summaryrefslogtreecommitdiff
path: root/lib/math/log-overkill.myr
blob: 6c7448657d1574b5367e97bcc773c25b35355212 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
use std

use "fpmath"
use "impls"
use "util"

/*
   This is an implementation of log(x) using the following idea, based on [Tan90]

     First, reduce to 2^e · xs, with xs ∈ [1, 2).

     xs = F1 + f1, with
       F1 = 1 + j1/2^5
       j1 ∈ {1, 2, …, 2^5 - 1}
       f1 ∈ [0, 2^-5)

     log(xs) = log(F1) + log(1 + f1/F1)

     1 + f1/F1 = F2 + f2, with
       F2 = 1 + j1/2^10
       j2 ∈ {1, 2, …, 2^5 - 1}
       f2 ∈ [0, 2^-10)

     log(xs) = log(F1) + log(F2) + log(1 + f2/F2)

     …

     log(xs) = log(F1) + log(F2) + log(F3) + log(F4) + log(1 + f4/F4)

     And f4/F4 < 2^-20, so we can get 100 bits of precision using a
     degree 5 polynomial.

     The specific choice of using 4 tables, each with 2^5 entries, may
     be improvable. It's a trade-off between storage for the tables and
     the number of floating point operations to chain the results
     together.
 */
pkg math =
	pkglocal const logoverkill32 : (x : flt32 -> (flt32, flt32))
	pkglocal const logoverkill64 : (x : flt64 -> (flt64, flt64))
;;



/*
   Ci is a table such that, for Ci[j] = (L1, L2, I1, I2),
     L1, L2 are log(1 + j·2^-(5i))
     I1, I2 are 1/(1 + j·2^-(5i))
 */
const C1 : (uint64, uint64, uint64, uint64)[32] = [
	(000000000000000000, 000000000000000000,     0x3ff0000000000000, 000000000000000000), /* j = 0 */
	(0x3f9f829b0e783300, 0x3c333e3f04f1ef23,     0x3fef07c1f07c1f08, 0xbc7f07c1f07c1f08), /* j = 1 */
	(0x3faf0a30c01162a6, 0x3c485f325c5bbacd,     0x3fee1e1e1e1e1e1e, 0x3c6e1e1e1e1e1e1e), /* j = 2 */
	(0x3fb6f0d28ae56b4c, 0xbc5906d99184b992,     0x3fed41d41d41d41d, 0x3c80750750750750), /* j = 3 */
	(0x3fbe27076e2af2e6, 0xbc361578001e0162,     0x3fec71c71c71c71c, 0x3c8c71c71c71c71c), /* j = 4 */
	(0x3fc29552f81ff523, 0x3c6301771c407dbf,     0x3febacf914c1bad0, 0xbc8bacf914c1bad0), /* j = 5 */
	(0x3fc5ff3070a793d4, 0xbc5bc60efafc6f6e,     0x3feaf286bca1af28, 0x3c8af286bca1af28), /* j = 6 */
	(0x3fc9525a9cf456b4, 0x3c6d904c1d4e2e26,     0x3fea41a41a41a41a, 0x3c80690690690690), /* j = 7 */
	(0x3fcc8ff7c79a9a22, 0xbc64f689f8434012,     0x3fe999999999999a, 0xbc8999999999999a), /* j = 8 */
	(0x3fcfb9186d5e3e2b, 0xbc6caaae64f21acb,     0x3fe8f9c18f9c18fa, 0xbc7f3831f3831f38), /* j = 9 */
	(0x3fd1675cababa60e, 0x3c2ce63eab883717,     0x3fe8618618618618, 0x3c88618618618618), /* j = 10 */
	(0x3fd2e8e2bae11d31, 0xbc78f4cdb95ebdf9,     0x3fe7d05f417d05f4, 0x3c67d05f417d05f4), /* j = 11 */
	(0x3fd4618bc21c5ec2, 0x3c7f42decdeccf1d,     0x3fe745d1745d1746, 0xbc7745d1745d1746), /* j = 12 */
	(0x3fd5d1bdbf5809ca, 0x3c74236383dc7fe1,     0x3fe6c16c16c16c17, 0xbc7f49f49f49f49f), /* j = 13 */
	(0x3fd739d7f6bbd007, 0xbc78c76ceb014b04,     0x3fe642c8590b2164, 0x3c7642c8590b2164), /* j = 14 */
	(0x3fd89a3386c1425b, 0xbc729639dfbbf0fb,     0x3fe5c9882b931057, 0x3c7310572620ae4c), /* j = 15 */
	(0x3fd9f323ecbf984c, 0xbc4a92e513217f5c,     0x3fe5555555555555, 0x3c85555555555555), /* j = 16 */
	(0x3fdb44f77bcc8f63, 0xbc7cd04495459c78,     0x3fe4e5e0a72f0539, 0x3c8e0a72f0539783), /* j = 17 */
	(0x3fdc8ff7c79a9a22, 0xbc74f689f8434012,     0x3fe47ae147ae147b, 0xbc6eb851eb851eb8), /* j = 18 */
	(0x3fddd46a04c1c4a1, 0xbc70467656d8b892,     0x3fe4141414141414, 0x3c64141414141414), /* j = 19 */
	(0x3fdf128f5faf06ed, 0xbc7328df13bb38c3,     0x3fe3b13b13b13b14, 0xbc83b13b13b13b14), /* j = 20 */
	(0x3fe02552a5a5d0ff, 0xbc7cb1cb51408c00,     0x3fe3521cfb2b78c1, 0x3c7a90e7d95bc60a), /* j = 21 */
	(0x3fe0be72e4252a83, 0xbc8259da11330801,     0x3fe2f684bda12f68, 0x3c82f684bda12f68), /* j = 22 */
	(0x3fe154c3d2f4d5ea, 0xbc859c33171a6876,     0x3fe29e4129e4129e, 0x3c804a7904a7904a), /* j = 23 */
	(0x3fe1e85f5e7040d0, 0x3c7ef62cd2f9f1e3,     0x3fe2492492492492, 0x3c82492492492492), /* j = 24 */
	(0x3fe2795e1289b11b, 0xbc6487c0c246978e,     0x3fe1f7047dc11f70, 0x3c81f7047dc11f70), /* j = 25 */
	(0x3fe307d7334f10be, 0x3c6fb590a1f566da,     0x3fe1a7b9611a7b96, 0x3c61a7b9611a7b96), /* j = 26 */
	(0x3fe393e0d3562a1a, 0xbc858eef67f2483a,     0x3fe15b1e5f75270d, 0x3c415b1e5f75270d), /* j = 27 */
	(0x3fe41d8fe84672ae, 0x3c89192f30bd1806,     0x3fe1111111111111, 0x3c61111111111111), /* j = 28 */
	(0x3fe4a4f85db03ebb, 0x3c313dfa3d3761b6,     0x3fe0c9714fbcda3b, 0xbc7f79b47582192e), /* j = 29 */
	(0x3fe52a2d265bc5ab, 0xbc61883750ea4d0a,     0x3fe0842108421084, 0x3c70842108421084), /* j = 30 */
	(0x3fe5ad404c359f2d, 0xbc435955683f7196,     0x3fe0410410410410, 0x3c80410410410410), /* j = 31 */
]

const C2 : (uint64, uint64, uint64, uint64)[32] = [
	(000000000000000000, 000000000000000000,     0x3ff0000000000000, 000000000000000000), /* j = 0 */
	(0x3f4ffc00aa8ab110, 0xbbe0fecbeb9b6cdb,     0x3feff801ff801ff8, 0x3c2ff801ff801ff8), /* j = 1 */
	(0x3f5ff802a9ab10e6, 0x3bfe29e3a153e3b2,     0x3feff007fc01ff00, 0x3c8ff007fc01ff00), /* j = 2 */
	(0x3f67f7047d7983da, 0x3c0a275a19204e80,     0x3fefe811f28a186e, 0xbc849093915301bf), /* j = 3 */
	(0x3f6ff00aa2b10bc0, 0x3c02821ad5a6d353,     0x3fefe01fe01fe020, 0xbc6fe01fe01fe020), /* j = 4 */
	(0x3f73f38a60f06489, 0x3c1693c937494046,     0x3fefd831c1cdbed1, 0x3c8e89d3b75ace7e), /* j = 5 */
	(0x3f77ee11ebd82e94, 0xbc161e96e2fc5d90,     0x3fefd04794a10e6a, 0x3c881bd63ea20ced), /* j = 6 */
	(0x3f7be79c70058ec9, 0xbbd964fefef02b62,     0x3fefc86155aa1659, 0xbc6b8fc468497f61), /* j = 7 */
	(0x3f7fe02a6b106789, 0xbbce44b7e3711ebf,     0x3fefc07f01fc07f0, 0x3c6fc07f01fc07f0), /* j = 8 */
	(0x3f81ebde2d1997e6, 0xbbfffa46e1b2ec81,     0x3fefb8a096acfacc, 0xbc82962e18495af3), /* j = 9 */
	(0x3f83e7295d25a7d9, 0xbbeff29a11443a06,     0x3fefb0c610d5e939, 0xbc5cb8337f41db5c), /* j = 10 */
	(0x3f85e1f703ecbe50, 0x3c23eb0bb43693b9,     0x3fefa8ef6d92aca5, 0x3c7cd0c1eaba7f22), /* j = 11 */
	(0x3f87dc475f810a77, 0xbc116d7687d3df21,     0x3fefa11caa01fa12, 0xbc7aaff02f71aaff), /* j = 12 */
	(0x3f89d61aadc6bd8d, 0xbc239b097b525947,     0x3fef994dc3455e8d, 0xbc82546d9bc5bd59), /* j = 13 */
	(0x3f8bcf712c74384c, 0xbc1f6842688f499a,     0x3fef9182b6813baf, 0x3c6b210c54d70f4a), /* j = 14 */
	(0x3f8dc84b19123815, 0xbc25f0e2d267d821,     0x3fef89bb80dcc421, 0xbc8e7da8c7156f9d), /* j = 15 */
	(0x3f8fc0a8b0fc03e4, 0xbc183092c59642a1,     0x3fef81f81f81f820, 0xbc8f81f81f81f820), /* j = 16 */
	(0x3f90dc4518afcc88, 0xbc379c0189fdfe78,     0x3fef7a388f9da20f, 0x3c7f99b2c82d3fb1), /* j = 17 */
	(0x3f91d7f7eb9eebe7, 0xbc2d41fe63d2dbf9,     0x3fef727cce5f530a, 0x3c84643cedd1cfd9), /* j = 18 */
	(0x3f92d36cefb557c3, 0xbc132fa3e4f20cf7,     0x3fef6ac4d8f95f7a, 0x3c8e8ed9770a8dde), /* j = 19 */
	(0x3f93cea44346a575, 0xbc10cb5a902b3a1c,     0x3fef6310aca0dbb5, 0x3c8d2e19807d8c43), /* j = 20 */
	(0x3f94c99e04901ded, 0xbc2cd10505ada0d6,     0x3fef5b60468d989f, 0xbc805a26b4cad717), /* j = 21 */
	(0x3f95c45a51b8d389, 0xbc3b10b6c3ec21b4,     0x3fef53b3a3fa204e, 0x3c8450467c5430f3), /* j = 22 */
	(0x3f96bed948d1b7d1, 0xbc1058290fde6de1,     0x3fef4c0ac223b2bc, 0x3c815c2df7afcd24), /* j = 23 */
	(0x3f97b91b07d5b11b, 0xbc35b602ace3a510,     0x3fef44659e4a4271, 0x3c85fc17734c36b8), /* j = 24 */
	(0x3f98b31faca9b00e, 0x3c1d5a46da6f6772,     0x3fef3cc435b0713c, 0x3c81d0a7e69ea094), /* j = 25 */
	(0x3f99ace7551cc514, 0x3c33409c1df8167f,     0x3fef3526859b8cec, 0x3c2f3526859b8cec), /* j = 26 */
	(0x3f9aa6721ee835aa, 0xbc24a3a50b6c5621,     0x3fef2d8c8b538c0f, 0xbc88a987ac35964a), /* j = 27 */
	(0x3f9b9fc027af9198, 0xbbf0ae69229dc868,     0x3fef25f644230ab5, 0x3c594ed8175c78b3), /* j = 28 */
	(0x3f9c98d18d00c814, 0xbc250589df0f25bf,     0x3fef1e63ad57473c, 0xbc8bf54d8dbc6a00), /* j = 29 */
	(0x3f9d91a66c543cc4, 0xbc1d34e608cbdaab,     0x3fef16d4c4401f17, 0xbc759ddff074959e), /* j = 30 */
	(0x3f9e8a3ee30cdcac, 0x3c07086b1c00b395,     0x3fef0f4986300ba6, 0xbc811b6b7ee8766a), /* j = 31 */
]

const C3 : (uint64, uint64, uint64, uint64)[32] = [
	(000000000000000000, 000000000000000000,     0x3ff0000000000000, 000000000000000000), /* j = 0 */
	(0x3effffe0002aaa6b, 0xbb953bbbe6661d42,     0x3fefffc0007fff00, 0x3c2fffc0007fff00), /* j = 1 */
	(0x3f0fffc000aaa8ab, 0xbba3bbc110fec82c,     0x3fefff8001fff800, 0x3c6fff8001fff800), /* j = 2 */
	(0x3f17ffb8011ffaf0, 0x3b984c534f3d9b6a,     0x3fefff40047fe501, 0xbc8780f2fa4e222b), /* j = 3 */
	(0x3f1fff8002aa9aab, 0x3b910e6678af0afc,     0x3fefff0007ffc002, 0xbbdfff0007ffc002), /* j = 4 */
	(0x3f23ff9c029a9723, 0x3bc1b965303b23b1,     0x3feffec00c7f8305, 0xbc6e30d217cb1211), /* j = 5 */
	(0x3f27ff70047fd782, 0xbbced098a5c0aff0,     0x3feffe8011ff280a, 0x3c6f8685b1bbab34), /* j = 6 */
	(0x3f2bff3c07250a51, 0xbbc89dd6d6bad8c1,     0x3feffe40187ea913, 0xbc7f8346d2208239), /* j = 7 */
	(0x3f2fff000aaa2ab1, 0x3ba0bbc04dc4e3dc,     0x3feffe001ffe0020, 0xbc2ffe001ffe0020), /* j = 8 */
	(0x3f31ff5e07979982, 0xbbce0e704817ebcd,     0x3feffdc0287d2733, 0x3c7f32ce6d7c4d43), /* j = 9 */
	(0x3f33ff380a6a0e74, 0x3bdb81fcb95bc1fe,     0x3feffd8031fc184e, 0x3c69e5fa087756ad), /* j = 10 */
	(0x3f35ff0e0ddc70a1, 0x3bacf6f3d97a3c05,     0x3feffd403c7acd72, 0x3c860b1b0bacff22), /* j = 11 */
	(0x3f37fee011febc18, 0x3bd2b9bcf5d3f323,     0x3feffd0047f940a2, 0xbc5e5d274451985a), /* j = 12 */
	(0x3f39feae16e0ec8b, 0xbbb6137aceeb34b1,     0x3feffcc054776bdf, 0x3c56b1b1f3ed39e8), /* j = 13 */
	(0x3f3bfe781c92fd4a, 0xbbc4ed10713cc126,     0x3feffc8061f5492c, 0xbc19fd284f974b74), /* j = 14 */
	(0x3f3dfe3e2324e946, 0x3bc0916462dd5deb,     0x3feffc407072d28b, 0x3c84eb0c748a57ca), /* j = 15 */
	(0x3f3ffe002aa6ab11, 0x3b999e2b62cc632d,     0x3feffc007ff00200, 0xbc7ffc007ff00200), /* j = 16 */
	(0x3f40fedf19941e6e, 0xbbb194c2e0aa6338,     0x3feffbc0906cd18c, 0x3c75b11e79f3cd9f), /* j = 17 */
	(0x3f41febc1e5ccc3c, 0x3bdc657d895d3592,     0x3feffb80a1e93b34, 0xbc84d11299626e29), /* j = 18 */
	(0x3f42fe9723b55bac, 0x3bd6cfb73e538464,     0x3feffb40b46538fa, 0xbc8d42a81b0bfc39), /* j = 19 */
	(0x3f43fe7029a5c947, 0xbbd4d578bf46e36a,     0x3feffb00c7e0c4e1, 0x3c7e673fde054f2c), /* j = 20 */
	(0x3f44fe4730361165, 0x3be400d77e93f2fd,     0x3feffac0dc5bd8ee, 0x3c8a38b2b2aeaf57), /* j = 21 */
	(0x3f45fe1c376e3031, 0xbbd524eb8a5ae7f6,     0x3feffa80f1d66f25, 0xbc6a5778f73582ce), /* j = 22 */
	(0x3f46fdef3f5621a3, 0xbbdf09d734886d52,     0x3feffa4108508189, 0xbc81a45478d24a37), /* j = 23 */
	(0x3f47fdc047f5e185, 0xbbebfa5c57d202d3,     0x3feffa011fca0a1e, 0x3c6a5b0eed338657), /* j = 24 */
	(0x3f48fd8f51556b70, 0xbbd0f4f2e08fd201,     0x3feff9c1384302e9, 0x3c8b9a1be68cf877), /* j = 25 */
	(0x3f49fd5c5b7cbace, 0x3beb6ed49f17d42d,     0x3feff98151bb65ef, 0x3c82d92be315df8f), /* j = 26 */
	(0x3f4afd276673cada, 0x3bd3222545da594f,     0x3feff9416c332d34, 0x3c8dbbba66ae573a), /* j = 27 */
	(0x3f4bfcf07242969d, 0x3bc5db4d2b3efe1c,     0x3feff90187aa52be, 0xbc698a69b8df8f19), /* j = 28 */
	(0x3f4cfcb77ef118f1, 0x3becc55406f300fb,     0x3feff8c1a420d091, 0xbc8032d47bdbf02c), /* j = 29 */
	(0x3f4dfc7c8c874c82, 0xbbe863e9d57a176f,     0x3feff881c196a0b2, 0x3c858cf2f70e18b2), /* j = 30 */
	(0x3f4efc3f9b0d2bc8, 0x3bd1e8e8a5f5b8b7,     0x3feff841e00bbd28, 0x3c782227ba60dc8b), /* j = 31 */
]

const C4 : (uint64, uint64, uint64, uint64)[32] = [
	(000000000000000000, 000000000000000000,     0x3ff0000000000000, 000000000000000000), /* j = 0 */
	(0x3eafffff00000aab, 0xbb45755553bbbbd1,     0x3feffffe00002000, 0xbc2ffffe00002000), /* j = 1 */
	(0x3ebffffe00002aab, 0xbb5655553bbbbe66,     0x3feffffc00008000, 0xbc5ffffc00008000), /* j = 2 */
	(0x3ec7fffdc0004800, 0xbb343ffcf666dfe6,     0x3feffffa00012000, 0xbc7afffaf000f300), /* j = 3 */
	(0x3ecffffc0000aaab, 0xbb6d5553bbbc1111,     0x3feffff800020000, 0xbc8ffff800020000), /* j = 4 */
	(0x3ed3fffce000a6ab, 0xbb7f1952e455f818,     0x3feffff600031fff, 0x3c4801387f9e581f), /* j = 5 */
	(0x3ed7fffb80012000, 0xbb743ff9ecceb2cc,     0x3feffff400047ffe, 0x3c8400287ff0d006), /* j = 6 */
	(0x3edbfff9e001c955, 0xbb702e9d89490dc5,     0x3feffff200061ffd, 0x3c84804b07df2c8e), /* j = 7 */
	(0x3edffff80002aaaa, 0xbb75553bbbc66662,     0x3feffff00007fffc, 0x3baffff00007fffc), /* j = 8 */
	(0x3ee1fffaf001e5ff, 0x3b797c2e21b72cff,     0x3fefffee000a1ffa, 0x3c8380cd078cabc1), /* j = 9 */
	(0x3ee3fff9c0029aa9, 0x3b8c8ad1ba965260,     0x3fefffec000c7ff8, 0x3c780270fe7960f4), /* j = 10 */
	(0x3ee5fff870037754, 0xbb8d0c6bc1b51bdd,     0x3fefffea000f1ff6, 0xbc897e36793a8ca8), /* j = 11 */
	(0x3ee7fff700047ffd, 0x3b8e006132f6735a,     0x3fefffe80011fff3, 0xbc8ffd7801e5fe94), /* j = 12 */
	(0x3ee9fff57005b8a7, 0x3b771277672a8835,     0x3fefffe600151fef, 0xbc74f906f5aa5866), /* j = 13 */
	(0x3eebfff3c0072551, 0xbb86c9d894dd7427,     0x3fefffe400187feb, 0xbc8bfb4f841a6c69), /* j = 14 */
	(0x3eedfff1f008c9fa, 0xbb7701aebecf7ae4,     0x3fefffe2001c1fe6, 0xbc8779d1fdcb2212), /* j = 15 */
	(0x3eeffff0000aaaa3, 0xbb8553bbbd110fec,     0x3fefffe0001fffe0, 0x3befffe0001fffe0), /* j = 16 */
	(0x3ef0fff6f80665a6, 0xbb9b95400571451d,     0x3fefffde00241fda, 0xbc8875ce02d51cfe), /* j = 17 */
	(0x3ef1fff5e00797fa, 0xbb9a0e8ef2f395cc,     0x3fefffdc00287fd2, 0x3c8c0cd071958038), /* j = 18 */
	(0x3ef2fff4b808ee4d, 0x3b984638f069f71f,     0x3fefffda002d1fca, 0x3c8a8fe8751bf4ef), /* j = 19 */
	(0x3ef3fff3800a6aa1, 0xbb794b915f81751a,     0x3fefffd80031ffc2, 0xbc8fec781869e17c), /* j = 20 */
	(0x3ef4fff2380c0ef4, 0x3b80a43b5348b6b9,     0x3fefffd600371fb8, 0xbc8668429728999b), /* j = 21 */
	(0x3ef5fff0e00ddd47, 0x3b624a1f136cc09c,     0x3fefffd4003c7fad, 0xbc77c6cf4ea2f3e0), /* j = 22 */
	(0x3ef6ffef780fd79a, 0xbb9a716c4210cdd0,     0x3fefffd200421fa1, 0xbc5aeeb948d5a74d), /* j = 23 */
	(0x3ef7ffee0011ffec, 0xbb8ff3d9a8c98613,     0x3fefffd00047ff94, 0x3c143fe1a02d8fbc), /* j = 24 */
	(0x3ef8ffec7814583d, 0x3b9f7bc8a4e1db73,     0x3fefffce004e1f86, 0xbc6141450a04205a), /* j = 25 */
	(0x3ef9ffeae016e28f, 0xbb8cb889999dd735,     0x3fefffcc00547f77, 0xbc83c837daa53cb3), /* j = 26 */
	(0x3efaffe93819a0e0, 0xbb9be60d8a0b5ba8,     0x3fefffca005b1f66, 0x3c7d81be350f0677), /* j = 27 */
	(0x3efbffe7801c9530, 0xbb873b12aed4646c,     0x3fefffc80061ff55, 0xbc8fb4f8834d1a39), /* j = 28 */
	(0x3efcffe5b81fc17f, 0x3b9fe950a87b2785,     0x3fefffc600691f41, 0x3c8dd655eb844520), /* j = 29 */
	(0x3efdffe3e02327cf, 0xbb9bfd7604f796f2,     0x3fefffc400707f2d, 0x3c618b7f1a71ae6b), /* j = 30 */
	(0x3efeffe1f826ca1d, 0xbb60ae99630e566e,     0x3fefffc200781f17, 0x3c80f0bb2d9557af), /* j = 31 */
]

const logoverkill32 = {x : flt32
	var x64 : flt64 = (x : flt64)
	var l64 : flt64 = log64(x64)
	var y1  : flt32 = (l64 : flt32)
	var y2  : flt32 = ((l64 - (y1 : flt64)) : flt32)
	-> (y1, y2)
}

const logoverkill64 = {x : flt64
	var xn, xe, xs
	(xn, xe, xs) = std.flt64explode(x)
	var xsf = std.flt64assem(false, 0, xs)
	var xb = std.flt64bits(x)
	var tn, te, ts
	var t1, t2

	/* Special cases */
	if std.isnan(x)
		-> (std.flt64frombits(0x7ff8000000000000), std.flt64frombits(0x7ff8000000000000))
	elif xe <= -1023 && xs == 0
		/* log (+/- 0) is -infinity */
		-> (std.flt64frombits(0xfff0000000000000), std.flt64frombits(0xfff0000000000000))
	elif xn
		/* log(-anything) is NaN */
		-> (std.flt64frombits(0x7ff8000000000000), std.flt64frombits(0x7ff8000000000000))
	;;

	if xe <= -1023
		/*
		   We depend on being able to pick bits out of xs as if it were normal, so
		   normalize any subnormals.
		 */
		xe++
		var check = 1 << 52
		while xs & check == 0
			xs <<= 1
			xe--
		;;
		xsf = std.flt64assem(false, 0, xs)
	;;

	var shift = 0
	var non_trivial = 0
	var then_invert = false
	var j1, F1, f1, logF1_hi, logF1_lo, F1_inv_hi, F1_inv_lo, fF1_hi, fF1_lo

	/* F1 */
	if xe == -1 && xs > 0x001d1ff05e41cfba
		/*
		   If we reduced to [1, 2) unconditionally, then values of x like 0.999… =
		   2^-1 · 1.999… would cause subtractive cancellation; we'd compute
		   log(1.999…), then subtract out log(2) at the end. They'd agree on the
		   first n bits, and we'd lose n bits of precision.

		   This is only a problem for exponent -1, and for xs large enough;
		   outside that, the numbers are so different that we won't lose precision
		   by cancelling. But here, we compute 1/x, proceed (with exponent 0), and
		   flip all the signs at the end.
		 */
		xe = 0
		var xinv_hi = 1.0 / x
		var xinv_lo = fma64(-1.0 * xinv_hi, x, 1.0) / x
		(tn, te, ts) = std.flt64explode(xinv_hi)
		non_trivial = ((47 >= te) : uint64) * ((47 - te < 64) : uint64)
		shift = non_trivial * ((47 - te) : uint64)
		j1 = non_trivial * ((ts >> shift) & 0x1f)
		var F1m1 = scale2((j1 : flt64), -5)
		F1 = 1.0 + F1m1
		var f1_hi, f1_lo
		(f1_hi, f1_lo) = fast2sum(xinv_hi - F1, xinv_lo)
		(logF1_hi, logF1_lo, F1_inv_hi, F1_inv_lo) = C1[j1]

		/* Compute 1 + f1/F1 */
		(fF1_hi, fF1_lo) = two_by_two64(f1_hi, std.flt64frombits(F1_inv_hi))
		(fF1_lo, t1) = slow2sum(fF1_lo, f1_lo * std.flt64frombits(F1_inv_hi))
		(fF1_lo, t2) = slow2sum(fF1_lo, f1_hi * std.flt64frombits(F1_inv_lo))
		(fF1_hi, fF1_lo) = fast2sum(fF1_hi, fF1_lo + (t1 + t2))
		then_invert = true
	else
		j1 = (xs & 0x000f800000000000) >> 47
		F1 = std.flt64assem(false, 0, xs & 0xffff800000000000)
		f1 = xsf - F1
		(logF1_hi, logF1_lo, F1_inv_hi, F1_inv_lo) = C1[j1]

		/* Compute 1 + f1/F1 */
		(fF1_hi, fF1_lo) = two_by_two64(f1, std.flt64frombits(F1_inv_hi))
		(fF1_lo, t1) = slow2sum(fF1_lo, f1 * std.flt64frombits(F1_inv_lo))
		(fF1_hi, fF1_lo) = fast2sum(fF1_hi, fF1_lo)
		fF1_lo += t1
	;;

	/* F2 */
	(tn, te, ts) = std.flt64explode(fF1_hi)
	non_trivial = ((42 >= te) : uint64) * ((42 - te < 64) : uint64)
	shift = non_trivial * ((42 - te) : uint64)
	var j2 = non_trivial * ((ts >> shift) & 0x1f)
	var F2m1 = scale2((j2 : flt64), -10)
	var F2 = 1.0 + F2m1
	var f2_hi, f2_lo
	(f2_hi, f2_lo) = fast2sum(fF1_hi - F2m1, fF1_lo)
	var logF2_hi, logF2_lo, F2_inv_hi, F2_inv_lo
	(logF2_hi, logF2_lo, F2_inv_hi, F2_inv_lo) = C2[j2]

	/* Compute 1 + f2/F2 */
	var fF2_hi, fF2_lo
	(fF2_hi, fF2_lo) = two_by_two64(f2_hi, std.flt64frombits(F2_inv_hi))
	(fF2_lo, t1) = slow2sum(fF2_lo, f2_lo * std.flt64frombits(F2_inv_hi))
	(fF2_lo, t2) = slow2sum(fF2_lo, f2_hi * std.flt64frombits(F2_inv_lo))
	(fF2_hi, fF2_lo) = fast2sum(fF2_hi, fF2_lo + (t1 + t2))

	/* F3 (just like F2) */
	(tn, te, ts) = std.flt64explode(fF2_hi)
	non_trivial = ((37 >= te) : uint64) * ((37 - te < 64) : uint64)
	shift = non_trivial * ((37 - te) : uint64)
	var j3 = non_trivial * ((ts >> shift) & 0x1f)
	var F3m1 = scale2((j3 : flt64), -15)
	var F3 = 1.0 + F3m1
	var f3_hi, f3_lo
	(f3_hi, f3_lo) = fast2sum(fF2_hi - F3m1, fF2_lo)
	var logF3_hi, logF3_lo, F3_inv_hi, F3_inv_lo
	(logF3_hi, logF3_lo, F3_inv_hi, F3_inv_lo) = C3[j3]

	/* Compute 1 + f3/F3 */
	var fF3_hi, fF3_lo
	(fF3_hi, fF3_lo) = two_by_two64(f3_hi, std.flt64frombits(F3_inv_hi))
	(fF3_lo, t1) = slow2sum(fF3_lo, f3_lo * std.flt64frombits(F3_inv_hi))
	(fF3_lo, t2) = slow2sum(fF3_lo, f3_hi * std.flt64frombits(F3_inv_lo))
	(fF3_hi, fF3_lo) = fast2sum(fF3_hi, fF3_lo + (t1 + t2))

	/* F4 (just like F2) */
	(tn, te, ts) = std.flt64explode(fF3_hi)
	non_trivial = ((32 >= te) : uint64) * ((32 - te < 64) : uint64)
	shift = non_trivial * ((32 - te) : uint64)
	var j4 = non_trivial * ((ts >> shift) & 0x1f)
	var F4m1 = scale2((j4 : flt64), -20)
	var F4 = 1.0 + F4m1
	var f4_hi, f4_lo
	(f4_hi, f4_lo) = fast2sum(fF3_hi - F4m1, fF3_lo)
	var logF4_hi, logF4_lo, F4_inv_hi, F4_inv_lo
	(logF4_hi, logF4_lo, F4_inv_hi, F4_inv_lo) = C4[j4]

	/* Compute 1 + f4/F4 */
	var fF4_hi, fF4_lo
	(fF4_hi, fF4_lo) = two_by_two64(f4_hi, std.flt64frombits(F4_inv_hi))
	(fF4_lo, t1) = slow2sum(fF4_lo, f4_lo * std.flt64frombits(F4_inv_hi))
	(fF4_lo, t2) = slow2sum(fF4_lo, f4_hi * std.flt64frombits(F4_inv_lo))
	(fF4_hi, fF4_lo) = fast2sum(fF4_hi, fF4_lo + (t1 + t2))

	/*
	   L = log(1 + f4/F4); we'd like to use horner_polyu, but since we have
	   _hi and _lo, it becomes more complicated.
	 */
	var L_hi, L_lo
	/* r = (1/5) · x */
	(L_hi, L_lo) = hl_mult(std.flt64frombits(0x3fc999999999999a), std.flt64frombits(0xbc6999999999999a), fF4_hi, fF4_lo)

	/* r = r - 1/4 */
	(t1, t2) = fast2sum(std.flt64frombits(0xbfd0000000000000), L_lo)
	(L_hi, L_lo) = fast2sum(t1, L_hi)
	L_lo += t2

	/* r = r · x */
	(L_hi, L_lo) = hl_mult(L_hi, L_lo, fF4_hi, fF4_lo)

	/* r = r + 1/3 */
	(L_hi, L_lo) = hl_add(std.flt64frombits(0x3fd5555555555555), std.flt64frombits(0x3c75555555555555), L_hi, L_lo)

	/* r = r · x */
	(L_hi, L_lo) = hl_mult(L_hi, L_lo, fF4_hi, fF4_lo)

	/* r = r - 1/2 */
	(t1, t2) = fast2sum(std.flt64frombits(0xbfe0000000000000), L_lo)
	(L_hi, L_lo) = fast2sum(t1, L_hi)
	L_lo += t2

	/* r = r · x */
	(L_hi, L_lo) = hl_mult(L_hi, L_lo, fF4_hi, fF4_lo)

	/* r = r + 1 */
	(t1, t2) = fast2sum(1.0, L_lo)
	(L_hi, L_lo) = fast2sum(t1, L_hi)
	L_lo += t2
	/* r = r · x */
	(L_hi, L_lo) = hl_mult(L_hi, L_lo, fF4_hi, fF4_lo)

	/*
	   Finally, compute log(F1) + log(F2) + log(F3) + log(F4) + L. We may
	   assume F1 > F2 > F3 > F4 > F5, since the only way this is disrupted is
	   if some Fi == 1.0, in which case the log is 0 and the fast2sum works
	   out either way. We can also assume each F1,2,3 > L. 
	 */
	var lsig_hi, lsig_lo
	
	/* log(F4) + L, slow because they're the same order of magnitude */
	(t1, t2) = slow2sum(std.flt64frombits(logF4_lo), L_lo)
	(lsig_lo, t1) = slow2sum(L_hi, t1)
	(lsig_hi, lsig_lo) = slow2sum(std.flt64frombits(logF4_hi), lsig_lo)

	(lsig_hi, lsig_lo) = hl_add(std.flt64frombits(logF3_hi), std.flt64frombits(logF3_lo), lsig_hi, lsig_lo + (t1 + t2))
	(lsig_hi, lsig_lo) = hl_add(std.flt64frombits(logF2_hi), std.flt64frombits(logF2_lo), lsig_hi, lsig_lo)
	(lsig_hi, lsig_lo) = hl_add(std.flt64frombits(logF1_hi), std.flt64frombits(logF1_lo), lsig_hi, lsig_lo)

	/* Oh yeah, and we need xe * log(2) */
	var xel2_hi, xel2_lo, lx_hi, lx_lo
	(xel2_hi, xel2_lo) = hl_mult((xe : flt64), 0.0, std.flt64frombits(0x3fe62e42fefa39ef), std.flt64frombits(0x3c7abc9e3b39803f))

	(t1, t2) = slow2sum(xel2_lo, lsig_lo)
	(lx_lo, t1) = slow2sum(lsig_hi, t1)
	(lx_hi, lx_lo) = slow2sum(xel2_hi, lx_lo)
	(lx_hi, lx_lo) = slow2sum(lx_hi, lx_lo + (t1 + t2))

	if then_invert
		-> (-1.0 * lx_hi, -1.0 * lx_lo)
	;;

	-> (lx_hi, lx_lo)
}