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.defs" |
---|
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 |
---|