|
| 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