Commit | Line | Data |
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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 | | | |
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 |