pxfm/logs/
log2p1_tables.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 6/2025. All rights reserved.
3 * //
4 * // Redistribution and use in source and binary forms, with or without modification,
5 * // are permitted provided that the following conditions are met:
6 * //
7 * // 1.  Redistributions of source code must retain the above copyright notice, this
8 * // list of conditions and the following disclaimer.
9 * //
10 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
11 * // this list of conditions and the following disclaimer in the documentation
12 * // and/or other materials provided with the distribution.
13 * //
14 * // 3.  Neither the name of the copyright holder nor the names of its
15 * // contributors may be used to endorse or promote products derived from
16 * // this software without specific prior written permission.
17 * //
18 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29
30pub(crate) static LOG2P1_EXACT: [u64; 53] = [
31    0x3ff0000000000000,
32    0x4008000000000000,
33    0x401c000000000000,
34    0x402e000000000000,
35    0x403f000000000000,
36    0x404f800000000000,
37    0x405fc00000000000,
38    0x406fe00000000000,
39    0x407ff00000000000,
40    0x408ff80000000000,
41    0x409ffc0000000000,
42    0x40affe0000000000,
43    0x40bfff0000000000,
44    0x40cfff8000000000,
45    0x40dfffc000000000,
46    0x40efffe000000000,
47    0x40fffff000000000,
48    0x410ffff800000000,
49    0x411ffffc00000000,
50    0x412ffffe00000000,
51    0x413fffff00000000,
52    0x414fffff80000000,
53    0x415fffffc0000000,
54    0x416fffffe0000000,
55    0x417ffffff0000000,
56    0x418ffffff8000000,
57    0x419ffffffc000000,
58    0x41affffffe000000,
59    0x41bfffffff000000,
60    0x41cfffffff800000,
61    0x41dfffffffc00000,
62    0x41efffffffe00000,
63    0x41fffffffff00000,
64    0x420ffffffff80000,
65    0x421ffffffffc0000,
66    0x422ffffffffe0000,
67    0x423fffffffff0000,
68    0x424fffffffff8000,
69    0x425fffffffffc000,
70    0x426fffffffffe000,
71    0x427ffffffffff000,
72    0x428ffffffffff800,
73    0x429ffffffffffc00,
74    0x42affffffffffe00,
75    0x42bfffffffffff00,
76    0x42cfffffffffff80,
77    0x42dfffffffffffc0,
78    0x42efffffffffffe0,
79    0x42fffffffffffff0,
80    0x430ffffffffffff8,
81    0x431ffffffffffffc,
82    0x432ffffffffffffe,
83    0x433fffffffffffff,
84];
85
86/* For 362 <= i <= 724, r[i] = LOG2P1_INVERSE[i-362] is a 10-bit approximation of
871/x[i], where i*2^-9 <= x[i] < (i+1)*2^-9.
88More precisely r[i] is a 10-bit value such that r[i]*y-1 is representable
89exactly on 53 bits for any y, i*2^-9 <= y < (i+1)*2^-9.
90Moreover |r[i]*y-1| <= 0.00212097167968735. */
91
92pub(crate) static LOG2P1_INVERSE: [u64; 363] = [
93    0x3ff6980000000000,
94    0x3ff6880000000000,
95    0x3ff6780000000000,
96    0x3ff6680000000000,
97    0x3ff6580000000000,
98    0x3ff6480000000000,
99    0x3ff6380000000000,
100    0x3ff6300000000000,
101    0x3ff6200000000000,
102    0x3ff6100000000000,
103    0x3ff6000000000000,
104    0x3ff5f00000000000,
105    0x3ff5e00000000000,
106    0x3ff5d00000000000,
107    0x3ff5c00000000000,
108    0x3ff5b00000000000,
109    0x3ff5a80000000000,
110    0x3ff5980000000000,
111    0x3ff5880000000000,
112    0x3ff5780000000000,
113    0x3ff5680000000000,
114    0x3ff5600000000000,
115    0x3ff5500000000000,
116    0x3ff5400000000000,
117    0x3ff5300000000000,
118    0x3ff5200000000000,
119    0x3ff5180000000000,
120    0x3ff5080000000000,
121    0x3ff4f80000000000,
122    0x3ff4f00000000000,
123    0x3ff4e00000000000,
124    0x3ff4d00000000000,
125    0x3ff4c00000000000,
126    0x3ff4b80000000000,
127    0x3ff4a80000000000,
128    0x3ff4a00000000000,
129    0x3ff4900000000000,
130    0x3ff4800000000000,
131    0x3ff4780000000000,
132    0x3ff4680000000000,
133    0x3ff4580000000000,
134    0x3ff4500000000000,
135    0x3ff4400000000000,
136    0x3ff4300000000000,
137    0x3ff4280000000000,
138    0x3ff4180000000000,
139    0x3ff4100000000000,
140    0x3ff4000000000000,
141    0x3ff3f80000000000,
142    0x3ff3e80000000000,
143    0x3ff3e00000000000,
144    0x3ff3d00000000000,
145    0x3ff3c00000000000,
146    0x3ff3b80000000000,
147    0x3ff3a80000000000,
148    0x3ff3a00000000000,
149    0x3ff3900000000000,
150    0x3ff3880000000000,
151    0x3ff3780000000000,
152    0x3ff3700000000000,
153    0x3ff3600000000000,
154    0x3ff3580000000000,
155    0x3ff3500000000000,
156    0x3ff3400000000000,
157    0x3ff3380000000000,
158    0x3ff3280000000000,
159    0x3ff3200000000000,
160    0x3ff3100000000000,
161    0x3ff3080000000000,
162    0x3ff3000000000000,
163    0x3ff2f00000000000,
164    0x3ff2e80000000000,
165    0x3ff2d80000000000,
166    0x3ff2d00000000000,
167    0x3ff2c80000000000,
168    0x3ff2b80000000000,
169    0x3ff2b00000000000,
170    0x3ff2a00000000000,
171    0x3ff2980000000000,
172    0x3ff2900000000000,
173    0x3ff2800000000000,
174    0x3ff2780000000000,
175    0x3ff2700000000000,
176    0x3ff2600000000000,
177    0x3ff2580000000000,
178    0x3ff2500000000000,
179    0x3ff2400000000000,
180    0x3ff2380000000000,
181    0x3ff2300000000000,
182    0x3ff2280000000000,
183    0x3ff2180000000000,
184    0x3ff2100000000000,
185    0x3ff2080000000000,
186    0x3ff2000000000000,
187    0x3ff1f00000000000,
188    0x3ff1e80000000000,
189    0x3ff1e00000000000,
190    0x3ff1d00000000000,
191    0x3ff1c80000000000,
192    0x3ff1c00000000000,
193    0x3ff1b80000000000,
194    0x3ff1b00000000000,
195    0x3ff1a00000000000,
196    0x3ff1980000000000,
197    0x3ff1900000000000,
198    0x3ff1880000000000,
199    0x3ff1800000000000,
200    0x3ff1700000000000,
201    0x3ff1680000000000,
202    0x3ff1600000000000,
203    0x3ff1580000000000,
204    0x3ff1500000000000,
205    0x3ff1400000000000,
206    0x3ff1380000000000,
207    0x3ff1300000000000,
208    0x3ff1280000000000,
209    0x3ff1200000000000,
210    0x3ff1180000000000,
211    0x3ff1100000000000,
212    0x3ff1000000000000,
213    0x3ff0f80000000000,
214    0x3ff0f00000000000,
215    0x3ff0e80000000000,
216    0x3ff0e00000000000,
217    0x3ff0d80000000000,
218    0x3ff0d00000000000,
219    0x3ff0c80000000000,
220    0x3ff0c00000000000,
221    0x3ff0b00000000000,
222    0x3ff0a80000000000,
223    0x3ff0a00000000000,
224    0x3ff0980000000000,
225    0x3ff0900000000000,
226    0x3ff0880000000000,
227    0x3ff0800000000000,
228    0x3ff0780000000000,
229    0x3ff0700000000000,
230    0x3ff0680000000000,
231    0x3ff0600000000000,
232    0x3ff0580000000000,
233    0x3ff0500000000000,
234    0x3ff0480000000000,
235    0x3ff0400000000000,
236    0x3ff0380000000000,
237    0x3ff0300000000000,
238    0x3ff0280000000000,
239    0x3ff0200000000000,
240    0x3ff0180000000000,
241    0x3ff0100000000000,
242    0x3ff0080000000000,
243    0x3feff80000000000,
244    0x3fefe80000000000,
245    0x3fefd80000000000,
246    0x3fefc80000000000,
247    0x3fefb80000000000,
248    0x3fefa80000000000,
249    0x3fef980000000000,
250    0x3fef880000000000,
251    0x3fef780000000000,
252    0x3fef680000000000,
253    0x3fef580000000000,
254    0x3fef500000000000,
255    0x3fef400000000000,
256    0x3fef300000000000,
257    0x3fef200000000000,
258    0x3fef100000000000,
259    0x3fef000000000000,
260    0x3feef00000000000,
261    0x3feee00000000000,
262    0x3feed00000000000,
263    0x3feec80000000000,
264    0x3feeb80000000000,
265    0x3feea80000000000,
266    0x3fee980000000000,
267    0x3fee880000000000,
268    0x3fee780000000000,
269    0x3fee700000000000,
270    0x3fee600000000000,
271    0x3fee500000000000,
272    0x3fee400000000000,
273    0x3fee300000000000,
274    0x3fee280000000000,
275    0x3fee180000000000,
276    0x3fee080000000000,
277    0x3fedf80000000000,
278    0x3fedf00000000000,
279    0x3fede00000000000,
280    0x3fedd00000000000,
281    0x3fedc00000000000,
282    0x3fedb80000000000,
283    0x3feda80000000000,
284    0x3fed980000000000,
285    0x3fed900000000000,
286    0x3fed800000000000,
287    0x3fed700000000000,
288    0x3fed600000000000,
289    0x3fed580000000000,
290    0x3fed480000000000,
291    0x3fed380000000000,
292    0x3fed300000000000,
293    0x3fed200000000000,
294    0x3fed100000000000,
295    0x3fed080000000000,
296    0x3fecf80000000000,
297    0x3fece80000000000,
298    0x3fece00000000000,
299    0x3fecd00000000000,
300    0x3fecc80000000000,
301    0x3fecb80000000000,
302    0x3feca80000000000,
303    0x3feca00000000000,
304    0x3fec900000000000,
305    0x3fec880000000000,
306    0x3fec780000000000,
307    0x3fec680000000000,
308    0x3fec600000000000,
309    0x3fec500000000000,
310    0x3fec480000000000,
311    0x3fec380000000000,
312    0x3fec300000000000,
313    0x3fec200000000000,
314    0x3fec180000000000,
315    0x3fec080000000000,
316    0x3febf80000000000,
317    0x3febf00000000000,
318    0x3febe00000000000,
319    0x3febd80000000000,
320    0x3febc80000000000,
321    0x3febc00000000000,
322    0x3febb00000000000,
323    0x3feba80000000000,
324    0x3feb980000000000,
325    0x3feb900000000000,
326    0x3feb800000000000,
327    0x3feb780000000000,
328    0x3feb680000000000,
329    0x3feb600000000000,
330    0x3feb580000000000,
331    0x3feb480000000000,
332    0x3feb400000000000,
333    0x3feb300000000000,
334    0x3feb280000000000,
335    0x3feb180000000000,
336    0x3feb100000000000,
337    0x3feb000000000000,
338    0x3feaf80000000000,
339    0x3feaf00000000000,
340    0x3feae00000000000,
341    0x3fead80000000000,
342    0x3feac80000000000,
343    0x3feac00000000000,
344    0x3feab80000000000,
345    0x3feaa80000000000,
346    0x3feaa00000000000,
347    0x3fea900000000000,
348    0x3fea880000000000,
349    0x3fea800000000000,
350    0x3fea700000000000,
351    0x3fea680000000000,
352    0x3fea600000000000,
353    0x3fea500000000000,
354    0x3fea480000000000,
355    0x3fea400000000000,
356    0x3fea300000000000,
357    0x3fea280000000000,
358    0x3fea200000000000,
359    0x3fea100000000000,
360    0x3fea080000000000,
361    0x3fea000000000000,
362    0x3fe9f00000000000,
363    0x3fe9e80000000000,
364    0x3fe9e00000000000,
365    0x3fe9d00000000000,
366    0x3fe9c80000000000,
367    0x3fe9c00000000000,
368    0x3fe9b00000000000,
369    0x3fe9a80000000000,
370    0x3fe9a00000000000,
371    0x3fe9980000000000,
372    0x3fe9880000000000,
373    0x3fe9800000000000,
374    0x3fe9780000000000,
375    0x3fe9680000000000,
376    0x3fe9600000000000,
377    0x3fe9580000000000,
378    0x3fe9500000000000,
379    0x3fe9400000000000,
380    0x3fe9380000000000,
381    0x3fe9300000000000,
382    0x3fe9280000000000,
383    0x3fe9200000000000,
384    0x3fe9100000000000,
385    0x3fe9080000000000,
386    0x3fe9000000000000,
387    0x3fe8f80000000000,
388    0x3fe8e80000000000,
389    0x3fe8e00000000000,
390    0x3fe8d80000000000,
391    0x3fe8d00000000000,
392    0x3fe8c80000000000,
393    0x3fe8b80000000000,
394    0x3fe8b00000000000,
395    0x3fe8a80000000000,
396    0x3fe8a00000000000,
397    0x3fe8980000000000,
398    0x3fe8880000000000,
399    0x3fe8800000000000,
400    0x3fe8780000000000,
401    0x3fe8700000000000,
402    0x3fe8680000000000,
403    0x3fe8600000000000,
404    0x3fe8500000000000,
405    0x3fe8480000000000,
406    0x3fe8400000000000,
407    0x3fe8380000000000,
408    0x3fe8300000000000,
409    0x3fe8280000000000,
410    0x3fe8200000000000,
411    0x3fe8100000000000,
412    0x3fe8080000000000,
413    0x3fe8000000000000,
414    0x3fe7f80000000000,
415    0x3fe7f00000000000,
416    0x3fe7e80000000000,
417    0x3fe7e00000000000,
418    0x3fe7d80000000000,
419    0x3fe7c80000000000,
420    0x3fe7c00000000000,
421    0x3fe7b80000000000,
422    0x3fe7b00000000000,
423    0x3fe7a80000000000,
424    0x3fe7a00000000000,
425    0x3fe7980000000000,
426    0x3fe7900000000000,
427    0x3fe7880000000000,
428    0x3fe7800000000000,
429    0x3fe7780000000000,
430    0x3fe7700000000000,
431    0x3fe7600000000000,
432    0x3fe7580000000000,
433    0x3fe7500000000000,
434    0x3fe7480000000000,
435    0x3fe7400000000000,
436    0x3fe7380000000000,
437    0x3fe7300000000000,
438    0x3fe7280000000000,
439    0x3fe7200000000000,
440    0x3fe7180000000000,
441    0x3fe7100000000000,
442    0x3fe7080000000000,
443    0x3fe7000000000000,
444    0x3fe6f80000000000,
445    0x3fe6f00000000000,
446    0x3fe6e80000000000,
447    0x3fe6e00000000000,
448    0x3fe6d80000000000,
449    0x3fe6d00000000000,
450    0x3fe6c80000000000,
451    0x3fe6c00000000000,
452    0x3fe6b80000000000,
453    0x3fe6b00000000000,
454    0x3fe6a80000000000,
455    0x3fe6a00000000000,
456];
457
458pub(crate) static LOG2P1_LOG_DD_INVERSE: [(u64, u64); 363] = [
459    (0xbd13c7ca90bc04b2, 0xbfd615ddb4bec000),
460    (0xbd3527d18f7738fa, 0xbfd5e87b20c29000),
461    (0x3d339ae8f873fa41, 0xbfd5baf846aa2000),
462    (0xbd2791f30a795215, 0xbfd58d54f86e0000),
463    (0x3d11e64778df4a62, 0xbfd55f9107a44000),
464    (0xbd3df83b7d931501, 0xbfd531ac457ee000),
465    (0x3d2a68c8f16f9b5d, 0xbfd503a682cb2000),
466    (0xbd234d7aaf04d104, 0xbfd4ec9732600000),
467    (0x3d3d7c92cd9ad824, 0xbfd4be5f95778000),
468    (0x3d38bccffe1a0f8c, 0xbfd4900680401000),
469    (0x3d13d82f484c84cc, 0xbfd4618bc21c6000),
470    (0x3d3fb129931715ad, 0xbfd432ef2a04f000),
471    (0xbd3f8ef43049f7d3, 0xbfd404308686a000),
472    (0xbd3c3e1cd9a395e3, 0xbfd3d54fa5c1f000),
473    (0xbd37a71cbcd735d0, 0xbfd3a64c55694000),
474    (0x3d3e9436ac53b023, 0xbfd3772662bfe000),
475    (0x3d3b07de4ea1a54a, 0xbfd35f865c933000),
476    (0xbd36217dc2a3e08b, 0xbfd3302c16586000),
477    (0xbd342f568b75fcac, 0xbfd300aead063000),
478    (0xbd360c61f7088353, 0xbfd2d10dec508000),
479    (0x3d30dbbf51f3aadc, 0xbfd2a1499f763000),
480    (0xbd3a8d7ad24c13f0, 0xbfd2895a13de8000),
481    (0xbd38e7bc224ea3e3, 0xbfd2596010df7000),
482    (0x3d3a6976f5eb0963, 0xbfd22941fbcf8000),
483    (0xbd27946c040cbe77, 0xbfd1f8ff9e48a000),
484    (0x3d381410e5c62aff, 0xbfd1c898c169a000),
485    (0x3d32dd466dc55e2d, 0xbfd1b05791f08000),
486    (0x3d3a8a8ba74a2684, 0xbfd17fb98e151000),
487    (0x3d3e97a65dfc9794, 0xbfd14ef67f887000),
488    (0x3d3d3e8499d67123, 0xbfd136870293b000),
489    (0x3d34ab9d817d52cd, 0xbfd1058bf9ae5000),
490    (0xbd3d2c81f640e1e6, 0xbfd0d46b579ab000),
491    (0xbd0c6bee7ef4030e, 0xbfd0a324e2739000),
492    (0xbd3ebc1d40c5a329, 0xbfd08a73667c5000),
493    (0x3d30e866bcd236ad, 0xbfd058f3c703f000),
494    (0xbcf036b89ef42d7f, 0xbfd0402594b4d000),
495    (0xbcdcc68d52e01203, 0xbfd00e6c45ad5000),
496    (0x3d0d572aab993c87, 0xbfcfb9186d5e4000),
497    (0x3d3f75fd6a526efe, 0xbfcf871b28956000),
498    (0x3d3f454f1417e41f, 0xbfcf22e5e72f2000),
499    (0x3d23d45330fdca4d, 0xbfcebe61f4dd8000),
500    (0x3d26805b80e8e6ff, 0xbfce8c0252aa6000),
501    (0x3d3a342c2af0003c, 0xbfce27076e2b0000),
502    (0xbd38fac1a628ccc6, 0xbfcdc1bca0abe000),
503    (0x3d15105fc364c784, 0xbfcd8ef91af32000),
504    (0x3d383270128aaa5f, 0xbfcd293581b6c000),
505    (0xbd2771239a07d55b, 0xbfccf6354e09c000),
506    (0x3d27794f689f8434, 0xbfcc8ff7c79aa000),
507    (0xbd20929decb454fc, 0xbfcc5cba543ae000),
508    (0xbd2386a947c378b5, 0xbfcbf601bb0e4000),
509    (0xbd39ac53f39d121c, 0xbfcbc286742d8000),
510    (0x3d34b722ec011f31, 0xbfcb5b519e8fc000),
511    (0x3cba4e633fcd9066, 0xbfcaf3c94e80c000),
512    (0x3d3b68f5395f139d, 0xbfcabfe5ae462000),
513    (0xbd3b99c8ca1d9abb, 0xbfca57df28244000),
514    (0x3d3539cd91dc9f0b, 0xbfca23bc1fe2c000),
515    (0x3d21f2a8a1ce0ffc, 0xbfc9bb362e7e0000),
516    (0xbcf93b564dd44000, 0xbfc986d322818000),
517    (0xbd37bc6abddeff46, 0xbfc91dcc8c340000),
518    (0xbd3a8154b13d72d5, 0xbfc8e928de886000),
519    (0xbd322120401202fc, 0xbfc87fa06520c000),
520    (0x3d3d8daadf4e2bd2, 0xbfc84abb75866000),
521    (0x3d302a52f9201ce8, 0xbfc815c0a1436000),
522    (0x3d2bdb9072534a58, 0xbfc7ab890210e000),
523    (0xbd0274903479e3d1, 0xbfc7764c128f2000),
524    (0xbd34ea64f6a95bef, 0xbfc70b8f97a1a000),
525    (0x3d3bc6e557134767, 0xbfc6d60fe719e000),
526    (0xbd3aa1bdbfc6c785, 0xbfc66acd4272a000),
527    (0xbd2d5ec0ab8163af, 0xbfc6350a28aaa000),
528    (0x3d38586f183bebf2, 0xbfc5ff3070a7a000),
529    (0xbcf0ba68b7555d4a, 0xbfc59338d9982000),
530    (0xbd3add94dda647e8, 0xbfc55d1ad4232000),
531    (0x3d3e9bf2fafeaf27, 0xbfc4f099f4a24000),
532    (0x3d34354bb3f219e5, 0xbfc4ba36f39a6000),
533    (0xbd1eea52723f6369, 0xbfc483bccce6e000),
534    (0x3d210047081f849d, 0xbfc41682bf728000),
535    (0xbd28a72a62b8c13f, 0xbfc3dfc2b0ecc000),
536    (0xbd3ee8779b2d8abc, 0xbfc371fc201e8000),
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807    (0xbd3fc158cb3124b9, 0x3fd4f637ebbaa000),
808    (0xbd3a0e6b7e827c2c, 0x3fd50c6f1d11c000),
809    (0x3d2ebe708164c759, 0x3fd522ae0738a000),
810    (0x3d27ec02e45547ce, 0x3fd538f4af8f7000),
811    (0x3d1a8954c0910952, 0x3fd54f431b7be000),
812    (0x3d14c5fd2badc774, 0x3fd5659950695000),
813    (0x3d1fadedee5d40ef, 0x3fd57bf753c8d000),
814    (0xbd369bf5a7a56f34, 0x3fd5925d2b113000),
815    (0xbcf7c79b0af7ecf8, 0x3fd5a8cadbbee000),
816    (0xbd227023eb68981c, 0x3fd5bf406b544000),
817    (0xbd0a0b2a08a465dc, 0x3fd5d5bddf596000),
818    (0x3d36b71a1229d17f, 0x3fd5ec433d5c3000),
819    (0x3d1ebe9176df3f65, 0x3fd602d08af09000),
820    (0xbd2f08ad603c488e, 0x3fd61965cdb03000),
821    (0xbd2db623e731ae00, 0x3fd630030b3ab000),
822];
pxfm/logs/log2p1_tables.rs

pxfm/logs/
log2p1_tables.rs
