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
72SREM_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
93Scale:     .long	0x00010000,0x80000000,0x00000000,0x00000000
94
95	|xref	t_avoid_unsupp
96
97        .global        smod
98smod:
99
100   movel               #0,Mod_Flag(%a6)
101   bras                Mod_Rem
102
103        .global        srem
104srem:
105
106   movel               #1,Mod_Flag(%a6)
107
108Mod_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
126HiY_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
137HiY_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
151Y_Normal:
152   addil               #0x00003FFE,%d3   | ...(D3,D4,D5) normalized
153|                                       ...with bias $7FFD
154
155Chk_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
171HiX_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
182HiX_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
196X_Normal:
197   addil               #0x00003FFE,%d0   | ...(D0,D1,D2) normalized
198|                                       ...with bias $7FFD
199
200Init:
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
222Mod_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
235R_NE_Y:
236|..use the borrow of the previous compare
237   bcss                R_LT_Y          | ...borrow is set iff R < Y
238
239R_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
247R_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
262PostLoop:
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
270HiR_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
281HiR_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|
295Get_Mod:
296   cmpil		#0x000041FE,%d0
297   bges		No_Scale
298Do_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
311No_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
329ModOrRem:
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
345Not_EQ:
346   bcss                Fix_Sign
347
348Last_Sub:
349|
350   fsubx		Y(%a6),%fp0		| ...no exceptions
351   addql               #1,%d3           | ...Q := Q + 1
352
353|
354
355Fix_Sign:
356|..Get sign of X
357   movew               SignX(%a6),%d6
358   bges		Get_Q
359   fnegx		%fp0
360
361|..Get Q
362|
363Get_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|
377Restore:
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
386Finish:
387	fmovex		%fp0,%fp0		|capture exceptions & round
388	rts
389
390Rem_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
399Q_Big:
400   clrl                %d3
401
402Set_R_0:
403   fmoves		#0x00000000,%fp0
404   movel		#0,Sc_Flag(%a6)
405   bra                Fix_Sign
406
407Tie_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
422