srem_mod.S
12 KB
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
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
|
| srem_mod.sa 3.1 12/10/90
|
| The entry point sMOD computes the floating point MOD of the
| input values X and Y. The entry point sREM computes the floating
| point (IEEE) REM of the input values X and Y.
|
| INPUT
| -----
| Double-extended value Y is pointed to by address in register
| A0. Double-extended value X is located in -12(A0). The values
| of X and Y are both nonzero and finite; although either or both
| of them can be denormalized. The special cases of zeros, NaNs,
| and infinities are handled elsewhere.
|
| OUTPUT
| ------
| FREM(X,Y) or FMOD(X,Y), depending on entry point.
|
| ALGORITHM
| ---------
|
| Step 1. Save and strip signs of X and Y: signX := sign(X),
| signY := sign(Y), X := |X|, Y := |Y|,
| signQ := signX EOR signY. Record whether MOD or REM
| is requested.
|
| Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0.
| If (L < 0) then
| R := X, go to Step 4.
| else
| R := 2^(-L)X, j := L.
| endif
|
| Step 3. Perform MOD(X,Y)
| 3.1 If R = Y, go to Step 9.
| 3.2 If R > Y, then { R := R - Y, Q := Q + 1}
| 3.3 If j = 0, go to Step 4.
| 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
| Step 3.1.
|
| Step 4. At this point, R = X - QY = MOD(X,Y). Set
| Last_Subtract := false (used in Step 7 below). If
| MOD is requested, go to Step 6.
|
| Step 5. R = MOD(X,Y), but REM(X,Y) is requested.
| 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
| Step 6.
| 5.2 If R > Y/2, then { set Last_Subtract := true,
| Q := Q + 1, Y := signY*Y }. Go to Step 6.
| 5.3 This is the tricky case of R = Y/2. If Q is odd,
| then { Q := Q + 1, signX := -signX }.
|
| Step 6. R := signX*R.
|
| Step 7. If Last_Subtract = true, R := R - Y.
|
| Step 8. Return signQ, last 7 bits of Q, and R as required.
|
| Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus,
| X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
| R := 0. Return signQ, last 7 bits of Q, and R.
|
|
| Copyright (C) Motorola, Inc. 1990
| All Rights Reserved
|
| For details on the license for this file, please see the
| file, README, in this same directory.
SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
#include "fpsp.h"
.set Mod_Flag,L_SCR3
.set SignY,FP_SCR3+4
.set SignX,FP_SCR3+8
.set SignQ,FP_SCR3+12
.set Sc_Flag,FP_SCR4
.set Y,FP_SCR1
.set Y_Hi,Y+4
.set Y_Lo,Y+8
.set R,FP_SCR2
.set R_Hi,R+4
.set R_Lo,R+8
Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000
|xref t_avoid_unsupp
.global smod
smod:
movel #0,Mod_Flag(%a6)
bras Mod_Rem
.global srem
srem:
movel #1,Mod_Flag(%a6)
Mod_Rem:
|..Save sign of X and Y
moveml %d2-%d7,-(%a7) | ...save data registers
movew (%a0),%d3
movew %d3,SignY(%a6)
andil #0x00007FFF,%d3 | ...Y := |Y|
|
movel 4(%a0),%d4
movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y|
tstl %d3
bnes Y_Normal
movel #0x00003FFE,%d3 | ...$3FFD + 1
tstl %d4
bnes HiY_not0
HiY_0:
movel %d5,%d4
clrl %d5
subil #32,%d3
clrl %d6
bfffo %d4{#0:#32},%d6
lsll %d6,%d4
subl %d6,%d3 | ...(D3,D4,D5) is normalized
| ...with bias $7FFD
bras Chk_X
HiY_not0:
clrl %d6
bfffo %d4{#0:#32},%d6
subl %d6,%d3
lsll %d6,%d4
movel %d5,%d7 | ...a copy of D5
lsll %d6,%d5
negl %d6
addil #32,%d6
lsrl %d6,%d7
orl %d7,%d4 | ...(D3,D4,D5) normalized
| ...with bias $7FFD
bras Chk_X
Y_Normal:
addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized
| ...with bias $7FFD
Chk_X:
movew -12(%a0),%d0
movew %d0,SignX(%a6)
movew SignY(%a6),%d1
eorl %d0,%d1
andil #0x00008000,%d1
movew %d1,SignQ(%a6) | ...sign(Q) obtained
andil #0x00007FFF,%d0
movel -8(%a0),%d1
movel -4(%a0),%d2 | ...(D0,D1,D2) is |X|
tstl %d0
bnes X_Normal
movel #0x00003FFE,%d0
tstl %d1
bnes HiX_not0
HiX_0:
movel %d2,%d1
clrl %d2
subil #32,%d0
clrl %d6
bfffo %d1{#0:#32},%d6
lsll %d6,%d1
subl %d6,%d0 | ...(D0,D1,D2) is normalized
| ...with bias $7FFD
bras Init
HiX_not0:
clrl %d6
bfffo %d1{#0:#32},%d6
subl %d6,%d0
lsll %d6,%d1
movel %d2,%d7 | ...a copy of D2
lsll %d6,%d2
negl %d6
addil #32,%d6
lsrl %d6,%d7
orl %d7,%d1 | ...(D0,D1,D2) normalized
| ...with bias $7FFD
bras Init
X_Normal:
addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized
| ...with bias $7FFD
Init:
|
movel %d3,L_SCR1(%a6) | ...save biased expo(Y)
movel %d0,L_SCR2(%a6) |save d0
subl %d3,%d0 | ...L := expo(X)-expo(Y)
| Move.L D0,L ...D0 is j
clrl %d6 | ...D6 := carry <- 0
clrl %d3 | ...D3 is Q
moveal #0,%a1 | ...A1 is k; j+k=L, Q=0
|..(Carry,D1,D2) is R
tstl %d0
bges Mod_Loop
|..expo(X) < expo(Y). Thus X = mod(X,Y)
|
movel L_SCR2(%a6),%d0 |restore d0
bra Get_Mod
|..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
Mod_Loop:
tstl %d6 | ...test carry bit
bgts R_GT_Y
|..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
cmpl %d4,%d1 | ...compare hi(R) and hi(Y)
bnes R_NE_Y
cmpl %d5,%d2 | ...compare lo(R) and lo(Y)
bnes R_NE_Y
|..At this point, R = Y
bra Rem_is_0
R_NE_Y:
|..use the borrow of the previous compare
bcss R_LT_Y | ...borrow is set iff R < Y
R_GT_Y:
|..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
|..and Y < (D1,D2) < 2Y. Either way, perform R - Y
subl %d5,%d2 | ...lo(R) - lo(Y)
subxl %d4,%d1 | ...hi(R) - hi(Y)
clrl %d6 | ...clear carry
addql #1,%d3 | ...Q := Q + 1
R_LT_Y:
|..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
tstl %d0 | ...see if j = 0.
beqs PostLoop
addl %d3,%d3 | ...Q := 2Q
addl %d2,%d2 | ...lo(R) = 2lo(R)
roxll #1,%d1 | ...hi(R) = 2hi(R) + carry
scs %d6 | ...set Carry if 2(R) overflows
addql #1,%a1 | ...k := k+1
subql #1,%d0 | ...j := j - 1
|..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
bras Mod_Loop
PostLoop:
|..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
|..normalize R.
movel L_SCR1(%a6),%d0 | ...new biased expo of R
tstl %d1
bnes HiR_not0
HiR_0:
movel %d2,%d1
clrl %d2
subil #32,%d0
clrl %d6
bfffo %d1{#0:#32},%d6
lsll %d6,%d1
subl %d6,%d0 | ...(D0,D1,D2) is normalized
| ...with bias $7FFD
bras Get_Mod
HiR_not0:
clrl %d6
bfffo %d1{#0:#32},%d6
bmis Get_Mod | ...already normalized
subl %d6,%d0
lsll %d6,%d1
movel %d2,%d7 | ...a copy of D2
lsll %d6,%d2
negl %d6
addil #32,%d6
lsrl %d6,%d7
orl %d7,%d1 | ...(D0,D1,D2) normalized
|
Get_Mod:
cmpil #0x000041FE,%d0
bges No_Scale
Do_Scale:
movew %d0,R(%a6)
clrw R+2(%a6)
movel %d1,R_Hi(%a6)
movel %d2,R_Lo(%a6)
movel L_SCR1(%a6),%d6
movew %d6,Y(%a6)
clrw Y+2(%a6)
movel %d4,Y_Hi(%a6)
movel %d5,Y_Lo(%a6)
fmovex R(%a6),%fp0 | ...no exception
movel #1,Sc_Flag(%a6)
bras ModOrRem
No_Scale:
movel %d1,R_Hi(%a6)
movel %d2,R_Lo(%a6)
subil #0x3FFE,%d0
movew %d0,R(%a6)
clrw R+2(%a6)
movel L_SCR1(%a6),%d6
subil #0x3FFE,%d6
movel %d6,L_SCR1(%a6)
fmovex R(%a6),%fp0
movew %d6,Y(%a6)
movel %d4,Y_Hi(%a6)
movel %d5,Y_Lo(%a6)
movel #0,Sc_Flag(%a6)
|
ModOrRem:
movel Mod_Flag(%a6),%d6
beqs Fix_Sign
movel L_SCR1(%a6),%d6 | ...new biased expo(Y)
subql #1,%d6 | ...biased expo(Y/2)
cmpl %d6,%d0
blts Fix_Sign
bgts Last_Sub
cmpl %d4,%d1
bnes Not_EQ
cmpl %d5,%d2
bnes Not_EQ
bra Tie_Case
Not_EQ:
bcss Fix_Sign
Last_Sub:
|
fsubx Y(%a6),%fp0 | ...no exceptions
addql #1,%d3 | ...Q := Q + 1
|
Fix_Sign:
|..Get sign of X
movew SignX(%a6),%d6
bges Get_Q
fnegx %fp0
|..Get Q
|
Get_Q:
clrl %d6
movew SignQ(%a6),%d6 | ...D6 is sign(Q)
movel #8,%d7
lsrl %d7,%d6
andil #0x0000007F,%d3 | ...7 bits of Q
orl %d6,%d3 | ...sign and bits of Q
swap %d3
fmovel %fpsr,%d6
andil #0xFF00FFFF,%d6
orl %d3,%d6
fmovel %d6,%fpsr | ...put Q in fpsr
|
Restore:
moveml (%a7)+,%d2-%d7
fmovel USER_FPCR(%a6),%fpcr
movel Sc_Flag(%a6),%d0
beqs Finish
fmulx Scale(%pc),%fp0 | ...may cause underflow
bra t_avoid_unsupp |check for denorm as a
| ;result of the scaling
Finish:
fmovex %fp0,%fp0 |capture exceptions & round
rts
Rem_is_0:
|..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
addql #1,%d3
cmpil #8,%d0 | ...D0 is j
bges Q_Big
lsll %d0,%d3
bras Set_R_0
Q_Big:
clrl %d3
Set_R_0:
fmoves #0x00000000,%fp0
movel #0,Sc_Flag(%a6)
bra Fix_Sign
Tie_Case:
|..Check parity of Q
movel %d3,%d6
andil #0x00000001,%d6
tstl %d6
beq Fix_Sign | ...Q is even
|..Q is odd, Q := Q + 1, signX := -signX
addql #1,%d3
movew SignX(%a6),%d6
eoril #0x00008000,%d6
movew %d6,SignX(%a6)
bra Fix_Sign
|end