| <!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/j0.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>j0.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_j0.c */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| /* j0(x), y0(x) |
| * Bessel function of the first and second kinds of order zero. |
| * Method -- j0(x): |
| * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
| * 2. Reduce x to |x| since j0(x)=j0(-x), and |
| * for x in (0,2) |
| * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
| * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
| * for x in (2,inf) |
| * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
| * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
| * as follow: |
| * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
| * = 1/sqrt(2) * (cos(x) + sin(x)) |
| * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
| * = 1/sqrt(2) * (sin(x) - cos(x)) |
| * (To avoid cancellation, use |
| * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
| * to compute the worse one.) |
| * |
| * 3 Special cases |
| * j0(nan)= nan |
| * j0(0) = 1 |
| * j0(inf) = 0 |
| * |
| * Method -- y0(x): |
| * 1. For x<2. |
| * Since |
| * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
| * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
| * We use the following function to approximate y0, |
| * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
| * where |
| * U(z) = u00 + u01*z + ... + u06*z^6 |
| * V(z) = 1 + v01*z + ... + v04*z^4 |
| * with absolute approximation error bounded by 2**-72. |
| * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
| * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
| * 2. For x>=2. |
| * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
| * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
| * by the method mentioned above. |
| * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
| */ |
| |
| </span><span class="kw">use super</span>::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt}; |
| <span class="kw">const </span>INVSQRTPI: f64 = <span class="number">5.64189583547756279280e-01</span>; <span class="comment">/* 0x3FE20DD7, 0x50429B6D */ |
| </span><span class="kw">const </span>TPI: f64 = <span class="number">6.36619772367581382433e-01</span>; <span class="comment">/* 0x3FE45F30, 0x6DC9C883 */ |
| |
| /* common method when |x|>=2 */ |
| </span><span class="kw">fn </span>common(ix: u32, x: f64, y0: bool) -> f64 { |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>c: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>ss: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>cc: f64; |
| <span class="kw">let </span>z: f64; |
| |
| <span class="comment">/* |
| * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4)) |
| * y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4)) |
| * |
| * sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2) |
| * cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2) |
| * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
| */ |
| </span>s = sin(x); |
| c = cos(x); |
| <span class="kw">if </span>y0 { |
| c = -c; |
| } |
| cc = s + c; |
| <span class="comment">/* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x7fe00000 </span>{ |
| ss = s - c; |
| z = -cos(<span class="number">2.0 </span>* x); |
| <span class="kw">if </span>s * c < <span class="number">0.0 </span>{ |
| cc = z / ss; |
| } <span class="kw">else </span>{ |
| ss = z / cc; |
| } |
| <span class="kw">if </span>ix < <span class="number">0x48000000 </span>{ |
| <span class="kw">if </span>y0 { |
| ss = -ss; |
| } |
| cc = pzero(x) * cc - qzero(x) * ss; |
| } |
| } |
| <span class="kw">return </span>INVSQRTPI * cc / sqrt(x); |
| } |
| |
| <span class="comment">/* R0/S0 on [0, 2.00] */ |
| </span><span class="kw">const </span>R02: f64 = <span class="number">1.56249999999999947958e-02</span>; <span class="comment">/* 0x3F8FFFFF, 0xFFFFFFFD */ |
| </span><span class="kw">const </span>R03: f64 = -<span class="number">1.89979294238854721751e-04</span>; <span class="comment">/* 0xBF28E6A5, 0xB61AC6E9 */ |
| </span><span class="kw">const </span>R04: f64 = <span class="number">1.82954049532700665670e-06</span>; <span class="comment">/* 0x3EBEB1D1, 0x0C503919 */ |
| </span><span class="kw">const </span>R05: f64 = -<span class="number">4.61832688532103189199e-09</span>; <span class="comment">/* 0xBE33D5E7, 0x73D63FCE */ |
| </span><span class="kw">const </span>S01: f64 = <span class="number">1.56191029464890010492e-02</span>; <span class="comment">/* 0x3F8FFCE8, 0x82C8C2A4 */ |
| </span><span class="kw">const </span>S02: f64 = <span class="number">1.16926784663337450260e-04</span>; <span class="comment">/* 0x3F1EA6D2, 0xDD57DBF4 */ |
| </span><span class="kw">const </span>S03: f64 = <span class="number">5.13546550207318111446e-07</span>; <span class="comment">/* 0x3EA13B54, 0xCE84D5A9 */ |
| </span><span class="kw">const </span>S04: f64 = <span class="number">1.16614003333790000205e-09</span>; <span class="comment">/* 0x3E1408BC, 0xF4745D8F */ |
| |
| </span><span class="kw">pub fn </span>j0(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span>r: f64; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix: u32; |
| |
| ix = get_high_word(x); |
| ix &= <span class="number">0x7fffffff</span>; |
| |
| <span class="comment">/* j0(+-inf)=0, j0(nan)=nan */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x7ff00000 </span>{ |
| <span class="kw">return </span><span class="number">1.0 </span>/ (x * x); |
| } |
| x = fabs(x); |
| |
| <span class="kw">if </span>ix >= <span class="number">0x40000000 </span>{ |
| <span class="comment">/* |x| >= 2 */ |
| /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */ |
| </span><span class="kw">return </span>common(ix, x, <span class="bool-val">false</span>); |
| } |
| |
| <span class="comment">/* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x3f200000 </span>{ |
| <span class="comment">/* |x| >= 2**-13 */ |
| /* up to 4ulp error close to 2 */ |
| </span>z = x * x; |
| r = z * (R02 + z * (R03 + z * (R04 + z * R05))); |
| s = <span class="number">1.0 </span>+ z * (S01 + z * (S02 + z * (S03 + z * S04))); |
| <span class="kw">return </span>(<span class="number">1.0 </span>+ x / <span class="number">2.0</span>) * (<span class="number">1.0 </span>- x / <span class="number">2.0</span>) + z * (r / s); |
| } |
| |
| <span class="comment">/* 1 - x*x/4 */ |
| /* prevent underflow */ |
| /* inexact should be raised when x!=0, this is not done correctly */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x38000000 </span>{ |
| <span class="comment">/* |x| >= 2**-127 */ |
| </span>x = <span class="number">0.25 </span>* x * x; |
| } |
| <span class="kw">return </span><span class="number">1.0 </span>- x; |
| } |
| |
| <span class="kw">const </span>U00: f64 = -<span class="number">7.38042951086872317523e-02</span>; <span class="comment">/* 0xBFB2E4D6, 0x99CBD01F */ |
| </span><span class="kw">const </span>U01: f64 = <span class="number">1.76666452509181115538e-01</span>; <span class="comment">/* 0x3FC69D01, 0x9DE9E3FC */ |
| </span><span class="kw">const </span>U02: f64 = -<span class="number">1.38185671945596898896e-02</span>; <span class="comment">/* 0xBF8C4CE8, 0xB16CFA97 */ |
| </span><span class="kw">const </span>U03: f64 = <span class="number">3.47453432093683650238e-04</span>; <span class="comment">/* 0x3F36C54D, 0x20B29B6B */ |
| </span><span class="kw">const </span>U04: f64 = -<span class="number">3.81407053724364161125e-06</span>; <span class="comment">/* 0xBECFFEA7, 0x73D25CAD */ |
| </span><span class="kw">const </span>U05: f64 = <span class="number">1.95590137035022920206e-08</span>; <span class="comment">/* 0x3E550057, 0x3B4EABD4 */ |
| </span><span class="kw">const </span>U06: f64 = -<span class="number">3.98205194132103398453e-11</span>; <span class="comment">/* 0xBDC5E43D, 0x693FB3C8 */ |
| </span><span class="kw">const </span>V01: f64 = <span class="number">1.27304834834123699328e-02</span>; <span class="comment">/* 0x3F8A1270, 0x91C9C71A */ |
| </span><span class="kw">const </span>V02: f64 = <span class="number">7.60068627350353253702e-05</span>; <span class="comment">/* 0x3F13ECBB, 0xF578C6C1 */ |
| </span><span class="kw">const </span>V03: f64 = <span class="number">2.59150851840457805467e-07</span>; <span class="comment">/* 0x3E91642D, 0x7FF202FD */ |
| </span><span class="kw">const </span>V04: f64 = <span class="number">4.41110311332675467403e-10</span>; <span class="comment">/* 0x3DFE5018, 0x3BD6D9EF */ |
| |
| </span><span class="kw">pub fn </span>y0(x: f64) -> f64 { |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span>u: f64; |
| <span class="kw">let </span>v: f64; |
| <span class="kw">let </span>ix: u32; |
| <span class="kw">let </span>lx: u32; |
| |
| ix = get_high_word(x); |
| lx = get_low_word(x); |
| |
| <span class="comment">/* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */ |
| </span><span class="kw">if </span>((ix << <span class="number">1</span>) | lx) == <span class="number">0 </span>{ |
| <span class="kw">return </span>-<span class="number">1.0 </span>/ <span class="number">0.0</span>; |
| } |
| <span class="kw">if </span>(ix >> <span class="number">31</span>) != <span class="number">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">0x7ff00000 </span>{ |
| <span class="kw">return </span><span class="number">1.0 </span>/ x; |
| } |
| |
| <span class="kw">if </span>ix >= <span class="number">0x40000000 </span>{ |
| <span class="comment">/* x >= 2 */ |
| /* large ulp errors near zeros: 3.958, 7.086,.. */ |
| </span><span class="kw">return </span>common(ix, x, <span class="bool-val">true</span>); |
| } |
| |
| <span class="comment">/* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x3e400000 </span>{ |
| <span class="comment">/* x >= 2**-27 */ |
| /* large ulp error near the first zero, x ~= 0.89 */ |
| </span>z = x * x; |
| u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06))))); |
| v = <span class="number">1.0 </span>+ z * (V01 + z * (V02 + z * (V03 + z * V04))); |
| <span class="kw">return </span>u / v + TPI * (j0(x) * log(x)); |
| } |
| <span class="kw">return </span>U00 + TPI * log(x); |
| } |
| |
| <span class="comment">/* The asymptotic expansions of pzero is |
| * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
| * For x >= 2, We approximate pzero by |
| * pzero(x) = 1 + (R/S) |
| * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
| * S = 1 + pS0*s^2 + ... + pS4*s^10 |
| * and |
| * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
| */ |
| </span><span class="kw">const </span>PR8: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [inf, 8]=1/[0,0.125] */ |
| </span><span class="number">0.00000000000000000000e+00</span>, <span class="comment">/* 0x00000000, 0x00000000 */ |
| </span>-<span class="number">7.03124999999900357484e-02</span>, <span class="comment">/* 0xBFB1FFFF, 0xFFFFFD32 */ |
| </span>-<span class="number">8.08167041275349795626e+00</span>, <span class="comment">/* 0xC02029D0, 0xB44FA779 */ |
| </span>-<span class="number">2.57063105679704847262e+02</span>, <span class="comment">/* 0xC0701102, 0x7B19E863 */ |
| </span>-<span class="number">2.48521641009428822144e+03</span>, <span class="comment">/* 0xC0A36A6E, 0xCD4DCAFC */ |
| </span>-<span class="number">5.25304380490729545272e+03</span>, <span class="comment">/* 0xC0B4850B, 0x36CC643D */ |
| </span>]; |
| <span class="kw">const </span>PS8: [f64; <span class="number">5</span>] = [ |
| <span class="number">1.16534364619668181717e+02</span>, <span class="comment">/* 0x405D2233, 0x07A96751 */ |
| </span><span class="number">3.83374475364121826715e+03</span>, <span class="comment">/* 0x40ADF37D, 0x50596938 */ |
| </span><span class="number">4.05978572648472545552e+04</span>, <span class="comment">/* 0x40E3D2BB, 0x6EB6B05F */ |
| </span><span class="number">1.16752972564375915681e+05</span>, <span class="comment">/* 0x40FC810F, 0x8F9FA9BD */ |
| </span><span class="number">4.76277284146730962675e+04</span>, <span class="comment">/* 0x40E74177, 0x4F2C49DC */ |
| </span>]; |
| |
| <span class="kw">const </span>PR5: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| </span>-<span class="number">1.14125464691894502584e-11</span>, <span class="comment">/* 0xBDA918B1, 0x47E495CC */ |
| </span>-<span class="number">7.03124940873599280078e-02</span>, <span class="comment">/* 0xBFB1FFFF, 0xE69AFBC6 */ |
| </span>-<span class="number">4.15961064470587782438e+00</span>, <span class="comment">/* 0xC010A370, 0xF90C6BBF */ |
| </span>-<span class="number">6.76747652265167261021e+01</span>, <span class="comment">/* 0xC050EB2F, 0x5A7D1783 */ |
| </span>-<span class="number">3.31231299649172967747e+02</span>, <span class="comment">/* 0xC074B3B3, 0x6742CC63 */ |
| </span>-<span class="number">3.46433388365604912451e+02</span>, <span class="comment">/* 0xC075A6EF, 0x28A38BD7 */ |
| </span>]; |
| <span class="kw">const </span>PS5: [f64; <span class="number">5</span>] = [ |
| <span class="number">6.07539382692300335975e+01</span>, <span class="comment">/* 0x404E6081, 0x0C98C5DE */ |
| </span><span class="number">1.05125230595704579173e+03</span>, <span class="comment">/* 0x40906D02, 0x5C7E2864 */ |
| </span><span class="number">5.97897094333855784498e+03</span>, <span class="comment">/* 0x40B75AF8, 0x8FBE1D60 */ |
| </span><span class="number">9.62544514357774460223e+03</span>, <span class="comment">/* 0x40C2CCB8, 0xFA76FA38 */ |
| </span><span class="number">2.40605815922939109441e+03</span>, <span class="comment">/* 0x40A2CC1D, 0xC70BE864 */ |
| </span>]; |
| |
| <span class="kw">const </span>PR3: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
| </span>-<span class="number">2.54704601771951915620e-09</span>, <span class="comment">/* 0xBE25E103, 0x6FE1AA86 */ |
| </span>-<span class="number">7.03119616381481654654e-02</span>, <span class="comment">/* 0xBFB1FFF6, 0xF7C0E24B */ |
| </span>-<span class="number">2.40903221549529611423e+00</span>, <span class="comment">/* 0xC00345B2, 0xAEA48074 */ |
| </span>-<span class="number">2.19659774734883086467e+01</span>, <span class="comment">/* 0xC035F74A, 0x4CB94E14 */ |
| </span>-<span class="number">5.80791704701737572236e+01</span>, <span class="comment">/* 0xC04D0A22, 0x420A1A45 */ |
| </span>-<span class="number">3.14479470594888503854e+01</span>, <span class="comment">/* 0xC03F72AC, 0xA892D80F */ |
| </span>]; |
| <span class="kw">const </span>PS3: [f64; <span class="number">5</span>] = [ |
| <span class="number">3.58560338055209726349e+01</span>, <span class="comment">/* 0x4041ED92, 0x84077DD3 */ |
| </span><span class="number">3.61513983050303863820e+02</span>, <span class="comment">/* 0x40769839, 0x464A7C0E */ |
| </span><span class="number">1.19360783792111533330e+03</span>, <span class="comment">/* 0x4092A66E, 0x6D1061D6 */ |
| </span><span class="number">1.12799679856907414432e+03</span>, <span class="comment">/* 0x40919FFC, 0xB8C39B7E */ |
| </span><span class="number">1.73580930813335754692e+02</span>, <span class="comment">/* 0x4065B296, 0xFC379081 */ |
| </span>]; |
| |
| <span class="kw">const </span>PR2: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| </span>-<span class="number">8.87534333032526411254e-08</span>, <span class="comment">/* 0xBE77D316, 0xE927026D */ |
| </span>-<span class="number">7.03030995483624743247e-02</span>, <span class="comment">/* 0xBFB1FF62, 0x495E1E42 */ |
| </span>-<span class="number">1.45073846780952986357e+00</span>, <span class="comment">/* 0xBFF73639, 0x8A24A843 */ |
| </span>-<span class="number">7.63569613823527770791e+00</span>, <span class="comment">/* 0xC01E8AF3, 0xEDAFA7F3 */ |
| </span>-<span class="number">1.11931668860356747786e+01</span>, <span class="comment">/* 0xC02662E6, 0xC5246303 */ |
| </span>-<span class="number">3.23364579351335335033e+00</span>, <span class="comment">/* 0xC009DE81, 0xAF8FE70F */ |
| </span>]; |
| <span class="kw">const </span>PS2: [f64; <span class="number">5</span>] = [ |
| <span class="number">2.22202997532088808441e+01</span>, <span class="comment">/* 0x40363865, 0x908B5959 */ |
| </span><span class="number">1.36206794218215208048e+02</span>, <span class="comment">/* 0x4061069E, 0x0EE8878F */ |
| </span><span class="number">2.70470278658083486789e+02</span>, <span class="comment">/* 0x4070E786, 0x42EA079B */ |
| </span><span class="number">1.53875394208320329881e+02</span>, <span class="comment">/* 0x40633C03, 0x3AB6FAFF */ |
| </span><span class="number">1.46576176948256193810e+01</span>, <span class="comment">/* 0x402D50B3, 0x44391809 */ |
| </span>]; |
| |
| <span class="kw">fn </span>pzero(x: f64) -> f64 { |
| <span class="kw">let </span>p: <span class="kw-2">&</span>[f64; <span class="number">6</span>]; |
| <span class="kw">let </span>q: <span class="kw-2">&</span>[f64; <span class="number">5</span>]; |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span>r: f64; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix: u32; |
| |
| ix = get_high_word(x); |
| ix &= <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x40200000 </span>{ |
| p = <span class="kw-2">&</span>PR8; |
| q = <span class="kw-2">&</span>PS8; |
| } <span class="kw">else if </span>ix >= <span class="number">0x40122E8B </span>{ |
| p = <span class="kw-2">&</span>PR5; |
| q = <span class="kw-2">&</span>PS5; |
| } <span class="kw">else if </span>ix >= <span class="number">0x4006DB6D </span>{ |
| p = <span class="kw-2">&</span>PR3; |
| q = <span class="kw-2">&</span>PS3; |
| } <span class="kw">else |
| </span><span class="comment">/*ix >= 0x40000000*/ |
| </span>{ |
| p = <span class="kw-2">&</span>PR2; |
| q = <span class="kw-2">&</span>PS2; |
| } |
| z = <span class="number">1.0 </span>/ (x * x); |
| r = p[<span class="number">0</span>] + z * (p[<span class="number">1</span>] + z * (p[<span class="number">2</span>] + z * (p[<span class="number">3</span>] + z * (p[<span class="number">4</span>] + z * p[<span class="number">5</span>])))); |
| s = <span class="number">1.0 </span>+ z * (q[<span class="number">0</span>] + z * (q[<span class="number">1</span>] + z * (q[<span class="number">2</span>] + z * (q[<span class="number">3</span>] + z * q[<span class="number">4</span>])))); |
| <span class="kw">return </span><span class="number">1.0 </span>+ r / s; |
| } |
| |
| <span class="comment">/* For x >= 8, the asymptotic expansions of qzero is |
| * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
| * We approximate pzero by |
| * qzero(x) = s*(-1.25 + (R/S)) |
| * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
| * S = 1 + qS0*s^2 + ... + qS5*s^12 |
| * and |
| * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
| */ |
| </span><span class="kw">const </span>QR8: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [inf, 8]=1/[0,0.125] */ |
| </span><span class="number">0.00000000000000000000e+00</span>, <span class="comment">/* 0x00000000, 0x00000000 */ |
| </span><span class="number">7.32421874999935051953e-02</span>, <span class="comment">/* 0x3FB2BFFF, 0xFFFFFE2C */ |
| </span><span class="number">1.17682064682252693899e+01</span>, <span class="comment">/* 0x40278952, 0x5BB334D6 */ |
| </span><span class="number">5.57673380256401856059e+02</span>, <span class="comment">/* 0x40816D63, 0x15301825 */ |
| </span><span class="number">8.85919720756468632317e+03</span>, <span class="comment">/* 0x40C14D99, 0x3E18F46D */ |
| </span><span class="number">3.70146267776887834771e+04</span>, <span class="comment">/* 0x40E212D4, 0x0E901566 */ |
| </span>]; |
| <span class="kw">const </span>QS8: [f64; <span class="number">6</span>] = [ |
| <span class="number">1.63776026895689824414e+02</span>, <span class="comment">/* 0x406478D5, 0x365B39BC */ |
| </span><span class="number">8.09834494656449805916e+03</span>, <span class="comment">/* 0x40BFA258, 0x4E6B0563 */ |
| </span><span class="number">1.42538291419120476348e+05</span>, <span class="comment">/* 0x41016652, 0x54D38C3F */ |
| </span><span class="number">8.03309257119514397345e+05</span>, <span class="comment">/* 0x412883DA, 0x83A52B43 */ |
| </span><span class="number">8.40501579819060512818e+05</span>, <span class="comment">/* 0x4129A66B, 0x28DE0B3D */ |
| </span>-<span class="number">3.43899293537866615225e+05</span>, <span class="comment">/* 0xC114FD6D, 0x2C9530C5 */ |
| </span>]; |
| |
| <span class="kw">const </span>QR5: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| </span><span class="number">1.84085963594515531381e-11</span>, <span class="comment">/* 0x3DB43D8F, 0x29CC8CD9 */ |
| </span><span class="number">7.32421766612684765896e-02</span>, <span class="comment">/* 0x3FB2BFFF, 0xD172B04C */ |
| </span><span class="number">5.83563508962056953777e+00</span>, <span class="comment">/* 0x401757B0, 0xB9953DD3 */ |
| </span><span class="number">1.35111577286449829671e+02</span>, <span class="comment">/* 0x4060E392, 0x0A8788E9 */ |
| </span><span class="number">1.02724376596164097464e+03</span>, <span class="comment">/* 0x40900CF9, 0x9DC8C481 */ |
| </span><span class="number">1.98997785864605384631e+03</span>, <span class="comment">/* 0x409F17E9, 0x53C6E3A6 */ |
| </span>]; |
| <span class="kw">const </span>QS5: [f64; <span class="number">6</span>] = [ |
| <span class="number">8.27766102236537761883e+01</span>, <span class="comment">/* 0x4054B1B3, 0xFB5E1543 */ |
| </span><span class="number">2.07781416421392987104e+03</span>, <span class="comment">/* 0x40A03BA0, 0xDA21C0CE */ |
| </span><span class="number">1.88472887785718085070e+04</span>, <span class="comment">/* 0x40D267D2, 0x7B591E6D */ |
| </span><span class="number">5.67511122894947329769e+04</span>, <span class="comment">/* 0x40EBB5E3, 0x97E02372 */ |
| </span><span class="number">3.59767538425114471465e+04</span>, <span class="comment">/* 0x40E19118, 0x1F7A54A0 */ |
| </span>-<span class="number">5.35434275601944773371e+03</span>, <span class="comment">/* 0xC0B4EA57, 0xBEDBC609 */ |
| </span>]; |
| |
| <span class="kw">const </span>QR3: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
| </span><span class="number">4.37741014089738620906e-09</span>, <span class="comment">/* 0x3E32CD03, 0x6ADECB82 */ |
| </span><span class="number">7.32411180042911447163e-02</span>, <span class="comment">/* 0x3FB2BFEE, 0x0E8D0842 */ |
| </span><span class="number">3.34423137516170720929e+00</span>, <span class="comment">/* 0x400AC0FC, 0x61149CF5 */ |
| </span><span class="number">4.26218440745412650017e+01</span>, <span class="comment">/* 0x40454F98, 0x962DAEDD */ |
| </span><span class="number">1.70808091340565596283e+02</span>, <span class="comment">/* 0x406559DB, 0xE25EFD1F */ |
| </span><span class="number">1.66733948696651168575e+02</span>, <span class="comment">/* 0x4064D77C, 0x81FA21E0 */ |
| </span>]; |
| <span class="kw">const </span>QS3: [f64; <span class="number">6</span>] = [ |
| <span class="number">4.87588729724587182091e+01</span>, <span class="comment">/* 0x40486122, 0xBFE343A6 */ |
| </span><span class="number">7.09689221056606015736e+02</span>, <span class="comment">/* 0x40862D83, 0x86544EB3 */ |
| </span><span class="number">3.70414822620111362994e+03</span>, <span class="comment">/* 0x40ACF04B, 0xE44DFC63 */ |
| </span><span class="number">6.46042516752568917582e+03</span>, <span class="comment">/* 0x40B93C6C, 0xD7C76A28 */ |
| </span><span class="number">2.51633368920368957333e+03</span>, <span class="comment">/* 0x40A3A8AA, 0xD94FB1C0 */ |
| </span>-<span class="number">1.49247451836156386662e+02</span>, <span class="comment">/* 0xC062A7EB, 0x201CF40F */ |
| </span>]; |
| |
| <span class="kw">const </span>QR2: [f64; <span class="number">6</span>] = [ |
| <span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| </span><span class="number">1.50444444886983272379e-07</span>, <span class="comment">/* 0x3E84313B, 0x54F76BDB */ |
| </span><span class="number">7.32234265963079278272e-02</span>, <span class="comment">/* 0x3FB2BEC5, 0x3E883E34 */ |
| </span><span class="number">1.99819174093815998816e+00</span>, <span class="comment">/* 0x3FFFF897, 0xE727779C */ |
| </span><span class="number">1.44956029347885735348e+01</span>, <span class="comment">/* 0x402CFDBF, 0xAAF96FE5 */ |
| </span><span class="number">3.16662317504781540833e+01</span>, <span class="comment">/* 0x403FAA8E, 0x29FBDC4A */ |
| </span><span class="number">1.62527075710929267416e+01</span>, <span class="comment">/* 0x403040B1, 0x71814BB4 */ |
| </span>]; |
| <span class="kw">const </span>QS2: [f64; <span class="number">6</span>] = [ |
| <span class="number">3.03655848355219184498e+01</span>, <span class="comment">/* 0x403E5D96, 0xF7C07AED */ |
| </span><span class="number">2.69348118608049844624e+02</span>, <span class="comment">/* 0x4070D591, 0xE4D14B40 */ |
| </span><span class="number">8.44783757595320139444e+02</span>, <span class="comment">/* 0x408A6645, 0x22B3BF22 */ |
| </span><span class="number">8.82935845112488550512e+02</span>, <span class="comment">/* 0x408B977C, 0x9C5CC214 */ |
| </span><span class="number">2.12666388511798828631e+02</span>, <span class="comment">/* 0x406A9553, 0x0E001365 */ |
| </span>-<span class="number">5.31095493882666946917e+00</span>, <span class="comment">/* 0xC0153E6A, 0xF8B32931 */ |
| </span>]; |
| |
| <span class="kw">fn </span>qzero(x: f64) -> f64 { |
| <span class="kw">let </span>p: <span class="kw-2">&</span>[f64; <span class="number">6</span>]; |
| <span class="kw">let </span>q: <span class="kw-2">&</span>[f64; <span class="number">6</span>]; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span>r: f64; |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix: u32; |
| |
| ix = get_high_word(x); |
| ix &= <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x40200000 </span>{ |
| p = <span class="kw-2">&</span>QR8; |
| q = <span class="kw-2">&</span>QS8; |
| } <span class="kw">else if </span>ix >= <span class="number">0x40122E8B </span>{ |
| p = <span class="kw-2">&</span>QR5; |
| q = <span class="kw-2">&</span>QS5; |
| } <span class="kw">else if </span>ix >= <span class="number">0x4006DB6D </span>{ |
| p = <span class="kw-2">&</span>QR3; |
| q = <span class="kw-2">&</span>QS3; |
| } <span class="kw">else |
| </span><span class="comment">/*ix >= 0x40000000*/ |
| </span>{ |
| p = <span class="kw-2">&</span>QR2; |
| q = <span class="kw-2">&</span>QS2; |
| } |
| z = <span class="number">1.0 </span>/ (x * x); |
| r = p[<span class="number">0</span>] + z * (p[<span class="number">1</span>] + z * (p[<span class="number">2</span>] + z * (p[<span class="number">3</span>] + z * (p[<span class="number">4</span>] + z * p[<span class="number">5</span>])))); |
| s = <span class="number">1.0 </span>+ z * (q[<span class="number">0</span>] + z * (q[<span class="number">1</span>] + z * (q[<span class="number">2</span>] + z * (q[<span class="number">3</span>] + z * (q[<span class="number">4</span>] + z * q[<span class="number">5</span>]))))); |
| <span class="kw">return </span>(-<span class="number">0.125 </span>+ r / s) / x; |
| } |
| </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> |
