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