| | |
| | 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 |