1|
2| srem_mod.sa 3.1 12/10/90
3|
4| The entry point sMOD computes the floating point MOD of the
5| input values X and Y. The entry point sREM computes the floating
6| point (IEEE) REM of the input values X and Y.
7|
8| INPUT
9| -----
10| Double-extended value Y is pointed to by address in register
11| A0. Double-extended value X is located in -12(A0). The values
12| of X and Y are both nonzero and finite; although either or both
13| of them can be denormalized. The special cases of zeros, NaNs,
14| and infinities are handled elsewhere.
15|
16| OUTPUT
17| ------
18| FREM(X,Y) or FMOD(X,Y), depending on entry point.
19|
20| ALGORITHM
21| ---------
22|
23| Step 1. Save and strip signs of X and Y: signX := sign(X),
24| signY := sign(Y), X := |X|, Y := |Y|,
25| signQ := signX EOR signY. Record whether MOD or REM
26| is requested.
27|
28| Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0.
29| If (L < 0) then
30| R := X, go to Step 4.
31| else
32| R := 2^(-L)X, j := L.
33| endif
34|
35| Step 3. Perform MOD(X,Y)
36| 3.1 If R = Y, go to Step 9.
37| 3.2 If R > Y, then { R := R - Y, Q := Q + 1}
38| 3.3 If j = 0, go to Step 4.
39| 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
40| Step 3.1.
41|
42| Step 4. At this point, R = X - QY = MOD(X,Y). Set
43| Last_Subtract := false (used in Step 7 below). If
44| MOD is requested, go to Step 6.
45|
46| Step 5. R = MOD(X,Y), but REM(X,Y) is requested.
47| 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
48| Step 6.
49| 5.2 If R > Y/2, then { set Last_Subtract := true,
50| Q := Q + 1, Y := signY*Y }. Go to Step 6.
51| 5.3 This is the tricky case of R = Y/2. If Q is odd,
52| then { Q := Q + 1, signX := -signX }.
53|
54| Step 6. R := signX*R.
55|
56| Step 7. If Last_Subtract = true, R := R - Y.
57|
58| Step 8. Return signQ, last 7 bits of Q, and R as required.
59|
60| Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus,
61| X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
62| R := 0. Return signQ, last 7 bits of Q, and R.
63|
64|
65
66| Copyright (C) Motorola, Inc. 1990
67| All Rights Reserved
68|
69| For details on the license for this file, please see the
70| file, README, in this same directory.
71
72SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package
73
74 |section 8
75
76#include "fpsp.h"
77
78 .set Mod_Flag,L_SCR3
79 .set SignY,FP_SCR3+4
80 .set SignX,FP_SCR3+8
81 .set SignQ,FP_SCR3+12
82 .set Sc_Flag,FP_SCR4
83
84 .set Y,FP_SCR1
85 .set Y_Hi,Y+4
86 .set Y_Lo,Y+8
87
88 .set R,FP_SCR2
89 .set R_Hi,R+4
90 .set R_Lo,R+8
91
92
93Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000
94
95 |xref t_avoid_unsupp
96
97 .global smod
98smod:
99
100 movel
101 bras Mod_Rem
102
103 .global srem
104srem:
105
106 movel
107
108Mod_Rem:
109|..Save sign of X and Y
110 moveml %d2-%d7,-(%a7) | ...save data registers
111 movew (%a0),%d3
112 movew %d3,SignY(%a6)
113 andil
114
115|
116 movel 4(%a0),%d4
117 movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y|
118
119 tstl %d3
120 bnes Y_Normal
121
122 movel
123 tstl %d4
124 bnes HiY_not0
125
126HiY_0:
127 movel %d5,%d4
128 clrl %d5
129 subil
130 clrl %d6
131 bfffo %d4{
132 lsll %d6,%d4
133 subl %d6,%d3 | ...(D3,D4,D5) is normalized
134| ...with bias $7FFD
135 bras Chk_X
136
137HiY_not0:
138 clrl %d6
139 bfffo %d4{
140 subl %d6,%d3
141 lsll %d6,%d4
142 movel %d5,%d7 | ...a copy of D5
143 lsll %d6,%d5
144 negl %d6
145 addil
146 lsrl %d6,%d7
147 orl %d7,%d4 | ...(D3,D4,D5) normalized
148| ...with bias $7FFD
149 bras Chk_X
150
151Y_Normal:
152 addil
153| ...with bias $7FFD
154
155Chk_X:
156 movew -12(%a0),%d0
157 movew %d0,SignX(%a6)
158 movew SignY(%a6),%d1
159 eorl %d0,%d1
160 andil
161 movew %d1,SignQ(%a6) | ...sign(Q) obtained
162 andil
163 movel -8(%a0),%d1
164 movel -4(%a0),%d2 | ...(D0,D1,D2) is |X|
165 tstl %d0
166 bnes X_Normal
167 movel
168 tstl %d1
169 bnes HiX_not0
170
171HiX_0:
172 movel %d2,%d1
173 clrl %d2
174 subil
175 clrl %d6
176 bfffo %d1{
177 lsll %d6,%d1
178 subl %d6,%d0 | ...(D0,D1,D2) is normalized
179| ...with bias $7FFD
180 bras Init
181
182HiX_not0:
183 clrl %d6
184 bfffo %d1{
185 subl %d6,%d0
186 lsll %d6,%d1
187 movel %d2,%d7 | ...a copy of D2
188 lsll %d6,%d2
189 negl %d6
190 addil
191 lsrl %d6,%d7
192 orl %d7,%d1 | ...(D0,D1,D2) normalized
193| ...with bias $7FFD
194 bras Init
195
196X_Normal:
197 addil
198| ...with bias $7FFD
199
200Init:
201|
202 movel %d3,L_SCR1(%a6) | ...save biased expo(Y)
203 movel %d0,L_SCR2(%a6) |save d0
204 subl %d3,%d0 | ...L := expo(X)-expo(Y)
205| Move.L D0,L ...D0 is j
206 clrl %d6 | ...D6 := carry <- 0
207 clrl %d3 | ...D3 is Q
208 moveal
209
210|..(Carry,D1,D2) is R
211 tstl %d0
212 bges Mod_Loop
213
214|..expo(X) < expo(Y). Thus X = mod(X,Y)
215|
216 movel L_SCR2(%a6),%d0 |restore d0
217 bra Get_Mod
218
219|..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
220
221
222Mod_Loop:
223 tstl %d6 | ...test carry bit
224 bgts R_GT_Y
225
226|..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
227 cmpl %d4,%d1 | ...compare hi(R) and hi(Y)
228 bnes R_NE_Y
229 cmpl %d5,%d2 | ...compare lo(R) and lo(Y)
230 bnes R_NE_Y
231
232|..At this point, R = Y
233 bra Rem_is_0
234
235R_NE_Y:
236|..use the borrow of the previous compare
237 bcss R_LT_Y | ...borrow is set iff R < Y
238
239R_GT_Y:
240|..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
241|..and Y < (D1,D2) < 2Y. Either way, perform R - Y
242 subl %d5,%d2 | ...lo(R) - lo(Y)
243 subxl %d4,%d1 | ...hi(R) - hi(Y)
244 clrl %d6 | ...clear carry
245 addql
246
247R_LT_Y:
248|..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
249 tstl %d0 | ...see if j = 0.
250 beqs PostLoop
251
252 addl %d3,%d3 | ...Q := 2Q
253 addl %d2,%d2 | ...lo(R) = 2lo(R)
254 roxll
255 scs %d6 | ...set Carry if 2(R) overflows
256 addql
257 subql
258|..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
259
260 bras Mod_Loop
261
262PostLoop:
263|..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
264
265|..normalize R.
266 movel L_SCR1(%a6),%d0 | ...new biased expo of R
267 tstl %d1
268 bnes HiR_not0
269
270HiR_0:
271 movel %d2,%d1
272 clrl %d2
273 subil
274 clrl %d6
275 bfffo %d1{
276 lsll %d6,%d1
277 subl %d6,%d0 | ...(D0,D1,D2) is normalized
278| ...with bias $7FFD
279 bras Get_Mod
280
281HiR_not0:
282 clrl %d6
283 bfffo %d1{
284 bmis Get_Mod | ...already normalized
285 subl %d6,%d0
286 lsll %d6,%d1
287 movel %d2,%d7 | ...a copy of D2
288 lsll %d6,%d2
289 negl %d6
290 addil
291 lsrl %d6,%d7
292 orl %d7,%d1 | ...(D0,D1,D2) normalized
293
294|
295Get_Mod:
296 cmpil
297 bges No_Scale
298Do_Scale:
299 movew %d0,R(%a6)
300 clrw R+2(%a6)
301 movel %d1,R_Hi(%a6)
302 movel %d2,R_Lo(%a6)
303 movel L_SCR1(%a6),%d6
304 movew %d6,Y(%a6)
305 clrw Y+2(%a6)
306 movel %d4,Y_Hi(%a6)
307 movel %d5,Y_Lo(%a6)
308 fmovex R(%a6),%fp0 | ...no exception
309 movel
310 bras ModOrRem
311No_Scale:
312 movel %d1,R_Hi(%a6)
313 movel %d2,R_Lo(%a6)
314 subil
315 movew %d0,R(%a6)
316 clrw R+2(%a6)
317 movel L_SCR1(%a6),%d6
318 subil
319 movel %d6,L_SCR1(%a6)
320 fmovex R(%a6),%fp0
321 movew %d6,Y(%a6)
322 movel %d4,Y_Hi(%a6)
323 movel %d5,Y_Lo(%a6)
324 movel
325
326|
327
328
329ModOrRem:
330 movel Mod_Flag(%a6),%d6
331 beqs Fix_Sign
332
333 movel L_SCR1(%a6),%d6 | ...new biased expo(Y)
334 subql
335 cmpl %d6,%d0
336 blts Fix_Sign
337 bgts Last_Sub
338
339 cmpl %d4,%d1
340 bnes Not_EQ
341 cmpl %d5,%d2
342 bnes Not_EQ
343 bra Tie_Case
344
345Not_EQ:
346 bcss Fix_Sign
347
348Last_Sub:
349|
350 fsubx Y(%a6),%fp0 | ...no exceptions
351 addql
352
353|
354
355Fix_Sign:
356|..Get sign of X
357 movew SignX(%a6),%d6
358 bges Get_Q
359 fnegx %fp0
360
361|..Get Q
362|
363Get_Q:
364 clrl %d6
365 movew SignQ(%a6),%d6 | ...D6 is sign(Q)
366 movel
367 lsrl %d7,%d6
368 andil
369 orl %d6,%d3 | ...sign and bits of Q
370 swap %d3
371 fmovel %fpsr,%d6
372 andil
373 orl %d3,%d6
374 fmovel %d6,%fpsr | ...put Q in fpsr
375
376|
377Restore:
378 moveml (%a7)+,%d2-%d7
379 fmovel USER_FPCR(%a6),%fpcr
380 movel Sc_Flag(%a6),%d0
381 beqs Finish
382 fmulx Scale(%pc),%fp0 | ...may cause underflow
383 bra t_avoid_unsupp |check for denorm as a
384| ;result of the scaling
385
386Finish:
387 fmovex %fp0,%fp0 |capture exceptions & round
388 rts
389
390Rem_is_0:
391|..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
392 addql
393 cmpil
394 bges Q_Big
395
396 lsll %d0,%d3
397 bras Set_R_0
398
399Q_Big:
400 clrl %d3
401
402Set_R_0:
403 fmoves
404 movel
405 bra Fix_Sign
406
407Tie_Case:
408|..Check parity of Q
409 movel %d3,%d6
410 andil
411 tstl %d6
412 beq Fix_Sign | ...Q is even
413
414|..Q is odd, Q := Q + 1, signX := -signX
415 addql
416 movew SignX(%a6),%d6
417 eoril
418 movew %d6,SignX(%a6)
419 bra Fix_Sign
420
421 |end
422
