/* l_srem_mods.s - Motorola 68040 FP modulo/remainder routines (LIB) *//* Copyright 1991-1993 Wind River Systems, Inc. */	.data	.globl	_copyright_wind_river	.long	_copyright_wind_river/*modification history--------------------01f,21jul93,kdl  added .text (SPR #2372).01e,23aug92,jcf  changed bxxx to jxx.01d,26may92,rrr  the tree shuffle01c,10jan92,kdl  added modification history; general cleanup.01b,01jan92,jcf	 reversed order of cmp <reg>,<reg>01a,15aug91,kdl  original version, from Motorola FPSP v2.0.*//*DESCRIPTION	srem_modsa 3.1 12/10/90 WIND RIVER MODIFICATION HISTORY      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	A0@(-12). 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    8NOMANUAL*/#include "fpsp040L.h"#define	Mod_Flag  	L_SCR3#define	SignY     	FP_SCR3+4#define	SignX     	FP_SCR3+8#define	SignQ     	FP_SCR3+12#define	Sc_Flag   	FP_SCR4#define	Y         	FP_SCR1#define	Y_Hi      	Y+4#define	Y_Lo      	Y+8#define	R         	FP_SCR2#define	R_Hi      	R+4#define	R_Lo      	R+8Scale:     .long	0x00010000,0x80000000,0x00000000,0x00000000|	xref	__l_t_avoid_unsupp	.text        .globl        __l_smod__l_smod:   movel               #0,a6@(Mod_Flag)   jra                 Mod_Rem        .globl        __l_srem__l_srem:   movel               #1,a6@(Mod_Flag)Mod_Rem:|..Save sign of X and Y   moveml              d2-d7,A7@-     |...save data registers   movew              	A0@,d3   movew               d3,a6@(SignY)   andil               #0x00007FFF,d3   |...Y := |Y||   movel              	A0@(4),d4   movel              	A0@(8),d5        |...(D3,d4,d5) is |Y|   tstl                d3   jne                 Y_Normal   movel               #0x00003FFE,d3	|...0x3FFD + 1   tstl                d4   jne                 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 0x7FFD   jra                 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 0x7FFD   jra                 Chk_XY_Normal:   addil               #0x00003FFE,d3   |...(D3,d4,d5) normalized|                                       |...with bias 0x7FFDChk_X:   movew              	A0@(-12),d0   movew               d0,a6@(SignX)   movew              	a6@(SignY),d1   eorl                d0,d1   andil               #0x00008000,d1   movew               d1,a6@(SignQ)	|...sign(Q) obtained   andil               #0x00007FFF,d0   movel              	A0@(-8),d1   movel              	A0@(-4),d2       |...(D0,d1,d2) is |X|   tstl                d0   jne                 X_Normal   movel               #0x00003FFE,d0   tstl                d1   jne                 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 0x7FFD   jra                 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 0x7FFD   jra                 InitX_Normal:   addil               #0x00003FFE,d0   |...(D0,d1,d2) normalized|                                       |...with bias 0x7FFDInit:|   movel               d3,a6@(L_SCR1)   |...save biased expo(Y)   movel		d0,a6@(L_SCR2)	| save d0   subl                d3,d0           |...l := expo(X)-expo(Y)|   Movel               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   jge                 Mod_Loop|..expo(X) < expo(Y). Thus X = mod(X,Y)|   movel		a6@(L_SCR2),d0	| restore d0   jra                 Get_Mod|..At this point  R = 2^(-L)X|  Q = 0|  k = 0|  and  k+j = LMod_Loop:   tstl                d6              |...test carry bit   jgt                 R_GT_Y|..At this point carry = 0, R = (D1,D2), Y = (D4,D5)   cmpl                d1,d4           |...compare hi(R) and hi(Y)   jne                 R_NE_Y   cmpl                d2,d5           |...compare lo(R) and lo(Y)   jne                 R_NE_Y|..At this point, R = Y   jra                 Rem_is_0R_NE_Y:|..use the borrow of the previous compare   jcs                 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.   jeq                 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.   jra                 Mod_LoopPostLoop:|..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.|..normalize R.   movel              	a6@(L_SCR1),d0           |...new biased expo of R   tstl                d1   jne                 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 0x7FFD   jra                 Get_ModHiR_not0:   clrl                d6   bfffo                d1{#0:#32},d6   jmi                 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   jge 		No_ScaleDo_Scale:   movew		d0,a6@(R)   clrw		a6@(R+2)   movel		d1,a6@(R_Hi)   movel		d2,a6@(R_Lo)   movel		a6@(L_SCR1),d6   movew		d6,a6@(Y)   clrw		a6@(Y+2)   movel		d4,a6@(Y_Hi)   movel		d5,a6@(Y_Lo)   fmovex		a6@(R),fp0		|...no exception   movel		#1,a6@(Sc_Flag)   jra 		ModOrRemNo_Scale:   movel		d1,a6@(R_Hi)   movel		d2,a6@(R_Lo)   subil		#0x3FFE,d0   movew		d0,a6@(R)   clrw		a6@(R+2)   movel		a6@(L_SCR1),d6   subil		#0x3FFE,d6   movel		d6,a6@(L_SCR1)   fmovex		a6@(R),fp0   movew		d6,a6@(Y)   movel		d4,a6@(Y_Hi)   movel		d5,a6@(Y_Lo)   movel		#0,a6@(Sc_Flag)|ModOrRem:   movel              	a6@(Mod_Flag),d6   jeq                 Fix_Sign   movel              	a6@(L_SCR1),d6           |...new biased expo(Y)   subql               #1,d6           |...biased expo(Y/2)   cmpl                d0,d6   jlt                 Fix_Sign   jgt                 Last_Sub   cmpl                d1,d4   jne                 Not_EQ   cmpl                d2,d5   jne                 Not_EQ   jra                 Tie_CaseNot_EQ:   jcs                 Fix_SignLast_Sub:|   fsubx		a6@(Y),fp0		|...no exceptions   addql               #1,d3           |...Q := Q + 1|Fix_Sign:|..Get sign of X   movew              	a6@(SignX),d6   jge 		Get_Q   fnegx		fp0|..Get Q|Get_Q:   clrl		d6   movew              	a6@(SignQ),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             	a6@(USER_FPCR),fpcr   movel              	a6@(Sc_Flag),d0   jeq                 Finish   fmulx		pc@(Scale),fp0	|...may cause underflow   jra 			__l_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   jge                 Q_Big   lsll                d0,d3   jra                 Set_R_0Q_Big:   clrl                d3Set_R_0:   .long 0xf23c4400,0x00000000	 /* fmoves	&0x00000000,fp0 */   movel		#0,a6@(Sc_Flag)   jra                 Fix_SignTie_Case:|..Check parity of Q   movel               d3,d6   andil               #0x00000001,d6   tstl                d6   jeq                 Fix_Sign		|...Q is even|..Q is odd, Q := Q + 1, signX := -signX   addql               #1,d3   movew              	a6@(SignX),d6   eoril               #0x00008000,d6   movew               d6,a6@(SignX)   jra                 Fix_Sign|   end