📄 srem_mod.s
字号:
//// $Id: srem_mod.S,v 1.1 1998/12/14 23:15:28 joel Exp $//// 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 Return signQ, last 7 bits of Q, and R.//// // Copyright (C) Motorola, Inc. 1990// All Rights Reserved//// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA // The copyright notice above does not evidence any // actual or intended publication of such source code.SREM_MOD: //idnt 2,1 | Motorola 040 Floating Point Software Package |section 8#include "fpsp.defs" .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+8Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000 |xref t_avoid_unsupp .global smodsmod: movel #0,Mod_Flag(%a6) bras Mod_Rem .global sremsrem: 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_not0HiY_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_XHiY_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_XY_Normal: addil #0x00003FFE,%d3 // ...(D3,D4,D5) normalized// ...with bias $7FFDChk_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_not0HiX_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 InitHiX_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 InitX_Normal: addil #0x00003FFE,%d0 // ...(D0,D1,D2) normalized// ...with bias $7FFDInit:// 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 = LMod_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_0R_NE_Y://..use the borrow of the previous compare bcss R_LT_Y // ...borrow is set iff R < YR_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 + 1R_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_LoopPostLoop://..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_not0HiR_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_ModHiR_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_ScaleDo_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 ModOrRemNo_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_CaseNot_EQ: bcss Fix_SignLast_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 scalingFinish: fmovex %fp0,%fp0 //capture exceptions & round rtsRem_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_0Q_Big: clrl %d3Set_R_0: fmoves #0x00000000,%fp0 movel #0,Sc_Flag(%a6) bra Fix_SignTie_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⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -