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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */</span> |
| <span class="comment">/* |
| * jn(n, x), yn(n, x) |
| * floating point Bessel's function of the 1st and 2nd kind |
| * of order n |
| * |
| * Special cases: |
| * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; |
| * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. |
| * Note 2. About jn(n,x), yn(n,x) |
| * For n=0, j0(x) is called, |
| * for n=1, j1(x) is called, |
| * for n<=x, forward recursion is used starting |
| * from values of j0(x) and j1(x). |
| * for n>x, a continued fraction approximation to |
| * j(n,x)/j(n-1,x) is evaluated and then backward |
| * recursion is used starting from a supposed value |
| * for j(n,x). The resulting value of j(0,x) is |
| * compared with the actual value to correct the |
| * supposed value of j(n,x). |
| * |
| * yn(n,x) is similar in all respects, except |
| * that forward recursion is used for all |
| * values of n>1. |
| */</span> |
| |
| <span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">cos</span>, <span class="ident">fabs</span>, <span class="ident">get_high_word</span>, <span class="ident">get_low_word</span>, <span class="ident">j0</span>, <span class="ident">j1</span>, <span class="ident">log</span>, <span class="ident">sin</span>, <span class="ident">sqrt</span>, <span class="ident">y0</span>, <span class="ident">y1</span>}; |
| |
| <span class="kw">const</span> <span class="ident">INVSQRTPI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.64189583547756279280e-01</span>; <span class="comment">/* 0x3FE20DD7, 0x50429B6D */</span> |
| |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">jn</span>(<span class="ident">n</span>: <span class="ident">i32</span>, <span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">lx</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">nm1</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sign</span>: <span class="ident">bool</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">a</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">b</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">temp</span>: <span class="ident">f64</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>); |
| <span class="ident">lx</span> <span class="op">=</span> <span class="ident">get_low_word</span>(<span class="ident">x</span>); |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span>; |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| |
| <span class="comment">// -lx == !lx + 1</span> |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">|</span> (<span class="ident">lx</span> <span class="op">|</span> ((<span class="op">!</span><span class="ident">lx</span>).<span class="ident">wrapping_add</span>(<span class="number">1</span>))) <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">></span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* nan */</span> |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| |
| <span class="comment">/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) |
| * Thus, J(-n,x) = J(n,-x) |
| */</span> |
| <span class="comment">/* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */</span> |
| <span class="kw">if</span> <span class="ident">n</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="ident">j0</span>(<span class="ident">x</span>); |
| } |
| <span class="kw">if</span> <span class="ident">n</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="ident">nm1</span> <span class="op">=</span> <span class="op">-</span>(<span class="ident">n</span> <span class="op">+</span> <span class="number">1</span>); |
| <span class="ident">x</span> <span class="op">=</span> <span class="op">-</span><span class="ident">x</span>; |
| <span class="ident">sign</span> <span class="op">=</span> <span class="op">!</span><span class="ident">sign</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">nm1</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">-</span> <span class="number">1</span>; |
| } |
| <span class="kw">if</span> <span class="ident">nm1</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="ident">j1</span>(<span class="ident">x</span>); |
| } |
| |
| <span class="ident">sign</span> <span class="op">&=</span> (<span class="ident">n</span> <span class="op">&</span> <span class="number">1</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span>; <span class="comment">/* even n: 0, odd n: signbit(x) */</span> |
| <span class="ident">x</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">|</span> <span class="ident">lx</span>) <span class="op">==</span> <span class="number">0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* if x is 0 or inf */</span> |
| <span class="ident">b</span> <span class="op">=</span> <span class="number">0.0</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> (<span class="ident">nm1</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op"><</span> <span class="ident">x</span> { |
| <span class="comment">/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x52d00000</span> { |
| <span class="comment">/* x > 2**302 */</span> |
| <span class="comment">/* (x >> n**2) |
| * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) |
| * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) |
| * Let s=sin(x), c=cos(x), |
| * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then |
| * |
| * n sin(xn)*sqt2 cos(xn)*sqt2 |
| * ---------------------------------- |
| * 0 s-c c+s |
| * 1 -s-c -c+s |
| * 2 -s+c -c-s |
| * 3 s+c c-s |
| */</span> |
| <span class="ident">temp</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">nm1</span> <span class="op">&</span> <span class="number">3</span> { |
| <span class="number">0</span> => <span class="op">-</span><span class="ident">cos</span>(<span class="ident">x</span>) <span class="op">+</span> <span class="ident">sin</span>(<span class="ident">x</span>), |
| <span class="number">1</span> => <span class="op">-</span><span class="ident">cos</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="ident">sin</span>(<span class="ident">x</span>), |
| <span class="number">2</span> => <span class="ident">cos</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="ident">sin</span>(<span class="ident">x</span>), |
| <span class="number">3</span> <span class="op">|</span> <span class="kw">_</span> => <span class="ident">cos</span>(<span class="ident">x</span>) <span class="op">+</span> <span class="ident">sin</span>(<span class="ident">x</span>), |
| }; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">INVSQRTPI</span> <span class="op">*</span> <span class="ident">temp</span> <span class="op">/</span> <span class="ident">sqrt</span>(<span class="ident">x</span>); |
| } <span class="kw">else</span> { |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">j0</span>(<span class="ident">x</span>); |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">j1</span>(<span class="ident">x</span>); |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op"><</span> <span class="ident">nm1</span> { |
| <span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">temp</span> <span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">b</span> <span class="op">*</span> (<span class="number">2.0</span> <span class="op">*</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">/</span> <span class="ident">x</span>) <span class="op">-</span> <span class="ident">a</span>; <span class="comment">/* avoid underflow */</span> |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">temp</span>; |
| } |
| } |
| } <span class="kw">else</span> { |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3e100000</span> { |
| <span class="comment">/* x < 2**-29 */</span> |
| <span class="comment">/* 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> <span class="ident">nm1</span> <span class="op">></span> <span class="number">32</span> { |
| <span class="comment">/* underflow */</span> |
| <span class="ident">b</span> <span class="op">=</span> <span class="number">0.0</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">temp</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="number">0.5</span>; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">temp</span>; |
| <span class="ident">a</span> <span class="op">=</span> <span class="number">1.0</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">2</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op"><</span><span class="op">=</span> <span class="ident">nm1</span> <span class="op">+</span> <span class="number">1</span> { |
| <span class="ident">a</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>; <span class="comment">/* a = n! */</span> |
| <span class="ident">b</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">temp</span>; <span class="comment">/* b = (x/2)^n */</span> |
| <span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">b</span> <span class="op">/</span> <span class="ident">a</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="comment">/* use backward recurrence */</span> |
| <span class="comment">/* 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 |
| */</span> |
| <span class="comment">/* determine k */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">t</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">q0</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">q1</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">w</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">h</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">tmp</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">nf</span>: <span class="ident">f64</span>; |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span>: <span class="ident">i32</span>; |
| |
| <span class="ident">nf</span> <span class="op">=</span> (<span class="ident">nm1</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="number">1.0</span>; |
| <span class="ident">w</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">*</span> <span class="ident">nf</span> <span class="op">/</span> <span class="ident">x</span>; |
| <span class="ident">h</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">/</span> <span class="ident">x</span>; |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">w</span> <span class="op">+</span> <span class="ident">h</span>; |
| <span class="ident">q0</span> <span class="op">=</span> <span class="ident">w</span>; |
| <span class="ident">q1</span> <span class="op">=</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">z</span> <span class="op">-</span> <span class="number">1.0</span>; |
| <span class="ident">k</span> <span class="op">=</span> <span class="number">1</span>; |
| <span class="kw">while</span> <span class="ident">q1</span> <span class="op"><</span> <span class="number">1.0e9</span> { |
| <span class="ident">k</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">z</span> <span class="op">+</span><span class="op">=</span> <span class="ident">h</span>; |
| <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">q1</span> <span class="op">-</span> <span class="ident">q0</span>; |
| <span class="ident">q0</span> <span class="op">=</span> <span class="ident">q1</span>; |
| <span class="ident">q1</span> <span class="op">=</span> <span class="ident">tmp</span>; |
| } |
| <span class="ident">t</span> <span class="op">=</span> <span class="number">0.0</span>; |
| <span class="ident">i</span> <span class="op">=</span> <span class="ident">k</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">t</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="number">2.0</span> <span class="op">*</span> ((<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="ident">nf</span>) <span class="op">/</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">t</span>); |
| <span class="ident">i</span> <span class="op">-</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">t</span>; |
| <span class="ident">b</span> <span class="op">=</span> <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> |
| <span class="ident">tmp</span> <span class="op">=</span> <span class="ident">nf</span> <span class="op">*</span> <span class="ident">log</span>(<span class="ident">fabs</span>(<span class="ident">w</span>)); |
| <span class="kw">if</span> <span class="ident">tmp</span> <span class="op"><</span> <span class="number">7.09782712893383973096e+02</span> { |
| <span class="ident">i</span> <span class="op">=</span> <span class="ident">nm1</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="ident">temp</span> <span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">b</span> <span class="op">*</span> (<span class="number">2.0</span> <span class="op">*</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>)) <span class="op">/</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">a</span>; |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">temp</span>; |
| <span class="ident">i</span> <span class="op">-</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="ident">i</span> <span class="op">=</span> <span class="ident">nm1</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="ident">temp</span> <span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">b</span> <span class="op">*</span> (<span class="number">2.0</span> <span class="op">*</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>)) <span class="op">/</span> <span class="ident">x</span> <span class="op">-</span> <span class="ident">a</span>; |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">temp</span>; |
| <span class="comment">/* scale b to avoid spurious overflow */</span> |
| <span class="kw">let</span> <span class="ident">x1p500</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x5f30000000000000</span>); <span class="comment">// 0x1p500 == 2^500</span> |
| <span class="kw">if</span> <span class="ident">b</span> <span class="op">></span> <span class="ident">x1p500</span> { |
| <span class="ident">a</span> <span class="op">/</span><span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">t</span> <span class="op">/</span><span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">b</span> <span class="op">=</span> <span class="number">1.0</span>; |
| } |
| <span class="ident">i</span> <span class="op">-</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">j0</span>(<span class="ident">x</span>); |
| <span class="ident">w</span> <span class="op">=</span> <span class="ident">j1</span>(<span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">fabs</span>(<span class="ident">z</span>) <span class="op">></span><span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">w</span>) { |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">z</span> <span class="op">/</span> <span class="ident">b</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">t</span> <span class="op">*</span> <span class="ident">w</span> <span class="op">/</span> <span class="ident">a</span>; |
| } |
| } |
| } |
| |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="op">-</span><span class="ident">b</span> |
| } <span class="kw">else</span> { |
| <span class="ident">b</span> |
| } |
| } |
| |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">yn</span>(<span class="ident">n</span>: <span class="ident">i32</span>, <span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">lx</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ib</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">nm1</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sign</span>: <span class="ident">bool</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">a</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">b</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">temp</span>: <span class="ident">f64</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>); |
| <span class="ident">lx</span> <span class="op">=</span> <span class="ident">get_low_word</span>(<span class="ident">x</span>); |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span>; |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| |
| <span class="comment">// -lx == !lx + 1</span> |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">|</span> (<span class="ident">lx</span> <span class="op">|</span> ((<span class="op">!</span><span class="ident">lx</span>).<span class="ident">wrapping_add</span>(<span class="number">1</span>))) <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">></span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* nan */</span> |
| <span class="kw">return</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">&&</span> (<span class="ident">ix</span> <span class="op">|</span> <span class="ident">lx</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="comment">/* x < 0 */</span> |
| <span class="kw">return</span> <span class="number">0.0</span> <span class="op">/</span> <span class="number">0.0</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">==</span> <span class="number">0x7ff00000</span> { |
| <span class="kw">return</span> <span class="number">0.0</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">n</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="ident">y0</span>(<span class="ident">x</span>); |
| } |
| <span class="kw">if</span> <span class="ident">n</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="ident">nm1</span> <span class="op">=</span> <span class="op">-</span>(<span class="ident">n</span> <span class="op">+</span> <span class="number">1</span>); |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">&</span> <span class="number">1</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">nm1</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">-</span> <span class="number">1</span>; |
| <span class="ident">sign</span> <span class="op">=</span> <span class="bool-val">false</span>; |
| } |
| <span class="kw">if</span> <span class="ident">nm1</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="kw">return</span> <span class="op">-</span><span class="ident">y1</span>(<span class="ident">x</span>); |
| } <span class="kw">else</span> { |
| <span class="kw">return</span> <span class="ident">y1</span>(<span class="ident">x</span>); |
| } |
| } |
| |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x52d00000</span> { |
| <span class="comment">/* x > 2**302 */</span> |
| <span class="comment">/* (x >> n**2) |
| * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) |
| * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) |
| * Let s=sin(x), c=cos(x), |
| * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then |
| * |
| * n sin(xn)*sqt2 cos(xn)*sqt2 |
| * ---------------------------------- |
| * 0 s-c c+s |
| * 1 -s-c -c+s |
| * 2 -s+c -c-s |
| * 3 s+c c-s |
| */</span> |
| <span class="ident">temp</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">nm1</span> <span class="op">&</span> <span class="number">3</span> { |
| <span class="number">0</span> => <span class="op">-</span><span class="ident">sin</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="ident">cos</span>(<span class="ident">x</span>), |
| <span class="number">1</span> => <span class="op">-</span><span class="ident">sin</span>(<span class="ident">x</span>) <span class="op">+</span> <span class="ident">cos</span>(<span class="ident">x</span>), |
| <span class="number">2</span> => <span class="ident">sin</span>(<span class="ident">x</span>) <span class="op">+</span> <span class="ident">cos</span>(<span class="ident">x</span>), |
| <span class="number">3</span> <span class="op">|</span> <span class="kw">_</span> => <span class="ident">sin</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="ident">cos</span>(<span class="ident">x</span>), |
| }; |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">INVSQRTPI</span> <span class="op">*</span> <span class="ident">temp</span> <span class="op">/</span> <span class="ident">sqrt</span>(<span class="ident">x</span>); |
| } <span class="kw">else</span> { |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">y0</span>(<span class="ident">x</span>); |
| <span class="ident">b</span> <span class="op">=</span> <span class="ident">y1</span>(<span class="ident">x</span>); |
| <span class="comment">/* quit if b is -inf */</span> |
| <span class="ident">ib</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">b</span>); |
| <span class="ident">i</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">while</span> <span class="ident">i</span> <span class="op"><</span> <span class="ident">nm1</span> <span class="op">&&</span> <span class="ident">ib</span> <span class="op">!</span><span class="op">=</span> <span class="number">0xfff00000</span> { |
| <span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">temp</span> <span class="op">=</span> <span class="ident">b</span>; |
| <span class="ident">b</span> <span class="op">=</span> (<span class="number">2.0</span> <span class="op">*</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">/</span> <span class="ident">x</span>) <span class="op">*</span> <span class="ident">b</span> <span class="op">-</span> <span class="ident">a</span>; |
| <span class="ident">ib</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">b</span>); |
| <span class="ident">a</span> <span class="op">=</span> <span class="ident">temp</span>; |
| } |
| } |
| |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="op">-</span><span class="ident">b</span> |
| } <span class="kw">else</span> { |
| <span class="ident">b</span> |
| } |
| } |
| </code></pre></div> |
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