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| </pre><pre class="rust"><code><span class="attribute">#![<span class="ident">allow</span>(<span class="ident">unused_unsafe</span>)]</span> |
| <span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.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="kw">use</span> <span class="ident"><span class="kw">super</span>::floor</span>; |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::scalbn</span>; |
| |
| <span class="comment">// initial value for jk</span> |
| <span class="kw">const</span> <span class="ident">INIT_JK</span>: [<span class="ident">usize</span>; <span class="number">4</span>] <span class="op">=</span> [<span class="number">3</span>, <span class="number">4</span>, <span class="number">4</span>, <span class="number">6</span>]; |
| |
| <span class="comment">// Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi</span> |
| <span class="comment">//</span> |
| <span class="comment">// integer array, contains the (24*i)-th to (24*i+23)-th</span> |
| <span class="comment">// bit of 2/pi after binary point. The corresponding</span> |
| <span class="comment">// floating value is</span> |
| <span class="comment">//</span> |
| <span class="comment">// ipio2[i] * 2^(-24(i+1)).</span> |
| <span class="comment">//</span> |
| <span class="comment">// NB: This table must have at least (e0-3)/24 + jk terms.</span> |
| <span class="comment">// For quad precision (e0 <= 16360, jk = 6), this is 686.</span> |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">target_pointer_width</span> <span class="op">=</span> <span class="string">"32"</span>)]</span> |
| <span class="kw">const</span> <span class="ident">IPIO2</span>: [<span class="ident">i32</span>; <span class="number">66</span>] <span class="op">=</span> [ |
| <span class="number">0xA2F983</span>, <span class="number">0x6E4E44</span>, <span class="number">0x1529FC</span>, <span class="number">0x2757D1</span>, <span class="number">0xF534DD</span>, <span class="number">0xC0DB62</span>, <span class="number">0x95993C</span>, <span class="number">0x439041</span>, <span class="number">0xFE5163</span>, |
| <span class="number">0xABDEBB</span>, <span class="number">0xC561B7</span>, <span class="number">0x246E3A</span>, <span class="number">0x424DD2</span>, <span class="number">0xE00649</span>, <span class="number">0x2EEA09</span>, <span class="number">0xD1921C</span>, <span class="number">0xFE1DEB</span>, <span class="number">0x1CB129</span>, |
| <span class="number">0xA73EE8</span>, <span class="number">0x8235F5</span>, <span class="number">0x2EBB44</span>, <span class="number">0x84E99C</span>, <span class="number">0x7026B4</span>, <span class="number">0x5F7E41</span>, <span class="number">0x3991D6</span>, <span class="number">0x398353</span>, <span class="number">0x39F49C</span>, |
| <span class="number">0x845F8B</span>, <span class="number">0xBDF928</span>, <span class="number">0x3B1FF8</span>, <span class="number">0x97FFDE</span>, <span class="number">0x05980F</span>, <span class="number">0xEF2F11</span>, <span class="number">0x8B5A0A</span>, <span class="number">0x6D1F6D</span>, <span class="number">0x367ECF</span>, |
| <span class="number">0x27CB09</span>, <span class="number">0xB74F46</span>, <span class="number">0x3F669E</span>, <span class="number">0x5FEA2D</span>, <span class="number">0x7527BA</span>, <span class="number">0xC7EBE5</span>, <span class="number">0xF17B3D</span>, <span class="number">0x0739F7</span>, <span class="number">0x8A5292</span>, |
| <span class="number">0xEA6BFB</span>, <span class="number">0x5FB11F</span>, <span class="number">0x8D5D08</span>, <span class="number">0x560330</span>, <span class="number">0x46FC7B</span>, <span class="number">0x6BABF0</span>, <span class="number">0xCFBC20</span>, <span class="number">0x9AF436</span>, <span class="number">0x1DA9E3</span>, |
| <span class="number">0x91615E</span>, <span class="number">0xE61B08</span>, <span class="number">0x659985</span>, <span class="number">0x5F14A0</span>, <span class="number">0x68408D</span>, <span class="number">0xFFD880</span>, <span class="number">0x4D7327</span>, <span class="number">0x310606</span>, <span class="number">0x1556CA</span>, |
| <span class="number">0x73A8C9</span>, <span class="number">0x60E27B</span>, <span class="number">0xC08C6B</span>, |
| ]; |
| |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">target_pointer_width</span> <span class="op">=</span> <span class="string">"64"</span>)]</span> |
| <span class="kw">const</span> <span class="ident">IPIO2</span>: [<span class="ident">i32</span>; <span class="number">690</span>] <span class="op">=</span> [ |
| <span class="number">0xA2F983</span>, <span class="number">0x6E4E44</span>, <span class="number">0x1529FC</span>, <span class="number">0x2757D1</span>, <span class="number">0xF534DD</span>, <span class="number">0xC0DB62</span>, <span class="number">0x95993C</span>, <span class="number">0x439041</span>, <span class="number">0xFE5163</span>, |
| <span class="number">0xABDEBB</span>, <span class="number">0xC561B7</span>, <span class="number">0x246E3A</span>, <span class="number">0x424DD2</span>, <span class="number">0xE00649</span>, <span class="number">0x2EEA09</span>, <span class="number">0xD1921C</span>, <span class="number">0xFE1DEB</span>, <span class="number">0x1CB129</span>, |
| <span class="number">0xA73EE8</span>, <span class="number">0x8235F5</span>, <span class="number">0x2EBB44</span>, <span class="number">0x84E99C</span>, <span class="number">0x7026B4</span>, <span class="number">0x5F7E41</span>, <span class="number">0x3991D6</span>, <span class="number">0x398353</span>, <span class="number">0x39F49C</span>, |
| <span class="number">0x845F8B</span>, <span class="number">0xBDF928</span>, <span class="number">0x3B1FF8</span>, <span class="number">0x97FFDE</span>, <span class="number">0x05980F</span>, <span class="number">0xEF2F11</span>, <span class="number">0x8B5A0A</span>, <span class="number">0x6D1F6D</span>, <span class="number">0x367ECF</span>, |
| <span class="number">0x27CB09</span>, <span class="number">0xB74F46</span>, <span class="number">0x3F669E</span>, <span class="number">0x5FEA2D</span>, <span class="number">0x7527BA</span>, <span class="number">0xC7EBE5</span>, <span class="number">0xF17B3D</span>, <span class="number">0x0739F7</span>, <span class="number">0x8A5292</span>, |
| <span class="number">0xEA6BFB</span>, <span class="number">0x5FB11F</span>, <span class="number">0x8D5D08</span>, <span class="number">0x560330</span>, <span class="number">0x46FC7B</span>, <span class="number">0x6BABF0</span>, <span class="number">0xCFBC20</span>, <span class="number">0x9AF436</span>, <span class="number">0x1DA9E3</span>, |
| <span class="number">0x91615E</span>, <span class="number">0xE61B08</span>, <span class="number">0x659985</span>, <span class="number">0x5F14A0</span>, <span class="number">0x68408D</span>, <span class="number">0xFFD880</span>, <span class="number">0x4D7327</span>, <span class="number">0x310606</span>, <span class="number">0x1556CA</span>, |
| <span class="number">0x73A8C9</span>, <span class="number">0x60E27B</span>, <span class="number">0xC08C6B</span>, <span class="number">0x47C419</span>, <span class="number">0xC367CD</span>, <span class="number">0xDCE809</span>, <span class="number">0x2A8359</span>, <span class="number">0xC4768B</span>, <span class="number">0x961CA6</span>, |
| <span class="number">0xDDAF44</span>, <span class="number">0xD15719</span>, <span class="number">0x053EA5</span>, <span class="number">0xFF0705</span>, <span class="number">0x3F7E33</span>, <span class="number">0xE832C2</span>, <span class="number">0xDE4F98</span>, <span class="number">0x327DBB</span>, <span class="number">0xC33D26</span>, |
| <span class="number">0xEF6B1E</span>, <span class="number">0x5EF89F</span>, <span class="number">0x3A1F35</span>, <span class="number">0xCAF27F</span>, <span class="number">0x1D87F1</span>, <span class="number">0x21907C</span>, <span class="number">0x7C246A</span>, <span class="number">0xFA6ED5</span>, <span class="number">0x772D30</span>, |
| <span class="number">0x433B15</span>, <span class="number">0xC614B5</span>, <span class="number">0x9D19C3</span>, <span class="number">0xC2C4AD</span>, <span class="number">0x414D2C</span>, <span class="number">0x5D000C</span>, <span class="number">0x467D86</span>, <span class="number">0x2D71E3</span>, <span class="number">0x9AC69B</span>, |
| <span class="number">0x006233</span>, <span class="number">0x7CD2B4</span>, <span class="number">0x97A7B4</span>, <span class="number">0xD55537</span>, <span class="number">0xF63ED7</span>, <span class="number">0x1810A3</span>, <span class="number">0xFC764D</span>, <span class="number">0x2A9D64</span>, <span class="number">0xABD770</span>, |
| <span class="number">0xF87C63</span>, <span class="number">0x57B07A</span>, <span class="number">0xE71517</span>, <span class="number">0x5649C0</span>, <span class="number">0xD9D63B</span>, <span class="number">0x3884A7</span>, <span class="number">0xCB2324</span>, <span class="number">0x778AD6</span>, <span class="number">0x23545A</span>, |
| <span class="number">0xB91F00</span>, <span class="number">0x1B0AF1</span>, <span class="number">0xDFCE19</span>, <span class="number">0xFF319F</span>, <span class="number">0x6A1E66</span>, <span class="number">0x615799</span>, <span class="number">0x47FBAC</span>, <span class="number">0xD87F7E</span>, <span class="number">0xB76522</span>, |
| <span class="number">0x89E832</span>, <span class="number">0x60BFE6</span>, <span class="number">0xCDC4EF</span>, <span class="number">0x09366C</span>, <span class="number">0xD43F5D</span>, <span class="number">0xD7DE16</span>, <span class="number">0xDE3B58</span>, <span class="number">0x929BDE</span>, <span class="number">0x2822D2</span>, |
| <span class="number">0xE88628</span>, <span class="number">0x4D58E2</span>, <span class="number">0x32CAC6</span>, <span class="number">0x16E308</span>, <span class="number">0xCB7DE0</span>, <span class="number">0x50C017</span>, <span class="number">0xA71DF3</span>, <span class="number">0x5BE018</span>, <span class="number">0x34132E</span>, |
| <span class="number">0x621283</span>, <span class="number">0x014883</span>, <span class="number">0x5B8EF5</span>, <span class="number">0x7FB0AD</span>, <span class="number">0xF2E91E</span>, <span class="number">0x434A48</span>, <span class="number">0xD36710</span>, <span class="number">0xD8DDAA</span>, <span class="number">0x425FAE</span>, |
| <span class="number">0xCE616A</span>, <span class="number">0xA4280A</span>, <span class="number">0xB499D3</span>, <span class="number">0xF2A606</span>, <span class="number">0x7F775C</span>, <span class="number">0x83C2A3</span>, <span class="number">0x883C61</span>, <span class="number">0x78738A</span>, <span class="number">0x5A8CAF</span>, |
| <span class="number">0xBDD76F</span>, <span class="number">0x63A62D</span>, <span class="number">0xCBBFF4</span>, <span class="number">0xEF818D</span>, <span class="number">0x67C126</span>, <span class="number">0x45CA55</span>, <span class="number">0x36D9CA</span>, <span class="number">0xD2A828</span>, <span class="number">0x8D61C2</span>, |
| <span class="number">0x77C912</span>, <span class="number">0x142604</span>, <span class="number">0x9B4612</span>, <span class="number">0xC459C4</span>, <span class="number">0x44C5C8</span>, <span class="number">0x91B24D</span>, <span class="number">0xF31700</span>, <span class="number">0xAD43D4</span>, <span class="number">0xE54929</span>, |
| <span class="number">0x10D5FD</span>, <span class="number">0xFCBE00</span>, <span class="number">0xCC941E</span>, <span class="number">0xEECE70</span>, <span class="number">0xF53E13</span>, <span class="number">0x80F1EC</span>, <span class="number">0xC3E7B3</span>, <span class="number">0x28F8C7</span>, <span class="number">0x940593</span>, |
| <span class="number">0x3E71C1</span>, <span class="number">0xB3092E</span>, <span class="number">0xF3450B</span>, <span class="number">0x9C1288</span>, <span class="number">0x7B20AB</span>, <span class="number">0x9FB52E</span>, <span class="number">0xC29247</span>, <span class="number">0x2F327B</span>, <span class="number">0x6D550C</span>, |
| <span class="number">0x90A772</span>, <span class="number">0x1FE76B</span>, <span class="number">0x96CB31</span>, <span class="number">0x4A1679</span>, <span class="number">0xE27941</span>, <span class="number">0x89DFF4</span>, <span class="number">0x9794E8</span>, <span class="number">0x84E6E2</span>, <span class="number">0x973199</span>, |
| <span class="number">0x6BED88</span>, <span class="number">0x365F5F</span>, <span class="number">0x0EFDBB</span>, <span class="number">0xB49A48</span>, <span class="number">0x6CA467</span>, <span class="number">0x427271</span>, <span class="number">0x325D8D</span>, <span class="number">0xB8159F</span>, <span class="number">0x09E5BC</span>, |
| <span class="number">0x25318D</span>, <span class="number">0x3974F7</span>, <span class="number">0x1C0530</span>, <span class="number">0x010C0D</span>, <span class="number">0x68084B</span>, <span class="number">0x58EE2C</span>, <span class="number">0x90AA47</span>, <span class="number">0x02E774</span>, <span class="number">0x24D6BD</span>, |
| <span class="number">0xA67DF7</span>, <span class="number">0x72486E</span>, <span class="number">0xEF169F</span>, <span class="number">0xA6948E</span>, <span class="number">0xF691B4</span>, <span class="number">0x5153D1</span>, <span class="number">0xF20ACF</span>, <span class="number">0x339820</span>, <span class="number">0x7E4BF5</span>, |
| <span class="number">0x6863B2</span>, <span class="number">0x5F3EDD</span>, <span class="number">0x035D40</span>, <span class="number">0x7F8985</span>, <span class="number">0x295255</span>, <span class="number">0xC06437</span>, <span class="number">0x10D86D</span>, <span class="number">0x324832</span>, <span class="number">0x754C5B</span>, |
| <span class="number">0xD4714E</span>, <span class="number">0x6E5445</span>, <span class="number">0xC1090B</span>, <span class="number">0x69F52A</span>, <span class="number">0xD56614</span>, <span class="number">0x9D0727</span>, <span class="number">0x50045D</span>, <span class="number">0xDB3BB4</span>, <span class="number">0xC576EA</span>, |
| <span class="number">0x17F987</span>, <span class="number">0x7D6B49</span>, <span class="number">0xBA271D</span>, <span class="number">0x296996</span>, <span class="number">0xACCCC6</span>, <span class="number">0x5414AD</span>, <span class="number">0x6AE290</span>, <span class="number">0x89D988</span>, <span class="number">0x50722C</span>, |
| <span class="number">0xBEA404</span>, <span class="number">0x940777</span>, <span class="number">0x7030F3</span>, <span class="number">0x27FC00</span>, <span class="number">0xA871EA</span>, <span class="number">0x49C266</span>, <span class="number">0x3DE064</span>, <span class="number">0x83DD97</span>, <span class="number">0x973FA3</span>, |
| <span class="number">0xFD9443</span>, <span class="number">0x8C860D</span>, <span class="number">0xDE4131</span>, <span class="number">0x9D3992</span>, <span class="number">0x8C70DD</span>, <span class="number">0xE7B717</span>, <span class="number">0x3BDF08</span>, <span class="number">0x2B3715</span>, <span class="number">0xA0805C</span>, |
| <span class="number">0x93805A</span>, <span class="number">0x921110</span>, <span class="number">0xD8E80F</span>, <span class="number">0xAF806C</span>, <span class="number">0x4BFFDB</span>, <span class="number">0x0F9038</span>, <span class="number">0x761859</span>, <span class="number">0x15A562</span>, <span class="number">0xBBCB61</span>, |
| <span class="number">0xB989C7</span>, <span class="number">0xBD4010</span>, <span class="number">0x04F2D2</span>, <span class="number">0x277549</span>, <span class="number">0xF6B6EB</span>, <span class="number">0xBB22DB</span>, <span class="number">0xAA140A</span>, <span class="number">0x2F2689</span>, <span class="number">0x768364</span>, |
| <span class="number">0x333B09</span>, <span class="number">0x1A940E</span>, <span class="number">0xAA3A51</span>, <span class="number">0xC2A31D</span>, <span class="number">0xAEEDAF</span>, <span class="number">0x12265C</span>, <span class="number">0x4DC26D</span>, <span class="number">0x9C7A2D</span>, <span class="number">0x9756C0</span>, |
| <span class="number">0x833F03</span>, <span class="number">0xF6F009</span>, <span class="number">0x8C402B</span>, <span class="number">0x99316D</span>, <span class="number">0x07B439</span>, <span class="number">0x15200C</span>, <span class="number">0x5BC3D8</span>, <span class="number">0xC492F5</span>, <span class="number">0x4BADC6</span>, |
| <span class="number">0xA5CA4E</span>, <span class="number">0xCD37A7</span>, <span class="number">0x36A9E6</span>, <span class="number">0x9492AB</span>, <span class="number">0x6842DD</span>, <span class="number">0xDE6319</span>, <span class="number">0xEF8C76</span>, <span class="number">0x528B68</span>, <span class="number">0x37DBFC</span>, |
| <span class="number">0xABA1AE</span>, <span class="number">0x3115DF</span>, <span class="number">0xA1AE00</span>, <span class="number">0xDAFB0C</span>, <span class="number">0x664D64</span>, <span class="number">0xB705ED</span>, <span class="number">0x306529</span>, <span class="number">0xBF5657</span>, <span class="number">0x3AFF47</span>, |
| <span class="number">0xB9F96A</span>, <span class="number">0xF3BE75</span>, <span class="number">0xDF9328</span>, <span class="number">0x3080AB</span>, <span class="number">0xF68C66</span>, <span class="number">0x15CB04</span>, <span class="number">0x0622FA</span>, <span class="number">0x1DE4D9</span>, <span class="number">0xA4B33D</span>, |
| <span class="number">0x8F1B57</span>, <span class="number">0x09CD36</span>, <span class="number">0xE9424E</span>, <span class="number">0xA4BE13</span>, <span class="number">0xB52333</span>, <span class="number">0x1AAAF0</span>, <span class="number">0xA8654F</span>, <span class="number">0xA5C1D2</span>, <span class="number">0x0F3F0B</span>, |
| <span class="number">0xCD785B</span>, <span class="number">0x76F923</span>, <span class="number">0x048B7B</span>, <span class="number">0x721789</span>, <span class="number">0x53A6C6</span>, <span class="number">0xE26E6F</span>, <span class="number">0x00EBEF</span>, <span class="number">0x584A9B</span>, <span class="number">0xB7DAC4</span>, |
| <span class="number">0xBA66AA</span>, <span class="number">0xCFCF76</span>, <span class="number">0x1D02D1</span>, <span class="number">0x2DF1B1</span>, <span class="number">0xC1998C</span>, <span class="number">0x77ADC3</span>, <span class="number">0xDA4886</span>, <span class="number">0xA05DF7</span>, <span class="number">0xF480C6</span>, |
| <span class="number">0x2FF0AC</span>, <span class="number">0x9AECDD</span>, <span class="number">0xBC5C3F</span>, <span class="number">0x6DDED0</span>, <span class="number">0x1FC790</span>, <span class="number">0xB6DB2A</span>, <span class="number">0x3A25A3</span>, <span class="number">0x9AAF00</span>, <span class="number">0x9353AD</span>, |
| <span class="number">0x0457B6</span>, <span class="number">0xB42D29</span>, <span class="number">0x7E804B</span>, <span class="number">0xA707DA</span>, <span class="number">0x0EAA76</span>, <span class="number">0xA1597B</span>, <span class="number">0x2A1216</span>, <span class="number">0x2DB7DC</span>, <span class="number">0xFDE5FA</span>, |
| <span class="number">0xFEDB89</span>, <span class="number">0xFDBE89</span>, <span class="number">0x6C76E4</span>, <span class="number">0xFCA906</span>, <span class="number">0x70803E</span>, <span class="number">0x156E85</span>, <span class="number">0xFF87FD</span>, <span class="number">0x073E28</span>, <span class="number">0x336761</span>, |
| <span class="number">0x86182A</span>, <span class="number">0xEABD4D</span>, <span class="number">0xAFE7B3</span>, <span class="number">0x6E6D8F</span>, <span class="number">0x396795</span>, <span class="number">0x5BBF31</span>, <span class="number">0x48D784</span>, <span class="number">0x16DF30</span>, <span class="number">0x432DC7</span>, |
| <span class="number">0x356125</span>, <span class="number">0xCE70C9</span>, <span class="number">0xB8CB30</span>, <span class="number">0xFD6CBF</span>, <span class="number">0xA200A4</span>, <span class="number">0xE46C05</span>, <span class="number">0xA0DD5A</span>, <span class="number">0x476F21</span>, <span class="number">0xD21262</span>, |
| <span class="number">0x845CB9</span>, <span class="number">0x496170</span>, <span class="number">0xE0566B</span>, <span class="number">0x015299</span>, <span class="number">0x375550</span>, <span class="number">0xB7D51E</span>, <span class="number">0xC4F133</span>, <span class="number">0x5F6E13</span>, <span class="number">0xE4305D</span>, |
| <span class="number">0xA92E85</span>, <span class="number">0xC3B21D</span>, <span class="number">0x3632A1</span>, <span class="number">0xA4B708</span>, <span class="number">0xD4B1EA</span>, <span class="number">0x21F716</span>, <span class="number">0xE4698F</span>, <span class="number">0x77FF27</span>, <span class="number">0x80030C</span>, |
| <span class="number">0x2D408D</span>, <span class="number">0xA0CD4F</span>, <span class="number">0x99A520</span>, <span class="number">0xD3A2B3</span>, <span class="number">0x0A5D2F</span>, <span class="number">0x42F9B4</span>, <span class="number">0xCBDA11</span>, <span class="number">0xD0BE7D</span>, <span class="number">0xC1DB9B</span>, |
| <span class="number">0xBD17AB</span>, <span class="number">0x81A2CA</span>, <span class="number">0x5C6A08</span>, <span class="number">0x17552E</span>, <span class="number">0x550027</span>, <span class="number">0xF0147F</span>, <span class="number">0x8607E1</span>, <span class="number">0x640B14</span>, <span class="number">0x8D4196</span>, |
| <span class="number">0xDEBE87</span>, <span class="number">0x2AFDDA</span>, <span class="number">0xB6256B</span>, <span class="number">0x34897B</span>, <span class="number">0xFEF305</span>, <span class="number">0x9EBFB9</span>, <span class="number">0x4F6A68</span>, <span class="number">0xA82A4A</span>, <span class="number">0x5AC44F</span>, |
| <span class="number">0xBCF82D</span>, <span class="number">0x985AD7</span>, <span class="number">0x95C7F4</span>, <span class="number">0x8D4D0D</span>, <span class="number">0xA63A20</span>, <span class="number">0x5F57A4</span>, <span class="number">0xB13F14</span>, <span class="number">0x953880</span>, <span class="number">0x0120CC</span>, |
| <span class="number">0x86DD71</span>, <span class="number">0xB6DEC9</span>, <span class="number">0xF560BF</span>, <span class="number">0x11654D</span>, <span class="number">0x6B0701</span>, <span class="number">0xACB08C</span>, <span class="number">0xD0C0B2</span>, <span class="number">0x485551</span>, <span class="number">0x0EFB1E</span>, |
| <span class="number">0xC37295</span>, <span class="number">0x3B06A3</span>, <span class="number">0x3540C0</span>, <span class="number">0x7BDC06</span>, <span class="number">0xCC45E0</span>, <span class="number">0xFA294E</span>, <span class="number">0xC8CAD6</span>, <span class="number">0x41F3E8</span>, <span class="number">0xDE647C</span>, |
| <span class="number">0xD8649B</span>, <span class="number">0x31BED9</span>, <span class="number">0xC397A4</span>, <span class="number">0xD45877</span>, <span class="number">0xC5E369</span>, <span class="number">0x13DAF0</span>, <span class="number">0x3C3ABA</span>, <span class="number">0x461846</span>, <span class="number">0x5F7555</span>, |
| <span class="number">0xF5BDD2</span>, <span class="number">0xC6926E</span>, <span class="number">0x5D2EAC</span>, <span class="number">0xED440E</span>, <span class="number">0x423E1C</span>, <span class="number">0x87C461</span>, <span class="number">0xE9FD29</span>, <span class="number">0xF3D6E7</span>, <span class="number">0xCA7C22</span>, |
| <span class="number">0x35916F</span>, <span class="number">0xC5E008</span>, <span class="number">0x8DD7FF</span>, <span class="number">0xE26A6E</span>, <span class="number">0xC6FDB0</span>, <span class="number">0xC10893</span>, <span class="number">0x745D7C</span>, <span class="number">0xB2AD6B</span>, <span class="number">0x9D6ECD</span>, |
| <span class="number">0x7B723E</span>, <span class="number">0x6A11C6</span>, <span class="number">0xA9CFF7</span>, <span class="number">0xDF7329</span>, <span class="number">0xBAC9B5</span>, <span class="number">0x5100B7</span>, <span class="number">0x0DB2E2</span>, <span class="number">0x24BA74</span>, <span class="number">0x607DE5</span>, |
| <span class="number">0x8AD874</span>, <span class="number">0x2C150D</span>, <span class="number">0x0C1881</span>, <span class="number">0x94667E</span>, <span class="number">0x162901</span>, <span class="number">0x767A9F</span>, <span class="number">0xBEFDFD</span>, <span class="number">0xEF4556</span>, <span class="number">0x367ED9</span>, |
| <span class="number">0x13D9EC</span>, <span class="number">0xB9BA8B</span>, <span class="number">0xFC97C4</span>, <span class="number">0x27A831</span>, <span class="number">0xC36EF1</span>, <span class="number">0x36C594</span>, <span class="number">0x56A8D8</span>, <span class="number">0xB5A8B4</span>, <span class="number">0x0ECCCF</span>, |
| <span class="number">0x2D8912</span>, <span class="number">0x34576F</span>, <span class="number">0x89562C</span>, <span class="number">0xE3CE99</span>, <span class="number">0xB920D6</span>, <span class="number">0xAA5E6B</span>, <span class="number">0x9C2A3E</span>, <span class="number">0xCC5F11</span>, <span class="number">0x4A0BFD</span>, |
| <span class="number">0xFBF4E1</span>, <span class="number">0x6D3B8E</span>, <span class="number">0x2C86E2</span>, <span class="number">0x84D4E9</span>, <span class="number">0xA9B4FC</span>, <span class="number">0xD1EEEF</span>, <span class="number">0xC9352E</span>, <span class="number">0x61392F</span>, <span class="number">0x442138</span>, |
| <span class="number">0xC8D91B</span>, <span class="number">0x0AFC81</span>, <span class="number">0x6A4AFB</span>, <span class="number">0xD81C2F</span>, <span class="number">0x84B453</span>, <span class="number">0x8C994E</span>, <span class="number">0xCC2254</span>, <span class="number">0xDC552A</span>, <span class="number">0xD6C6C0</span>, |
| <span class="number">0x96190B</span>, <span class="number">0xB8701A</span>, <span class="number">0x649569</span>, <span class="number">0x605A26</span>, <span class="number">0xEE523F</span>, <span class="number">0x0F117F</span>, <span class="number">0x11B5F4</span>, <span class="number">0xF5CBFC</span>, <span class="number">0x2DBC34</span>, |
| <span class="number">0xEEBC34</span>, <span class="number">0xCC5DE8</span>, <span class="number">0x605EDD</span>, <span class="number">0x9B8E67</span>, <span class="number">0xEF3392</span>, <span class="number">0xB817C9</span>, <span class="number">0x9B5861</span>, <span class="number">0xBC57E1</span>, <span class="number">0xC68351</span>, |
| <span class="number">0x103ED8</span>, <span class="number">0x4871DD</span>, <span class="number">0xDD1C2D</span>, <span class="number">0xA118AF</span>, <span class="number">0x462C21</span>, <span class="number">0xD7F359</span>, <span class="number">0x987AD9</span>, <span class="number">0xC0549E</span>, <span class="number">0xFA864F</span>, |
| <span class="number">0xFC0656</span>, <span class="number">0xAE79E5</span>, <span class="number">0x362289</span>, <span class="number">0x22AD38</span>, <span class="number">0xDC9367</span>, <span class="number">0xAAE855</span>, <span class="number">0x382682</span>, <span class="number">0x9BE7CA</span>, <span class="number">0xA40D51</span>, |
| <span class="number">0xB13399</span>, <span class="number">0x0ED7A9</span>, <span class="number">0x480569</span>, <span class="number">0xF0B265</span>, <span class="number">0xA7887F</span>, <span class="number">0x974C88</span>, <span class="number">0x36D1F9</span>, <span class="number">0xB39221</span>, <span class="number">0x4A827B</span>, |
| <span class="number">0x21CF98</span>, <span class="number">0xDC9F40</span>, <span class="number">0x5547DC</span>, <span class="number">0x3A74E1</span>, <span class="number">0x42EB67</span>, <span class="number">0xDF9DFE</span>, <span class="number">0x5FD45E</span>, <span class="number">0xA4677B</span>, <span class="number">0x7AACBA</span>, |
| <span class="number">0xA2F655</span>, <span class="number">0x23882B</span>, <span class="number">0x55BA41</span>, <span class="number">0x086E59</span>, <span class="number">0x862A21</span>, <span class="number">0x834739</span>, <span class="number">0xE6E389</span>, <span class="number">0xD49EE5</span>, <span class="number">0x40FB49</span>, |
| <span class="number">0xE956FF</span>, <span class="number">0xCA0F1C</span>, <span class="number">0x8A59C5</span>, <span class="number">0x2BFA94</span>, <span class="number">0xC5C1D3</span>, <span class="number">0xCFC50F</span>, <span class="number">0xAE5ADB</span>, <span class="number">0x86C547</span>, <span class="number">0x624385</span>, |
| <span class="number">0x3B8621</span>, <span class="number">0x94792C</span>, <span class="number">0x876110</span>, <span class="number">0x7B4C2A</span>, <span class="number">0x1A2C80</span>, <span class="number">0x12BF43</span>, <span class="number">0x902688</span>, <span class="number">0x893C78</span>, <span class="number">0xE4C4A8</span>, |
| <span class="number">0x7BDBE5</span>, <span class="number">0xC23AC4</span>, <span class="number">0xEAF426</span>, <span class="number">0x8A67F7</span>, <span class="number">0xBF920D</span>, <span class="number">0x2BA365</span>, <span class="number">0xB1933D</span>, <span class="number">0x0B7CBD</span>, <span class="number">0xDC51A4</span>, |
| <span class="number">0x63DD27</span>, <span class="number">0xDDE169</span>, <span class="number">0x19949A</span>, <span class="number">0x9529A8</span>, <span class="number">0x28CE68</span>, <span class="number">0xB4ED09</span>, <span class="number">0x209F44</span>, <span class="number">0xCA984E</span>, <span class="number">0x638270</span>, |
| <span class="number">0x237C7E</span>, <span class="number">0x32B90F</span>, <span class="number">0x8EF5A7</span>, <span class="number">0xE75614</span>, <span class="number">0x08F121</span>, <span class="number">0x2A9DB5</span>, <span class="number">0x4D7E6F</span>, <span class="number">0x5119A5</span>, <span class="number">0xABF9B5</span>, |
| <span class="number">0xD6DF82</span>, <span class="number">0x61DD96</span>, <span class="number">0x023616</span>, <span class="number">0x9F3AC4</span>, <span class="number">0xA1A283</span>, <span class="number">0x6DED72</span>, <span class="number">0x7A8D39</span>, <span class="number">0xA9B882</span>, <span class="number">0x5C326B</span>, |
| <span class="number">0x5B2746</span>, <span class="number">0xED3400</span>, <span class="number">0x7700D2</span>, <span class="number">0x55F4FC</span>, <span class="number">0x4D5901</span>, <span class="number">0x8071E0</span>, |
| ]; |
| |
| <span class="kw">const</span> <span class="ident">PIO2</span>: [<span class="ident">f64</span>; <span class="number">8</span>] <span class="op">=</span> [ |
| <span class="number">1.57079625129699707031e+00</span>, <span class="comment">/* 0x3FF921FB, 0x40000000 */</span> |
| <span class="number">7.54978941586159635335e-08</span>, <span class="comment">/* 0x3E74442D, 0x00000000 */</span> |
| <span class="number">5.39030252995776476554e-15</span>, <span class="comment">/* 0x3CF84698, 0x80000000 */</span> |
| <span class="number">3.28200341580791294123e-22</span>, <span class="comment">/* 0x3B78CC51, 0x60000000 */</span> |
| <span class="number">1.27065575308067607349e-29</span>, <span class="comment">/* 0x39F01B83, 0x80000000 */</span> |
| <span class="number">1.22933308981111328932e-36</span>, <span class="comment">/* 0x387A2520, 0x40000000 */</span> |
| <span class="number">2.73370053816464559624e-44</span>, <span class="comment">/* 0x36E38222, 0x80000000 */</span> |
| <span class="number">2.16741683877804819444e-51</span>, <span class="comment">/* 0x3569F31D, 0x00000000 */</span> |
| ]; |
| |
| <span class="comment">// fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize) -> i32</span> |
| <span class="comment">//</span> |
| <span class="comment">// Input parameters:</span> |
| <span class="comment">// x[] The input value (must be positive) is broken into nx</span> |
| <span class="comment">// pieces of 24-bit integers in double precision format.</span> |
| <span class="comment">// x[i] will be the i-th 24 bit of x. The scaled exponent</span> |
| <span class="comment">// of x[0] is given in input parameter e0 (i.e., x[0]*2^e0</span> |
| <span class="comment">// match x's up to 24 bits.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Example of breaking a double positive z into x[0]+x[1]+x[2]:</span> |
| <span class="comment">// e0 = ilogb(z)-23</span> |
| <span class="comment">// z = scalbn(z,-e0)</span> |
| <span class="comment">// for i = 0,1,2</span> |
| <span class="comment">// x[i] = floor(z)</span> |
| <span class="comment">// z = (z-x[i])*2**24</span> |
| <span class="comment">//</span> |
| <span class="comment">// y[] ouput result in an array of double precision numbers.</span> |
| <span class="comment">// The dimension of y[] is:</span> |
| <span class="comment">// 24-bit precision 1</span> |
| <span class="comment">// 53-bit precision 2</span> |
| <span class="comment">// 64-bit precision 2</span> |
| <span class="comment">// 113-bit precision 3</span> |
| <span class="comment">// The actual value is the sum of them. Thus for 113-bit</span> |
| <span class="comment">// precison, one may have to do something like:</span> |
| <span class="comment">//</span> |
| <span class="comment">// long double t,w,r_head, r_tail;</span> |
| <span class="comment">// t = (long double)y[2] + (long double)y[1];</span> |
| <span class="comment">// w = (long double)y[0];</span> |
| <span class="comment">// r_head = t+w;</span> |
| <span class="comment">// r_tail = w - (r_head - t);</span> |
| <span class="comment">//</span> |
| <span class="comment">// e0 The exponent of x[0]. Must be <= 16360 or you need to</span> |
| <span class="comment">// expand the ipio2 table.</span> |
| <span class="comment">//</span> |
| <span class="comment">// prec an integer indicating the precision:</span> |
| <span class="comment">// 0 24 bits (single)</span> |
| <span class="comment">// 1 53 bits (double)</span> |
| <span class="comment">// 2 64 bits (extended)</span> |
| <span class="comment">// 3 113 bits (quad)</span> |
| <span class="comment">//</span> |
| <span class="comment">// Here is the description of some local variables:</span> |
| <span class="comment">//</span> |
| <span class="comment">// jk jk+1 is the initial number of terms of ipio2[] needed</span> |
| <span class="comment">// in the computation. The minimum and recommended value</span> |
| <span class="comment">// for jk is 3,4,4,6 for single, double, extended, and quad.</span> |
| <span class="comment">// jk+1 must be 2 larger than you might expect so that our</span> |
| <span class="comment">// recomputation test works. (Up to 24 bits in the integer</span> |
| <span class="comment">// part (the 24 bits of it that we compute) and 23 bits in</span> |
| <span class="comment">// the fraction part may be lost to cancelation before we</span> |
| <span class="comment">// recompute.)</span> |
| <span class="comment">//</span> |
| <span class="comment">// jz local integer variable indicating the number of</span> |
| <span class="comment">// terms of ipio2[] used.</span> |
| <span class="comment">//</span> |
| <span class="comment">// jx nx - 1</span> |
| <span class="comment">//</span> |
| <span class="comment">// jv index for pointing to the suitable ipio2[] for the</span> |
| <span class="comment">// computation. In general, we want</span> |
| <span class="comment">// ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8</span> |
| <span class="comment">// is an integer. Thus</span> |
| <span class="comment">// e0-3-24*jv >= 0 or (e0-3)/24 >= jv</span> |
| <span class="comment">// Hence jv = max(0,(e0-3)/24).</span> |
| <span class="comment">//</span> |
| <span class="comment">// jp jp+1 is the number of terms in PIo2[] needed, jp = jk.</span> |
| <span class="comment">//</span> |
| <span class="comment">// q[] double array with integral value, representing the</span> |
| <span class="comment">// 24-bits chunk of the product of x and 2/pi.</span> |
| <span class="comment">//</span> |
| <span class="comment">// q0 the corresponding exponent of q[0]. Note that the</span> |
| <span class="comment">// exponent for q[i] would be q0-24*i.</span> |
| <span class="comment">//</span> |
| <span class="comment">// PIo2[] double precision array, obtained by cutting pi/2</span> |
| <span class="comment">// into 24 bits chunks.</span> |
| <span class="comment">//</span> |
| <span class="comment">// f[] ipio2[] in floating point</span> |
| <span class="comment">//</span> |
| <span class="comment">// iq[] integer array by breaking up q[] in 24-bits chunk.</span> |
| <span class="comment">//</span> |
| <span class="comment">// fq[] final product of x*(2/pi) in fq[0],..,fq[jk]</span> |
| <span class="comment">//</span> |
| <span class="comment">// ih integer. If >0 it indicates q[] is >= 0.5, hence</span> |
| <span class="comment">// it also indicates the *sign* of the result.</span> |
| |
| <span class="doccomment">/// Return the last three digits of N with y = x - N*pi/2</span> |
| <span class="doccomment">/// so that |y| < pi/2.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// The method is to compute the integer (mod 8) and fraction parts of</span> |
| <span class="doccomment">/// (2/pi)*x without doing the full multiplication. In general we</span> |
| <span class="doccomment">/// skip the part of the product that are known to be a huge integer (</span> |
| <span class="doccomment">/// more accurately, = 0 mod 8 ). Thus the number of operations are</span> |
| <span class="doccomment">/// independent of the exponent of the input.</span> |
| <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">all</span>(<span class="ident">test</span>, <span class="ident">assert_no_panic</span>), <span class="ident">no_panic::no_panic</span>)]</span> |
| <span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn</span> <span class="ident">rem_pio2_large</span>(<span class="ident">x</span>: <span class="kw-2">&</span>[<span class="ident">f64</span>], <span class="ident">y</span>: <span class="kw-2">&mut</span> [<span class="ident">f64</span>], <span class="ident">e0</span>: <span class="ident">i32</span>, <span class="ident">prec</span>: <span class="ident">usize</span>) -> <span class="ident">i32</span> { |
| <span class="kw">let</span> <span class="ident">x1p24</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x4170000000000000</span>); <span class="comment">// 0x1p24 === 2 ^ 24</span> |
| <span class="kw">let</span> <span class="ident">x1p_24</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x3e70000000000000</span>); <span class="comment">// 0x1p_24 === 2 ^ (-24)</span> |
| |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">all</span>(<span class="ident">target_pointer_width</span> <span class="op">=</span> <span class="string">"64"</span>, <span class="ident">feature</span> <span class="op">=</span> <span class="string">"checked"</span>))]</span> |
| <span class="macro">assert!</span>(<span class="ident">e0</span> <span class="op"><</span><span class="op">=</span> <span class="number">16360</span>); |
| |
| <span class="kw">let</span> <span class="ident">nx</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">len</span>(); |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">fw</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">n</span>: <span class="ident">i32</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ih</span>: <span class="ident">i32</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">f</span>: [<span class="ident">f64</span>; <span class="number">20</span>] <span class="op">=</span> [<span class="number">0.</span>; <span class="number">20</span>]; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">fq</span>: [<span class="ident">f64</span>; <span class="number">20</span>] <span class="op">=</span> [<span class="number">0.</span>; <span class="number">20</span>]; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">q</span>: [<span class="ident">f64</span>; <span class="number">20</span>] <span class="op">=</span> [<span class="number">0.</span>; <span class="number">20</span>]; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">iq</span>: [<span class="ident">i32</span>; <span class="number">20</span>] <span class="op">=</span> [<span class="number">0</span>; <span class="number">20</span>]; |
| |
| <span class="comment">/* initialize jk*/</span> |
| <span class="kw">let</span> <span class="ident">jk</span> <span class="op">=</span> <span class="ident">INIT_JK</span>[<span class="ident">prec</span>]; |
| <span class="kw">let</span> <span class="ident">jp</span> <span class="op">=</span> <span class="ident">jk</span>; |
| |
| <span class="comment">/* determine jx,jv,q0, note that 3>q0 */</span> |
| <span class="kw">let</span> <span class="ident">jx</span> <span class="op">=</span> <span class="ident">nx</span> <span class="op">-</span> <span class="number">1</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">jv</span> <span class="op">=</span> (<span class="ident">e0</span> <span class="op">-</span> <span class="number">3</span>) <span class="op">/</span> <span class="number">24</span>; |
| <span class="kw">if</span> <span class="ident">jv</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="ident">jv</span> <span class="op">=</span> <span class="number">0</span>; |
| } |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">q0</span> <span class="op">=</span> <span class="ident">e0</span> <span class="op">-</span> <span class="number">24</span> <span class="op">*</span> (<span class="ident">jv</span> <span class="op">+</span> <span class="number">1</span>); |
| <span class="kw">let</span> <span class="ident">jv</span> <span class="op">=</span> <span class="ident">jv</span> <span class="kw">as</span> <span class="ident">usize</span>; |
| |
| <span class="comment">/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">j</span> <span class="op">=</span> (<span class="ident">jv</span> <span class="kw">as</span> <span class="ident">i32</span>) <span class="op">-</span> (<span class="ident">jx</span> <span class="kw">as</span> <span class="ident">i32</span>); |
| <span class="kw">let</span> <span class="ident">m</span> <span class="op">=</span> <span class="ident">jx</span> <span class="op">+</span> <span class="ident">jk</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="op">=</span><span class="ident">m</span> { |
| <span class="macro">i!</span>(<span class="ident">f</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="kw">if</span> <span class="ident">j</span> <span class="op"><</span> <span class="number">0</span> { |
| <span class="number">0.</span> |
| } <span class="kw">else</span> { |
| <span class="macro">i!</span>(<span class="ident">IPIO2</span>, <span class="ident">j</span> <span class="kw">as</span> <span class="ident">usize</span>) <span class="kw">as</span> <span class="ident">f64</span> |
| }); |
| <span class="ident">j</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| |
| <span class="comment">/* compute q[0],q[1],...q[jk] */</span> |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="op">=</span><span class="ident">jk</span> { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="number">0</span>..<span class="op">=</span><span class="ident">jx</span> { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">x</span>, <span class="ident">j</span>) <span class="op">*</span> <span class="macro">i!</span>(<span class="ident">f</span>, <span class="ident">jx</span> <span class="op">+</span> <span class="ident">i</span> <span class="op">-</span> <span class="ident">j</span>); |
| } |
| <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">jz</span> <span class="op">=</span> <span class="ident">jk</span>; |
| |
| <span class="lifetime">'recompute</span>: <span class="kw">loop</span> { |
| <span class="comment">/* distill q[] into iq[] reversingly */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="number">0i32</span>; |
| <span class="ident">z</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">jz</span>); |
| <span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> (<span class="number">1</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">=</span> (<span class="ident">x1p_24</span> <span class="op">*</span> <span class="ident">z</span>) <span class="kw">as</span> <span class="ident">i32</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span> <span class="kw">as</span> <span class="ident">usize</span>, <span class="op">=</span>, (<span class="ident">z</span> <span class="op">-</span> <span class="ident">x1p24</span> <span class="op">*</span> <span class="ident">fw</span>) <span class="kw">as</span> <span class="ident">i32</span>); |
| <span class="ident">z</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">j</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">+</span> <span class="ident">fw</span>; |
| <span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| |
| <span class="comment">/* compute n */</span> |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">scalbn</span>(<span class="ident">z</span>, <span class="ident">q0</span>); <span class="comment">/* actual value of z */</span> |
| <span class="ident">z</span> <span class="op">-</span><span class="op">=</span> <span class="number">8.0</span> <span class="op">*</span> <span class="ident">floor</span>(<span class="ident">z</span> <span class="op">*</span> <span class="number">0.125</span>); <span class="comment">/* trim off integer >= 8 */</span> |
| <span class="ident">n</span> <span class="op">=</span> <span class="ident">z</span> <span class="kw">as</span> <span class="ident">i32</span>; |
| <span class="ident">z</span> <span class="op">-</span><span class="op">=</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">ih</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">if</span> <span class="ident">q0</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="comment">/* need iq[jz-1] to determine n */</span> |
| <span class="ident">i</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">></span><span class="op">></span> (<span class="number">24</span> <span class="op">-</span> <span class="ident">q0</span>); |
| <span class="ident">n</span> <span class="op">+</span><span class="op">=</span> <span class="ident">i</span>; |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>, <span class="op">-</span><span class="op">=</span>, <span class="ident">i</span> <span class="op"><</span><span class="op"><</span> (<span class="number">24</span> <span class="op">-</span> <span class="ident">q0</span>)); |
| <span class="ident">ih</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">></span><span class="op">></span> (<span class="number">23</span> <span class="op">-</span> <span class="ident">q0</span>); |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">q0</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">ih</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">></span><span class="op">></span> <span class="number">23</span>; |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">z</span> <span class="op">></span><span class="op">=</span> <span class="number">0.5</span> { |
| <span class="ident">ih</span> <span class="op">=</span> <span class="number">2</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">ih</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="comment">/* q > 0.5 */</span> |
| <span class="ident">n</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">carry</span> <span class="op">=</span> <span class="number">0i32</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">jz</span> { |
| <span class="comment">/* compute 1-q */</span> |
| <span class="kw">let</span> <span class="ident">j</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span>); |
| <span class="kw">if</span> <span class="ident">carry</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="kw">if</span> <span class="ident">j</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">carry</span> <span class="op">=</span> <span class="number">1</span>; |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="number">0x1000000</span> <span class="op">-</span> <span class="ident">j</span>); |
| } |
| } <span class="kw">else</span> { |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="number">0xffffff</span> <span class="op">-</span> <span class="ident">j</span>); |
| } |
| } |
| <span class="kw">if</span> <span class="ident">q0</span> <span class="op">></span> <span class="number">0</span> { |
| <span class="comment">/* rare case: chance is 1 in 12 */</span> |
| <span class="kw">match</span> <span class="ident">q0</span> { |
| <span class="number">1</span> => { |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>, <span class="op">&=</span>, <span class="number">0x7fffff</span>); |
| } |
| <span class="number">2</span> => { |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>, <span class="op">&=</span>, <span class="number">0x3fffff</span>); |
| } |
| <span class="kw">_</span> => {} |
| } |
| } |
| <span class="kw">if</span> <span class="ident">ih</span> <span class="op">==</span> <span class="number">2</span> { |
| <span class="ident">z</span> <span class="op">=</span> <span class="number">1.</span> <span class="op">-</span> <span class="ident">z</span>; |
| <span class="kw">if</span> <span class="ident">carry</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">z</span> <span class="op">-</span><span class="op">=</span> <span class="ident">scalbn</span>(<span class="number">1.</span>, <span class="ident">q0</span>); |
| } |
| } |
| } |
| |
| <span class="comment">/* check if recomputation is needed */</span> |
| <span class="kw">if</span> <span class="ident">z</span> <span class="op">==</span> <span class="number">0.</span> { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">j</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">jk</span>..<span class="op">=</span><span class="ident">jz</span> <span class="op">-</span> <span class="number">1</span>).<span class="ident">rev</span>() { |
| <span class="ident">j</span> <span class="op">|</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span>); |
| } |
| <span class="kw">if</span> <span class="ident">j</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="comment">/* need recomputation */</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span> <span class="op">=</span> <span class="number">1</span>; |
| <span class="kw">while</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jk</span> <span class="op">-</span> <span class="ident">k</span>, <span class="op">==</span>, <span class="number">0</span>) { |
| <span class="ident">k</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; <span class="comment">/* k = no. of terms needed */</span> |
| } |
| |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">jz</span> <span class="op">+</span> <span class="number">1</span>)..<span class="op">=</span>(<span class="ident">jz</span> <span class="op">+</span> <span class="ident">k</span>) { |
| <span class="comment">/* add q[jz+1] to q[jz+k] */</span> |
| <span class="macro">i!</span>(<span class="ident">f</span>, <span class="ident">jx</span> <span class="op">+</span> <span class="ident">i</span>, <span class="op">=</span>, <span class="macro">i!</span>(<span class="ident">IPIO2</span>, <span class="ident">jv</span> <span class="op">+</span> <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span>); |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">for</span> <span class="ident">j</span> <span class="kw">in</span> <span class="number">0</span>..<span class="op">=</span><span class="ident">jx</span> { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">x</span>, <span class="ident">j</span>) <span class="op">*</span> <span class="macro">i!</span>(<span class="ident">f</span>, <span class="ident">jx</span> <span class="op">+</span> <span class="ident">i</span> <span class="op">-</span> <span class="ident">j</span>); |
| } |
| <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } |
| <span class="ident">jz</span> <span class="op">+</span><span class="op">=</span> <span class="ident">k</span>; |
| <span class="kw">continue</span> <span class="lifetime">'recompute</span>; |
| } |
| } |
| |
| <span class="kw">break</span>; |
| } |
| |
| <span class="comment">/* chop off zero terms */</span> |
| <span class="kw">if</span> <span class="ident">z</span> <span class="op">==</span> <span class="number">0.</span> { |
| <span class="ident">jz</span> <span class="op">-</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">q0</span> <span class="op">-</span><span class="op">=</span> <span class="number">24</span>; |
| <span class="kw">while</span> <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span>) <span class="op">==</span> <span class="number">0</span> { |
| <span class="ident">jz</span> <span class="op">-</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">q0</span> <span class="op">-</span><span class="op">=</span> <span class="number">24</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="comment">/* break z into 24-bit if necessary */</span> |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">scalbn</span>(<span class="ident">z</span>, <span class="op">-</span><span class="ident">q0</span>); |
| <span class="kw">if</span> <span class="ident">z</span> <span class="op">></span><span class="op">=</span> <span class="ident">x1p24</span> { |
| <span class="ident">fw</span> <span class="op">=</span> (<span class="ident">x1p_24</span> <span class="op">*</span> <span class="ident">z</span>) <span class="kw">as</span> <span class="ident">i32</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span>, <span class="op">=</span>, (<span class="ident">z</span> <span class="op">-</span> <span class="ident">x1p24</span> <span class="op">*</span> <span class="ident">fw</span>) <span class="kw">as</span> <span class="ident">i32</span>); |
| <span class="ident">jz</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">q0</span> <span class="op">+</span><span class="op">=</span> <span class="number">24</span>; |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span>, <span class="op">=</span>, <span class="ident">fw</span> <span class="kw">as</span> <span class="ident">i32</span>); |
| } <span class="kw">else</span> { |
| <span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">jz</span>, <span class="op">=</span>, <span class="ident">z</span> <span class="kw">as</span> <span class="ident">i32</span>); |
| } |
| } |
| |
| <span class="comment">/* convert integer "bit" chunk to floating-point value */</span> |
| <span class="ident">fw</span> <span class="op">=</span> <span class="ident">scalbn</span>(<span class="number">1.</span>, <span class="ident">q0</span>); |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">i</span>, <span class="op">=</span>, <span class="ident">fw</span> <span class="op">*</span> (<span class="macro">i!</span>(<span class="ident">iq</span>, <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span>)); |
| <span class="ident">fw</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">x1p_24</span>; |
| } |
| |
| <span class="comment">/* compute PIo2[0,...,jp]*q[jz,...,0] */</span> |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>; |
| <span class="kw">while</span> (<span class="ident">k</span> <span class="op"><</span><span class="op">=</span> <span class="ident">jp</span>) <span class="op">&&</span> (<span class="ident">k</span> <span class="op"><</span><span class="op">=</span> <span class="ident">jz</span> <span class="op">-</span> <span class="ident">i</span>) { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">PIO2</span>, <span class="ident">k</span>) <span class="op">*</span> <span class="macro">i!</span>(<span class="ident">q</span>, <span class="ident">i</span> <span class="op">+</span> <span class="ident">k</span>); |
| <span class="ident">k</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">jz</span> <span class="op">-</span> <span class="ident">i</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } |
| |
| <span class="comment">/* compress fq[] into y[] */</span> |
| <span class="kw">match</span> <span class="ident">prec</span> { |
| <span class="number">0</span> => { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| } |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">0</span>, <span class="op">=</span>, <span class="kw">if</span> <span class="ident">ih</span> <span class="op">==</span> <span class="number">0</span> { <span class="ident">fw</span> } <span class="kw">else</span> { <span class="op">-</span><span class="ident">fw</span> }); |
| } |
| <span class="number">1</span> <span class="op">|</span> <span class="number">2</span> => { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">0</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| } |
| <span class="comment">// TODO: drop excess precision here once double_t is used</span> |
| <span class="ident">fw</span> <span class="op">=</span> <span class="ident">fw</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">0</span>, <span class="op">=</span>, <span class="kw">if</span> <span class="ident">ih</span> <span class="op">==</span> <span class="number">0</span> { <span class="ident">fw</span> } <span class="kw">else</span> { <span class="op">-</span><span class="ident">fw</span> }); |
| <span class="ident">fw</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="number">0</span>) <span class="op">-</span> <span class="ident">fw</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">1</span>..<span class="op">=</span><span class="ident">jz</span> { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| } |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">1</span>, <span class="op">=</span>, <span class="kw">if</span> <span class="ident">ih</span> <span class="op">==</span> <span class="number">0</span> { <span class="ident">fw</span> } <span class="kw">else</span> { <span class="op">-</span><span class="ident">fw</span> }); |
| } |
| <span class="number">3</span> => { |
| <span class="comment">/* painful */</span> |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">1</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">+</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>, <span class="op">+</span><span class="op">=</span>, <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">-</span> <span class="ident">fw</span>); |
| <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">2</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">+</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>, <span class="op">+</span><span class="op">=</span>, <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>) <span class="op">-</span> <span class="ident">fw</span>); |
| <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span> <span class="op">-</span> <span class="number">1</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } |
| <span class="ident">fw</span> <span class="op">=</span> <span class="number">0f64</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="number">2</span>..<span class="op">=</span><span class="ident">jz</span>).<span class="ident">rev</span>() { |
| <span class="ident">fw</span> <span class="op">+</span><span class="op">=</span> <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="ident">i</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ih</span> <span class="op">==</span> <span class="number">0</span> { |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">0</span>, <span class="op">=</span>, <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="number">0</span>)); |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">1</span>, <span class="op">=</span>, <span class="macro">i!</span>(<span class="ident">fq</span>, <span class="number">1</span>)); |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">2</span>, <span class="op">=</span>, <span class="ident">fw</span>); |
| } <span class="kw">else</span> { |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">0</span>, <span class="op">=</span>, <span class="op">-</span><span class="macro">i!</span>(<span class="ident">fq</span>, <span class="number">0</span>)); |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">1</span>, <span class="op">=</span>, <span class="op">-</span><span class="macro">i!</span>(<span class="ident">fq</span>, <span class="number">1</span>)); |
| <span class="macro">i!</span>(<span class="ident">y</span>, <span class="number">2</span>, <span class="op">=</span>, <span class="op">-</span><span class="ident">fw</span>); |
| } |
| } |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">debug_assertions</span>)]</span> |
| <span class="kw">_</span> => <span class="macro">unreachable!</span>(), |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">not</span>(<span class="ident">debug_assertions</span>))]</span> |
| <span class="kw">_</span> => {} |
| } |
| <span class="ident">n</span> <span class="op">&</span> <span class="number">7</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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