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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