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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */</span> |
| <span class="comment">/* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */</span> |
| |
| <span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">cosf</span>, <span class="ident">fabsf</span>, <span class="ident">logf</span>, <span class="ident">sinf</span>, <span class="ident">sqrtf</span>}; |
| |
| <span class="kw">const</span> <span class="ident">INVSQRTPI</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">5.6418961287e-01</span>; <span class="comment">/* 0x3f106ebb */</span> |
| <span class="kw">const</span> <span class="ident">TPI</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">6.3661974669e-01</span>; <span class="comment">/* 0x3f22f983 */</span> |
| |
| <span class="kw">fn</span> <span class="ident">common</span>(<span class="ident">ix</span>: <span class="ident">u32</span>, <span class="ident">x</span>: <span class="ident">f32</span>, <span class="ident">y1</span>: <span class="ident">bool</span>, <span class="ident">sign</span>: <span class="ident">bool</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</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">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">c</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ss</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">cc</span>: <span class="ident">f64</span>; |
| |
| <span class="ident">s</span> <span class="op">=</span> <span class="ident">sinf</span>(<span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">if</span> <span class="ident">y1</span> { |
| <span class="ident">s</span> <span class="op">=</span> <span class="op">-</span><span class="ident">s</span>; |
| } |
| <span class="ident">c</span> <span class="op">=</span> <span class="ident">cosf</span>(<span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">cc</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">-</span> <span class="ident">c</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x7f000000</span> { |
| <span class="ident">ss</span> <span class="op">=</span> <span class="op">-</span><span class="ident">s</span> <span class="op">-</span> <span class="ident">c</span>; |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">cosf</span>(<span class="number">2.0</span> <span class="op">*</span> <span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">if</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">c</span> <span class="op">></span> <span class="number">0.0</span> { |
| <span class="ident">cc</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">/</span> <span class="ident">ss</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">ss</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">/</span> <span class="ident">cc</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x58800000</span> { |
| <span class="kw">if</span> <span class="ident">y1</span> { |
| <span class="ident">ss</span> <span class="op">=</span> <span class="op">-</span><span class="ident">ss</span>; |
| } |
| <span class="ident">cc</span> <span class="op">=</span> (<span class="ident">ponef</span>(<span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="ident">cc</span> <span class="op">-</span> (<span class="ident">qonef</span>(<span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="ident">ss</span>; |
| } |
| } |
| <span class="kw">if</span> <span class="ident">sign</span> { |
| <span class="ident">cc</span> <span class="op">=</span> <span class="op">-</span><span class="ident">cc</span>; |
| } |
| <span class="kw">return</span> (((<span class="ident">INVSQRTPI</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="ident">cc</span>) <span class="op">/</span> (<span class="ident">sqrtf</span>(<span class="ident">x</span>) <span class="kw">as</span> <span class="ident">f64</span>)) <span class="kw">as</span> <span class="ident">f32</span>; |
| } |
| |
| <span class="comment">/* R0/S0 on [0,2] */</span> |
| <span class="kw">const</span> <span class="ident">R00</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.2500000000e-02</span>; <span class="comment">/* 0xbd800000 */</span> |
| <span class="kw">const</span> <span class="ident">R01</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.4070566976e-03</span>; <span class="comment">/* 0x3ab86cfd */</span> |
| <span class="kw">const</span> <span class="ident">R02</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.5995563444e-05</span>; <span class="comment">/* 0xb7862e36 */</span> |
| <span class="kw">const</span> <span class="ident">R03</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">4.9672799207e-08</span>; <span class="comment">/* 0x335557d2 */</span> |
| <span class="kw">const</span> <span class="ident">S01</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.9153760746e-02</span>; <span class="comment">/* 0x3c9ce859 */</span> |
| <span class="kw">const</span> <span class="ident">S02</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.8594678841e-04</span>; <span class="comment">/* 0x3942fab6 */</span> |
| <span class="kw">const</span> <span class="ident">S03</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.1771846857e-06</span>; <span class="comment">/* 0x359dffc2 */</span> |
| <span class="kw">const</span> <span class="ident">S04</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">5.0463624390e-09</span>; <span class="comment">/* 0x31ad6446 */</span> |
| <span class="kw">const</span> <span class="ident">S05</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="number">1.2354227016e-11</span>; <span class="comment">/* 0x2d59567e */</span> |
| |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">j1f</span>(<span class="ident">x</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f32</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">sign</span>: <span class="ident">bool</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</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="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7f800000</span> { |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</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">0x40000000</span> { |
| <span class="comment">/* |x| >= 2 */</span> |
| <span class="kw">return</span> <span class="ident">common</span>(<span class="ident">ix</span>, <span class="ident">fabsf</span>(<span class="ident">x</span>), <span class="bool-val">false</span>, <span class="ident">sign</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x39000000</span> { |
| <span class="comment">/* |x| >= 2**-13 */</span> |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R00</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R01</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">R02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">R03</span>))); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S01</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S02</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S03</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">S04</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">S05</span>)))); |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>; |
| } <span class="kw">else</span> { |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">0.5</span>; |
| } |
| <span class="kw">return</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">x</span>; |
| } |
| |
| <span class="kw">const</span> <span class="ident">U0</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="op">-</span><span class="number">1.9605709612e-01</span>, <span class="comment">/* 0xbe48c331 */</span> |
| <span class="number">5.0443872809e-02</span>, <span class="comment">/* 0x3d4e9e3c */</span> |
| <span class="op">-</span><span class="number">1.9125689287e-03</span>, <span class="comment">/* 0xbafaaf2a */</span> |
| <span class="number">2.3525259166e-05</span>, <span class="comment">/* 0x37c5581c */</span> |
| <span class="op">-</span><span class="number">9.1909917899e-08</span>, <span class="comment">/* 0xb3c56003 */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">V0</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="number">1.9916731864e-02</span>, <span class="comment">/* 0x3ca3286a */</span> |
| <span class="number">2.0255257550e-04</span>, <span class="comment">/* 0x3954644b */</span> |
| <span class="number">1.3560879779e-06</span>, <span class="comment">/* 0x35b602d4 */</span> |
| <span class="number">6.2274145840e-09</span>, <span class="comment">/* 0x31d5f8eb */</span> |
| <span class="number">1.6655924903e-11</span>, <span class="comment">/* 0x2d9281cf */</span> |
| ]; |
| |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">y1f</span>(<span class="ident">x</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">v</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>(); |
| <span class="kw">if</span> (<span class="ident">ix</span> <span class="op">&</span> <span class="number">0x7fffffff</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="op">-</span><span class="number">1.0</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="op">></span> <span class="number">31</span>) <span class="op">!</span><span class="op">=</span> <span class="number">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="op">=</span> <span class="number">0x7f800000</span> { |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">/</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">0x40000000</span> { |
| <span class="comment">/* |x| >= 2.0 */</span> |
| <span class="kw">return</span> <span class="ident">common</span>(<span class="ident">ix</span>, <span class="ident">x</span>, <span class="bool-val">true</span>, <span class="bool-val">false</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x33000000</span> { |
| <span class="comment">/* x < 2**-25 */</span> |
| <span class="kw">return</span> <span class="op">-</span><span class="ident">TPI</span> <span class="op">/</span> <span class="ident">x</span>; |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="ident">u</span> <span class="op">=</span> <span class="ident">U0</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U0</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U0</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">U0</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">U0</span>[<span class="number">4</span>]))); |
| <span class="ident">v</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V0</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V0</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V0</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">V0</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">V0</span>[<span class="number">4</span>])))); |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">*</span> (<span class="ident">u</span> <span class="op">/</span> <span class="ident">v</span>) <span class="op">+</span> <span class="ident">TPI</span> <span class="op">*</span> (<span class="ident">j1f</span>(<span class="ident">x</span>) <span class="op">*</span> <span class="ident">logf</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span>); |
| } |
| |
| <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> <span class="ident">PR8</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [inf, 8]=1/[0,0.125] */</span> |
| <span class="number">0.0000000000e+00</span>, <span class="comment">/* 0x00000000 */</span> |
| <span class="number">1.1718750000e-01</span>, <span class="comment">/* 0x3df00000 */</span> |
| <span class="number">1.3239480972e+01</span>, <span class="comment">/* 0x4153d4ea */</span> |
| <span class="number">4.1205184937e+02</span>, <span class="comment">/* 0x43ce06a3 */</span> |
| <span class="number">3.8747453613e+03</span>, <span class="comment">/* 0x45722bed */</span> |
| <span class="number">7.9144794922e+03</span>, <span class="comment">/* 0x45f753d6 */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">PS8</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="number">1.1420736694e+02</span>, <span class="comment">/* 0x42e46a2c */</span> |
| <span class="number">3.6509309082e+03</span>, <span class="comment">/* 0x45642ee5 */</span> |
| <span class="number">3.6956207031e+04</span>, <span class="comment">/* 0x47105c35 */</span> |
| <span class="number">9.7602796875e+04</span>, <span class="comment">/* 0x47bea166 */</span> |
| <span class="number">3.0804271484e+04</span>, <span class="comment">/* 0x46f0a88b */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">PR5</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */</span> |
| <span class="number">1.3199052094e-11</span>, <span class="comment">/* 0x2d68333f */</span> |
| <span class="number">1.1718749255e-01</span>, <span class="comment">/* 0x3defffff */</span> |
| <span class="number">6.8027510643e+00</span>, <span class="comment">/* 0x40d9b023 */</span> |
| <span class="number">1.0830818176e+02</span>, <span class="comment">/* 0x42d89dca */</span> |
| <span class="number">5.1763616943e+02</span>, <span class="comment">/* 0x440168b7 */</span> |
| <span class="number">5.2871520996e+02</span>, <span class="comment">/* 0x44042dc6 */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">PS5</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="number">5.9280597687e+01</span>, <span class="comment">/* 0x426d1f55 */</span> |
| <span class="number">9.9140142822e+02</span>, <span class="comment">/* 0x4477d9b1 */</span> |
| <span class="number">5.3532670898e+03</span>, <span class="comment">/* 0x45a74a23 */</span> |
| <span class="number">7.8446904297e+03</span>, <span class="comment">/* 0x45f52586 */</span> |
| <span class="number">1.5040468750e+03</span>, <span class="comment">/* 0x44bc0180 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">PR3</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="number">3.0250391081e-09</span>, <span class="comment">/* 0x314fe10d */</span> |
| <span class="number">1.1718686670e-01</span>, <span class="comment">/* 0x3defffab */</span> |
| <span class="number">3.9329774380e+00</span>, <span class="comment">/* 0x407bb5e7 */</span> |
| <span class="number">3.5119403839e+01</span>, <span class="comment">/* 0x420c7a45 */</span> |
| <span class="number">9.1055007935e+01</span>, <span class="comment">/* 0x42b61c2a */</span> |
| <span class="number">4.8559066772e+01</span>, <span class="comment">/* 0x42423c7c */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">PS3</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="number">3.4791309357e+01</span>, <span class="comment">/* 0x420b2a4d */</span> |
| <span class="number">3.3676245117e+02</span>, <span class="comment">/* 0x43a86198 */</span> |
| <span class="number">1.0468714600e+03</span>, <span class="comment">/* 0x4482dbe3 */</span> |
| <span class="number">8.9081134033e+02</span>, <span class="comment">/* 0x445eb3ed */</span> |
| <span class="number">1.0378793335e+02</span>, <span class="comment">/* 0x42cf936c */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">PR2</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */</span> |
| <span class="number">1.0771083225e-07</span>, <span class="comment">/* 0x33e74ea8 */</span> |
| <span class="number">1.1717621982e-01</span>, <span class="comment">/* 0x3deffa16 */</span> |
| <span class="number">2.3685150146e+00</span>, <span class="comment">/* 0x401795c0 */</span> |
| <span class="number">1.2242610931e+01</span>, <span class="comment">/* 0x4143e1bc */</span> |
| <span class="number">1.7693971634e+01</span>, <span class="comment">/* 0x418d8d41 */</span> |
| <span class="number">5.0735230446e+00</span>, <span class="comment">/* 0x40a25a4d */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">PS2</span>: [<span class="ident">f32</span>; <span class="number">5</span>] <span class="op">=</span> [ |
| <span class="number">2.1436485291e+01</span>, <span class="comment">/* 0x41ab7dec */</span> |
| <span class="number">1.2529022980e+02</span>, <span class="comment">/* 0x42fa9499 */</span> |
| <span class="number">2.3227647400e+02</span>, <span class="comment">/* 0x436846c7 */</span> |
| <span class="number">1.1767937469e+02</span>, <span class="comment">/* 0x42eb5bd7 */</span> |
| <span class="number">8.3646392822e+00</span>, <span class="comment">/* 0x4105d590 */</span> |
| ]; |
| |
| <span class="kw">fn</span> <span class="ident">ponef</span>(<span class="ident">x</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="ident">p</span>: <span class="kw-2">&</span>[<span class="ident">f32</span>; <span class="number">6</span>]; |
| <span class="kw">let</span> <span class="ident">q</span>: <span class="kw-2">&</span>[<span class="ident">f32</span>; <span class="number">5</span>]; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>(); |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x41000000</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR8</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS8</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x409173eb</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR5</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS5</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4036d917</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR3</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS3</span>; |
| } <span class="kw">else</span> |
| <span class="comment">/*ix >= 0x40000000*/</span> |
| { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PR2</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">PS2</span>; |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>); |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">p</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p</span>[<span class="number">5</span>])))); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">q</span>[<span class="number">4</span>])))); |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>; |
| } |
| |
| <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> <span class="ident">QR8</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [inf, 8]=1/[0,0.125] */</span> |
| <span class="number">0.0000000000e+00</span>, <span class="comment">/* 0x00000000 */</span> |
| <span class="op">-</span><span class="number">1.0253906250e-01</span>, <span class="comment">/* 0xbdd20000 */</span> |
| <span class="op">-</span><span class="number">1.6271753311e+01</span>, <span class="comment">/* 0xc1822c8d */</span> |
| <span class="op">-</span><span class="number">7.5960174561e+02</span>, <span class="comment">/* 0xc43de683 */</span> |
| <span class="op">-</span><span class="number">1.1849806641e+04</span>, <span class="comment">/* 0xc639273a */</span> |
| <span class="op">-</span><span class="number">4.8438511719e+04</span>, <span class="comment">/* 0xc73d3683 */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">QS8</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="number">1.6139537048e+02</span>, <span class="comment">/* 0x43216537 */</span> |
| <span class="number">7.8253862305e+03</span>, <span class="comment">/* 0x45f48b17 */</span> |
| <span class="number">1.3387534375e+05</span>, <span class="comment">/* 0x4802bcd6 */</span> |
| <span class="number">7.1965775000e+05</span>, <span class="comment">/* 0x492fb29c */</span> |
| <span class="number">6.6660125000e+05</span>, <span class="comment">/* 0x4922be94 */</span> |
| <span class="op">-</span><span class="number">2.9449025000e+05</span>, <span class="comment">/* 0xc88fcb48 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">QR5</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [8,4.5454]=1/[0.125,0.22001] */</span> |
| <span class="op">-</span><span class="number">2.0897993405e-11</span>, <span class="comment">/* 0xadb7d219 */</span> |
| <span class="op">-</span><span class="number">1.0253904760e-01</span>, <span class="comment">/* 0xbdd1fffe */</span> |
| <span class="op">-</span><span class="number">8.0564479828e+00</span>, <span class="comment">/* 0xc100e736 */</span> |
| <span class="op">-</span><span class="number">1.8366960144e+02</span>, <span class="comment">/* 0xc337ab6b */</span> |
| <span class="op">-</span><span class="number">1.3731937256e+03</span>, <span class="comment">/* 0xc4aba633 */</span> |
| <span class="op">-</span><span class="number">2.6124443359e+03</span>, <span class="comment">/* 0xc523471c */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">QS5</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="number">8.1276550293e+01</span>, <span class="comment">/* 0x42a28d98 */</span> |
| <span class="number">1.9917987061e+03</span>, <span class="comment">/* 0x44f8f98f */</span> |
| <span class="number">1.7468484375e+04</span>, <span class="comment">/* 0x468878f8 */</span> |
| <span class="number">4.9851425781e+04</span>, <span class="comment">/* 0x4742bb6d */</span> |
| <span class="number">2.7948074219e+04</span>, <span class="comment">/* 0x46da5826 */</span> |
| <span class="op">-</span><span class="number">4.7191835938e+03</span>, <span class="comment">/* 0xc5937978 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">QR3</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="op">-</span><span class="number">5.0783124372e-09</span>, <span class="comment">/* 0xb1ae7d4f */</span> |
| <span class="op">-</span><span class="number">1.0253783315e-01</span>, <span class="comment">/* 0xbdd1ff5b */</span> |
| <span class="op">-</span><span class="number">4.6101160049e+00</span>, <span class="comment">/* 0xc0938612 */</span> |
| <span class="op">-</span><span class="number">5.7847221375e+01</span>, <span class="comment">/* 0xc267638e */</span> |
| <span class="op">-</span><span class="number">2.2824453735e+02</span>, <span class="comment">/* 0xc3643e9a */</span> |
| <span class="op">-</span><span class="number">2.1921012878e+02</span>, <span class="comment">/* 0xc35b35cb */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">QS3</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="number">4.7665153503e+01</span>, <span class="comment">/* 0x423ea91e */</span> |
| <span class="number">6.7386511230e+02</span>, <span class="comment">/* 0x4428775e */</span> |
| <span class="number">3.3801528320e+03</span>, <span class="comment">/* 0x45534272 */</span> |
| <span class="number">5.5477290039e+03</span>, <span class="comment">/* 0x45ad5dd5 */</span> |
| <span class="number">1.9031191406e+03</span>, <span class="comment">/* 0x44ede3d0 */</span> |
| <span class="op">-</span><span class="number">1.3520118713e+02</span>, <span class="comment">/* 0xc3073381 */</span> |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">QR2</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="comment">/* for x in [2.8570,2]=1/[0.3499,0.5] */</span> |
| <span class="op">-</span><span class="number">1.7838172539e-07</span>, <span class="comment">/* 0xb43f8932 */</span> |
| <span class="op">-</span><span class="number">1.0251704603e-01</span>, <span class="comment">/* 0xbdd1f475 */</span> |
| <span class="op">-</span><span class="number">2.7522056103e+00</span>, <span class="comment">/* 0xc0302423 */</span> |
| <span class="op">-</span><span class="number">1.9663616180e+01</span>, <span class="comment">/* 0xc19d4f16 */</span> |
| <span class="op">-</span><span class="number">4.2325313568e+01</span>, <span class="comment">/* 0xc2294d1f */</span> |
| <span class="op">-</span><span class="number">2.1371921539e+01</span>, <span class="comment">/* 0xc1aaf9b2 */</span> |
| ]; |
| <span class="kw">const</span> <span class="ident">QS2</span>: [<span class="ident">f32</span>; <span class="number">6</span>] <span class="op">=</span> [ |
| <span class="number">2.9533363342e+01</span>, <span class="comment">/* 0x41ec4454 */</span> |
| <span class="number">2.5298155212e+02</span>, <span class="comment">/* 0x437cfb47 */</span> |
| <span class="number">7.5750280762e+02</span>, <span class="comment">/* 0x443d602e */</span> |
| <span class="number">7.3939318848e+02</span>, <span class="comment">/* 0x4438d92a */</span> |
| <span class="number">1.5594900513e+02</span>, <span class="comment">/* 0x431bf2f2 */</span> |
| <span class="op">-</span><span class="number">4.9594988823e+00</span>, <span class="comment">/* 0xc09eb437 */</span> |
| ]; |
| |
| <span class="kw">fn</span> <span class="ident">qonef</span>(<span class="ident">x</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="ident">p</span>: <span class="kw-2">&</span>[<span class="ident">f32</span>; <span class="number">6</span>]; |
| <span class="kw">let</span> <span class="ident">q</span>: <span class="kw-2">&</span>[<span class="ident">f32</span>; <span class="number">6</span>]; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>(); |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x41000000</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR8</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS8</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x409173eb</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR5</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS5</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x4036d917</span> { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR3</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS3</span>; |
| } <span class="kw">else</span> |
| <span class="comment">/*ix >= 0x40000000*/</span> |
| { |
| <span class="ident">p</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QR2</span>; |
| <span class="ident">q</span> <span class="op">=</span> <span class="kw-2">&</span><span class="ident">QS2</span>; |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>); |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">p</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">p</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">p</span>[<span class="number">5</span>])))); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">0</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">1</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">2</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">3</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">q</span>[<span class="number">4</span>] <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">q</span>[<span class="number">5</span>]))))); |
| <span class="kw">return</span> (<span class="number">0.375</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>) <span class="op">/</span> <span class="ident">x</span>; |
| } |
| |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span> |
| <span class="kw">mod</span> <span class="ident">tests</span> { |
| <span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">j1f</span>, <span class="ident">y1f</span>}; |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_j1f_2488</span>() { |
| <span class="comment">// 0x401F3E49</span> |
| <span class="macro">assert_eq!</span>(<span class="ident">j1f</span>(<span class="number">2.4881766_f32</span>), <span class="number">0.49999475_f32</span>); |
| } |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_y1f_2002</span>() { |
| <span class="macro">assert_eq!</span>(<span class="ident">y1f</span>(<span class="number">2.0000002_f32</span>), <span class="op">-</span><span class="number">0.10703229_f32</span>); |
| } |
| } |
| </code></pre></div> |
| </section><section id="search" class="content hidden"></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="1.60.0-nightly (1bd4fdc94 2022-01-12)" ></div> |
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