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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
| |
| | For details on the license for this file, please see the
| | file, README, in this same directory.
|
| 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
|
|
