<span class="number">0x5d800000</span>); <span class="comment">// 0x1p60 == 2^60
</span><span class="kw">if </span>b > x1p60 {
a /= b;
t /= b;
b = <span class="number">1.0</span>;
}
i -= <span class="number">1</span>;
}
}
z = j0f(x);
w = j1f(x);
<span class="kw">if </span>fabsf(z) >= fabsf(w) {
b = t * z / b;
} <span class="kw">else </span>{
b = t * w / a;
}
}
}
<span class="kw">if </span>sign {
-b
} <span class="kw">else </span>{
b
}
}
<span class="kw">pub fn </span>ynf(n: i32, x: f32) -> f32 {
<span class="kw">let </span><span class="kw-2">mut </span>ix: u32;
<span class="kw">let </span><span class="kw-2">mut </span>ib: u32;
<span class="kw">let </span>nm1: i32;
<span class="kw">let </span><span class="kw-2">mut </span>sign: bool;
<span class="kw">let </span><span class="kw-2">mut </span>i: i32;
<span class="kw">let </span><span class="kw-2">mut </span>a: f32;
<span class="kw">let </span><span class="kw-2">mut </span>b: f32;
<span class="kw">let </span><span class="kw-2">mut </span>temp: f32;
ix = x.to_bits();
sign = (ix >> <span class="number">31</span>) != <span class="number">0</span>;
ix &= <span class="number">0x7fffffff</span>;
<span class="kw">if </span>ix > <span class="number">0x7f800000 </span>{
<span class="comment">/* nan */
</span><span class="kw">return </span>x;
}
<span class="kw">if </span>sign && ix != <span class="number">0 </span>{
<span class="comment">/* x < 0 */
</span><span class="kw">return </span><span class="number">0.0 </span>/ <span class="number">0.0</span>;
}
<span class="kw">if </span>ix == <span class="number">0x7f800000 </span>{
<span class="kw">return </span><span class="number">0.0</span>;
}
<span class="kw">if </span>n == <span class="number">0 </span>{
<span class="kw">return </span>y0f(x);
}
<span class="kw">if </span>n < <span class="number">0 </span>{
nm1 = -(n + <span class="number">1</span>);
sign = (n & <span class="number">1</span>) != <span class="number">0</span>;
} <span class="kw">else </span>{
nm1 = n - <span class="number">1</span>;
sign = <span class="bool-val">false</span>;
}
<span class="kw">if </span>nm1 == <span class="number">0 </span>{
<span class="kw">if </span>sign {
<span class="kw">return </span>-y1f(x);
} <span class="kw">else </span>{
<span class="kw">return </span>y1f(x);
}
}
a = y0f(x);
b = y1f(x);
<span class="comment">/* quit if b is -inf */
</span>ib = b.to_bits();
i = <span class="number">0</span>;
<span class="kw">while </span>i < nm1 && ib != <span class="number">0xff800000 </span>{
i += <span class="number">1</span>;
temp = b;
b = (<span class="number">2.0 </span>* (i <span class="kw">as </span>f32) / x) * b - a;
ib = b.to_bits();
a = temp;
}
<span class="kw">if </span>sign {
-b
} <span class="kw">else </span>{
b
}
}
</code></pre></div>
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