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
72 SREM_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
93 Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000
94
95 |xref t_avoid_unsupp
96
97 .global smod
98 smod:
99
100 movel #0,Mod_Flag(%a6)
101 bras Mod_Rem
102
103 .global srem
104 srem:
105
106 movel #1,Mod_Flag(%a6)
107
108 Mod_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 #0x00007FFF,%d3 | ...Y := |Y|
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 #0x00003FFE,%d3 | ...$3FFD + 1
123 tstl %d4
124 bnes HiY_not0
125
126 HiY_0:
127 movel %d5,%d4
128 clrl %d5
129 subil #32,%d3
130 clrl %d6
131 bfffo %d4{#0:#32},%d6
132 lsll %d6,%d4
133 subl %d6,%d3 | ...(D3,D4,D5) is normalized
134 | ...with bias $7FFD
135 bras Chk_X
136
137 HiY_not0:
138 clrl %d6
139 bfffo %d4{#0:#32},%d6
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 #32,%d6
146 lsrl %d6,%d7
147 orl %d7,%d4 | ...(D3,D4,D5) normalized
148 | ...with bias $7FFD
149 bras Chk_X
150
151 Y_Normal:
152 addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized
153 | ...with bias $7FFD
154
155 Chk_X:
156 movew -12(%a0),%d0
157 movew %d0,SignX(%a6)
158 movew SignY(%a6),%d1
159 eorl %d0,%d1
160 andil #0x00008000,%d1
161 movew %d1,SignQ(%a6) | ...sign(Q) obtained
162 andil #0x00007FFF,%d0
163 movel -8(%a0),%d1
164 movel -4(%a0),%d2 | ...(D0,D1,D2) is |X|
165 tstl %d0
166 bnes X_Normal
167 movel #0x00003FFE,%d0
168 tstl %d1
169 bnes HiX_not0
170
171 HiX_0:
172 movel %d2,%d1
173 clrl %d2
174 subil #32,%d0
175 clrl %d6
176 bfffo %d1{#0:#32},%d6
177 lsll %d6,%d1
178 subl %d6,%d0 | ...(D0,D1,D2) is normalized
179 | ...with bias $7FFD
180 bras Init
181
182 HiX_not0:
183 clrl %d6
184 bfffo %d1{#0:#32},%d6
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 #32,%d6
191 lsrl %d6,%d7
192 orl %d7,%d1 | ...(D0,D1,D2) normalized
193 | ...with bias $7FFD
194 bras Init
195
196 X_Normal:
197 addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized
198 | ...with bias $7FFD
199
200 Init:
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 #0,%a1 | ...A1 is k; j+k=L, Q=0
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
222 Mod_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
235 R_NE_Y:
236 |..use the borrow of the previous compare
237 bcss R_LT_Y | ...borrow is set iff R < Y
238
239 R_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 #1,%d3 | ...Q := Q + 1
246
247 R_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 #1,%d1 | ...hi(R) = 2hi(R) + carry
255 scs %d6 | ...set Carry if 2(R) overflows
256 addql #1,%a1 | ...k := k+1
257 subql #1,%d0 | ...j := j - 1
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
262 PostLoop:
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
270 HiR_0:
271 movel %d2,%d1
272 clrl %d2
273 subil #32,%d0
274 clrl %d6
275 bfffo %d1{#0:#32},%d6
276 lsll %d6,%d1
277 subl %d6,%d0 | ...(D0,D1,D2) is normalized
278 | ...with bias $7FFD
279 bras Get_Mod
280
281 HiR_not0:
282 clrl %d6
283 bfffo %d1{#0:#32},%d6
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 #32,%d6
291 lsrl %d6,%d7
292 orl %d7,%d1 | ...(D0,D1,D2) normalized
293
294 |
295 Get_Mod:
296 cmpil #0x000041FE,%d0
297 bges No_Scale
298 Do_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 #1,Sc_Flag(%a6)
310 bras ModOrRem
311 No_Scale:
312 movel %d1,R_Hi(%a6)
313 movel %d2,R_Lo(%a6)
314 subil #0x3FFE,%d0
315 movew %d0,R(%a6)
316 clrw R+2(%a6)
317 movel L_SCR1(%a6),%d6
318 subil #0x3FFE,%d6
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 #0,Sc_Flag(%a6)
325
326 |
327
328
329 ModOrRem:
330 movel Mod_Flag(%a6),%d6
331 beqs Fix_Sign
332
333 movel L_SCR1(%a6),%d6 | ...new biased expo(Y)
334 subql #1,%d6 | ...biased expo(Y/2)
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
345 Not_EQ:
346 bcss Fix_Sign
347
348 Last_Sub:
349 |
350 fsubx Y(%a6),%fp0 | ...no exceptions
351 addql #1,%d3 | ...Q := Q + 1
352
353 |
354
355 Fix_Sign:
356 |..Get sign of X
357 movew SignX(%a6),%d6
358 bges Get_Q
359 fnegx %fp0
360
361 |..Get Q
362 |
363 Get_Q:
364 clrl %d6
365 movew SignQ(%a6),%d6 | ...D6 is sign(Q)
366 movel #8,%d7
367 lsrl %d7,%d6
368 andil #0x0000007F,%d3 | ...7 bits of Q
369 orl %d6,%d3 | ...sign and bits of Q
370 swap %d3
371 fmovel %fpsr,%d6
372 andil #0xFF00FFFF,%d6
373 orl %d3,%d6
374 fmovel %d6,%fpsr | ...put Q in fpsr
375
376 |
377 Restore:
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
386 Finish:
387 fmovex %fp0,%fp0 |capture exceptions & round
388 rts
389
390 Rem_is_0:
391 |..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
392 addql #1,%d3
393 cmpil #8,%d0 | ...D0 is j
394 bges Q_Big
395
396 lsll %d0,%d3
397 bras Set_R_0
398
399 Q_Big:
400 clrl %d3
401
402 Set_R_0:
403 fmoves #0x00000000,%fp0
404 movel #0,Sc_Flag(%a6)
405 bra Fix_Sign
406
407 Tie_Case:
408 |..Check parity of Q
409 movel %d3,%d6
410 andil #0x00000001,%d6
411 tstl %d6
412 beq Fix_Sign | ...Q is even
413
414 |..Q is odd, Q := Q + 1, signX := -signX
415 addql #1,%d3
416 movew SignX(%a6),%d6
417 eoril #0x00008000,%d6
418 movew %d6,SignX(%a6)
419 bra Fix_Sign
420
421 |end