| <!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/j1.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>j1.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_j1.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. |
| * ==================================================== |
| */ |
| /* j1(x), y1(x) |
| * Bessel function of the first and second kinds of order zero. |
| * Method -- j1(x): |
| * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
| * 2. Reduce x to |x| since j1(x)=-j1(-x), and |
| * for x in (0,2) |
| * j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
| * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
| * for x in (2,inf) |
| * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
| * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
| * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
| * as follow: |
| * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
| * = 1/sqrt(2) * (sin(x) - cos(x)) |
| * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/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 |
| * j1(nan)= nan |
| * j1(0) = 0 |
| * j1(inf) = 0 |
| * |
| * Method -- y1(x): |
| * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
| * 2. For x<2. |
| * Since |
| * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
| * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
| * We use the following function to approximate y1, |
| * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
| * where for x in [0,2] (abs err less than 2**-65.89) |
| * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
| * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
| * Note: For tiny x, 1/x dominate y1 and hence |
| * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
| * 3. For x>=2. |
| * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
| * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
| * by method mentioned above. |
| */ |
| |
| </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 */ |
| |
| </span><span class="kw">fn </span>common(ix: u32, x: f64, y1: bool, sign: bool) -> f64 { |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>s: f64; |
| <span class="kw">let </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="comment">/* |
| * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x-3pi/4)-q1(x)*sin(x-3pi/4)) |
| * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x-3pi/4)+q1(x)*cos(x-3pi/4)) |
| * |
| * sin(x-3pi/4) = -(sin(x) + cos(x))/sqrt(2) |
| * cos(x-3pi/4) = (sin(x) - cos(x))/sqrt(2) |
| * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
| */ |
| </span>s = sin(x); |
| <span class="kw">if </span>y1 { |
| s = -s; |
| } |
| c = cos(x); |
| cc = s - c; |
| <span class="kw">if </span>ix < <span class="number">0x7fe00000 </span>{ |
| <span class="comment">/* avoid overflow in 2*x */ |
| </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>y1 { |
| ss = -ss; |
| } |
| cc = pone(x) * cc - qone(x) * ss; |
| } |
| } |
| <span class="kw">if </span>sign { |
| cc = -cc; |
| } |
| <span class="kw">return </span>INVSQRTPI * cc / sqrt(x); |
| } |
| |
| <span class="comment">/* R0/S0 on [0,2] */ |
| </span><span class="kw">const </span>R00: f64 = -<span class="number">6.25000000000000000000e-02</span>; <span class="comment">/* 0xBFB00000, 0x00000000 */ |
| </span><span class="kw">const </span>R01: f64 = <span class="number">1.40705666955189706048e-03</span>; <span class="comment">/* 0x3F570D9F, 0x98472C61 */ |
| </span><span class="kw">const </span>R02: f64 = -<span class="number">1.59955631084035597520e-05</span>; <span class="comment">/* 0xBEF0C5C6, 0xBA169668 */ |
| </span><span class="kw">const </span>R03: f64 = <span class="number">4.96727999609584448412e-08</span>; <span class="comment">/* 0x3E6AAAFA, 0x46CA0BD9 */ |
| </span><span class="kw">const </span>S01: f64 = <span class="number">1.91537599538363460805e-02</span>; <span class="comment">/* 0x3F939D0B, 0x12637E53 */ |
| </span><span class="kw">const </span>S02: f64 = <span class="number">1.85946785588630915560e-04</span>; <span class="comment">/* 0x3F285F56, 0xB9CDF664 */ |
| </span><span class="kw">const </span>S03: f64 = <span class="number">1.17718464042623683263e-06</span>; <span class="comment">/* 0x3EB3BFF8, 0x333F8498 */ |
| </span><span class="kw">const </span>S04: f64 = <span class="number">5.04636257076217042715e-09</span>; <span class="comment">/* 0x3E35AC88, 0xC97DFF2C */ |
| </span><span class="kw">const </span>S05: f64 = <span class="number">1.23542274426137913908e-11</span>; <span class="comment">/* 0x3DAB2ACF, 0xCFB97ED8 */ |
| |
| </span><span class="kw">pub fn </span>j1(x: f64) -> f64 { |
| <span class="kw">let </span><span class="kw-2">mut </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; |
| <span class="kw">let </span>sign: bool; |
| |
| ix = get_high_word(x); |
| 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">0x7ff00000 </span>{ |
| <span class="kw">return </span><span class="number">1.0 </span>/ (x * x); |
| } |
| <span class="kw">if </span>ix >= <span class="number">0x40000000 </span>{ |
| <span class="comment">/* |x| >= 2 */ |
| </span><span class="kw">return </span>common(ix, fabs(x), <span class="bool-val">false</span>, sign); |
| } |
| <span class="kw">if </span>ix >= <span class="number">0x38000000 </span>{ |
| <span class="comment">/* |x| >= 2**-127 */ |
| </span>z = x * x; |
| r = z * (R00 + z * (R01 + z * (R02 + z * R03))); |
| s = <span class="number">1.0 </span>+ z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05)))); |
| z = r / s; |
| } <span class="kw">else </span>{ |
| <span class="comment">/* avoid underflow, raise inexact if x!=0 */ |
| </span>z = x; |
| } |
| <span class="kw">return </span>(<span class="number">0.5 </span>+ z) * x; |
| } |
| |
| <span class="kw">const </span>U0: [f64; <span class="number">5</span>] = [ |
| -<span class="number">1.96057090646238940668e-01</span>, <span class="comment">/* 0xBFC91866, 0x143CBC8A */ |
| </span><span class="number">5.04438716639811282616e-02</span>, <span class="comment">/* 0x3FA9D3C7, 0x76292CD1 */ |
| </span>-<span class="number">1.91256895875763547298e-03</span>, <span class="comment">/* 0xBF5F55E5, 0x4844F50F */ |
| </span><span class="number">2.35252600561610495928e-05</span>, <span class="comment">/* 0x3EF8AB03, 0x8FA6B88E */ |
| </span>-<span class="number">9.19099158039878874504e-08</span>, <span class="comment">/* 0xBE78AC00, 0x569105B8 */ |
| </span>]; |
| <span class="kw">const </span>V0: [f64; <span class="number">5</span>] = [ |
| <span class="number">1.99167318236649903973e-02</span>, <span class="comment">/* 0x3F94650D, 0x3F4DA9F0 */ |
| </span><span class="number">2.02552581025135171496e-04</span>, <span class="comment">/* 0x3F2A8C89, 0x6C257764 */ |
| </span><span class="number">1.35608801097516229404e-06</span>, <span class="comment">/* 0x3EB6C05A, 0x894E8CA6 */ |
| </span><span class="number">6.22741452364621501295e-09</span>, <span class="comment">/* 0x3E3ABF1D, 0x5BA69A86 */ |
| </span><span class="number">1.66559246207992079114e-11</span>, <span class="comment">/* 0x3DB25039, 0xDACA772A */ |
| </span>]; |
| |
| <span class="kw">pub fn </span>y1(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">/* y1(nan)=nan, y1(<0)=nan, y1(0)=-inf, y1(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 */ |
| </span><span class="kw">return </span>common(ix, x, <span class="bool-val">true</span>, <span class="bool-val">false</span>); |
| } |
| <span class="kw">if </span>ix < <span class="number">0x3c900000 </span>{ |
| <span class="comment">/* x < 2**-54 */ |
| </span><span class="kw">return </span>-TPI / x; |
| } |
| z = x * x; |
| u = U0[<span class="number">0</span>] + z * (U0[<span class="number">1</span>] + z * (U0[<span class="number">2</span>] + z * (U0[<span class="number">3</span>] + z * U0[<span class="number">4</span>]))); |
| v = <span class="number">1.0 </span>+ z * (V0[<span class="number">0</span>] + z * (V0[<span class="number">1</span>] + z * (V0[<span class="number">2</span>] + z * (V0[<span class="number">3</span>] + z * V0[<span class="number">4</span>])))); |
| <span class="kw">return </span>x * (u / v) + TPI * (j1(x) * log(x) - <span class="number">1.0 </span>/ x); |
| } |
| |
| <span class="comment">/* For x >= 8, the asymptotic expansions of pone is |
| * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
| * We approximate pone by |
| * pone(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 |
| * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
| */ |
| |
| </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">1.17187499999988647970e-01</span>, <span class="comment">/* 0x3FBDFFFF, 0xFFFFFCCE */ |
| </span><span class="number">1.32394806593073575129e+01</span>, <span class="comment">/* 0x402A7A9D, 0x357F7FCE */ |
| </span><span class="number">4.12051854307378562225e+02</span>, <span class="comment">/* 0x4079C0D4, 0x652EA590 */ |
| </span><span class="number">3.87474538913960532227e+03</span>, <span class="comment">/* 0x40AE457D, 0xA3A532CC */ |
| </span><span class="number">7.91447954031891731574e+03</span>, <span class="comment">/* 0x40BEEA7A, 0xC32782DD */ |
| </span>]; |
| <span class="kw">const </span>PS8: [f64; <span class="number">5</span>] = [ |
| <span class="number">1.14207370375678408436e+02</span>, <span class="comment">/* 0x405C8D45, 0x8E656CAC */ |
| </span><span class="number">3.65093083420853463394e+03</span>, <span class="comment">/* 0x40AC85DC, 0x964D274F */ |
| </span><span class="number">3.69562060269033463555e+04</span>, <span class="comment">/* 0x40E20B86, 0x97C5BB7F */ |
| </span><span class="number">9.76027935934950801311e+04</span>, <span class="comment">/* 0x40F7D42C, 0xB28F17BB */ |
| </span><span class="number">3.08042720627888811578e+04</span>, <span class="comment">/* 0x40DE1511, 0x697A0B2D */ |
| </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">1.31990519556243522749e-11</span>, <span class="comment">/* 0x3DAD0667, 0xDAE1CA7D */ |
| </span><span class="number">1.17187493190614097638e-01</span>, <span class="comment">/* 0x3FBDFFFF, 0xE2C10043 */ |
| </span><span class="number">6.80275127868432871736e+00</span>, <span class="comment">/* 0x401B3604, 0x6E6315E3 */ |
| </span><span class="number">1.08308182990189109773e+02</span>, <span class="comment">/* 0x405B13B9, 0x452602ED */ |
| </span><span class="number">5.17636139533199752805e+02</span>, <span class="comment">/* 0x40802D16, 0xD052D649 */ |
| </span><span class="number">5.28715201363337541807e+02</span>, <span class="comment">/* 0x408085B8, 0xBB7E0CB7 */ |
| </span>]; |
| <span class="kw">const </span>PS5: [f64; <span class="number">5</span>] = [ |
| <span class="number">5.92805987221131331921e+01</span>, <span class="comment">/* 0x404DA3EA, 0xA8AF633D */ |
| </span><span class="number">9.91401418733614377743e+02</span>, <span class="comment">/* 0x408EFB36, 0x1B066701 */ |
| </span><span class="number">5.35326695291487976647e+03</span>, <span class="comment">/* 0x40B4E944, 0x5706B6FB */ |
| </span><span class="number">7.84469031749551231769e+03</span>, <span class="comment">/* 0x40BEA4B0, 0xB8A5BB15 */ |
| </span><span class="number">1.50404688810361062679e+03</span>, <span class="comment">/* 0x40978030, 0x036F5E51 */ |
| </span>]; |
| |
| <span class="kw">const </span>PR3: [f64; <span class="number">6</span>] = [ |
| <span class="number">3.02503916137373618024e-09</span>, <span class="comment">/* 0x3E29FC21, 0xA7AD9EDD */ |
| </span><span class="number">1.17186865567253592491e-01</span>, <span class="comment">/* 0x3FBDFFF5, 0x5B21D17B */ |
| </span><span class="number">3.93297750033315640650e+00</span>, <span class="comment">/* 0x400F76BC, 0xE85EAD8A */ |
| </span><span class="number">3.51194035591636932736e+01</span>, <span class="comment">/* 0x40418F48, 0x9DA6D129 */ |
| </span><span class="number">9.10550110750781271918e+01</span>, <span class="comment">/* 0x4056C385, 0x4D2C1837 */ |
| </span><span class="number">4.85590685197364919645e+01</span>, <span class="comment">/* 0x4048478F, 0x8EA83EE5 */ |
| </span>]; |
| <span class="kw">const </span>PS3: [f64; <span class="number">5</span>] = [ |
| <span class="number">3.47913095001251519989e+01</span>, <span class="comment">/* 0x40416549, 0xA134069C */ |
| </span><span class="number">3.36762458747825746741e+02</span>, <span class="comment">/* 0x40750C33, 0x07F1A75F */ |
| </span><span class="number">1.04687139975775130551e+03</span>, <span class="comment">/* 0x40905B7C, 0x5037D523 */ |
| </span><span class="number">8.90811346398256432622e+02</span>, <span class="comment">/* 0x408BD67D, 0xA32E31E9 */ |
| </span><span class="number">1.03787932439639277504e+02</span>, <span class="comment">/* 0x4059F26D, 0x7C2EED53 */ |
| </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">1.07710830106873743082e-07</span>, <span class="comment">/* 0x3E7CE9D4, 0xF65544F4 */ |
| </span><span class="number">1.17176219462683348094e-01</span>, <span class="comment">/* 0x3FBDFF42, 0xBE760D83 */ |
| </span><span class="number">2.36851496667608785174e+00</span>, <span class="comment">/* 0x4002F2B7, 0xF98FAEC0 */ |
| </span><span class="number">1.22426109148261232917e+01</span>, <span class="comment">/* 0x40287C37, 0x7F71A964 */ |
| </span><span class="number">1.76939711271687727390e+01</span>, <span class="comment">/* 0x4031B1A8, 0x177F8EE2 */ |
| </span><span class="number">5.07352312588818499250e+00</span>, <span class="comment">/* 0x40144B49, 0xA574C1FE */ |
| </span>]; |
| <span class="kw">const </span>PS2: [f64; <span class="number">5</span>] = [ |
| <span class="number">2.14364859363821409488e+01</span>, <span class="comment">/* 0x40356FBD, 0x8AD5ECDC */ |
| </span><span class="number">1.25290227168402751090e+02</span>, <span class="comment">/* 0x405F5293, 0x14F92CD5 */ |
| </span><span class="number">2.32276469057162813669e+02</span>, <span class="comment">/* 0x406D08D8, 0xD5A2DBD9 */ |
| </span><span class="number">1.17679373287147100768e+02</span>, <span class="comment">/* 0x405D6B7A, 0xDA1884A9 */ |
| </span><span class="number">8.36463893371618283368e+00</span>, <span class="comment">/* 0x4020BAB1, 0xF44E5192 */ |
| </span>]; |
| |
| <span class="kw">fn </span>pone(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 qone is |
| * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
| * We approximate pone by |
| * qone(x) = s*(0.375 + (R/S)) |
| * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
| * S = 1 + qs1*s^2 + ... + qs6*s^12 |
| * and |
| * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
| */ |
| |
| </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">1.02539062499992714161e-01</span>, <span class="comment">/* 0xBFBA3FFF, 0xFFFFFDF3 */ |
| </span>-<span class="number">1.62717534544589987888e+01</span>, <span class="comment">/* 0xC0304591, 0xA26779F7 */ |
| </span>-<span class="number">7.59601722513950107896e+02</span>, <span class="comment">/* 0xC087BCD0, 0x53E4B576 */ |
| </span>-<span class="number">1.18498066702429587167e+04</span>, <span class="comment">/* 0xC0C724E7, 0x40F87415 */ |
| </span>-<span class="number">4.84385124285750353010e+04</span>, <span class="comment">/* 0xC0E7A6D0, 0x65D09C6A */ |
| </span>]; |
| <span class="kw">const </span>QS8: [f64; <span class="number">6</span>] = [ |
| <span class="number">1.61395369700722909556e+02</span>, <span class="comment">/* 0x40642CA6, 0xDE5BCDE5 */ |
| </span><span class="number">7.82538599923348465381e+03</span>, <span class="comment">/* 0x40BE9162, 0xD0D88419 */ |
| </span><span class="number">1.33875336287249578163e+05</span>, <span class="comment">/* 0x4100579A, 0xB0B75E98 */ |
| </span><span class="number">7.19657723683240939863e+05</span>, <span class="comment">/* 0x4125F653, 0x72869C19 */ |
| </span><span class="number">6.66601232617776375264e+05</span>, <span class="comment">/* 0x412457D2, 0x7719AD5C */ |
| </span>-<span class="number">2.94490264303834643215e+05</span>, <span class="comment">/* 0xC111F969, 0x0EA5AA18 */ |
| </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">2.08979931141764104297e-11</span>, <span class="comment">/* 0xBDB6FA43, 0x1AA1A098 */ |
| </span>-<span class="number">1.02539050241375426231e-01</span>, <span class="comment">/* 0xBFBA3FFF, 0xCB597FEF */ |
| </span>-<span class="number">8.05644828123936029840e+00</span>, <span class="comment">/* 0xC0201CE6, 0xCA03AD4B */ |
| </span>-<span class="number">1.83669607474888380239e+02</span>, <span class="comment">/* 0xC066F56D, 0x6CA7B9B0 */ |
| </span>-<span class="number">1.37319376065508163265e+03</span>, <span class="comment">/* 0xC09574C6, 0x6931734F */ |
| </span>-<span class="number">2.61244440453215656817e+03</span>, <span class="comment">/* 0xC0A468E3, 0x88FDA79D */ |
| </span>]; |
| <span class="kw">const </span>QS5: [f64; <span class="number">6</span>] = [ |
| <span class="number">8.12765501384335777857e+01</span>, <span class="comment">/* 0x405451B2, 0xFF5A11B2 */ |
| </span><span class="number">1.99179873460485964642e+03</span>, <span class="comment">/* 0x409F1F31, 0xE77BF839 */ |
| </span><span class="number">1.74684851924908907677e+04</span>, <span class="comment">/* 0x40D10F1F, 0x0D64CE29 */ |
| </span><span class="number">4.98514270910352279316e+04</span>, <span class="comment">/* 0x40E8576D, 0xAABAD197 */ |
| </span><span class="number">2.79480751638918118260e+04</span>, <span class="comment">/* 0x40DB4B04, 0xCF7C364B */ |
| </span>-<span class="number">4.71918354795128470869e+03</span>, <span class="comment">/* 0xC0B26F2E, 0xFCFFA004 */ |
| </span>]; |
| |
| <span class="kw">const </span>QR3: [f64; <span class="number">6</span>] = [ |
| -<span class="number">5.07831226461766561369e-09</span>, <span class="comment">/* 0xBE35CFA9, 0xD38FC84F */ |
| </span>-<span class="number">1.02537829820837089745e-01</span>, <span class="comment">/* 0xBFBA3FEB, 0x51AEED54 */ |
| </span>-<span class="number">4.61011581139473403113e+00</span>, <span class="comment">/* 0xC01270C2, 0x3302D9FF */ |
| </span>-<span class="number">5.78472216562783643212e+01</span>, <span class="comment">/* 0xC04CEC71, 0xC25D16DA */ |
| </span>-<span class="number">2.28244540737631695038e+02</span>, <span class="comment">/* 0xC06C87D3, 0x4718D55F */ |
| </span>-<span class="number">2.19210128478909325622e+02</span>, <span class="comment">/* 0xC06B66B9, 0x5F5C1BF6 */ |
| </span>]; |
| <span class="kw">const </span>QS3: [f64; <span class="number">6</span>] = [ |
| <span class="number">4.76651550323729509273e+01</span>, <span class="comment">/* 0x4047D523, 0xCCD367E4 */ |
| </span><span class="number">6.73865112676699709482e+02</span>, <span class="comment">/* 0x40850EEB, 0xC031EE3E */ |
| </span><span class="number">3.38015286679526343505e+03</span>, <span class="comment">/* 0x40AA684E, 0x448E7C9A */ |
| </span><span class="number">5.54772909720722782367e+03</span>, <span class="comment">/* 0x40B5ABBA, 0xA61D54A6 */ |
| </span><span class="number">1.90311919338810798763e+03</span>, <span class="comment">/* 0x409DBC7A, 0x0DD4DF4B */ |
| </span>-<span class="number">1.35201191444307340817e+02</span>, <span class="comment">/* 0xC060E670, 0x290A311F */ |
| </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">1.78381727510958865572e-07</span>, <span class="comment">/* 0xBE87F126, 0x44C626D2 */ |
| </span>-<span class="number">1.02517042607985553460e-01</span>, <span class="comment">/* 0xBFBA3E8E, 0x9148B010 */ |
| </span>-<span class="number">2.75220568278187460720e+00</span>, <span class="comment">/* 0xC0060484, 0x69BB4EDA */ |
| </span>-<span class="number">1.96636162643703720221e+01</span>, <span class="comment">/* 0xC033A9E2, 0xC168907F */ |
| </span>-<span class="number">4.23253133372830490089e+01</span>, <span class="comment">/* 0xC04529A3, 0xDE104AAA */ |
| </span>-<span class="number">2.13719211703704061733e+01</span>, <span class="comment">/* 0xC0355F36, 0x39CF6E52 */ |
| </span>]; |
| <span class="kw">const </span>QS2: [f64; <span class="number">6</span>] = [ |
| <span class="number">2.95333629060523854548e+01</span>, <span class="comment">/* 0x403D888A, 0x78AE64FF */ |
| </span><span class="number">2.52981549982190529136e+02</span>, <span class="comment">/* 0x406F9F68, 0xDB821CBA */ |
| </span><span class="number">7.57502834868645436472e+02</span>, <span class="comment">/* 0x4087AC05, 0xCE49A0F7 */ |
| </span><span class="number">7.39393205320467245656e+02</span>, <span class="comment">/* 0x40871B25, 0x48D4C029 */ |
| </span><span class="number">1.55949003336666123687e+02</span>, <span class="comment">/* 0x40637E5E, 0x3C3ED8D4 */ |
| </span>-<span class="number">4.95949898822628210127e+00</span>, <span class="comment">/* 0xC013D686, 0xE71BE86B */ |
| </span>]; |
| |
| <span class="kw">fn </span>qone(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">0.375 </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> |
