pxfm/logs/
log1p_dyadic_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 */
29use crate::dyadic_float::{DyadicFloat128, DyadicSign};
30
31// Logarithm range reduction - Step 3:
32//   s(k) = 2^-21 round( 2^21 / (1 + k*2^-21) ) - 1 for k = -69 .. 69
33// Output range:
34//   [-0x1.012bb800000800114p-22, 0x1p-22 ]
35pub(crate) static LOG1P_S3: [u64; 139] = [
36    0x3f01400000000000,
37    0x3f01000000000000,
38    0x3f00c00000000000,
39    0x3f00800000000000,
40    0x3f00400000000000,
41    0x3f00000000000000,
42    0x3eff800000000000,
43    0x3eff000000000000,
44    0x3efe800000000000,
45    0x3efe000000000000,
46    0x3efd800000000000,
47    0x3efd000000000000,
48    0x3efc800000000000,
49    0x3efc000000000000,
50    0x3efb800000000000,
51    0x3efb000000000000,
52    0x3efa800000000000,
53    0x3efa000000000000,
54    0x3ef9800000000000,
55    0x3ef9000000000000,
56    0x3ef8800000000000,
57    0x3ef8000000000000,
58    0x3ef7800000000000,
59    0x3ef7000000000000,
60    0x3ef6800000000000,
61    0x3ef6000000000000,
62    0x3ef5800000000000,
63    0x3ef5000000000000,
64    0x3ef4800000000000,
65    0x3ef4000000000000,
66    0x3ef3800000000000,
67    0x3ef3000000000000,
68    0x3ef2800000000000,
69    0x3ef2000000000000,
70    0x3ef1800000000000,
71    0x3ef1000000000000,
72    0x3ef0800000000000,
73    0x3ef0000000000000,
74    0x3eef000000000000,
75    0x3eee000000000000,
76    0x3eed000000000000,
77    0x3eec000000000000,
78    0x3eeb000000000000,
79    0x3eea000000000000,
80    0x3ee9000000000000,
81    0x3ee8000000000000,
82    0x3ee7000000000000,
83    0x3ee6000000000000,
84    0x3ee5000000000000,
85    0x3ee4000000000000,
86    0x3ee3000000000000,
87    0x3ee2000000000000,
88    0x3ee1000000000000,
89    0x3ee0000000000000,
90    0x3ede000000000000,
91    0x3edc000000000000,
92    0x3eda000000000000,
93    0x3ed8000000000000,
94    0x3ed6000000000000,
95    0x3ed4000000000000,
96    0x3ed2000000000000,
97    0x3ed0000000000000,
98    0x3ecc000000000000,
99    0x3ec8000000000000,
100    0x3ec4000000000000,
101    0x3ec0000000000000,
102    0x3eb8000000000000,
103    0x3eb0000000000000,
104    0x3ea0000000000000,
105    0x0000000000000000,
106    0xbea0000000000000,
107    0xbeb0000000000000,
108    0xbeb8000000000000,
109    0xbec0000000000000,
110    0xbec4000000000000,
111    0xbec8000000000000,
112    0xbecc000000000000,
113    0xbed0000000000000,
114    0xbed2000000000000,
115    0xbed4000000000000,
116    0xbed6000000000000,
117    0xbed8000000000000,
118    0xbeda000000000000,
119    0xbedc000000000000,
120    0xbede000000000000,
121    0xbee0000000000000,
122    0xbee1000000000000,
123    0xbee2000000000000,
124    0xbee3000000000000,
125    0xbee4000000000000,
126    0xbee5000000000000,
127    0xbee6000000000000,
128    0xbee7000000000000,
129    0xbee8000000000000,
130    0xbee9000000000000,
131    0xbeea000000000000,
132    0xbeeb000000000000,
133    0xbeec000000000000,
134    0xbeed000000000000,
135    0xbeee000000000000,
136    0xbeef000000000000,
137    0xbef0000000000000,
138    0xbef0800000000000,
139    0xbef1000000000000,
140    0xbef1800000000000,
141    0xbef2000000000000,
142    0xbef2800000000000,
143    0xbef3000000000000,
144    0xbef3800000000000,
145    0xbef4000000000000,
146    0xbef4800000000000,
147    0xbef5000000000000,
148    0xbef5800000000000,
149    0xbef6000000000000,
150    0xbef6800000000000,
151    0xbef7000000000000,
152    0xbef7800000000000,
153    0xbef8000000000000,
154    0xbef8800000000000,
155    0xbef9000000000000,
156    0xbef9800000000000,
157    0xbefa000000000000,
158    0xbefa800000000000,
159    0xbefb000000000000,
160    0xbefb800000000000,
161    0xbefc000000000000,
162    0xbefc800000000000,
163    0xbefd000000000000,
164    0xbefd800000000000,
165    0xbefe000000000000,
166    0xbefe800000000000,
167    0xbeff000000000000,
168    0xbeff800000000000,
169    0xbf00000000000000,
170    0xbf00400000000000,
171    0xbf00800000000000,
172    0xbf00c00000000000,
173    0xbf01000000000000,
174    0xbf01400000000000,
175];
176
177// Logarithm range reduction - Step 2:
178//   s(k) = 2^-18 round( 2^18 / (1 + k*2^-14) ) - 1 for k = -91 .. 96
179// Output range:
180//   [-0x1.1037c00000040271p-15 , 0x1.108480000008096cp-15]
181pub(crate) static LOG1P_S2: [u64; 188] = [
182    0x3f76e00000000000,
183    0x3f76a00000000000,
184    0x3f76600000000000,
185    0x3f76200000000000,
186    0x3f75dc0000000000,
187    0x3f759c0000000000,
188    0x3f755c0000000000,
189    0x3f751c0000000000,
190    0x3f74dc0000000000,
191    0x3f749c0000000000,
192    0x3f74580000000000,
193    0x3f74180000000000,
194    0x3f73d80000000000,
195    0x3f73980000000000,
196    0x3f73580000000000,
197    0x3f73180000000000,
198    0x3f72d80000000000,
199    0x3f72940000000000,
200    0x3f72540000000000,
201    0x3f72140000000000,
202    0x3f71d40000000000,
203    0x3f71940000000000,
204    0x3f71540000000000,
205    0x3f71140000000000,
206    0x3f70d00000000000,
207    0x3f70900000000000,
208    0x3f70500000000000,
209    0x3f70100000000000,
210    0x3f6fa00000000000,
211    0x3f6f200000000000,
212    0x3f6ea00000000000,
213    0x3f6e200000000000,
214    0x3f6d980000000000,
215    0x3f6d180000000000,
216    0x3f6c980000000000,
217    0x3f6c180000000000,
218    0x3f6b980000000000,
219    0x3f6b180000000000,
220    0x3f6a980000000000,
221    0x3f6a180000000000,
222    0x3f69980000000000,
223    0x3f69100000000000,
224    0x3f68900000000000,
225    0x3f68100000000000,
226    0x3f67900000000000,
227    0x3f67100000000000,
228    0x3f66900000000000,
229    0x3f66100000000000,
230    0x3f65900000000000,
231    0x3f65100000000000,
232    0x3f64900000000000,
233    0x3f64100000000000,
234    0x3f63880000000000,
235    0x3f63080000000000,
236    0x3f62880000000000,
237    0x3f62080000000000,
238    0x3f61880000000000,
239    0x3f61080000000000,
240    0x3f60880000000000,
241    0x3f60080000000000,
242    0x3f5f100000000000,
243    0x3f5e100000000000,
244    0x3f5d100000000000,
245    0x3f5c100000000000,
246    0x3f5b100000000000,
247    0x3f5a100000000000,
248    0x3f59100000000000,
249    0x3f58100000000000,
250    0x3f57100000000000,
251    0x3f56000000000000,
252    0x3f55000000000000,
253    0x3f54000000000000,
254    0x3f53000000000000,
255    0x3f52000000000000,
256    0x3f51000000000000,
257    0x3f50000000000000,
258    0x3f4e000000000000,
259    0x3f4c000000000000,
260    0x3f4a000000000000,
261    0x3f48000000000000,
262    0x3f46000000000000,
263    0x3f44000000000000,
264    0x3f42000000000000,
265    0x3f40000000000000,
266    0x3f3c000000000000,
267    0x3f38000000000000,
268    0x3f34000000000000,
269    0x3f30000000000000,
270    0x3f28000000000000,
271    0x3f20000000000000,
272    0x3f10000000000000,
273    0x0000000000000000,
274    0xbf10000000000000,
275    0xbf20000000000000,
276    0xbf28000000000000,
277    0xbf30000000000000,
278    0xbf34000000000000,
279    0xbf38000000000000,
280    0xbf3c000000000000,
281    0xbf40000000000000,
282    0xbf42000000000000,
283    0xbf44000000000000,
284    0xbf46000000000000,
285    0xbf48000000000000,
286    0xbf4a000000000000,
287    0xbf4c000000000000,
288    0xbf4e000000000000,
289    0xbf50000000000000,
290    0xbf51000000000000,
291    0xbf52000000000000,
292    0xbf53000000000000,
293    0xbf54000000000000,
294    0xbf55000000000000,
295    0xbf56000000000000,
296    0xbf56f00000000000,
297    0xbf57f00000000000,
298    0xbf58f00000000000,
299    0xbf59f00000000000,
300    0xbf5af00000000000,
301    0xbf5bf00000000000,
302    0xbf5cf00000000000,
303    0xbf5df00000000000,
304    0xbf5ef00000000000,
305    0xbf5ff00000000000,
306    0xbf60780000000000,
307    0xbf60f80000000000,
308    0xbf61780000000000,
309    0xbf61f80000000000,
310    0xbf62780000000000,
311    0xbf62f80000000000,
312    0xbf63780000000000,
313    0xbf63f00000000000,
314    0xbf64700000000000,
315    0xbf64f00000000000,
316    0xbf65700000000000,
317    0xbf65f00000000000,
318    0xbf66700000000000,
319    0xbf66f00000000000,
320    0xbf67700000000000,
321    0xbf67f00000000000,
322    0xbf68700000000000,
323    0xbf68f00000000000,
324    0xbf69680000000000,
325    0xbf69e80000000000,
326    0xbf6a680000000000,
327    0xbf6ae80000000000,
328    0xbf6b680000000000,
329    0xbf6be80000000000,
330    0xbf6c680000000000,
331    0xbf6ce80000000000,
332    0xbf6d680000000000,
333    0xbf6de00000000000,
334    0xbf6e600000000000,
335    0xbf6ee00000000000,
336    0xbf6f600000000000,
337    0xbf6fe00000000000,
338    0xbf70300000000000,
339    0xbf70700000000000,
340    0xbf70b00000000000,
341    0xbf70f00000000000,
342    0xbf712c0000000000,
343    0xbf716c0000000000,
344    0xbf71ac0000000000,
345    0xbf71ec0000000000,
346    0xbf722c0000000000,
347    0xbf726c0000000000,
348    0xbf72ac0000000000,
349    0xbf72e80000000000,
350    0xbf73280000000000,
351    0xbf73680000000000,
352    0xbf73a80000000000,
353    0xbf73e80000000000,
354    0xbf74280000000000,
355    0xbf74640000000000,
356    0xbf74a40000000000,
357    0xbf74e40000000000,
358    0xbf75240000000000,
359    0xbf75640000000000,
360    0xbf75a40000000000,
361    0xbf75e00000000000,
362    0xbf76200000000000,
363    0xbf76600000000000,
364    0xbf76a00000000000,
365    0xbf76e00000000000,
366    0xbf77200000000000,
367    0xbf775c0000000000,
368    0xbf779c0000000000,
369    0xbf77dc0000000000,
370];
371
372//def format_hex(value):
373//     l = hex(value)[2:]
374//     n = 8
375//     x = [l[i:i + n] for i in range(0, len(l), n)]
376//     return "0x" + "_".join(x) + "_u128"
377// for i in range(129):
378//     r = 2^-8 * round( 2^8 / (1 + i*2^(-7)) );
379//     s, m, e = RealField(128)(r).log().sign_mantissa_exponent();
380//     print("DyadicFloat {sign: DyadicDyadicSign::Pos, exponent: ", e, ",mantissa:", format_hex(m), "},");
381#[rustfmt::skip]
382pub(crate) static LOG1P_R1: [DyadicFloat128; 129] = [
383DyadicFloat128 {sign: DyadicSign::Pos,exponent: 0,   mantissa: 0_u128},
384DyadicFloat128 {sign: DyadicSign::Pos,exponent: -134,mantissa: 0x8080abac_46f38946_662d417c_ed007a46_u128},
385DyadicFloat128 {sign: DyadicSign::Pos,exponent: -133,mantissa: 0x8102b2c4_9ac23a4f_91d082dc_e3ddcd38_u128},
386DyadicFloat128 {sign: DyadicSign::Pos,exponent: -133,mantissa: 0xc2492946_4655f45c_da5f3cc0_b3251dbd_u128},
387DyadicFloat128 {sign: DyadicSign::Pos,exponent: -132,mantissa: 0x820aec4f_3a222380_b9e3aea6_c444ef07_u128},
388DyadicFloat128 {sign: DyadicSign::Pos,exponent: -132,mantissa: 0xa33576a1_6f1f4c64_521016bd_904dc968_u128},
389DyadicFloat128 {sign: DyadicSign::Pos,exponent: -132,mantissa: 0xb3e4a796_a5dac208_27cca0bc_c06c2f92_u128},
390DyadicFloat128 {sign: DyadicSign::Pos,exponent: -132,mantissa: 0xd5779687_d887e0d1_a9dda170_56e45ed5_u128},
391DyadicFloat128 {sign: DyadicSign::Pos,exponent: -132,mantissa: 0xf7518e00_35c3dd83_606d8909_3278a939_u128},
392DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0x8cb9de8a_32ab368a_a7c98595_30a45153_u128},
393DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0x9defad3e_8f73217a_976d3b5b_45f6ca0b_u128},
394DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xa6988ae9_03f562ed_3e858f08_597b3a69_u128},
395DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xb8069857_560707a3_6a677b4c_8bec22e1_u128},
396DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xc99af2ea_ca4c4570_eaf51f66_692844ba_u128},
397DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xd273b205_8de1bd49_46bbf837_b4d320c6_u128},
398DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xe442c00d_e2591b47_196ab34c_e0bccd12_u128},
399DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xed393b1c_22351280_3f4e2e66_0317d55f_u128},
400DyadicFloat128 {sign: DyadicSign::Pos,exponent: -131,mantissa: 0xff4489ce_deab2ca6_c17bd40d_8d9291ec_u128},
401DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0x88bc7411_3f23def1_9c5a0fe3_96f40f1e_u128},
402DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0x8d515bf1_1fb94f1c_88713268_840cbcc0_u128},
403DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0x968b0864_3409ceb6_65c0da50_6a088484_u128},
404DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0x9b2fe580_ac80b17d_411a5b94_4aca8708_u128},
405DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xa489ec19_9dab06f2_a9fb6cf0_ecb411b7_u128},
406DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xa93f2f25_0dac67d1_cad2fb8d_48054ae0_u128},
407DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xadfa035a_a1ed8fdc_149767e4_10316d2c_u128},
408DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xb780945b_ab55dce4_34c7bc3d_32750fde_u128},
409DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xbc4c6c2a_226399ef_8f6ebcfb_2016a439_u128},
410DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xc5f57f59_c7f46155_aa8b6997_a402bf30_u128},
411DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xcad2d6e7_b80bf914_2c507fb7_a3d0bf6a_u128},
412DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xcfb62038_44b3209a_d0cb02f3_3f79c16c_u128},
413DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xd98ec2ba_de71e539_58a98f2a_d65bee9b_u128},
414DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xde8439c1_dec56877_4d57da94_5b5d0aaa_u128},
415DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xe37fde37_807b84e3_4e9a750b_6b68781d_u128},
416DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xe881bf93_2af3dac0_c524848e_3443e040_u128},
417DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xf29877ff_38809091_3b020fa1_820c9492_u128},
418DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xf7ad6f26_e7ff2ef7_54d2238f_75f969b1_u128},
419DyadicFloat128 {sign: DyadicSign::Pos,exponent: -130,mantissa: 0xfcc8e365_9d9bcbec_ca0cdf30_1431b60f_u128},
420DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x80f572b1_363487b9_f5bd0b5b_3479d5f4_u128},
421DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x86216b3b_0b17188b_163ceae8_8f720f1e_u128},
422DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x88bc7411_3f23def1_9c5a0fe3_96f40f1e_u128},
423DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x8b5ae65d_67db9acd_f7a51681_26a58b9a_u128},
424DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x8dfccb1a_d35ca6ed_5147bdb6_ddcaf59c_u128},
425DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x90a22b68_75c6a1f7_ae91aeba_609c8877_u128},
426DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x934b1089_a6dc93c1_df5bb3b6_0554e152_u128},
427DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x95f783e6_e49a9cfa_4a5004f3_ef063313_u128},
428DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x9b5b3bb5_f088b766_d878bbe3_d392be25_u128},
429DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0x9e1293b9_998c1daa_5b035eae_273a855f_u128},
430DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xa0cda11e_af46390d_bb243827_3918db7e_u128},
431DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xa38c6e13_8e20d831_f698298a_dddd7f32_u128},
432DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xa64f04f0_b961df76_e4f5275c_2d15c21f_u128},
433DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xa9157039_c51ebe70_8164c759_686a2209_u128},
434DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xabdfba9e_468fd6f6_f72ea077_49ce6bd3_u128},
435DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xaeadeefa_caf97d35_7dd6e688_ebb13b03_u128},
436DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xb1801859_d56249dc_18ce51ff_f99479cd_u128},
437DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xb45641f4_e350a0d3_2756eba0_0bc33978_u128},
438DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xb7307735_78cb90b2_be1116c3_466beb6d_u128},
439DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xba0ec3b6_33dd8b09_49dc60b2_b059a60b_u128},
440DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xbcf13343_e7d9ec7d_2efd1778_1bb3afec_u128},
441DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xbfd7d1de_c0a8df6f_37eda996_244bccb0_u128},
442DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xc2c2abbb_6e5fd56f_33337789_d592e296_u128},
443DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xc5b1cd44_596fa51e_1a18fb8f_9f9ef280_u128},
444DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xc8a5431a_dfb44ca5_688ce7c1_a75e341a_u128},
445DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xcb9d1a18_9ab56e76_2d7e9307_c70c0668_u128},
446DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xcb9d1a18_9ab56e76_2d7e9307_c70c0668_u128},
447DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xce995f50_af69d861_ef2f3f4f_861ad6a9_u128},
448DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xd19a2011_27d3c645_7f9d79f5_1dcc7301_u128},
449DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xd49f69e4_56cf1b79_5f53bd2e_406e66e7_u128},
450DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xd7a94a92_466e833a_ad88bba7_d0cee8e0_u128},
451DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xdab7d022_31484a92_96c20cca_6efe2ac5_u128},
452DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xddcb08dc_0717d85b_f40a666c_87842843_u128},
453DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xe0e30349_fd1cec80_7fe8e180_2aba24d6_u128},
454DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xe0e30349_fd1cec80_7fe8e180_2aba24d6_u128},
455DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xe3ffce3a_2aa64922_3eadb651_b49ac53a_u128},
456DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xe72178c0_323a1a0f_304e1653_e71d9973_u128},
457DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xea481236_f7d35baf_e9a767a8_0d6d97e8_u128},
458DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xed73aa42_64b0ade9_4f91cf4b_33e42998_u128},
459DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xed73aa42_64b0ade9_4f91cf4b_33e42998_u128},
460DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xf0a450d1_39366ca6_fc66eb64_08ff6433_u128},
461DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xf3da161e_ed6b9aaf_ac8d42f7_8d3e65d3_u128},
462DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xf7150ab5_a09f27f4_5a470250_d40ebe90_u128},
463DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xf7150ab5_a09f27f4_5a470250_d40ebe90_u128},
464DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xfa553f70_18c966f2_b780a545_a1b54dcf_u128},
465DyadicFloat128 {sign: DyadicSign::Pos,exponent: -129,mantissa: 0xfd9ac57b_d244217e_8f05924d_258c14c5_u128},
466DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8072d72d_903d588b_89d1b09c_70c4010a_u128},
467DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8072d72d_903d588b_89d1b09c_70c4010a_u128},
468DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x821b05f3_b01d6774_030d58c3_f7e2ea1f_u128},
469DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x83c5f829_9e2b4091_20f6fafe_8fbb68b9_u128},
470DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8573b716_82a7d21a_e21f9f89_c1ab80b2_u128},
471DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8573b716_82a7d21a_e21f9f89_c1ab80b2_u128},
472DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x87244c30_8e670a66_01e005d0_6dbfa8f8_u128},
473DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x88d7c11e_3ad53cdc_223111a7_07b6de2c_u128},
474DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x88d7c11e_3ad53cdc_223111a7_07b6de2c_u128},
475DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8a8e1fb7_94b09134_2eb628db_a173c82d_u128},
476DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8c477207_91e53313_be2ad194_15fe25a5_u128},
477DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8c477207_91e53313_be2ad194_15fe25a5_u128},
478DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8e03c24d_73003959_bddae1cc_ce247838_u128},
479DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8fc31afe_30b2c6de_9b00bf16_7e95da67_u128},
480DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x8fc31afe_30b2c6de_9b00bf16_7e95da67_u128},
481DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x918586c5_f5e4bf01_9b92199e_d1a4bab1_u128},
482DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x934b1089_a6dc93c1_df5bb3b6_0554e152_u128},
483DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x934b1089_a6dc93c1_df5bb3b6_0554e152_u128},
484DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9513c368_76083695_f3cbc416_a2418012_u128},
485DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x96dfaabd_86fa1646_be1188fb_c94e2f15_u128},
486DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x96dfaabd_86fa1646_be1188fb_c94e2f15_u128},
487DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x98aed221_a03458b6_1d2f8932_1647b358_u128},
488DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x98aed221_a03458b6_1d2f8932_1647b358_u128},
489DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9a81456c_ec642e0f_e549f9aa_ea3cb5e1_u128},
490DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9c5710b8_cbb73a42_a2554b2d_d4619e63_u128},
491DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9c5710b8_cbb73a42_a2554b2d_d4619e63_u128},
492DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9e304061_b5fda919_30603d87_b6df81ad_u128},
493DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0x9e304061_b5fda919_30603d87_b6df81ad_u128},
494DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa00ce109_2e5498c3_67879c5a_30cd1242_u128},
495DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa00ce109_2e5498c3_67879c5a_30cd1242_u128},
496DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa1ecff97_c91e267b_0b7efae0_8e597e16_u128},
497DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa3d0a93f_45169a4a_83594fab_088c0d65_u128},
498DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa3d0a93f_45169a4a_83594fab_088c0d65_u128},
499DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa5b7eb7c_b860fb88_af6a62a0_dec6e073_u128},
500DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa5b7eb7c_b860fb88_af6a62a0_dec6e073_u128},
501DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa7a2d41a_d270c9d7_49362382_a768847a_u128},
502DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa7a2d41a_d270c9d7_49362382_a768847a_u128},
503DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa9917134_33c2b998_8ba4aea6_14d05701_u128},
504DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xa9917134_33c2b998_8ba4aea6_14d05701_u128},
505DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xab83d135_dc633301_7fe6607b_a902ef3c_u128},
506DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xab83d135_dc633301_7fe6607b_a902ef3c_u128},
507DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xad7a02e1_b24efd31_d60864fd_949b4bd3_u128},
508DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xad7a02e1_b24efd31_d60864fd_949b4bd3_u128},
509DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xaf741551_20c9011c_066d235e_e63073dd_u128},
510DyadicFloat128 {sign: DyadicSign::Pos,exponent: -128,mantissa: 0xaf741551_20c9011c_066d235e_e63073dd_u128},
511DyadicFloat128 {sign: DyadicSign::Pos,exponent: 0,   mantissa: 0_u128}
512];
513
514// -log(r) for the second step, generated by SageMath with:
515// def format_hex(value):
516//     l = hex(value)[2:]
517//     n = 8
518//     x = [l[i:i + n] for i in range(0, len(l), n)]
519//     return "0x" + "_".join(x) + "_u128"
520// for i in range(-91, 97):
521//   r = 2^-18 * round( 2^18 / (1 + i*2^(-14)) );
522//   s, m, e = RealField(128)(r).log().sign_mantissa_exponent();
523//   print("{sign: DyadicDyadicSign::Pos," if (s == -1) else "{sign: DyadicDyadicSign::Neg, exponent: ", e, ", mantissa: "
524//         format_hex(m), "},");
525#[rustfmt::skip]
526pub(crate) static LOG1P_R2: [DyadicFloat128; 188] = [
527    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xb67dab2a_1a5742a4_a0e061c5_f7431c5e_u128},
528    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xb4807f24_af682939_5d5bfe7b_969ed6ec_u128},
529    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xb2834b35_b4d54d5f_4d08702d_dfabc23f_u128},
530    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xb0860f5c_eba9be95_d4d36650_8b9953df_u128},
531    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xae68f71a_a09e8847_ac18a289_f8f214a9_u128},
532    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xac6baaee_d676e8f1_d5b42054_abb88c45_u128},
533    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xaa6e56d8_7cd632d6_09809d58_ee484964_u128},
534    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xa870fad7_54bb8791_b9e6fc7c_72f06d73_u128},
535    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xa67396eb_1f231892_6f78d6d0_105c00e2_u128},
536    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xa4762b13_9d0626e7_028f7126_29209148_u128},
537    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xa258dfd1_0aedaa67_c98d898e_f172df02_u128},
538    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0xa05b63a3_73e60a83_fcc37c3c_3062bfa1_u128},
539    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x9e5ddf89_cf42f501_3eb450db_05763c36_u128},
540    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x9c605383_ddf1b88c_7146a86f_d458b775_u128},
541    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x9a62bf91_60dcb286_c20a0c92_81474436_u128},
542    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x986523b2_18eb4ed6_cdc57316_ec4aebc3_u128},
543    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x96677fe5_c70207b9_c060dad7_4cef4273_u128},
544    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x9449f92d_2ff44633_ed8def1a_3e433499_u128},
545    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x924c4507_3220b5e0_3ce7a1f8_5c27b4fc_u128},
546    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x904e88f3_68fea63f_f2ca8934_49f7f2cb_u128},
547    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x8e50c4f1_956699ed_8d77d9fa_bd2853cf_u128},
548    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x8c52f901_782e20ec_93e828d7_5b58ded4_u128},
549    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x8a552522_d227d87a_9f9605b0_53c5acf0_u128},
550    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x88574955_64236ae0_62a14939_3bca7241_u128},
551    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x86398719_b66bac7c_aea6b56c_e89203d4_u128},
552    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x843b9aef_044e4dcc_0242bd86_d00609b2_u128},
553    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x823da6d4_c89c6927_daabf927_74bac84e_u128},
554    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -135, mantissa: 0x803faaca_c419abf2_a1c6f3fc_242ef8d0_u128},
555    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xfc834da1_6f0d9f57_a225ebc0_2e6d9dd4_u128},
556    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xf88735cc_c7433381_c33f6ad3_40ae18a9_u128},
557    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xf48b0e17_1249b6bc_70b2a4d3_8a242244_u128},
558    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xf08ed67f_d190e280_1d548190_48b811b0_u128},
559    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xec52ca07_ed95f236_9c21b650_afe9ede0_u128},
560    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xe85671ad_ecd28aac_935519c9_6d30e463_u128},
561    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xe45a0970_dc912ca7_ba88f6f2_e2672cfe_u128},
562    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xe05d9150_3e298bc8_0b1a8b84_657ae069_u128},
563    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xdc61094b_92ed70ef_ea3bff8d_197b20a1_u128},
564    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xd8647162_5c28b9e5_cdbb931d_6fecc249_u128},
565    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xd467c994_1b2158f5_d971d560_d5f00820_u128},
566    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xd06b11e0_51175493_75563561_244c090b_u128},
567    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xcc6e4a46_7f44c6fa_dc393c9a_3f3b380f_u128},
568    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xc831a4c6_f6fa709d_e6abe6e9_e4ee2096_u128},
569    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xc434bc61_24a0f16e_3ce3c822_8583a66e_u128},
570    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xc037c413_c61bfd93_b96a79f5_c5a4963a_u128},
571    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xbc3abbde_5c8d9bde_aaef2733_7008679f_u128},
572    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xb83da3c0_6911e509_a49a3fca_ddc8bc5a_u128},
573    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xb4407bb9_6cbf035a_e0254feb_785362fa_u128},
574    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xb04343c8_e8a53245_9893a4e2_5ab9dc95_u128},
575    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xac45fbee_5dcebe0b_5d8b0f40_a3708915_u128},
576    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xa848a429_4d40035d_5f4c11c2_c7a58c69_u128},
577    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xa44b3c79_37f76efd_b348cc5d_f706ffba_u128},
578    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0xa04dc4dd_9eed7d60_9159f2c5_5a18befd_u128},
579    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x9c106456_3058bef3_bdfdee41_fe6a5a02_u128},
580    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x9812cbe3_46475a24_4580ddf8_9853254d_u128},
581    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x94152383_53489ffb_ac75e10d_61fc3ee8_u128},
582    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x90176b35_d83ce8e2_cad9b30b_29736155_u128},
583    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x8c19a2fa_55fe9b14_6f881deb_98fc45f3_u128},
584    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x881bcad0_4d622a3e_70a04b63_b7248c96_u128},
585    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x841de2b7_3f361722_b4823fb4_8035eddd_u128},
586    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -136, mantissa: 0x801feaae_ac42ef38_3364ccb5_b13cd47f_u128},
587    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xf843c56c_2a969897_e306977b_049f0ad5_u128},
588    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xf0479599_f617a843_e3c4d9e9_619bc045_u128},
589    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xe84b45e5_bc76702c_4356d525_b5e6432d_u128},
590    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xe04ed64e_7f14697a_7839dcd7_989339ab_u128},
591    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xd85246d3_3f47230b_4e21f045_ecb76f23_u128},
592    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xd0559772_fe5840b0_902e248d_d4ba9b28_u128},
593    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xc858c82c_bd857a72_a4444906_7ef92e01_u128},
594    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xc05bd8ff_7e009bd2_17926207_cc22e4e6_u128},
595    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xb85ec9ea_40ef8309_1c349622_f3fa5d82_u128},
596    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xafe1c6ec_e1a058dd_97fa2fd0_c9dc723e_u128},
597    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0xa7e47606_048b1a65_983e8089_7cf1e60f_u128},
598    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0x9fe70534_1d236102_7199cd06_ae5d39b3_u128},
599    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0x97e97476_2c5e8f58_43cd18a7_2a051a96_u128},
600    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0x8febc3cb_332616ff_7b6d1248_c3e1fd40_u128},
601    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -137, mantissa: 0x87edf332_325777c5_f5572a88_14c703af_u128},
602    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xffe00554_55887de0_26828c92_649a3a39_u128},
603    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xefe3e464_3a640cf3_82c550bd_1216d82a_u128},
604    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xdfe78392_14b4e8ae_da6959f7_f0e01bf0_u128},
605    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xcfeae2db_e5d6736d_da93e2fa_85a8f214_u128},
606    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xbfee023f_af0c2480_b47505bf_a5a03b06_u128},
607    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0xaff0e1bb_718186ad_b1475a51_80a43520_u128},
608    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0x9ff3814d_2e4a36b2_a8740b91_c95df537_u128},
609    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -138, mantissa: 0x8ff5e0f2_e661e1c6_57d895d3_5921b59c_u128},
610    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -139, mantissa: 0xfff00155_35588833_3c56c598_c659c2a3_u128},
611    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -139, mantissa: 0xdff3c0e4_97ea4eb1_2ef8ec33_ed9d782a_u128},
612    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -139, mantissa: 0xbff7008f_f5e0c257_379eba7e_6465ff63_u128},
613    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -139, mantissa: 0x9ff9c053_5073a370_3f972b78_3fcab757_u128},
614    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -140, mantissa: 0xfff80055_51558885_de026e27_1ee0549d_u128},
615    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -140, mantissa: 0xbffb8023_febc0c25_eceb47ea_01f6c632_u128},
616    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -141, mantissa: 0xfffc0015_54d55888_7333c578_57e1ed52_u128},
617    DyadicFloat128 { sign: DyadicSign::Neg, exponent: -142, mantissa: 0xfffe0005_55455588_87dde026_fa704374_u128},
618    DyadicFloat128 { sign: DyadicSign::Pos, exponent: 0,    mantissa: 0_u128},
619    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -141, mantissa: 0x80010002_aab2aac4_44999abe_2fe2cc65_u128},
620    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -140, mantissa: 0x8002000a_aaeaac44_4eef3815_81464ccb_u128},
621    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -140, mantissa: 0xc0048024_01440c26_dfeb4850_85f6f454_u128},
622    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -139, mantissa: 0x8004002a_acaac445_99abe3be_3a1c6e93_u128},
623    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -139, mantissa: 0xa0064053_5a37a37a_6bc1e20e_ac8448b4_u128},
624    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -139, mantissa: 0xc0090090_0a20c275_979eedc0_64c242fd_u128},
625    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -139, mantissa: 0xe00c40e4_bd6e4efd_c72446cc_1bf728bd_u128},
626    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0x800800aa_baac446e_f381b821_bbb569e5_u128},
627    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0x900a20f3_19a3e273_569b26aa_a485ea5c_u128},
628    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xa00c814d_7c6a37f8_2dcf56c8_3c80b028_u128},
629    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xb00f21bb_e3e388ee_5f697682_84463b9b_u128},
630    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xc0120240_510c284c_b48ea6c0_5e2773a1_u128},
631    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xd01522dc_c4f87991_14d9d761_96d8043a_u128},
632    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xe0188393_40d4f241_e016a611_a4415d72_u128},
633    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -138, mantissa: 0xf01c2465_c5e61b6f_661e135f_49a47c40_u128},
634    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0x801002ab_2ac4499a_be6bf0fa_435e8383_u128},
635    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0x88121333_7898871e_9a31ba0c_bc030353_u128},
636    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0x901443cc_cd362c9f_54b57dfe_0c4c840f_u128},
637    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0x98169478_296fad41_7ad1e9c3_15328f7e_u128},
638    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xa0190536_8e2389b3_1f3f686c_f3d6be22_u128},
639    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xa81b9608_fc3c50ec_f105b66e_c4703ede_u128},
640    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xb01e46f0_74b0a0f3_610848c6_8df4d233_u128},
641    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xb7a0e9ed_7613acb0_2e0efddf_33a20464_u128},
642    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xbfa3d900_8e042ffb_c2cdb3c7_50f127b4_u128},
643    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xc7a6e82b_a36a7073_bd953378_6d3f4c49_u128},
644    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xcfaa176f_b76c8eb1_82e237c9_a4d450e3_u128},
645    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xd7ad66cd_cb3cbe14_c00b46a4_d0e3dfd0_u128},
646    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xdfb0d646_e0194584_ea999c0d_f8546710_u128},
647    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xe7b465db_f74c8032_cec6c2a9_ad974f4f_u128},
648    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xefb8158e_122cde5a_2d2045da_1570a07c_u128},
649    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xf7bbe55e_321ce603_6752e9b2_381e3edc_u128},
650    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -137, mantissa: 0xffbfd54d_588b33c5_3c1ed527_28e00e40_u128},
651    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x83e1f2ae_43793dc3_493b0d87_3fb9a340_u128},
652    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x87e40ac6_5f6cc4a0_29e38750_c9d26893_u128},
653    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x8be632ef_80e9a0df_aab9e832_7258ac3f_u128},
654    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x8fe86b2a_28bf51b3_28bc403d_8a5f3c63_u128},
655    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x93eab376_d7c36377_f720c1c9_7227fcdc_u128},
656    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x97ed0bd6_0ed17018_6ad9a3e3_d11b66c1_u128},
657    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x9bef7448_4ecb1f6c_edb27b79_c90b4019_u128},
658    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0x9fb1c4cd_27012e19_a092a0d7_ab21722a_u128},
659    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xa3b44c65_b71c2d85_535d52f0_939a4d02_u128},
660    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xa7b6e412_cadcb3dc_90a57e11_edc1864e_u128},
661    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xabb98bd4_e33c4381_68e9c901_60031159_u128},
662    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xafbc43ac_813a6ea3_bf60594f_929adeb8_u128},
663    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xb3bf0b9a_25dcd7a2_8a421588_86775205_u128},
664    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xb7c1e39e_522f316d_1ab45417_663dee9e_u128},
665    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xbbc4cbb9_87433fe4_6c51ae3c_e1aea68a_u128},
666    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xbfc7c3ec_4630d83c_7c52ae8b_40ebabb7_u128},
667    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xc3cacc37_1015e15d_a857126f_7cfaaa67_u128},
668    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xc7cde49a_66165446_14d05662_cd29464a_u128},
669    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xcb90da16_44d29bb7_8379db06_ef3cd6bb_u128},
670    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xcf9411aa_99ddb7de_9025f4c6_7dd38bb6_u128},
671    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xd3975958_f681086d_d6f8a61c_892032ee_u128},
672    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xd79ab121_dbf8714c_9a2f20b4_e2332d47_u128},
673    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xdb9e1905_cb85ea59_3c767d61_f51d375b_u128},
674    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xdfa19105_46717fca_d4b2bd65_bb25493c_u128},
675    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xe3a51920_ce095292_c96c1254_a30ef91f_u128},
676    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xe7a8b158_e3a198be_73e324ce_0946b214_u128},
677    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xebac59ae_08949dd8_cacd125a_12bac62c_u128},
678    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xef6fd620_b2b7a503_cafdc272_27b71eaa_u128},
679    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xf3739daf_959aaafc_688d4282_f6026aa3_u128},
680    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xf777755d_03f4e0b6_e54e9e38_04464cdd_u128},
681    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xfb7b5d29_7f388a12_cb78b383_f4b59dce_u128},
682    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -136, mantissa: 0xff7f5515_88de024f_ee055fc5_15062c04_u128},
683    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x81c1ae90_d131de38_207812b4_3382acdd_u128},
684    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x83c3baa7_26a721cc_dc90c4c4_b61f3a87_u128},
685    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x85c5cece_05941dbc_1a03f13f_b2c978b1_u128},
686    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x87c7eb05_aec1304f_b36f282e_83a7dc36_u128},
687    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x89a9eccd_56a980c0_d82a4661_6d4c393f_u128},
688    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x8bac18a6_40185360_bc6ff847_13c9babd_u128},
689    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x8dae4c90_b22574f4_9f7942a5_16fc2d8a_u128},
690    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x8fb0888c_eda546ab_15e50cfd_9b29b427_u128},
691    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x91b2cc9b_336f3718_9f465296_ae7dd49a_u128},
692    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x93b518bb_c45dc268_b49c1eb9_b348e6e4_u128},
693    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x95b76cee_e14e728e_daa320cd_64c9d9c7_u128},
694    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x9799a333_de49b963_75a91950_ffe1e3b5_u128},
695    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x999c070b_a32068cd_5c6abcbf_43f03f14_u128},
696    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x9b9e72f6_b295ad4f_5a9e7f26_5d1ed157_u128},
697    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x9da0e6f5_4d9318fd_efeb98d0_2a195c17_u128},
698    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0x9fa36307_b5054ca8_2aa503a3_110ab5a7_u128},
699    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xa1a5e72e_29dbf808_d0fe7e05_869eb825_u128},
700    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xa3884a68_a750cb10_e80a28f4_e1e500d2_u128},
701    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xa58ade36_aeef9f0b_53106415_1ca6e30b_u128},
702    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xa78d7a19_82c4b08f_27c01ffa_8e2e3c4b_u128},
703    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xa9901e11_63cbbbf5_7ba9408d_c857d568_u128},
704    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xab92ca1e_93038d76_104d1e33_31d3b4fa_u128},
705    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xad957e41_516e0158_9343c846_fcdf9137_u128},
706    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xaf780e79_b2514889_3977e89a_ec59bfa2_u128},
707    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xb17ad246_ef3713bc_913d4e3d_c55c3e6e_u128},
708    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xb37d9e2a_7a56b09d_777b52a9_e70d8bcc_u128},
709    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xb5807224_94be0c91_55de916f_d30591de_u128},
710    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xb7834e35_7f7e2600_e79cfb37_be2861e4_u128},
711    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xb986325d_7bab0c89_90983104_d3805389_u128},
712    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xbb68ef9c_254aa378_59e3b2ec_71ce64f4_u128},
713    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xbd6be371_8c77636f_e83183bf_3dd612ef_u128},
714    DyadicFloat128 { sign: DyadicSign::Pos, exponent: -135, mantissa: 0xbf6edf5e_c44d9d35_c4e3b0ac_2fd52b7f_u128},
715];
716
717// -log(r) for the third step, generated by SageMath with:
718//
719// for i in range(-69, 70):
720//   r = 2^-21 * round( 2^21 / (1 + i*2^(-21)) );
721//   s, m, e = RealField(128)(r).log().sign_mantissa_exponent();
722//   print("{sign: DyadicDyadicSign::Pos," if (s == -1) else "{sign: DyadicDyadicSign::Neg, exponent: ", e, ", mantissa:"
723//         format_hex(m), "},");
724#[rustfmt::skip]
725pub(crate) static LOGP1_R3: [DyadicFloat128; 139] =[
726   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -142, mantissa: 0x89ff6b38_d5de2622_e39d3faf_42340ed7_u128},
727   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -142, mantissa: 0x87ff6f80_ccb40f16_7ff33266_82c02485_u128},
728   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -142, mantissa: 0x85ff73b8_c3cdf731_5caf4fbe_343cf928_u128},
729   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -142, mantissa: 0x83ff77e0_bb2ade79_cdb6e554_348f7fe8_u128},
730   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -142, mantissa: 0x81ff7bf8_b2c9c4f6_0ef009c2_457de25d_u128},
731   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xffff0001_55535558_8883333c_57b57c74_u128},
732   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xfbff07f1_45931f44_f32668f3_9c70d183_u128},
733   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xf7ff0fc1_3650e7bd_459a73c6_a6486fe3_u128},
734   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xf3ff1771_278aaecd_37b18cca_7dd3a29f_u128},
735   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xefff1f01_193e7480_513f610d_21bcfc78_u128},
736   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xebff2671_0b6a38e1_ea190b95_c0690b7b_u128},
737   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xe7ff2dc0_fe0bfbfd_2a150f64_f0ad1743_u128},
738   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xe3ff34f0_f121bddd_090b5174_e995e9d1_u128},
739   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xdfff3c00_e4a97e8c_4ed512b9_b93ea2bf_u128},
740   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xdbff42f0_d8a13e15_934cea21_7ab794a2_u128},
741   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xd7ff49c0_cd06fc83_3e4ebe94_8afd2c76_u128},
742   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xd3ff5070_c1d8b9df_87b7c0f5_bcfee2e1_u128},
743   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xcfff5700_b7147634_77666622_8cb6371b_u128},
744   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xcbff5d70_acb8318b_e53a60f3_514db358_u128},
745   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xc7ff63c0_a2c1ebef_79149c3b_6e57fa86_u128},
746   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xc3ff69f0_992fa568_aad734c9_8416df2a_u128},
747   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xbfff7000_8fff5e00_c2657367_9ed28334_u128},
748   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xbbff75f0_872f15c0_d7a3c6db_6540809f_u128},
749   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xb7ff7bc0_7ebcccb1_d277bde6_45fb1aad_u128},
750   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xb3ff8170_76a682dc_6ac80145_a4087793_u128},
751   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xafff8700_6eea3849_287c4db3_0271e265_u128},
752   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xabff8c70_6785ed00_637d6de4_2eeb151e_u128},
753   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xa7ff91c0_6077a10a_43b5348b_6b898a8c_u128},
754   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0xa3ff96f0_59bd546e_c10e7657_978bd7f6_u128},
755   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x9fff9c00_53550735_a37503f4_57310e59_u128},
756   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x9bffa0f0_4d3cb966_82d5a40a_3aa022ff_u128},
757   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x97ffa5c0_47726b08_c71e0d3e_e3df5f4d_u128},
758   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x93ffaa70_41f41c23_a83ce035_2bdbd79b_u128},
759   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x8fffaf00_3cbfccbe_2e21a18d_4680e8e4_u128},
760   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x8bffb370_37d37cdf_30bcb3e4_e5dfbd28_u128},
761   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x87ffb7c0_332d2c8d_57ff51d7_5c66d64a_u128},
762   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -143, mantissa: 0x83ffbbf0_2ecadbcf_1bdb87fd_be299f43_u128},
763   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xffff8000_55551555_88885dde_02700703_u128},
764   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xf7ff87e0_4d94724c_d259ca80_3a0c1870_u128},
765   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xefff8f80_464fce8f_e5141308_51c7070a_u128},
766   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xe7ff96e0_3f832a2a_30a16898_f3073a64_u128},
767   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xdfff9e00_392a8526_c4ed6451_7b2949ce_u128},
768   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xd7ffa4e0_3341df90_51e4fb4e_32cf6350_u128},
769   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xcfffab80_2dc53971_277672a8_8350bcce_u128},
770   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xc7ffb1e0_28b092d3_35915377_2a490f06_u128},
771   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xbfffb800_23ffebc0_0c265ece_6b481a0e_u128},
772   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xb7ffbde0_1faf4440_db2781c0_3fa132f6_u128},
773   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xafffc380_1bba9c5e_7287c95c_845ada33_u128},
774   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0xa7ffc8e0_181df421_423b56b1_263e5a77_u128},
775   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0x9fffce00_14d54b91_5a3752ca_4c076fa3_u128},
776   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0x97ffd2e0_11dca2b6_6a71e2b2_7eb3f573_u128},
777   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0x8fffd780_0f2ff997_c2e21b72_cff39d8f_u128},
778   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -144, mantissa: 0x87ffdbe0_0ccb503c_537ff612_feb7ac9e_u128},
779   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xffffc000_15554d55_58888733_33c57c18_u128},
780   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xefffc7c0_1193f9d1_fa514218_42311c42_u128},
781   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xdfffcf00_0e4aa5fa_2c4ed6de_475b942c_u128},
782   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xcfffd5c0_0b7151d8_ce77678c_bb6fcb88_u128},
783   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xbfffdc00_08fffd78_00c26629_a679ed3b_u128},
784   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0xafffe1c0_06eea8e1_23287cb9_d3072728_u128},
785   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0x9fffe700_0535541c_d5a37540_fd057315_u128},
786   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -145, mantissa: 0x8fffebc0_03cbff32_f82e21c1_fce36810_u128},
787   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -146, mantissa: 0xffffe000_05555455_5588887d_dde02702_u128},
788   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -146, mantissa: 0xdfffe780_0392aa14_9ac4ed72_adf5b295_u128},
789   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -146, mantissa: 0xbfffee00_023fffaf_000c2664_8066b482_u128},
790   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -146, mantissa: 0x9ffff380_014d552e_455a3754_b292c077_u128},
791   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -147, mantissa: 0xfffff000_01555535_55588888_33333c58_u128},
792   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -147, mantissa: 0xbffff700_008ffff5_e000c266_5736679f_u128},
793   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -148, mantissa: 0xfffff800_00555551_55558888_85ddde02_u128},
794   DyadicFloat128 {sign: DyadicSign::Neg, exponent: -149, mantissa: 0xfffffc00_00155554_d5555888_88733334_u128},
795   DyadicFloat128 {sign: DyadicSign::Pos, exponent: 0,    mantissa: 0_u128},
796   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -148, mantissa: 0x80000200_000aaaaa_eaaaac44_444eeeef_u128},
797   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -147, mantissa: 0x80000400_002aaaac_aaaac444_459999ac_u128},
798   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -147, mantissa: 0xc0000900_0090000a_2000c266_7596679f_u128},
799   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -146, mantissa: 0x80000800_00aaaaba_aaac4444_6eeef381_u128},
800   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -146, mantissa: 0xa0000c80_014d557c_655a3755_f81815cc_u128},
801   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -146, mantissa: 0xc0001200_02400051_000c2668_4c66b482_u128},
802   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -146, mantissa: 0xe0001880_0392ab40_bac4ed7c_40fb07eb_u128},
803   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0x80001000_02aaab2a_aac44449_999abe2c_u128},
804   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0x90001440_03cc00cd_082e21d7_9cbb6812_u128},
805   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xa0001900_0535568d_d5a37569_adb01dc3_u128},
806   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xb0001e40_06eeac74_33287d01_e8c9d1d9_u128},
807   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xc0002400_09000288_00c266a3_2679ed48_u128},
808   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xd0002a40_0b7158d1_de776851_22b2764b_u128},
809   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xe0003100_0e4aaf5b_2c4ed810_a8063f03_u128},
810   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -145, mantissa: 0xf0003840_1194062e_0a5143e7_be891c8f_u128},
811   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0x80002000_0aaaaeaa_ac4444ee_ef3813a1_u128},
812   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0x88002420_0ccb5a6e_5b7ff7fe_1339025b_u128},
813   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0x90002880_0f300668_42e21e26_caf39e33_u128},
814   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0x98002d20_11dcb29e_f271e66f_a5554bc6_u128},
815   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xa0003200_14d55f19_5a3757e0_615cc676_u128},
816   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xa8003720_181e0bde_ca3b5d82_10ca5cab_u128},
817   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xb0003c80_1bbab8f6_f287d25f_3cb032bb_u128},
818   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xb8004220_1faf6669_e3278d84_0be28cdb_u128},
819   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xc0004800_24001440_0c266dfe_6b482076_u128},
820   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xc8004e20_28b0c282_3d9166de_380a6d3d_u128},
821   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xd0005480_2dc57139_a7768b35_6ba61e4b_u128},
822   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xd8005b20_3342206f_d9e51a18_49db73c1_u128},
823   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xe0006200_392ad02e_c4ed8a9d_907eb521_u128},
824   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xe8006920_3f838080_b8a197de_a928acd7_u128},
825   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xf0007080_46503170_65144cf7_dcc72d3b_u128},
826   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -144, mantissa: 0xf8007820_4d94e308_da5a1108_890d9f6a_u128},
827   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x80004000_2aaacaaa_c4445999_abe2ce2c_u128},
828   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x84004410_2ecb2431_1fdbbb4f_3bffc832_u128},
829   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x88004840_332d7e1d_97ff8f39_ec91b4ee_u128},
830   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x8c004c90_37d3d876_74bcfcf0_b3f0a95d_u128},
831   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x90005100_3cc03342_2e21f80c_a6813aff_u128},
832   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x94005590_41f48e87_6c3d4629_170ce87f_u128},
833   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x98005a40_4772ea4d_071e84e3_b80a8881_u128},
834   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0x9c005f10_4d3d469a_06d62fdc_bdd6bec3_u128},
835   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xa0006400_5355a375_a375a6b7_01dc77c0_u128},
836   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xa4006910_59be00e7_450f3318_26ad6b05_u128},
837   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xa8006e40_60785ef6_83b60ea8_bd0aa459_u128},
838   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xac007390_6786bdab_277e6914_69dd13f5_u128},
839   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xb0007900_6eeb1d0d_287d6e0a_0d1e25eb_u128},
840   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xb4007e90_76a77d24_aec94b3b_e9b060f5_u128},
841   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xb8008440_7ebdddfa_1279365f_ce280cce_u128},
842   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xbc008a10_87303f95_dba5732f_3e83e04a_u128},
843   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xc0009000_9000a200_c2675967_9ed5b754_u128},
844   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xc4009610_99310543_aed95aca_5edb5109_u128},
845   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xc8009c40_a2c36967_b917091d_2687160f_u128},
846   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xcc00a290_acb9ce76_293d1c2a_0378e75d_u128},
847   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xd000a900_b7163478_776977bf_9766f5a7_u128},
848   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xd400af90_c1da9b78_4bbb31b1_4776a18b_u128},
849   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xd800b640_cd09037f_7e5297d7_6c8564ba_u128},
850   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xdc00bd10_d8a36c98_1751360f_8461c447_u128},
851   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xe000c400_e4abd6cc_4ed9dc3c_63f44c41_u128},
852   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xe400cb10_f1244226_8d10a446_6a5894d5_u128},
853   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xe800d240_fe0eaeb1_6a1af81b_b4e6510e_u128},
854   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xec00d991_0b6d1c77_ae1f97b0_542a677a_u128},
855   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xf000e101_19418b84_51469efe_81d014cc_u128},
856   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xf400e891_278dfbe2_7bb98c06_d77a18b4_u128},
857   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xf800f041_36546d9d_85a344d0_868bed17_u128},
858   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -143, mantissa: 0xfc00f811_4596e0c0_f7301d69_90e307cc_u128},
859   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x80008000_aaabaaac_4446eef3_8140138f_u128},
860   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x82008408_b2cbe5b8_10f5e432_96105497_u128},
861   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x84008820_bb2d2189_edbd4f83_ef63f730_u128},
862   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x86008c48_c3d05e27_feb654fd_541c638e_u128},
863   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x88009080_ccb69b98_7ffadeb8_882f7674_u128},
864   DyadicFloat128 {sign: DyadicSign::Pos, exponent: -142, mantissa: 0x8a0094c8_d5e0d9e1_c5a59fd3_6bd44397_u128},
865];
pxfm/logs/log1p_dyadic_tables.rs

pxfm/logs/
log1p_dyadic_tables.rs
