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1da177e4 LT |
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 | | | |
e00d82d0 MW |
69 | | For details on the license for this file, please see the |
70 | | file, README, in this same directory. | |
1da177e4 LT |
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 |