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69 | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
70 | The copyright notice above does not evidence any
71 | actual or intended publication of such source code.
72
73 SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package
74
75 |section 8
76
77 .include "fpsp.h"
78
79 .set Mod_Flag,L_SCR3
80 .set SignY,FP_SCR3+4
81 .set SignX,FP_SCR3+8
82 .set SignQ,FP_SCR3+12
83 .set Sc_Flag,FP_SCR4
84
85 .set Y,FP_SCR1
86 .set Y_Hi,Y+4
87 .set Y_Lo,Y+8
88
89 .set R,FP_SCR2
90 .set R_Hi,R+4
91 .set R_Lo,R+8
92
93
94 Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000
95
96 |xref t_avoid_unsupp
97
98 .global smod
99 smod:
100
101 movel #0,Mod_Flag(%a6)
102 bras Mod_Rem
103
104 .global srem
105 srem:
106
107 movel #1,Mod_Flag(%a6)
108
109 Mod_Rem:
110 |..Save sign of X and Y
111 moveml %d2-%d7,-(%a7) | ...save data registers
112 movew (%a0),%d3
113 movew %d3,SignY(%a6)
114 andil #0x00007FFF,%d3 | ...Y := |Y|
115
116 |
117 movel 4(%a0),%d4
118 movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y|
119
120 tstl %d3
121 bnes Y_Normal
122
123 movel #0x00003FFE,%d3 | ...$3FFD + 1
124 tstl %d4
125 bnes HiY_not0
126
127 HiY_0:
128 movel %d5,%d4
129 clrl %d5
130 subil #32,%d3
131 clrl %d6
132 bfffo %d4{#0:#32},%d6
133 lsll %d6,%d4
134 subl %d6,%d3 | ...(D3,D4,D5) is normalized
135 | ...with bias $7FFD
136 bras Chk_X
137
138 HiY_not0:
139 clrl %d6
140 bfffo %d4{#0:#32},%d6
141 subl %d6,%d3
142 lsll %d6,%d4
143 movel %d5,%d7 | ...a copy of D5
144 lsll %d6,%d5
145 negl %d6
146 addil #32,%d6
147 lsrl %d6,%d7
148 orl %d7,%d4 | ...(D3,D4,D5) normalized
149 | ...with bias $7FFD
150 bras Chk_X
151
152 Y_Normal:
153 addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized
154 | ...with bias $7FFD
155
156 Chk_X:
157 movew -12(%a0),%d0
158 movew %d0,SignX(%a6)
159 movew SignY(%a6),%d1
160 eorl %d0,%d1
161 andil #0x00008000,%d1
162 movew %d1,SignQ(%a6) | ...sign(Q) obtained
163 andil #0x00007FFF,%d0
164 movel -8(%a0),%d1
165 movel -4(%a0),%d2 | ...(D0,D1,D2) is |X|
166 tstl %d0
167 bnes X_Normal
168 movel #0x00003FFE,%d0
169 tstl %d1
170 bnes HiX_not0
171
172 HiX_0:
173 movel %d2,%d1
174 clrl %d2
175 subil #32,%d0
176 clrl %d6
177 bfffo %d1{#0:#32},%d6
178 lsll %d6,%d1
179 subl %d6,%d0 | ...(D0,D1,D2) is normalized
180 | ...with bias $7FFD
181 bras Init
182
183 HiX_not0:
184 clrl %d6
185 bfffo %d1{#0:#32},%d6
186 subl %d6,%d0
187 lsll %d6,%d1
188 movel %d2,%d7 | ...a copy of D2
189 lsll %d6,%d2
190 negl %d6
191 addil #32,%d6
192 lsrl %d6,%d7
193 orl %d7,%d1 | ...(D0,D1,D2) normalized
194 | ...with bias $7FFD
195 bras Init
196
197 X_Normal:
198 addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized
199 | ...with bias $7FFD
200
201 Init:
202 |
203 movel %d3,L_SCR1(%a6) | ...save biased expo(Y)
204 movel %d0,L_SCR2(%a6) |save d0
205 subl %d3,%d0 | ...L := expo(X)-expo(Y)
206 | Move.L D0,L ...D0 is j
207 clrl %d6 | ...D6 := carry <- 0
208 clrl %d3 | ...D3 is Q
209 moveal #0,%a1 | ...A1 is k; j+k=L, Q=0
210
211 |..(Carry,D1,D2) is R
212 tstl %d0
213 bges Mod_Loop
214
215 |..expo(X) < expo(Y). Thus X = mod(X,Y)
216 |
217 movel L_SCR2(%a6),%d0 |restore d0
218 bra Get_Mod
219
220 |..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
221
222
223 Mod_Loop:
224 tstl %d6 | ...test carry bit
225 bgts R_GT_Y
226
227 |..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
228 cmpl %d4,%d1 | ...compare hi(R) and hi(Y)
229 bnes R_NE_Y
230 cmpl %d5,%d2 | ...compare lo(R) and lo(Y)
231 bnes R_NE_Y
232
233 |..At this point, R = Y
234 bra Rem_is_0
235
236 R_NE_Y:
237 |..use the borrow of the previous compare
238 bcss R_LT_Y | ...borrow is set iff R < Y
239
240 R_GT_Y:
241 |..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
242 |..and Y < (D1,D2) < 2Y. Either way, perform R - Y
243 subl %d5,%d2 | ...lo(R) - lo(Y)
244 subxl %d4,%d1 | ...hi(R) - hi(Y)
245 clrl %d6 | ...clear carry
246 addql #1,%d3 | ...Q := Q + 1
247
248 R_LT_Y:
249 |..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
250 tstl %d0 | ...see if j = 0.
251 beqs PostLoop
252
253 addl %d3,%d3 | ...Q := 2Q
254 addl %d2,%d2 | ...lo(R) = 2lo(R)
255 roxll #1,%d1 | ...hi(R) = 2hi(R) + carry
256 scs %d6 | ...set Carry if 2(R) overflows
257 addql #1,%a1 | ...k := k+1
258 subql #1,%d0 | ...j := j - 1
259 |..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
260
261 bras Mod_Loop
262
263 PostLoop:
264 |..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
265
266 |..normalize R.
267 movel L_SCR1(%a6),%d0 | ...new biased expo of R
268 tstl %d1
269 bnes HiR_not0
270
271 HiR_0:
272 movel %d2,%d1
273 clrl %d2
274 subil #32,%d0
275 clrl %d6
276 bfffo %d1{#0:#32},%d6
277 lsll %d6,%d1
278 subl %d6,%d0 | ...(D0,D1,D2) is normalized
279 | ...with bias $7FFD
280 bras Get_Mod
281
282 HiR_not0:
283 clrl %d6
284 bfffo %d1{#0:#32},%d6
285 bmis Get_Mod | ...already normalized
286 subl %d6,%d0
287 lsll %d6,%d1
288 movel %d2,%d7 | ...a copy of D2
289 lsll %d6,%d2
290 negl %d6
291 addil #32,%d6
292 lsrl %d6,%d7
293 orl %d7,%d1 | ...(D0,D1,D2) normalized
294
295 |
296 Get_Mod:
297 cmpil #0x000041FE,%d0
298 bges No_Scale
299 Do_Scale:
300 movew %d0,R(%a6)
301 clrw R+2(%a6)
302 movel %d1,R_Hi(%a6)
303 movel %d2,R_Lo(%a6)
304 movel L_SCR1(%a6),%d6
305 movew %d6,Y(%a6)
306 clrw Y+2(%a6)
307 movel %d4,Y_Hi(%a6)
308 movel %d5,Y_Lo(%a6)
309 fmovex R(%a6),%fp0 | ...no exception
310 movel #1,Sc_Flag(%a6)
311 bras ModOrRem
312 No_Scale:
313 movel %d1,R_Hi(%a6)
314 movel %d2,R_Lo(%a6)
315 subil #0x3FFE,%d0
316 movew %d0,R(%a6)
317 clrw R+2(%a6)
318 movel L_SCR1(%a6),%d6
319 subil #0x3FFE,%d6
320 movel %d6,L_SCR1(%a6)
321 fmovex R(%a6),%fp0
322 movew %d6,Y(%a6)
323 movel %d4,Y_Hi(%a6)
324 movel %d5,Y_Lo(%a6)
325 movel #0,Sc_Flag(%a6)
326
327 |
328
329
330 ModOrRem:
331 movel Mod_Flag(%a6),%d6
332 beqs Fix_Sign
333
334 movel L_SCR1(%a6),%d6 | ...new biased expo(Y)
335 subql #1,%d6 | ...biased expo(Y/2)
336 cmpl %d6,%d0
337 blts Fix_Sign
338 bgts Last_Sub
339
340 cmpl %d4,%d1
341 bnes Not_EQ
342 cmpl %d5,%d2
343 bnes Not_EQ
344 bra Tie_Case
345
346 Not_EQ:
347 bcss Fix_Sign
348
349 Last_Sub:
350 |
351 fsubx Y(%a6),%fp0 | ...no exceptions
352 addql #1,%d3 | ...Q := Q + 1
353
354 |
355
356 Fix_Sign:
357 |..Get sign of X
358 movew SignX(%a6),%d6
359 bges Get_Q
360 fnegx %fp0
361
362 |..Get Q
363 |
364 Get_Q:
365 clrl %d6
366 movew SignQ(%a6),%d6 | ...D6 is sign(Q)
367 movel #8,%d7
368 lsrl %d7,%d6
369 andil #0x0000007F,%d3 | ...7 bits of Q
370 orl %d6,%d3 | ...sign and bits of Q
371 swap %d3
372 fmovel %fpsr,%d6
373 andil #0xFF00FFFF,%d6
374 orl %d3,%d6
375 fmovel %d6,%fpsr | ...put Q in fpsr
376
377 |
378 Restore:
379 moveml (%a7)+,%d2-%d7
380 fmovel USER_FPCR(%a6),%fpcr
381 movel Sc_Flag(%a6),%d0
382 beqs Finish
383 fmulx Scale(%pc),%fp0 | ...may cause underflow
384 bra t_avoid_unsupp |check for denorm as a
385 | ;result of the scaling
386
387 Finish:
388 fmovex %fp0,%fp0 |capture exceptions & round
389 rts
390
391 Rem_is_0:
392 |..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
393 addql #1,%d3
394 cmpil #8,%d0 | ...D0 is j
395 bges Q_Big
396
397 lsll %d0,%d3
398 bras Set_R_0
399
400 Q_Big:
401 clrl %d3
402
403 Set_R_0:
404 fmoves #0x00000000,%fp0
405 movel #0,Sc_Flag(%a6)
406 bra Fix_Sign
407
408 Tie_Case:
409 |..Check parity of Q
410 movel %d3,%d6
411 andil #0x00000001,%d6
412 tstl %d6
413 beq Fix_Sign | ...Q is even
414
415 |..Q is odd, Q := Q + 1, signX := -signX
416 addql #1,%d3
417 movew SignX(%a6),%d6
418 eoril #0x00008000,%d6
419 movew %d6,SignX(%a6)
420 bra Fix_Sign
421
422 |end
![[bottom]](../icons/bottom.png){kind=icon}
![[previous]](../icons/n_left.png){kind=icon}
![[next]](../icons/n_right.png){kind=icon}
![[first]](../icons/n_first.png){kind=icon}
![[last]](../icons/n_last.png){kind=icon}
![[top]](../icons/n_top.png){kind=icon}
![[index]](../icons/index.png){kind=icon}
![[help]](../icons/help.png){kind=icon}
*/
![[top]](../icons/top.png){kind=icon}
![[bottom]](../icons/n_bottom.png){kind=icon}