****************************************************************************** * CyberPI_Calc * * 68K calculation routines * * © 1997 HAAGE&PARTNER Computer GmbH * ****************************************************************************** ;// XREF / XDEF xref Area_Quotient xref Area_Quotient2 xref Area_Quotient3 xref Area_Quotient4 xref Area_ArcTan xref Area_Result xref Area_Q_Actual xref Len_Q_Actual xref Area_Q2_Actual xref Len_Q2_Actual xref Area_Q3_Actual xref Len_Q3_Actual xref Area_Q4_Actual xref Len_Q4_Actual xref Area_AT_Actual xref Len_AT_Actual xref Num_ArcTan_57 xref Num_ArcTan_239 xref Num_ArcTan_682 xref Num_ArcTan_12943 xref ConvertMem xref Count xref _060Flag xdef BinToASCII xdef Calculation ;;/ mc68020 near a4,-1 near code section "code",code ;// BinToASCII ****************************************************************************** * d2 = BinToASCII (d0,d1,a0,a1) * * Conversion of the result area in a ASCII-String * * a0 [.L] -> source area (result area) * a1 [.L] -> destination area for ASCII-String * d0 [.L] = number of decimals * d1 [.L] = length of the areas in longwords ****************************************************************************** BinToASCII movem.l d0/d1,-(sp) move.l ConvertMem(a4),a3 move #"3 ",(a1)+ tst d0 ; when number of decimals is 0 beq.w BTA_exit ; then only write a "3" move.b #".",-1(a1) addq.l #4,a0 moveq #0,d7 subq.l #1,d1 BTA_loop ; in this loop the area will be lea 0(a0,d1.l*4),a2 ; multiplied with 1000000000 tst.l -4(a2) bne.b BTA_cont lea -4(a2),a2 subq.l #1,d1 BTA_cont tst.b _060Flag(a4) bne.b BTA_060 move.l #1000000000,d3 moveq #0,d5 moveq #0,d6 BTA_loop2 move.l -(a2),d2 mulu.l d3,d4:d2 add.l d5,d2 addx.l d6,d4 move.l d4,d5 move.l d2,(a2) cmp.l a0,a2 bgt.w BTA_loop2 bra.b BTA_Not060 BTA_060 move.l #50000,d3 moveq #0,d5 moveq #0,d6 move.l a2,d4 BTA_loop2a move -(a2),d2 mulu d3,d2 add d5,d2 move d2,(a2) swap d2 addx d6,d2 move d2,d5 cmp.l a0,a2 bgt.w BTA_loop2a move.l d4,a2 move d5,d4 move.l #20000,d3 moveq #0,d5 BTA_loop2b move -(a2),d2 mulu d3,d2 add d5,d2 move d2,(a2) swap d2 addx d6,d2 move d2,d5 cmp.l a0,a2 bgt.w BTA_loop2b mulu d3,d4 add.l d5,d4 move.l d4,d5 BTA_Not060 divul.l #10000,d5:d4 ; turbo conversion divu #10000,d4 add.b #"0",d4 move.b d4,(a1)+ swap d4 move.l 0(a3,d4.w*4),(a1)+ ; read a ASCII-longword move.l 0(a3,d5.w*4),(a1)+ ; and a second BTA_cont2 add.l #9,d7 cmp.l d0,d7 blt BTA_loop BTA_exit movem.l (sp)+,d0/d1 rts ;;/ ;// Calculation ****************************************************************************** * Calculation (d1) * * Binary Calculation of PI * stores the final result in the result area * * d1 [.L] = length of the areas in Longwords ****************************************************************************** Calculation tst.l Count(a4) ; don't calc anything when bne.w Calc_start ; count is 0 moveq #-1,d0 rts Calc_start movem.l d1-d4/a0,-(sp) move.l d1,d0 bsr FirstCalc ; 4*44/57+4*7/239+4*12/682+4*24/12943 moveq #1,d5 ; term counter move.l Num_ArcTan_57(a4),d3 ; num of terms for arctan(57) subq.l #1,d3 ; are we already finished? beq.w Calc_exit ; then leave moveq #3,d4 ; 2n-1 moveq #1,d6 ; flag (1=subtraction,0=add.) NextTerm lea Area_Q_Actual(a4),a2 move.l Area_Q_Actual(a4),a0 move.l a0,a1 move.l Len_Q_Actual(a4),d0 move.l #57*57,d1 bsr Division16 move.l Area_Q_Actual(a4),a0 move.l Area_ArcTan(a4),a1 move.l Area_Quotient(a4),a2 ; copy Area_Quotient to bsr CopyArea ; Area_ArcTan clr.l -4(a1) ; optimization trick cmp.l Num_ArcTan_239(a4),d5 ; do we need more terms of bhi.b NoSecond ; arctan(239)? no -> jump move.l Area_Q2_Actual(a4),a0 lea Area_Q2_Actual(a4),a2 move.l a0,a1 move.l Len_Q2_Actual(a4),d0 move.l #239*239,d1 bsr Division16 move.l Area_Q2_Actual(a4),a0 move.l Area_ArcTan(a4),a1 move.l Area_Quotient2(a4),a2 bsr Addition ; add Area_Quotient2 to NoSecond cmp.l Num_ArcTan_682(a4),d5 ; more terms of arctan(682)? bhi.b NoThird ; no -> jump lea Area_Q3_Actual(a4),a2 move.l Area_Q3_Actual(a4),a0 move.l a0,a1 move.l Len_Q3_Actual(a4),d0 tst.b _060Flag(a4) bne.b .060a move.l #682*682,d1 bsr Division ; calc Area_Quotient / 57^2 bra.b .not060a .060a move.l #682,d1 bsr Division16 move.l Area_Q3_Actual(a4),a0 move.l a0,a1 move.l Len_Q3_Actual(a4),d0 bsr Division16 .not060a move.l Area_Q3_Actual(a4),a0 move.l Area_ArcTan(a4),a1 move.l Area_Quotient3(a4),a2 bsr Subtraction ; sub Area_Quotient3 from NoThird cmp.l Num_ArcTan_12943(a4),d5 ; more terms of arctan(12943)? bhi.b NoFourth ; no -> jump lea Area_Q4_Actual(a4),a2 move.l Area_Q4_Actual(a4),a0 move.l a0,a1 move.l Len_Q4_Actual(a4),d0 tst.b _060Flag(a4) bne.b .060b move.l #12943*12943,d1 bsr Division ; calc Area_Quotient / 12943^2 bra.b .not060b .060b move.l #12943,d1 bsr Division16 move.l Area_Q4_Actual(a4),a0 move.l a0,a1 move.l Len_Q4_Actual(a4),d0 bsr Division16 .not060b move.l Area_Q4_Actual(a4),a0 move.l Area_ArcTan(a4),a1 move.l Area_Quotient4(a4),a2 bsr Addition ; add Area_Quotient4 to NoFourth lea Area_AT_Actual(a4),a2 move.l Area_AT_Actual(a4),a0 move.l a0,a1 move.l d4,d1 move.l Len_AT_Actual(a4),d0 tst.b _060Flag(a4) bne.b .060c bsr Division ; Area_ArcTan / d4 bra.b .not060c .060c cmp.l #$ffff,d4 bhi.b .slow bsr Division16 bra.b .not060c .slow bsr Division .not060c move.l Area_AT_Actual(a4),a0 move.l Area_Result(a4),a1 move.l Area_ArcTan(a4),a2 tst d6 bne.b Subtract bsr Addition ; add new term to result area bra.b NoSubtract Subtract bsr Subtraction ; sub new term from res. area NoSubtract addq.l #1,d5 eor #1,d6 ; change add./sub. addq.l #2,d4 ; divisor + 2 subq.l #1,d3 ; counter bne.w NextTerm Calc_exit moveq #-1,d0 Calc_End movem.l (sp)+,d1-d4/a0 rts ;;/ ;// FirstCalc ****************************************************************************** * FirstCalc (d0) * * calculation of 4*44/57 + 4*7*239 + 4*12*682 + 4*24*12943 * * d0 [.L] = length of the areas in Longwords ****************************************************************************** FirstCalc movem.l d1/a0,-(sp) move.l Area_Quotient(a4),a0 move.l #44*4,d1 bsr IntToArea ; first term = 44*4 move.l Area_Quotient2(a4),a0 move.l #7*4,d1 bsr IntToArea ; second term = 7*4 move.l Area_Quotient3(a4),a0 move.l #12*4,d1 bsr IntToArea ; third term = 12*4 move.l Area_Quotient4(a4),a0 move.l #24*4,d1 bsr IntToArea ; fourth term = 24*4 move.l Area_Quotient(a4),a0 lea Area_Q_Actual(a4),a2 move.l a0,a1 move.l #57,d1 bsr Division16 move.l Area_Quotient2(a4),a0 lea Area_Q2_Actual(a4),a2 move.l a0,a1 move.l #239,d1 bsr Division16 move.l Area_Quotient3(a4),a0 lea Area_Q3_Actual(a4),a2 move.l a0,a1 move.l #682,d1 bsr Division16 move.l Area_Quotient4(a4),a0 lea Area_Q4_Actual(a4),a2 move.l a0,a1 move.l #12943,d1 bsr Division16 move.l Area_Quotient(a4),a0 move.l Area_Result(a4),a1 move.l a0,a2 bsr CopyArea ; copy (we only have addition move.l Area_Quotient2(a4),a0 ; operation with two operands) move.l Area_Result(a4),a1 move.l a0,a2 bsr Addition ; calc 44*4/57 + 7*4/239 move.l Area_Quotient3(a4),a0 move.l Area_Result(a4),a1 move.l a0,a2 bsr Subtraction ; calc previous - 12*4/682 move.l Area_Quotient4(a4),a0 move.l Area_Result(a4),a1 move.l a0,a2 bsr Addition ; calc previous + 24*4/12943 movem.l (sp)+,d1/a0 rts ;;/ ;// IntToArea ****************************************************************************** * IntToArea (a0,d0,d1) * * Converts the integer (d1) to an area of the length d0 * * a0 [.L] -> destination area * d0 [.L] = length of the area in Longwords * d1 [.W] = integer value to convert * ****************************************************************************** IntToArea movem.l d0-d2/a0,-(sp) ext.l d1 move.l a0,d2 ITA_clear clr.l (a0)+ ; clear the whole area (=0) subq.l #1,d0 bne.b ITA_clear move.l d2,a0 move.l d1,(a0) ; write integer movem.l (sp)+,d0-d2/a0 rts ;;/ ;// CopyArea ****************************************************************************** * CopyArea (a0,a1,a2,d0) * * Copies the source area to dest area * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to beginning of the source area * d0 [.L] = length of the area in Longwords * ****************************************************************************** CopyArea movem.l d0-d2/a0-a2,-(sp) move.l a0,d2 sub.l a2,d2 add.l d2,a1 move.l d0,d2 and.l #$f,d2 lsr.l #4,d0 beq.b CA_copy2 CA_copy rept 16 move.l (a0)+,(a1)+ endr subq.l #1,d0 bne.b CA_copy tst.l d2 beq.b CA_nocopy2 CA_copy2 move.l (a0)+,(a1)+ subq #1,d2 bne.b CA_copy2 CA_nocopy2 movem.l (sp)+,d0-d2/a0-a2 rts ;;/ ;// Addition ****************************************************************************** * Addition (a0,a1,a2,d0) * * Performs the addition a1-> + a0-> and stores the result in a1-> * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to beginning of the source area * d0 [.L] = length of the area in Longwords * ****************************************************************************** Addition movem.l d0-d4/a0/a1,-(sp) move.l a0,d2 sub.l a2,d2 add.l d2,a1 move.l d0,d1 lsl.l #2,d0 add.l d0,a0 add.l d0,a1 move.l d1,d0 swap d0 move d1,d3 lsr #4,d1 and #$f,d3 subq #1,d3 move d3,d4 subq #1,d1 and.b #$ef,ccr move d1,d2 Add_Loop bmi.b Add_Next Add_Loop1 rept 16 addx.l -(a0),-(a1) endr dbra d1,Add_Loop1 Add_Next tst d3 bmi.b Add_Next2 Add_Next1 addx.l -(a0),-(a1) dbra d3,Add_Next1 Add_Next2 move d4,d3 move d2,d1 dbra d0,Add_Loop move ccr,d0 ; do we have an carry out? btst #4,d0 beq.b Add_End ; no -> jump Add_last addx.l -(a0),-(a1) ; then another addition bcs.b Add_last Add_End movem.l (sp)+,d0-d4/a0/a1 rts ;;/ ;// Subtraction ****************************************************************************** * Subtraction (a0,a1,a2,d0) * * Performs the subtraction a1-> - a0-> and stores the result in a1-> * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to beginning of the source area * d0 [.L] = length of the area in Longwords * ****************************************************************************** Subtraction movem.l d0-d4/a0-a2,-(sp) move.l a0,d2 sub.l a2,d2 add.l d2,a1 move.l d0,d1 lsl.l #2,d0 add.l d0,a0 add.l d0,a1 move.l d1,d0 swap d0 move d1,d3 lsr #4,d1 and #$f,d3 subq #1,d3 move d3,d4 subq #1,d1 and.b #$ef,ccr move d1,d2 Sub_Loop bmi.b Sub_Next Sub_Loop1 rept 16 subx.l -(a0),-(a1) endr dbra d1,Sub_Loop1 Sub_Next tst d3 bmi.b Sub_Next2 Sub_Next1 subx.l -(a0),-(a1) dbra d3,Sub_Next1 Sub_Next2 move d4,d3 move d2,d1 dbra d0,Sub_Loop move CCR,d0 btst #4,d0 ;carry-out ? beq.b Sub_End Sub_last subx.l -(a0),-(a1) ;another subtraction bcs.b Sub_last Sub_End movem.l (sp)+,d0-d4/a0-a2 rts ;;/ ;// Division ****************************************************************************** * Division (a0,a1,a2,d0,d1) * * Performs the division a0-> / d1 and stores the result in a1-> * optimized for 68020-040 * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to Area_x_Actual * d0 [.L] = length of the area in Longwords * d1 [.L] = divisor * ****************************************************************************** Division tst.b _060Flag(a4) bne.w Division060 movem.l d0-d6/a0-a2,-(sp) tst.l (a0) bne.b Division_cont tst.l a2 beq.b Division_cont lea 4(a0),a0 clr.l (a1)+ subq.l #1,d0 addq.l #4,(a2) subq.l #1,4(a2) Division_cont moveq #0,d3 ; first high 32 bits = 0 move.l d0,d4 and.l #$3,d4 lsr.l #2,d0 beq.b Division_next Division_loop rept 4 move.l (a0)+,d2 ; get first longword divu.l d1,d3:d2 ; divide move.l d2,(a1)+ ; write result (d3 is automatically ; the new remainder) endr subq.l #1,d0 bne.b Division_loop ; repeat Division_next subq #1,d4 bmi.b Division_end Division_loop2 move.l (a0)+,d2 divu.l d1,d3:d2 ; divide move.l d2,(a1)+ dbra d4,Division_loop2 Division_end movem.l (sp)+,d0-d6/a0-a2 rts ;;/ ;// Division060 ****************************************************************************** * Division060 (a0,a1,a2,d0,d1) * * Performs the division a0-> / d1 and stores the result in a1-> * optimized for 68060 * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to Area_x_Actual * d0 [.L] = length of the area in Longwords * d1 [.L] = divisor * ****************************************************************************** Division060 movem.l d0-d6/a0-a2,-(sp) tst.l (a0) bne.b Division0_cont tst.l a2 beq.b Division0_cont lea 4(a0),a0 clr.l (a1)+ subq.l #1,d0 addq.l #4,(a2) subq.l #1,4(a2) Division0_cont moveq #0,d3 ; first high 32 bits = 0 move.l d0,d4 and.l #$3,d4 lsr.l #2,d0 beq.b Division0_next Division0_loop rept 4 move.l (a0)+,d2 ; get first longword bsr Div64 move.l d2,(a1)+ ; write result endr subq.l #1,d0 bne.b Division0_loop ; repeat Division0_next subq #1,d4 bmi.b Division0_end Division0_loop2 move.l (a0)+,d2 bsr Div64 move.l d2,(a1)+ dbra d4,Division0_loop2 Division0_end movem.l (sp)+,d0-d6/a0-a2 rts ;;/ ;// Division16 ****************************************************************************** * Division16 (a0,a1,a2,d0,d1) * * Performs the division a0-> / d1 and stores the result in a1-> * optimized for 68060 * divisor must be 16 Bit!! * * a0 [.L] -> source area * a1 [.L] -> destination area * a2 [.L] -> ptr to Area_x_Actual * d0 [.L] = length of the area in Longwords * d1 [.L] = divisor * ****************************************************************************** Division16 tst.b _060Flag(a4) beq.w Division movem.l d0-d4/a0-a2,-(sp) tst.l (a0) bne.b Division6_cont tst.l a2 beq.b Division6_cont lea 4(a0),a0 clr.l (a1)+ subq.l #1,d0 addq.l #4,(a2) subq.l #1,4(a2) Division6_cont moveq #0,d3 ; first high 16 bits = 0 move.l d0,d4 and.l #$3,d4 lsr.l #2,d0 beq.b Division6_next Division6_loop rept 8 move (a0)+,d3 divu d1,d3 move d3,(a1)+ endr subq.l #1,d0 bne.b Division6_loop ; repeat Division6_next subq #1,d4 bmi.b Division6_end Division6_loop2 rept 2 move (a0)+,d3 divu d1,d3 move d3,(a1)+ endr dbra d4,Division6_loop2 Division6_end movem.l (sp)+,d0-d4/a0-a2 rts ;;/ ;// Div64 ****************************************************************************** * d2,d3 = Div64 (d1,d2,d3) * * Performs the 64 bit division on 68060 systems * this emulation is not 100% (no OV, no DIV0, unsigned ...)! * d5-d7 are trashed! * * d3 [.L] = high word of dividend * d2 [.L] = low word of dividend * d1 [.L] = divisor * * d2 [.L] = quotient * d3 [.L] = remainder ****************************************************************************** DivCore macro add.l d2,d2 addx.l d3,d3 bcs.b .do\@ cmp.l d3,d1 bhi.b .cont\@ .do\@ sub.l d1,d3 neg.l d6 .cont\@ addx.l d5,d5 endm Div64 move.l d1,-(sp) moveq #0,d5 moveq #1,d6 rept 32 DivCore endr move.l d5,d2 move.l (sp)+,d1 rts ;;/