1 |
2 | slogn.sa 3.1 12/10/90
3 |
4 | slogn computes the natural logarithm o
5 | input value. slognd does the same exce
6 | denormalized number. slognp1 computes
7 | computes log(1+X) for denormalized X.
8 |
9 | Input: Double-extended value in memory
10 | register a0.
11 |
12 | Output: log(X) or log(1+X) returned in
13 |
14 | Accuracy and Monotonicity: The returne
15 | 64 significant bit, i.e. withi
16 | result is subsequently rounded
17 | result is provably monotonic i
18 |
19 | Speed: The program slogn takes approxi
20 | argument X such that |X-1| >=
21 | situation. For those arguments
22 | 210 cycles. For the less comm
23 | run no worse than 10% slower.
24 |
25 | Algorithm:
26 | LOGN:
27 | Step 1. If |X-1| < 1/16, approximate l
28 | u, where u = 2(X-1)/(X+1). Oth
29 |
30 | Step 2. X = 2**k * Y where 1 <= Y < 2.
31 | significant bits of Y plus 2**
32 | 2 where the six "x" match thos
33 |
34 | Step 3. Define u = (Y-F)/F. Approximat
35 | log(1+u) = poly.
36 |
37 | Step 4. Reconstruct log(X) = log( 2**k
38 | by k*log(2) + (log(F) + poly).
39 | beforehand and stored in the p
40 |
41 | lognp1:
42 | Step 1: If |X| < 1/16, approximate log
43 | u where u = 2X/(2+X). Otherwis
44 |
45 | Step 2: Let 1+X = 2**k * Y, where 1 <=
46 | of the algorithm for LOGN and
47 | k*log(2) + log(F) + poly where
48 | u = (Y-F)/F.
49 |
50 | Implementation Notes:
51 | Note 1. There are 64 different possibl
52 | need to be tabulated. Moreover
53 | tabulated so that the division
54 | multiplication.
55 |
56 | Note 2. In Step 2 of lognp1, in order
57 | Y-F has to be calculated caref
58 |
59 | Note 3. To fully exploit the pipeline,
60 | into two parts evaluated indep
61 |
62
63 | Copyright (C) Motorola, Inc. 1
64 | All Rights Reserved
65 |
66 | For details on the license for this fi
67 | file, README, in this same directory.
68
69 |slogn idnt 2,1 | Motorola 040 Floating Po
70
71 |section 8
72
73 #include "fpsp.h"
74
75 BOUNDS1: .long 0x3FFEF07D,0x3FFF8841
76 BOUNDS2: .long 0x3FFE8000,0x3FFFC000
77
78 LOGOF2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC
79
80 one: .long 0x3F800000
81 zero: .long 0x00000000
82 infty: .long 0x7F800000
83 negone: .long 0xBF800000
84
85 LOGA6: .long 0x3FC2499A,0xB5E4040B
86 LOGA5: .long 0xBFC555B5,0x848CB7DB
87
88 LOGA4: .long 0x3FC99999,0x987D8730
89 LOGA3: .long 0xBFCFFFFF,0xFF6F7E97
90
91 LOGA2: .long 0x3FD55555,0x555555a4
92 LOGA1: .long 0xBFE00000,0x00000008
93
94 LOGB5: .long 0x3F175496,0xADD7DAD6
95 LOGB4: .long 0x3F3C71C2,0xFE80C7E0
96
97 LOGB3: .long 0x3F624924,0x928BCCFF
98 LOGB2: .long 0x3F899999,0x999995EC
99
100 LOGB1: .long 0x3FB55555,0x55555555
101 TWO: .long 0x40000000,0x00000000
102
103 LTHOLD: .long 0x3f990000,0x80000000,0x00000000
104
105 LOGTBL:
106 .long 0x3FFE0000,0xFE03F80F,0xE03F80F
107 .long 0x3FF70000,0xFF015358,0x833C47E
108 .long 0x3FFE0000,0xFA232CF2,0x52138AC
109 .long 0x3FF90000,0xBDC8D83E,0xAD88D54
110 .long 0x3FFE0000,0xF6603D98,0x0F6603D
111 .long 0x3FFA0000,0x9CF43DCF,0xF5EAFD4
112 .long 0x3FFE0000,0xF2B9D648,0x0F2B9D6
113 .long 0x3FFA0000,0xDA16EB88,0xCB8DF61
114 .long 0x3FFE0000,0xEF2EB71F,0xC434523
115 .long 0x3FFB0000,0x8B29B775,0x1BD7074
116 .long 0x3FFE0000,0xEBBDB2A5,0xC1619C8
117 .long 0x3FFB0000,0xA8D839F8,0x30C1FB4
118 .long 0x3FFE0000,0xE865AC7B,0x7603A19
119 .long 0x3FFB0000,0xC61A2EB1,0x8CD907A
120 .long 0x3FFE0000,0xE525982A,0xF70C880
121 .long 0x3FFB0000,0xE2F2A47A,0xDE3A18A
122 .long 0x3FFE0000,0xE1FC780E,0x1FC780E
123 .long 0x3FFB0000,0xFF64898E,0xDF55D55
124 .long 0x3FFE0000,0xDEE95C4C,0xA037BA5
125 .long 0x3FFC0000,0x8DB956A9,0x7B3D014
126 .long 0x3FFE0000,0xDBEB61EE,0xD19C595
127 .long 0x3FFC0000,0x9B8FE100,0xF47BA1D
128 .long 0x3FFE0000,0xD901B203,0x6406C80
129 .long 0x3FFC0000,0xA9372F1D,0x0DA1BD1
130 .long 0x3FFE0000,0xD62B80D6,0x2B80D62
131 .long 0x3FFC0000,0xB6B07F38,0xCE90E46
132 .long 0x3FFE0000,0xD3680D36,0x80D3680
133 .long 0x3FFC0000,0xC3FD0329,0x0648848
134 .long 0x3FFE0000,0xD0B69FCB,0xD2580D0
135 .long 0x3FFC0000,0xD11DE0FF,0x15AB18C
136 .long 0x3FFE0000,0xCE168A77,0x25080CE
137 .long 0x3FFC0000,0xDE1433A1,0x6C66B15
138 .long 0x3FFE0000,0xCB8727C0,0x65C393E
139 .long 0x3FFC0000,0xEAE10B5A,0x7DDC8AD
140 .long 0x3FFE0000,0xC907DA4E,0x871146A
141 .long 0x3FFC0000,0xF7856E5E,0xE2C9B29
142 .long 0x3FFE0000,0xC6980C69,0x80C6980
143 .long 0x3FFD0000,0x82012CA5,0xA68206D
144 .long 0x3FFE0000,0xC4372F85,0x5D824CA
145 .long 0x3FFD0000,0x882C5FCD,0x7256A8C
146 .long 0x3FFE0000,0xC1E4BBD5,0x95F6E94
147 .long 0x3FFD0000,0x8E44C60B,0x4CCFD7D
148 .long 0x3FFE0000,0xBFA02FE8,0x0BFA02F
149 .long 0x3FFD0000,0x944AD09E,0xF4351AF
150 .long 0x3FFE0000,0xBD691047,0x07661AA
151 .long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B
152 .long 0x3FFE0000,0xBB3EE721,0xA54D880
153 .long 0x3FFD0000,0xA0218434,0x353F1DE
154 .long 0x3FFE0000,0xB92143FA,0x36F5E02
155 .long 0x3FFD0000,0xA5F2FCAB,0xBBC506D
156 .long 0x3FFE0000,0xB70FBB5A,0x19BE365
157 .long 0x3FFD0000,0xABB3B8BA,0x2AD362A
158 .long 0x3FFE0000,0xB509E68A,0x9B94821
159 .long 0x3FFD0000,0xB1641795,0xCE3CA97
160 .long 0x3FFE0000,0xB30F6352,0x8917C80
161 .long 0x3FFD0000,0xB7047551,0x5D0F1C6
162 .long 0x3FFE0000,0xB11FD3B8,0x0B11FD3
163 .long 0x3FFD0000,0xBC952AFE,0xEA3D13E
164 .long 0x3FFE0000,0xAF3ADDC6,0x80AF3AD
165 .long 0x3FFD0000,0xC2168ED0,0xF458BA4
166 .long 0x3FFE0000,0xAD602B58,0x0AD602B
167 .long 0x3FFD0000,0xC788F439,0xB3163BF
168 .long 0x3FFE0000,0xAB8F69E2,0x8359CD1
169 .long 0x3FFD0000,0xCCECAC08,0xBF04565
170 .long 0x3FFE0000,0xA9C84A47,0xA07F563
171 .long 0x3FFD0000,0xD2420487,0x2DD8516
172 .long 0x3FFE0000,0xA80A80A8,0x0A80A80
173 .long 0x3FFD0000,0xD7894992,0x3BC3588
174 .long 0x3FFE0000,0xA655C439,0x2D7B73A
175 .long 0x3FFD0000,0xDCC2C4B4,0x9887DAC
176 .long 0x3FFE0000,0xA4A9CF1D,0x9683375
177 .long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9
178 .long 0x3FFE0000,0xA3065E3F,0xAE7CD0E
179 .long 0x3FFD0000,0xE70D785C,0x2F9F5BD
180 .long 0x3FFE0000,0xA16B312E,0xA8FC377
181 .long 0x3FFD0000,0xEC1F392C,0x5179F28
182 .long 0x3FFE0000,0x9FD809FD,0x809FD80
183 .long 0x3FFD0000,0xF12440D3,0xE36130E
184 .long 0x3FFE0000,0x9E4CAD23,0xDD5F3A2
185 .long 0x3FFD0000,0xF61CCE92,0x346600B
186 .long 0x3FFE0000,0x9CC8E160,0xC3FB19B
187 .long 0x3FFD0000,0xFB091FD3,0x8145630
188 .long 0x3FFE0000,0x9B4C6F9E,0xF03A3CA
189 .long 0x3FFD0000,0xFFE97042,0xBFA4C2A
190 .long 0x3FFE0000,0x99D722DA,0xBDE58F0
191 .long 0x3FFE0000,0x825EFCED,0x4936933
192 .long 0x3FFE0000,0x9868C809,0x868C809
193 .long 0x3FFE0000,0x84C37A7A,0xB9A905C
194 .long 0x3FFE0000,0x97012E02,0x5C04B80
195 .long 0x3FFE0000,0x87224C2E,0x8E645FB
196 .long 0x3FFE0000,0x95A02568,0x095A025
197 .long 0x3FFE0000,0x897B8CAC,0x9F7DE29
198 .long 0x3FFE0000,0x94458094,0x4580944
199 .long 0x3FFE0000,0x8BCF55DE,0xC4CD05F
200 .long 0x3FFE0000,0x92F11384,0x0497889
201 .long 0x3FFE0000,0x8E1DC0FB,0x89E125E
202 .long 0x3FFE0000,0x91A2B3C4,0xD5E6F80
203 .long 0x3FFE0000,0x9066E68C,0x955B6C9
204 .long 0x3FFE0000,0x905A3863,0x3E06C43
205 .long 0x3FFE0000,0x92AADE74,0xC7BE59E
206 .long 0x3FFE0000,0x8F1779D9,0xFDC3A21
207 .long 0x3FFE0000,0x94E9BFF6,0x1584564
208 .long 0x3FFE0000,0x8DDA5202,0x3769480
209 .long 0x3FFE0000,0x9723A1B7,0x2013420
210 .long 0x3FFE0000,0x8CA29C04,0x6514E02
211 .long 0x3FFE0000,0x995899C8,0x90EB899
212 .long 0x3FFE0000,0x8B70344A,0x139BC75
213 .long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2
214 .long 0x3FFE0000,0x8A42F870,0x5669DB4
215 .long 0x3FFE0000,0x9DB4224F,0xFFE1157
216 .long 0x3FFE0000,0x891AC73A,0xE9819B5
217 .long 0x3FFE0000,0x9FDADC26,0x8B7A12D
218 .long 0x3FFE0000,0x87F78087,0xF78087F
219 .long 0x3FFE0000,0xA1FCFF17,0xCE733BD
220 .long 0x3FFE0000,0x86D90544,0x7A34ACC
221 .long 0x3FFE0000,0xA41A9E8F,0x5446FB9
222 .long 0x3FFE0000,0x85BF3761,0x2CEE3C9
223 .long 0x3FFE0000,0xA633CD7E,0x6771CD8
224 .long 0x3FFE0000,0x84A9F9C8,0x084A9F9
225 .long 0x3FFE0000,0xA8489E60,0x0B435A5
226 .long 0x3FFE0000,0x83993052,0x3FBE336
227 .long 0x3FFE0000,0xAA59233C,0xCCA4BD4
228 .long 0x3FFE0000,0x828CBFBE,0xB9A020A
229 .long 0x3FFE0000,0xAC656DAE,0x6BCC498
230 .long 0x3FFE0000,0x81848DA8,0xFAF0D27
231 .long 0x3FFE0000,0xAE6D8EE3,0x60BB246
232 .long 0x3FFE0000,0x80808080,0x8080808
233 .long 0x3FFE0000,0xB07197A2,0x3C46C65
234
235 .set ADJK,L_SCR1
236
237 .set X,FP_SCR1
238 .set XDCARE,X+2
239 .set XFRAC,X+4
240
241 .set F,FP_SCR2
242 .set FFRAC,F+4
243
244 .set KLOG2,FP_SCR3
245
246 .set SAVEU,FP_SCR4
247
248 | xref t_frcinx
249 |xref t_extdnrm
250 |xref t_operr
251 |xref t_dz
252
253 .global slognd
254 slognd:
255 |--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INP
256
257 movel #-100,ADJK(%a6) | ...I
258
259 |----normalize the input value by left shiftin
260 |----below), adjusting exponent and storing -k
261 |----the value TWOTO100 is no longer needed.
262 |----Note that this code assumes the denormali
263
264 moveml %d2-%d7,-(%a7) | ...s
265 movel #0x00000000,%d3 | ...D
266 movel 4(%a0),%d4
267 movel 8(%a0),%d5 | ...(
268 clrl %d2 | ...D
269
270 tstl %d4
271 bnes HiX_not0
272
273 HiX_0:
274 movel %d5,%d4
275 clrl %d5
276 movel #32,%d2
277 clrl %d6
278 bfffo %d4{#0:#32},%d6
279 lsll %d6,%d4
280 addl %d6,%d2 | ...(
281
282 movel %d3,X(%a6)
283 movel %d4,XFRAC(%a6)
284 movel %d5,XFRAC+4(%a6)
285 negl %d2
286 movel %d2,ADJK(%a6)
287 fmovex X(%a6),%fp0
288 moveml (%a7)+,%d2-%d7 | ...r
289 lea X(%a6),%a0
290 bras LOGBGN | ...b
291
292
293 HiX_not0:
294 clrl %d6
295 bfffo %d4{#0:#32},%d6 | ...f
296 movel %d6,%d2 | ...g
297 lsll %d6,%d4
298 movel %d5,%d7 | ...a
299 lsll %d6,%d5
300 negl %d6
301 addil #32,%d6
302 lsrl %d6,%d7
303 orl %d7,%d4 | ...(
304
305 movel %d3,X(%a6)
306 movel %d4,XFRAC(%a6)
307 movel %d5,XFRAC+4(%a6)
308 negl %d2
309 movel %d2,ADJK(%a6)
310 fmovex X(%a6),%fp0
311 moveml (%a7)+,%d2-%d7 | ...r
312 lea X(%a6),%a0
313 bras LOGBGN | ...b
314
315
316 .global slogn
317 slogn:
318 |--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZE
319
320 fmovex (%a0),%fp0 | ...L
321 movel #0x00000000,ADJK(%a6)
322
323 LOGBGN:
324 |--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*F
325 |--A FINITE, NON-ZERO, NORMALIZED NUMBER.
326
327 movel (%a0),%d0
328 movew 4(%a0),%d0
329
330 movel (%a0),X(%a6)
331 movel 4(%a0),X+4(%a6)
332 movel 8(%a0),X+8(%a6)
333
334 cmpil #0,%d0 | ...CHECK IF
335 blt LOGNEG | ...LOG OF NE
336 cmp2l BOUNDS1,%d0 | ...X IS POSI
337 bcc LOGNEAR1 | ...BOUNDS IS
338
339 LOGMAIN:
340 |--THIS SHOULD BE THE USUAL CASE, X NOT VERY C
341
342 |--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXX
343 |--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS
344 |--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
345 |-- = K*LOG2 + LOG(F) + L
346 |--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THU
347 |--LOG(1+U) CAN BE VERY EFFICIENT.
348 |--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A
349 |--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
350
351 |--GET K, Y, F, AND ADDRESS OF 1/F.
352 asrl #8,%d0
353 asrl #8,%d0 | ...SHIFTED 1
354 subil #0x3FFF,%d0 | ...THIS IS K
355 addl ADJK(%a6),%d0 | ...ADJUST K,
356 lea LOGTBL,%a0 | ...BASE ADDR
357 fmovel %d0,%fp1 | ...C
358
359 |--WHILE THE CONVERSION IS GOING ON, WE GET F
360 movel #0x3FFF0000,X(%a6) | ...X
361 movel XFRAC(%a6),FFRAC(%a6)
362 andil #0xFE000000,FFRAC(%a6) | ...FI
363 oril #0x01000000,FFRAC(%a6) | ...GE
364 movel FFRAC(%a6),%d0 | ...READY TO
365 andil #0x7E000000,%d0
366 asrl #8,%d0
367 asrl #8,%d0
368 asrl #4,%d0 | ...SHIFTED 2
369 addal %d0,%a0 | ...A0 IS THE
370
371 fmovex X(%a6),%fp0
372 movel #0x3fff0000,F(%a6)
373 clrl F+8(%a6)
374 fsubx F(%a6),%fp0 | ...Y
375 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...S
376 |--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F,
377 |--REGISTERS SAVED: FPCR, FP1, FP2
378
379 LP1CONT1:
380 |--AN RE-ENTRY POINT FOR LOGNP1
381 fmulx (%a0),%fp0 | ...FP0 IS U
382 fmulx LOGOF2,%fp1 | ...GET K*LOG
383 fmovex %fp0,%fp2
384 fmulx %fp2,%fp2 | ...F
385 fmovex %fp1,KLOG2(%a6) | ...PUT K*LOG
386
387 |--LOG(1+U) IS APPROXIMATED BY
388 |--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6)))))
389 |--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4
390
391 fmovex %fp2,%fp3
392 fmovex %fp2,%fp1
393
394 fmuld LOGA6,%fp1 | ...V*A6
395 fmuld LOGA5,%fp2 | ...V*A5
396
397 faddd LOGA4,%fp1 | ...A4+V*A6
398 faddd LOGA3,%fp2 | ...A3+V*A5
399
400 fmulx %fp3,%fp1 | ...V
401 fmulx %fp3,%fp2 | ...V
402
403 faddd LOGA2,%fp1 | ...A2+V*(A4+
404 faddd LOGA1,%fp2 | ...A1+V*(A3+
405
406 fmulx %fp3,%fp1 | ...V
407 addal #16,%a0 | ...ADDRESS O
408 fmulx %fp3,%fp2 | ...V
409
410 fmulx %fp0,%fp1 | ...U
411 faddx %fp2,%fp0 | ...U
412
413 faddx (%a0),%fp1 | ...LOG(F)+U*
414 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...R
415 faddx %fp1,%fp0 | ...F
416
417 fmovel %d1,%fpcr
418 faddx KLOG2(%a6),%fp0 | ...FINAL ADD
419 bra t_frcinx
420
421
422 LOGNEAR1:
423 |--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS TH
424 fmovex %fp0,%fp1
425 fsubs one,%fp1 | ...F
426 fadds one,%fp0 | ...F
427 faddx %fp1,%fp1 | ...F
428 |--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN
429 |--IN U, U = 2(X-1)/(X+1) = FP1/FP0
430
431 LP1CONT2:
432 |--THIS IS AN RE-ENTRY POINT FOR LOGNP1
433 fdivx %fp0,%fp1 | ...F
434 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...
435 |--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
436 |--LET V=U*U, W=V*V, CALCULATE
437 |--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)
438 |--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2
439 fmovex %fp1,%fp0
440 fmulx %fp0,%fp0 | ...FP0 IS V
441 fmovex %fp1,SAVEU(%a6) | ...STORE U I
442 fmovex %fp0,%fp1
443 fmulx %fp1,%fp1 | ...FP1 IS W
444
445 fmoved LOGB5,%fp3
446 fmoved LOGB4,%fp2
447
448 fmulx %fp1,%fp3 | ...W*B5
449 fmulx %fp1,%fp2 | ...W*B4
450
451 faddd LOGB3,%fp3 | ...B3+W*B5
452 faddd LOGB2,%fp2 | ...B2+W*B4
453
454 fmulx %fp3,%fp1 | ...W*(B3+W*B
455
456 fmulx %fp0,%fp2 | ...V*(B2+W*B
457
458 faddd LOGB1,%fp1 | ...B1+W*(B3+W*B5)
459 fmulx SAVEU(%a6),%fp0 | ...FP0 IS U*
460
461 faddx %fp2,%fp1 | ...B1+W*(B3+
462 fmovemx (%sp)+,%fp2-%fp2/%fp3 | ...FP2
463
464 fmulx %fp1,%fp0 | ...U*V*( [B1
465
466 fmovel %d1,%fpcr
467 faddx SAVEU(%a6),%fp0
468 bra t_frcinx
469 rts
470
471 LOGNEG:
472 |--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
473 bra t_operr
474
475 .global slognp1d
476 slognp1d:
477 |--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED I
478 | Simply return the denorm
479
480 bra t_extdnrm
481
482 .global slognp1
483 slognp1:
484 |--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-
485
486 fmovex (%a0),%fp0 | ...LOAD INPU
487 fabsx %fp0 |test magnitud
488 fcmpx LTHOLD,%fp0 |compare with
489 fbgt LP1REAL |if greater, c
490 fmovel #0,%fpsr |clr N
491 fmovel %d1,%fpcr
492 fmovex (%a0),%fp0 |return signed
493 bra t_frcinx
494
495 LP1REAL:
496 fmovex (%a0),%fp0 | ...LOAD INPU
497 movel #0x00000000,ADJK(%a6)
498 fmovex %fp0,%fp1 | ...FP1 IS IN
499 fadds one,%fp0 | ...X := ROUN
500 fmovex %fp0,X(%a6)
501 movew XFRAC(%a6),XDCARE(%a6)
502 movel X(%a6),%d0
503 cmpil #0,%d0
504 ble LP1NEG0 | ...LOG OF ZERO OR -V
505 cmp2l BOUNDS2,%d0
506 bcs LOGMAIN | ...BOUNDS2 IS [1/2,3
507 |--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS
508 |--CONTAINS AT LEAST 63 BITS OF INFORMATION OF
509 |--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
510
511 LP1NEAR1:
512 |--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
513 cmp2l BOUNDS1,%d0
514 bcss LP1CARE
515
516 LP1ONE16:
517 |--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(
518 |--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
519 faddx %fp1,%fp1 | ...FP1 IS 2Z
520 fadds one,%fp0 | ...FP0 IS 1+
521 |--U = FP1/FP0
522 bra LP1CONT2
523
524 LP1CARE:
525 |--HERE WE USE THE USUAL TABLE DRIVEN APPROACH
526 |--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFOR
527 |--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z I
528 |--THERE ARE ONLY TWO CASES.
529 |--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F
530 |--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F
531 |--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN
532 |--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
533
534 movel XFRAC(%a6),FFRAC(%a6)
535 andil #0xFE000000,FFRAC(%a6)
536 oril #0x01000000,FFRAC(%a6) | ...F
537 cmpil #0x3FFF8000,%d0 | ...SEE IF 1+
538 bges KISZERO
539
540 KISNEG1:
541 fmoves TWO,%fp0
542 movel #0x3fff0000,F(%a6)
543 clrl F+8(%a6)
544 fsubx F(%a6),%fp0 | ...2-F
545 movel FFRAC(%a6),%d0
546 andil #0x7E000000,%d0
547 asrl #8,%d0
548 asrl #8,%d0
549 asrl #4,%d0 | ...D0 CONTAI
550 faddx %fp1,%fp1 | ...G
551 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...S
552 faddx %fp1,%fp0 | ...F
553 lea LOGTBL,%a0 | ...A0 IS ADD
554 addal %d0,%a0
555 fmoves negone,%fp1 | ...FP1 IS K
556 bra LP1CONT1
557
558 KISZERO:
559 fmoves one,%fp0
560 movel #0x3fff0000,F(%a6)
561 clrl F+8(%a6)
562 fsubx F(%a6),%fp0 | ...1
563 movel FFRAC(%a6),%d0
564 andil #0x7E000000,%d0
565 asrl #8,%d0
566 asrl #8,%d0
567 asrl #4,%d0
568 faddx %fp1,%fp0 | ...F
569 fmovemx %fp2-%fp2/%fp3,-(%sp) | ...F
570 lea LOGTBL,%a0
571 addal %d0,%a0 | ...A0 IS ADD
572 fmoves zero,%fp1 | ...FP1 IS K
573 bra LP1CONT1
574
575 LP1NEG0:
576 |--FPCR SAVED. D0 IS X IN COMPACT FORM.
577 cmpil #0,%d0
578 blts LP1NEG
579 LP1ZERO:
580 fmoves negone,%fp0
581
582 fmovel %d1,%fpcr
583 bra t_dz
584
585 LP1NEG:
586 fmoves zero,%fp0
587
588 fmovel %d1,%fpcr
589 bra t_operr
590
591 |end
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