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
73SREM_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
94Scale:     .long	0x00010000,0x80000000,0x00000000,0x00000000
95
96	|xref	t_avoid_unsupp
97
98        .global        smod
99smod:
100
101   movel               #0,Mod_Flag(%a6)
102   bras                Mod_Rem
103
104        .global        srem
105srem:
106
107   movel               #1,Mod_Flag(%a6)
108
109Mod_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
127HiY_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
138HiY_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
152Y_Normal:
153   addil               #0x00003FFE,%d3   | ...(D3,D4,D5) normalized
154|                                       ...with bias $7FFD
155
156Chk_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
172HiX_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
183HiX_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
197X_Normal:
198   addil               #0x00003FFE,%d0   | ...(D0,D1,D2) normalized
199|                                       ...with bias $7FFD
200
201Init:
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
223Mod_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
236R_NE_Y:
237|..use the borrow of the previous compare
238   bcss                R_LT_Y          | ...borrow is set iff R < Y
239
240R_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
248R_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
263PostLoop:
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
271HiR_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
282HiR_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|
296Get_Mod:
297   cmpil		#0x000041FE,%d0
298   bges		No_Scale
299Do_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
312No_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
330ModOrRem:
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
346Not_EQ:
347   bcss                Fix_Sign
348
349Last_Sub:
350|
351   fsubx		Y(%a6),%fp0		| ...no exceptions
352   addql               #1,%d3           | ...Q := Q + 1
353
354|
355
356Fix_Sign:
357|..Get sign of X
358   movew               SignX(%a6),%d6
359   bges		Get_Q
360   fnegx		%fp0
361
362|..Get Q
363|
364Get_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|
378Restore:
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
387Finish:
388	fmovex		%fp0,%fp0		|capture exceptions & round
389	rts
390
391Rem_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
400Q_Big:
401   clrl                %d3
402
403Set_R_0:
404   fmoves		#0x00000000,%fp0
405   movel		#0,Sc_Flag(%a6)
406   bra                Fix_Sign
407
408Tie_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
423