| <!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 `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.7/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="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.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"><a class="sidebar-logo" href="../../../libm/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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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> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="libm" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
