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+|
+| srem_mod.sa 3.1 12/10/90
+|
+| The entry point sMOD computes the floating point MOD of the
+| input values X and Y. The entry point sREM computes the floating
+| point (IEEE) REM of the input values X and Y.
+|
+| INPUT
+| -----
+| Double-extended value Y is pointed to by address in register
+| A0. Double-extended value X is located in -12(A0). The values
+| of X and Y are both nonzero and finite; although either or both
+| of them can be denormalized. The special cases of zeros, NaNs,
+| and infinities are handled elsewhere.
+|
+| OUTPUT
+| ------
+| FREM(X,Y) or FMOD(X,Y), depending on entry point.
+|
+| ALGORITHM
+| ---------
+|
+| Step 1. Save and strip signs of X and Y: signX := sign(X),
+| signY := sign(Y), X := |X|, Y := |Y|,
+| signQ := signX EOR signY. Record whether MOD or REM
+| is requested.
+|
+| Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0.
+| If (L < 0) then
+| R := X, go to Step 4.
+| else
+| R := 2^(-L)X, j := L.
+| endif
+|
+| Step 3. Perform MOD(X,Y)
+| 3.1 If R = Y, go to Step 9.
+| 3.2 If R > Y, then { R := R - Y, Q := Q + 1}
+| 3.3 If j = 0, go to Step 4.
+| 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
+| Step 3.1.
+|
+| Step 4. At this point, R = X - QY = MOD(X,Y). Set
+| Last_Subtract := false (used in Step 7 below). If
+| MOD is requested, go to Step 6.
+|
+| Step 5. R = MOD(X,Y), but REM(X,Y) is requested.
+| 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
+| Step 6.
+| 5.2 If R > Y/2, then { set Last_Subtract := true,
+| Q := Q + 1, Y := signY*Y }. Go to Step 6.
+| 5.3 This is the tricky case of R = Y/2. If Q is odd,
+| then { Q := Q + 1, signX := -signX }.
+|
+| Step 6. R := signX*R.
+|
+| Step 7. If Last_Subtract = true, R := R - Y.
+|
+| Step 8. Return signQ, last 7 bits of Q, and R as required.
+|
+| Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus,
+| X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
+| R := 0. Return signQ, last 7 bits of Q, and R.
+|
+|
+
+| Copyright (C) Motorola, Inc. 1990
+| All Rights Reserved
+|
+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
+| The copyright notice above does not evidence any
+| actual or intended publication of such source code.
+
+SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package
+
+ |section 8
+
+#include "fpsp.h"
+
+ .set Mod_Flag,L_SCR3
+ .set SignY,FP_SCR3+4
+ .set SignX,FP_SCR3+8
+ .set SignQ,FP_SCR3+12
+ .set Sc_Flag,FP_SCR4
+
+ .set Y,FP_SCR1
+ .set Y_Hi,Y+4
+ .set Y_Lo,Y+8
+
+ .set R,FP_SCR2
+ .set R_Hi,R+4
+ .set R_Lo,R+8
+
+
+Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000
+
+ |xref t_avoid_unsupp
+
+ .global smod
+smod:
+
+ movel #0,Mod_Flag(%a6)
+ bras Mod_Rem
+
+ .global srem
+srem:
+
+ movel #1,Mod_Flag(%a6)
+
+Mod_Rem:
+|..Save sign of X and Y
+ moveml %d2-%d7,-(%a7) | ...save data registers
+ movew (%a0),%d3
+ movew %d3,SignY(%a6)
+ andil #0x00007FFF,%d3 | ...Y := |Y|
+
+|
+ movel 4(%a0),%d4
+ movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y|
+
+ tstl %d3
+ bnes Y_Normal
+
+ movel #0x00003FFE,%d3 | ...$3FFD + 1
+ tstl %d4
+ bnes HiY_not0
+
+HiY_0:
+ movel %d5,%d4
+ clrl %d5
+ subil #32,%d3
+ clrl %d6
+ bfffo %d4{#0:#32},%d6
+ lsll %d6,%d4
+ subl %d6,%d3 | ...(D3,D4,D5) is normalized
+| ...with bias $7FFD
+ bras Chk_X
+
+HiY_not0:
+ clrl %d6
+ bfffo %d4{#0:#32},%d6
+ subl %d6,%d3
+ lsll %d6,%d4
+ movel %d5,%d7 | ...a copy of D5
+ lsll %d6,%d5
+ negl %d6
+ addil #32,%d6
+ lsrl %d6,%d7
+ orl %d7,%d4 | ...(D3,D4,D5) normalized
+| ...with bias $7FFD
+ bras Chk_X
+
+Y_Normal:
+ addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized
+| ...with bias $7FFD
+
+Chk_X:
+ movew -12(%a0),%d0
+ movew %d0,SignX(%a6)
+ movew SignY(%a6),%d1
+ eorl %d0,%d1
+ andil #0x00008000,%d1
+ movew %d1,SignQ(%a6) | ...sign(Q) obtained
+ andil #0x00007FFF,%d0
+ movel -8(%a0),%d1
+ movel -4(%a0),%d2 | ...(D0,D1,D2) is |X|
+ tstl %d0
+ bnes X_Normal
+ movel #0x00003FFE,%d0
+ tstl %d1
+ bnes HiX_not0
+
+HiX_0:
+ movel %d2,%d1
+ clrl %d2
+ subil #32,%d0
+ clrl %d6
+ bfffo %d1{#0:#32},%d6
+ lsll %d6,%d1
+ subl %d6,%d0 | ...(D0,D1,D2) is normalized
+| ...with bias $7FFD
+ bras Init
+
+HiX_not0:
+ clrl %d6
+ bfffo %d1{#0:#32},%d6
+ subl %d6,%d0
+ lsll %d6,%d1
+ movel %d2,%d7 | ...a copy of D2
+ lsll %d6,%d2
+ negl %d6
+ addil #32,%d6
+ lsrl %d6,%d7
+ orl %d7,%d1 | ...(D0,D1,D2) normalized
+| ...with bias $7FFD
+ bras Init
+
+X_Normal:
+ addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized
+| ...with bias $7FFD
+
+Init:
+|
+ movel %d3,L_SCR1(%a6) | ...save biased expo(Y)
+ movel %d0,L_SCR2(%a6) |save d0
+ subl %d3,%d0 | ...L := expo(X)-expo(Y)
+| Move.L D0,L ...D0 is j
+ clrl %d6 | ...D6 := carry <- 0
+ clrl %d3 | ...D3 is Q
+ moveal #0,%a1 | ...A1 is k; j+k=L, Q=0
+
+|..(Carry,D1,D2) is R
+ tstl %d0
+ bges Mod_Loop
+
+|..expo(X) < expo(Y). Thus X = mod(X,Y)
+|
+ movel L_SCR2(%a6),%d0 |restore d0
+ bra Get_Mod
+
+|..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
+
+
+Mod_Loop:
+ tstl %d6 | ...test carry bit
+ bgts R_GT_Y
+
+|..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
+ cmpl %d4,%d1 | ...compare hi(R) and hi(Y)
+ bnes R_NE_Y
+ cmpl %d5,%d2 | ...compare lo(R) and lo(Y)
+ bnes R_NE_Y
+
+|..At this point, R = Y
+ bra Rem_is_0
+
+R_NE_Y:
+|..use the borrow of the previous compare
+ bcss R_LT_Y | ...borrow is set iff R < Y
+
+R_GT_Y:
+|..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
+|..and Y < (D1,D2) < 2Y. Either way, perform R - Y
+ subl %d5,%d2 | ...lo(R) - lo(Y)
+ subxl %d4,%d1 | ...hi(R) - hi(Y)
+ clrl %d6 | ...clear carry
+ addql #1,%d3 | ...Q := Q + 1
+
+R_LT_Y:
+|..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
+ tstl %d0 | ...see if j = 0.
+ beqs PostLoop
+
+ addl %d3,%d3 | ...Q := 2Q
+ addl %d2,%d2 | ...lo(R) = 2lo(R)
+ roxll #1,%d1 | ...hi(R) = 2hi(R) + carry
+ scs %d6 | ...set Carry if 2(R) overflows
+ addql #1,%a1 | ...k := k+1
+ subql #1,%d0 | ...j := j - 1
+|..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
+
+ bras Mod_Loop
+
+PostLoop:
+|..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
+
+|..normalize R.
+ movel L_SCR1(%a6),%d0 | ...new biased expo of R
+ tstl %d1
+ bnes HiR_not0
+
+HiR_0:
+ movel %d2,%d1
+ clrl %d2
+ subil #32,%d0
+ clrl %d6
+ bfffo %d1{#0:#32},%d6
+ lsll %d6,%d1
+ subl %d6,%d0 | ...(D0,D1,D2) is normalized
+| ...with bias $7FFD
+ bras Get_Mod
+
+HiR_not0:
+ clrl %d6
+ bfffo %d1{#0:#32},%d6
+ bmis Get_Mod | ...already normalized
+ subl %d6,%d0
+ lsll %d6,%d1
+ movel %d2,%d7 | ...a copy of D2
+ lsll %d6,%d2
+ negl %d6
+ addil #32,%d6
+ lsrl %d6,%d7
+ orl %d7,%d1 | ...(D0,D1,D2) normalized
+
+|
+Get_Mod:
+ cmpil #0x000041FE,%d0
+ bges No_Scale
+Do_Scale:
+ movew %d0,R(%a6)
+ clrw R+2(%a6)
+ movel %d1,R_Hi(%a6)
+ movel %d2,R_Lo(%a6)
+ movel L_SCR1(%a6),%d6
+ movew %d6,Y(%a6)
+ clrw Y+2(%a6)
+ movel %d4,Y_Hi(%a6)
+ movel %d5,Y_Lo(%a6)
+ fmovex R(%a6),%fp0 | ...no exception
+ movel #1,Sc_Flag(%a6)
+ bras ModOrRem
+No_Scale:
+ movel %d1,R_Hi(%a6)
+ movel %d2,R_Lo(%a6)
+ subil #0x3FFE,%d0
+ movew %d0,R(%a6)
+ clrw R+2(%a6)
+ movel L_SCR1(%a6),%d6
+ subil #0x3FFE,%d6
+ movel %d6,L_SCR1(%a6)
+ fmovex R(%a6),%fp0
+ movew %d6,Y(%a6)
+ movel %d4,Y_Hi(%a6)
+ movel %d5,Y_Lo(%a6)
+ movel #0,Sc_Flag(%a6)
+
+|
+
+
+ModOrRem:
+ movel Mod_Flag(%a6),%d6
+ beqs Fix_Sign
+
+ movel L_SCR1(%a6),%d6 | ...new biased expo(Y)
+ subql #1,%d6 | ...biased expo(Y/2)
+ cmpl %d6,%d0
+ blts Fix_Sign
+ bgts Last_Sub
+
+ cmpl %d4,%d1
+ bnes Not_EQ
+ cmpl %d5,%d2
+ bnes Not_EQ
+ bra Tie_Case
+
+Not_EQ:
+ bcss Fix_Sign
+
+Last_Sub:
+|
+ fsubx Y(%a6),%fp0 | ...no exceptions
+ addql #1,%d3 | ...Q := Q + 1
+
+|
+
+Fix_Sign:
+|..Get sign of X
+ movew SignX(%a6),%d6
+ bges Get_Q
+ fnegx %fp0
+
+|..Get Q
+|
+Get_Q:
+ clrl %d6
+ movew SignQ(%a6),%d6 | ...D6 is sign(Q)
+ movel #8,%d7
+ lsrl %d7,%d6
+ andil #0x0000007F,%d3 | ...7 bits of Q
+ orl %d6,%d3 | ...sign and bits of Q
+ swap %d3
+ fmovel %fpsr,%d6
+ andil #0xFF00FFFF,%d6
+ orl %d3,%d6
+ fmovel %d6,%fpsr | ...put Q in fpsr
+
+|
+Restore:
+ moveml (%a7)+,%d2-%d7
+ fmovel USER_FPCR(%a6),%fpcr
+ movel Sc_Flag(%a6),%d0
+ beqs Finish
+ fmulx Scale(%pc),%fp0 | ...may cause underflow
+ bra t_avoid_unsupp |check for denorm as a
+| ;result of the scaling
+
+Finish:
+ fmovex %fp0,%fp0 |capture exceptions & round
+ rts
+
+Rem_is_0:
+|..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
+ addql #1,%d3
+ cmpil #8,%d0 | ...D0 is j
+ bges Q_Big
+
+ lsll %d0,%d3
+ bras Set_R_0
+
+Q_Big:
+ clrl %d3
+
+Set_R_0:
+ fmoves #0x00000000,%fp0
+ movel #0,Sc_Flag(%a6)
+ bra Fix_Sign
+
+Tie_Case:
+|..Check parity of Q
+ movel %d3,%d6
+ andil #0x00000001,%d6
+ tstl %d6
+ beq Fix_Sign | ...Q is even
+
+|..Q is odd, Q := Q + 1, signX := -signX
+ addql #1,%d3
+ movew SignX(%a6),%d6
+ eoril #0x00008000,%d6
+ movew %d6,SignX(%a6)
+ bra Fix_Sign
+
+ |end
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