1 |
2 | stwotox.sa 3.1 12/10/90
3 |
4 | stwotox --- 2**X
5 | stwotoxd --- 2**X for denormalized X
6 | stentox --- 10**X
7 | stentoxd --- 10**X for denormalized X
8 |
9 | Input: Double-extended number X in loc
10 | by address register a0.
11 |
12 | Output: The function values are return
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 stwotox takes appro
20 | program stentox takes approxim
21 |
22 | Algorithm:
23 |
24 | twotox
25 | 1. If |X| > 16480, go to ExpBig.
26 |
27 | 2. If |X| < 2**(-70), go to ExpSm.
28 |
29 | 3. Decompose X as X = N/64 + r where |
30 | decompose N as
31 | N = 64(M + M') + j, j = 0,1,
32 |
33 | 4. Overwrite r := r * log2. Then
34 | 2**X = 2**(M') * 2**(M) * 2**(
35 | Go to expr to compute that exp
36 |
37 | tentox
38 | 1. If |X| > 16480*log_10(2) (base 10 l
39 |
40 | 2. If |X| < 2**(-70), go to ExpSm.
41 |
42 | 3. Set y := X*log_2(10)*64 (base 2 log
43 | N := round-to-int(y). Decompos
44 | N = 64(M + M') + j, j = 0,1,
45 |
46 | 4. Define r as
47 | r := ((X - N*L1)-N*L2) * L10
48 | where L1, L2 are the leading a
49 | and L10 is the natural log of
50 | 10**X = 2**(M') * 2**(M) * 2**
51 | Go to expr to compute that exp
52 |
53 | expr
54 | 1. Fetch 2**(j/64) from table as Fact1
55 |
56 | 2. Overwrite Fact1 and Fact2 by
57 | Fact1 := 2**(M) * Fact1
58 | Fact2 := 2**(M) * Fact2
59 | Thus Fact1 + Fact2 = 2**(M) *
60 |
61 | 3. Calculate P where 1 + P approximate
62 | P = r + r*r*(A1+r*(A2+...+r*A5
63 |
64 | 4. Let AdjFact := 2**(M'). Return
65 | AdjFact * ( Fact1 + ((Fact1*P)
66 | Exit.
67 |
68 | ExpBig
69 | 1. Generate overflow by Huge * Huge if
70 | underflow by Tiny * Tiny.
71 |
72 | ExpSm
73 | 1. Return 1 + X.
74 |
75
76 | Copyright (C) Motorola, Inc. 1
77 | All Rights Reserved
78 |
79 | For details on the license for this fi
80 | file, README, in this same directory.
81
82 |STWOTOX idnt 2,1 | Motorola 040 Flo
83
84 |section 8
85
86 #include "fpsp.h"
87
88 BOUNDS1: .long 0x3FB98000,0x400D80C0 |
89 BOUNDS2: .long 0x3FB98000,0x400B9B07 |
90
91 L2TEN64: .long 0x406A934F,0x0979A371 |
92 L10TWO1: .long 0x3F734413,0x509F8000 |
93
94 L10TWO2: .long 0xBFCD0000,0xC0219DC1,0x
95
96 LOG10: .long 0x40000000,0x935D8DDD,0xAAA8AC17
97
98 LOG2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC
99
100 EXPA5: .long 0x3F56C16D,0x6F7BD0B2
101 EXPA4: .long 0x3F811112,0x302C712C
102 EXPA3: .long 0x3FA55555,0x55554CC1
103 EXPA2: .long 0x3FC55555,0x55554A54
104 EXPA1: .long 0x3FE00000,0x00000000,0x00000000
105
106 HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF
107 TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF
108
109 EXPTBL:
110 .long 0x3FFF0000,0x80000000,0x0000000
111 .long 0x3FFF0000,0x8164D1F3,0xBC03077
112 .long 0x3FFF0000,0x82CD8698,0xAC2BA1D
113 .long 0x3FFF0000,0x843A28C3,0xACDE404
114 .long 0x3FFF0000,0x85AAC367,0xCC487B1
115 .long 0x3FFF0000,0x871F6196,0x9E8D101
116 .long 0x3FFF0000,0x88980E80,0x92DA852
117 .long 0x3FFF0000,0x8A14D575,0x496EFD9
118 .long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E
119 .long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E
120 .long 0x3FFF0000,0x8EA4398B,0x45CD53C
121 .long 0x3FFF0000,0x9031DC43,0x1466B1D
122 .long 0x3FFF0000,0x91C3D373,0xAB11C33
123 .long 0x3FFF0000,0x935A2B2F,0x13E6E92
124 .long 0x3FFF0000,0x94F4EFA8,0xFEF7096
125 .long 0x3FFF0000,0x96942D37,0x20185A0
126 .long 0x3FFF0000,0x9837F051,0x8DB8A96
127 .long 0x3FFF0000,0x99E04593,0x20B7FA6
128 .long 0x3FFF0000,0x9B8D39B9,0xD54E553
129 .long 0x3FFF0000,0x9D3ED9A7,0x2CFFB75
130 .long 0x3FFF0000,0x9EF53260,0x91A111A
131 .long 0x3FFF0000,0xA0B0510F,0xB9714FC
132 .long 0x3FFF0000,0xA2704303,0x0C49681
133 .long 0x3FFF0000,0xA43515AE,0x09E6809
134 .long 0x3FFF0000,0xA5FED6A9,0xB15138E
135 .long 0x3FFF0000,0xA7CD93B4,0xE965356
136 .long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF
137 .long 0x3FFF0000,0xAB7A39B5,0xA93ED33
138 .long 0x3FFF0000,0xAD583EEA,0x42A14AC
139 .long 0x3FFF0000,0xAF3B78AD,0x690A437
140 .long 0x3FFF0000,0xB123F581,0xD2AC259
141 .long 0x3FFF0000,0xB311C412,0xA911248
142 .long 0x3FFF0000,0xB504F333,0xF9DE648
143 .long 0x3FFF0000,0xB6FD91E3,0x28D1779
144 .long 0x3FFF0000,0xB8FBAF47,0x62FB9EE
145 .long 0x3FFF0000,0xBAFF5AB2,0x133E45F
146 .long 0x3FFF0000,0xBD08A39F,0x580C36B
147 .long 0x3FFF0000,0xBF1799B6,0x7A73108
148 .long 0x3FFF0000,0xC12C4CCA,0x6670945
149 .long 0x3FFF0000,0xC346CCDA,0x2497640
150 .long 0x3FFF0000,0xC5672A11,0x5506DAD
151 .long 0x3FFF0000,0xC78D74C8,0xABB9B15
152 .long 0x3FFF0000,0xC9B9BD86,0x6E2F27A
153 .long 0x3FFF0000,0xCBEC14FE,0xF2727C5
154 .long 0x3FFF0000,0xCE248C15,0x1F8480E
155 .long 0x3FFF0000,0xD06333DA,0xEF2B259
156 .long 0x3FFF0000,0xD2A81D91,0xF12AE45
157 .long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1
158 .long 0x3FFF0000,0xD744FCCA,0xD69D6AF
159 .long 0x3FFF0000,0xD99D15C2,0x78AFD7B
160 .long 0x3FFF0000,0xDBFBB797,0xDAF2375
161 .long 0x3FFF0000,0xDE60F482,0x5E0E912
162 .long 0x3FFF0000,0xE0CCDEEC,0x2A94E11
163 .long 0x3FFF0000,0xE33F8972,0xBE8A5A5
164 .long 0x3FFF0000,0xE5B906E7,0x7C8348A
165 .long 0x3FFF0000,0xE8396A50,0x3C4BDC6
166 .long 0x3FFF0000,0xEAC0C6E7,0xDD24392
167 .long 0x3FFF0000,0xED4F301E,0xD9942B8
168 .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5C
169 .long 0x3FFF0000,0xF281773C,0x59FFB13
170 .long 0x3FFF0000,0xF5257D15,0x2486CC2
171 .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB
172 .long 0x3FFF0000,0xFA83B2DB,0x722A033
173 .long 0x3FFF0000,0xFD3E0C0C,0xF486C17
174
175 .set N,L_SCR1
176
177 .set X,FP_SCR1
178 .set XDCARE,X+2
179 .set XFRAC,X+4
180
181 .set ADJFACT,FP_SCR2
182
183 .set FACT1,FP_SCR3
184 .set FACT1HI,FACT1+4
185 .set FACT1LOW,FACT1+8
186
187 .set FACT2,FP_SCR4
188 .set FACT2HI,FACT2+4
189 .set FACT2LOW,FACT2+8
190
191 | xref t_unfl
192 |xref t_ovfl
193 |xref t_frcinx
194
195 .global stwotoxd
196 stwotoxd:
197 |--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARG
198
199 fmovel %d1,%fpcr
200 fmoves #0x3F800000,%fp0 | ..
201 movel (%a0),%d0
202 orl #0x00800001,%d0
203 fadds %d0,%fp0
204 bra t_frcinx
205
206 .global stwotox
207 stwotox:
208 |--ENTRY POINT FOR 2**(X), HERE X IS FINITE, N
209 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPU
210
211 movel (%a0),%d0
212 movew 4(%a0),%d0
213 fmovex %fp0,X(%a6)
214 andil #0x7FFFFFFF,%d0
215
216 cmpil #0x3FB98000,%d0
217 bges TWOOK1
218 bra EXPBORS
219
220 TWOOK1:
221 cmpil #0x400D80C0,%d0
222 bles TWOMAIN
223 bra EXPBORS
224
225
226 TWOMAIN:
227 |--USUAL CASE, 2^(-70) <= |X| <= 16480
228
229 fmovex %fp0,%fp1
230 fmuls #0x42800000,%fp1 | ..
231
232 fmovel %fp1,N(%a6)
233 movel %d2,-(%sp)
234 lea EXPTBL,%a1 | ...L
235 fmovel N(%a6),%fp1
236 movel N(%a6),%d0
237 movel %d0,%d2
238 andil #0x3F,%d0
239 asll #4,%d0 | ...D
240 addal %d0,%a1 | ...A
241 asrl #6,%d2 | ...d
242 movel %d2,%d0
243 asrl #1,%d0 | ...D
244 subl %d0,%d2 | ...d
245 addil #0x3FFF,%d2
246 movew %d2,ADJFACT(%a6)
247 movel (%sp)+,%d2
248 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORT
249 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |
250 |--ADJFACT = 2^(M').
251 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR,
252
253 fmuls #0x3C800000,%fp1 | ..
254 movel (%a1)+,FACT1(%a6)
255 movel (%a1)+,FACT1HI(%a6)
256 movel (%a1)+,FACT1LOW(%a6)
257 movew (%a1)+,FACT2(%a6)
258 clrw FACT2+2(%a6)
259
260 fsubx %fp1,%fp0
261
262 movew (%a1)+,FACT2HI(%a6)
263 clrw FACT2HI+2(%a6)
264 clrl FACT2LOW(%a6)
265 addw %d0,FACT1(%a6)
266
267 fmulx LOG2,%fp0 | ...F
268 addw %d0,FACT2(%a6)
269
270 bra expr
271
272 EXPBORS:
273 |--FPCR, D0 SAVED
274 cmpil #0x3FFF8000,%d0
275 bgts EXPBIG
276
277 EXPSM:
278 |--|X| IS SMALL, RETURN 1 + X
279
280 fmovel %d1,%FPCR
281 fadds #0x3F800000,%fp0 | ..
282
283 bra t_frcinx
284
285 EXPBIG:
286 |--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; E
287 |--REGISTERS SAVE SO FAR ARE FPCR AND D0
288 movel X(%a6),%d0
289 cmpil #0,%d0
290 blts EXPNEG
291
292 bclrb #7,(%a0)
293 bra t_ovfl
294
295 EXPNEG:
296 bclrb #7,(%a0)
297 bra t_unfl
298
299 .global stentoxd
300 stentoxd:
301 |--ENTRY POINT FOR 10**(X) FOR DENORMALIZED AR
302
303 fmovel %d1,%fpcr
304 fmoves #0x3F800000,%fp0 | ..
305 movel (%a0),%d0
306 orl #0x00800001,%d0
307 fadds %d0,%fp0
308 bra t_frcinx
309
310 .global stentox
311 stentox:
312 |--ENTRY POINT FOR 10**(X), HERE X IS FINITE,
313 fmovemx (%a0),%fp0-%fp0 | ...LOAD INPU
314
315 movel (%a0),%d0
316 movew 4(%a0),%d0
317 fmovex %fp0,X(%a6)
318 andil #0x7FFFFFFF,%d0
319
320 cmpil #0x3FB98000,%d0
321 bges TENOK1
322 bra EXPBORS
323
324 TENOK1:
325 cmpil #0x400B9B07,%d0
326 bles TENMAIN
327 bra EXPBORS
328
329 TENMAIN:
330 |--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 /
331
332 fmovex %fp0,%fp1
333 fmuld L2TEN64,%fp1 | ...X
334
335 fmovel %fp1,N(%a6)
336 movel %d2,-(%sp)
337 lea EXPTBL,%a1 | ...L
338 fmovel N(%a6),%fp1
339 movel N(%a6),%d0
340 movel %d0,%d2
341 andil #0x3F,%d0
342 asll #4,%d0 | ...D
343 addal %d0,%a1 | ...A
344 asrl #6,%d2 | ...d
345 movel %d2,%d0
346 asrl #1,%d0 | ...D
347 subl %d0,%d2 | ...d
348 addil #0x3FFF,%d2
349 movew %d2,ADJFACT(%a6)
350 movel (%sp)+,%d2
351
352 |--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORT
353 |--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |
354 |--ADJFACT = 2^(M').
355 |--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR,
356
357 fmovex %fp1,%fp2
358
359 fmuld L10TWO1,%fp1 | ...N
360 movel (%a1)+,FACT1(%a6)
361
362 fmulx L10TWO2,%fp2 | ...N
363
364 movel (%a1)+,FACT1HI(%a6)
365 movel (%a1)+,FACT1LOW(%a6)
366 fsubx %fp1,%fp0
367 movew (%a1)+,FACT2(%a6)
368
369 fsubx %fp2,%fp0
370
371 clrw FACT2+2(%a6)
372 movew (%a1)+,FACT2HI(%a6)
373 clrw FACT2HI+2(%a6)
374 clrl FACT2LOW(%a6)
375
376 fmulx LOG10,%fp0 | ...F
377
378 addw %d0,FACT1(%a6)
379 addw %d0,FACT2(%a6)
380
381 expr:
382 |--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
383 |--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2
384 |--FP0 IS R. THE FOLLOWING CODE COMPUTES
385 |-- 2**(M'+M) * 2**(J/64) * EXP(R)
386
387 fmovex %fp0,%fp1
388 fmulx %fp1,%fp1
389
390 fmoved EXPA5,%fp2 | ...F
391 fmoved EXPA4,%fp3 | ...F
392
393 fmulx %fp1,%fp2
394 fmulx %fp1,%fp3
395
396 faddd EXPA3,%fp2 | ...F
397 faddd EXPA2,%fp3 | ...F
398
399 fmulx %fp1,%fp2
400 fmulx %fp1,%fp3
401
402 faddd EXPA1,%fp2 | ...F
403 fmulx %fp0,%fp3
404
405 fmulx %fp1,%fp2
406 faddx %fp3,%fp0
407
408 faddx %fp2,%fp0
409
410
411 |--FINAL RECONSTRUCTION PROCESS
412 |--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R
413
414 fmulx FACT1(%a6),%fp0
415 faddx FACT2(%a6),%fp0
416 faddx FACT1(%a6),%fp0
417
418 fmovel %d1,%FPCR
419 clrw ADJFACT+2(%a6)
420 movel #0x80000000,ADJFACT+4(
421 clrl ADJFACT+8(%a6)
422 fmulx ADJFACT(%a6),%fp0
423
424 bra t_frcinx
425
426 |end
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