****************************************************************************** * CyberPI_Calc_P * * PowerPC 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 BinToASCIIPPC xdef CalculationPPC ;;/ cpu POWERPC smalldata smallcode section "code",code ;// BinToASCIIPPC ****************************************************************************** * BinToASCIIPPC (_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 ****************************************************************************** BinToASCIIPPC prolog 1024,r18 pushgpr r3-r16 pushgpr _d0/_d1/_a0/_a1 popgpr r4-r7 liw r11,1000000000 liw r16,10000 lw r8,ConvertMem ;-> converter table li r3,"3 " sth r3,0(r7) ;store digits before decimal point addi r7,r7,2 tstw r4 ;when number of decimals is 0 beq BTA_exit ;then only write a "3" li r3,"." stb r3,-1(r7) ;store decimal point addi r6,r6,4 clrw r9 subi r5,r5,1 BTA_loop ;in this loop the area will be slwi r3,r5,2 ;multiplied with 1000000000 add r10,r6,r3 ;r10 -> end of area lwz r3,-4(r10) ;read first tstw r3 bne BTA_cont ;if not zero then jump subi r10,r10,4 ;else decrease end ptr subi r5,r5,1 BTA_cont clrw r12 BTA_loop2 lwzu r14,-4(r10) ;load one longword mulhwu r15,r11,r14 ;64 bit multiply (r11 = 10 ^ 9) mullw r14,r11,r14 addc r14,r14,r12 addze r12,r15 stw r14,0(r10) cmpw r10,r6 bgt BTA_loop2 divwu r13,r12,r16 ;now calc offsets to converter table mullw r3,r13,r16 subf r3,r3,r12 divwu r15,r13,r16 mullw r14,r15,r16 subf r14,r14,r13 addi r15,r15,"0" stb r15,0(r7) slwi r3,r3,2 slwi r14,r14,2 lwzx r13,r8,r14 ;read a ASCII longword stb r13,4(r7) srwi r13,r13,8 stb r13,3(r7) srwi r13,r13,8 stb r13,2(r7) srwi r13,r13,8 stb r13,1(r7) ; stw r13,1(r7) ;and store lwzx r13,r8,r3 ;once again stb r13,8(r7) srwi r13,r13,8 stb r13,7(r7) srwi r13,r13,8 stb r13,6(r7) srwi r13,r13,8 stb r13,5(r7) ; stw r13,5(r7) addi r7,r7,9 BTA_cont2 addi r9,r9,9 cmpw r9,r4 blt BTA_loop BTA_exit popgpr epilog ;;/ ;// CalculationPPC ****************************************************************************** * CalculationPPC (_d1) * * Binary Calculation of PI * stores the final result in the result area * * _d1 [.L] = length of the areas in Longwords ****************************************************************************** CalculationPPC prolog 1024,r18 pushgpr r3-r17 push _d1 pop r4 lw r0,Count tstw r0 beq Calc_End lw r14,Num_ArcTan_57 lw r15,Num_ArcTan_239 lw r16,Num_ArcTan_682 lw r17,Num_ArcTan_12943 mr r3,r4 bl FirstCalc ;4*44/57+4*7/239+4*12/682+4*24/12943 li r8,1 ;term counter mr r6,r14 ;num of terms for arctan(57) subic. r6,r6,1 ;are we already finished? beq Calc_End ;then leave mtctr r6 li r7,3 ;2n-1 li r9,1 ;flag (1=subtraction,0=add.) NextTerm la r13,Area_Q_Actual lw r11,Area_Q_Actual mr r12,r11 lw r3,Len_Q_Actual li r4,57*57 bl Division16 lw r11,Area_Q_Actual lw r12,Area_ArcTan lw r13,Area_Quotient ;copy Area_Quotient to bl CopyArea ;Area_ArcTan li r0,0 stw r0,-4(r12) ;optimization trick cmplw r8,r15 ;do we need more terms of bgt NoSecond ;arctan(239)? no -> jump la r13,Area_Q2_Actual lw r11,Area_Q2_Actual mr r12,r11 lw r3,Len_Q2_Actual li r4,239*239 bl Division16 lw r11,Area_Q2_Actual lw r12,Area_ArcTan lw r13,Area_Quotient2 bl Addition ;add Area_Quotient2 NoSecond cmplw r8,r16 ;more terms of arctan(682)? bgt NoThird ;no -> jump la r13,Area_Q3_Actual lw r11,Area_Q3_Actual mr r12,r11 lw r3,Len_Q3_Actual li r4,682 bl Division16 lw r11,Area_Q3_Actual mr r12,r11 lw r3,Len_Q3_Actual bl Division16 lw r11,Area_Q3_Actual lw r12,Area_ArcTan lw r13,Area_Quotient3 bl Subtraction ;sub Area_Quotient3 NoThird cmplw r8,r17 ;more terms of arctan(12943)? bgt NoFourth ;no -> jump la r13,Area_Q4_Actual lw r11,Area_Q4_Actual mr r12,r11 lw r3,Len_Q4_Actual li r4,12943 bl Division16 lw r11,Area_Q4_Actual mr r12,r11 lw r3,Len_Q4_Actual bl Division16 lw r11,Area_Q4_Actual lw r12,Area_ArcTan lw r13,Area_Quotient4 bl Addition ;add Area_Quotient4 NoFourth la r13,Area_AT_Actual lw r11,Area_AT_Actual mr r12,r11 lw r3,Len_AT_Actual mr r4,r7 cmplwi r7,$ffff bgt .slow bl Division16 b .fast .slow bl Division .fast lw r11,Area_AT_Actual lw r12,Area_Result lw r13,Area_ArcTan tstw r9 bne Subtract bl Addition ;add new term to result area b NoSubtract Subtract bl Subtraction ;sub new term from result area NoSubtract addi r8,r8,1 xori r9,r9,1 ;change add./sub. addi r7,r7,2 ;divisor + 2 bdnz NextTerm Calc_End popgpr epilog ;;/ ;// FirstCalc ****************************************************************************** * FirstCalc (r3) * * calculation of 4*44/57 + 4*7*239 + 4*12*682 + 4*24*12943 * * r3 [.L] = length of the areas in Longwords ****************************************************************************** FirstCalc pushlr lw r11,Area_Quotient li r4,44*4 bl IntToArea ; first term = 44*4 lw r11,Area_Quotient2 li r4,7*4 bl IntToArea ; second term = 7*4 lw r11,Area_Quotient3 li r4,12*4 bl IntToArea ; second term = 12*4 lw r11,Area_Quotient4 li r4,24*4 bl IntToArea ; second term = 24*4 la r13,Area_Q_Actual lw r11,Area_Quotient mr r12,r11 li r4,57 bl Division16 la r13,Area_Q2_Actual lw r11,Area_Quotient2 mr r12,r11 li r4,239 bl Division16 la r13,Area_Q3_Actual lw r11,Area_Quotient3 mr r12,r11 li r4,682 bl Division16 la r13,Area_Q4_Actual lw r11,Area_Quotient4 mr r12,r11 li r4,12943 bl Division16 lw r11,Area_Quotient lw r12,Area_Result mr r13,r11 bl CopyArea ;copy (we only have addition lw r11,Area_Quotient2 ;operation with two operands) lw r12,Area_Result mr r13,r11 bl Addition ;calc 44*4/57 + 7*4/239 lw r11,Area_Quotient3 ;operation with two operands) lw r12,Area_Result mr r13,r11 bl Subtraction ;calc previous - 12*4/682 lw r11,Area_Quotient4 lw r12,Area_Result mr r13,r11 bl Addition ;calc previous + 24*4/12943 poplr blr ;;/ ;// IntToArea ****************************************************************************** * IntToArea (r11,r3,r4) * * Converts the integer (r4) to an area of the length r3 * * r11 [.L] -> destination area * r3 [.L] = length of the area in Longwords * r4 [.W] = integer value to convert * ****************************************************************************** IntToArea pushctr pushgpr r3-r5/r11 extsh r4,r4 slwi r5,r3,2 add r11,r11,r5 mtctr r3 li r5,0 ITA_clear stwu r5,-4(r11) ;clear the whole area (=0) bdnz ITA_clear stw r4,0(r11) ;write integer popgpr popctr blr ;;/ ;// CopyArea ****************************************************************************** * CopyArea (r11,r12,r13,r3) * * Copies the source area to dest area * * r11 [.L] -> source area * r12 [.L] -> destination area * r13 [.L] -> ptr to beginning of the source area * r3 [.L] = length of the area in Longwords * ****************************************************************************** CopyArea pushctr pushgpr r3/r5/r6/r11/r12 pushf f0 subf r5,r13,r11 add r12,r5,r12 slwi r6,r3,2 add r11,r11,r6 add r12,r12,r6 andi. r5,r3,$1f srwi. r3,r3,5 beq CA_copy1 mtctr r3 CA_copy rept 16 lfdu f0,-8(r11) stfdu f0,-8(r12) endr bdnz CA_copy tstw r5 beq CA_nocopy2 CA_copy1 mtctr r5 CA_copy2 lwzu r0,-4(r11) stwu r0,-4(r12) bdnz CA_copy2 CA_nocopy2 popf f0 popgpr popctr blr ;;/ ;// Addition ****************************************************************************** * Addition (r11,r12,r13,r3) * * Performs the addition r12-> + r11-> and stores the result in r12-> * * r11 [.L] -> source area * r12 [.L] -> destination area * r13 [.L] -> ptr to beginning of the source area * r3 [.L] = length of the area in Longwords * ****************************************************************************** Addition pushctr pushgpr r3-r7/r11/r12 subf r4,r13,r11 add r12,r12,r4 slwi r4,r3,2 add r11,r11,r4 add r12,r12,r4 addic r3,r3,0 ;clear carry! srwi. r4,r3,4 beq Add_Next mtctr r4 Add_Loop1 rept 16 lwzu r7,-4(r11) lwzu r5,-4(r12) adde r7,r7,r5 stw r7,0(r12) endr bdnz Add_Loop1 Add_Next andi. r6,r3,$f beq Add_Last mtctr r6 Add_Loop2 lwzu r7,-4(r11) lwzu r5,-4(r12) adde r7,r7,r5 stw r7,0(r12) bdnz Add_Loop2 Add_Last li r0,-1 addze. r0,r0 bne Add_End lwzu r7,-4(r11) lwzu r5,-4(r12) adde r7,r7,r5 stw r7,0(r12) b Add_Last Add_End popgpr popctr blr ;;/ ;// Subtraction ****************************************************************************** * Subtraction (r11,r12,r13,r3) * * Performs the subtraction r12-> - r11-> and stores the result in r12-> * * r11 [.L] -> source area * r12 [.L] -> destination area * r13 [.L] -> ptr to beginning of the source area * r3 [.L] = length of the area in Longwords * ****************************************************************************** Subtraction pushctr pushgpr r3-r7/r11/r12 subf r4,r13,r11 add r12,r12,r4 slwi r4,r3,2 add r11,r11,r4 add r12,r12,r4 subfc r7,r7,r7 ;set carry to 1!! srwi. r4,r3,4 beq Sub_Next mtctr r4 Sub_Loop1 rept 16 lwzu r7,-4(r11) lwzu r5,-4(r12) subfe r7,r7,r5 stw r7,0(r12) endr bdnz Sub_Loop1 Sub_Next andi. r6,r3,$f beq Sub_Last mtctr r6 Sub_Loop2 lwzu r7,-4(r11) lwzu r5,-4(r12) subfe r7,r7,r5 stw r7,0(r12) bdnz Sub_Loop2 Sub_Last li r0,-1 addze. r0,r0 beq Sub_End lwzu r7,-4(r11) lwzu r5,-4(r12) subfe r7,r7,r5 stw r7,0(r12) b Sub_Last Sub_End popgpr popctr blr ;;/ ;// Division ****************************************************************************** * Division (r11,r12,r13,r3,r4) * * Performs the division r11-> / r12 and stores the result in r12-> * * r11 [.L] -> source area * r12 [.L] -> destination area * r13 [.L] -> ptr to Area_x_Actual * r3 [.L] = length of the area in Longwords * r4 [.L] = divisor * ****************************************************************************** Division pushlr pushctr pushgpr r3-r9/r11-r13 lwz r5,0(r11) tstw r5 bne Division_cont tstw r13 beq Division_cont addi r11,r11,4 li r5,0 stw r5,0(r12) addi r12,r12,4 subic r3,r3,1 lwz r5,0(r13) addi r5,r5,4 stw r5,0(r13) lwz r5,4(r13) subi r5,r5,4 stw r5,4(r13) Division_cont subi r11,r11,4 ;prepare for lhzu subi r12,r12,4 ;prepare for sthu li r6,0 ;first high 32 bits = 0 srwi. r7,r3,2 beq Division_next mtctr r7 Division_loop rept 4 lwzu r5,4(r11) ;get first longword bl Div64 stwu r5,4(r12) ;write result endr bdnz Division_loop Division_next andi. r3,r3,$3 beq Division_end mtctr r3 Division_loop2 lwzu r5,4(r11) bl Div64 stwu r5,4(r12) bdnz Division_loop2 Division_end popgpr popctr poplr blr ;;/ ;// Division16 ****************************************************************************** * Division16 (r11,r12,r13,r3,r4) * * Performs the division r11-> / r12 and stores the result in r12-> * divisor must be 16 Bit!! * * r11 [.L] -> source area * r12 [.L] -> destination area * r13 [.L] -> ptr to Area_x_Actual * r3 [.L] = length of the area in Longwords * r4 [.L] = divisor * ****************************************************************************** Division16 pushctr pushgpr r3-r7/r11-r13 andi. r4,r4,$ffff lwz r5,0(r11) tstw r5 bne Division6_cont tstw r13 beq Division6_cont addi r11,r11,4 li r5,0 stw r5,0(r12) addi r12,r12,4 subic r3,r3,1 lwz r5,0(r13) addi r5,r5,4 stw r5,0(r13) lwz r5,4(r13) subi r5,r5,1 stw r5,4(r13) Division6_cont subi r11,r11,2 ;prepare for lhzu subi r12,r12,2 ;prepare for sthu li r6,0 srwi. r7,r3,2 beq Division6_next mtctr r7 Division6_loop rept 8 lhzu r5,2(r11) mh r6,r5 divwu r5,r6,r4 sthu r5,2(r12) mullw r5,r5,r4 subf r6,r5,r6 slwi r6,r6,16 endr bdnz Division6_loop Division6_next andi. r3,r3,$3 beq Division6_end mtctr r3 Division6_loop2 rept 2 lhzu r5,2(r11) mh r6,r5 divwu r5,r6,r4 sthu r5,2(r12) mullw r5,r5,r4 subf r6,r5,r6 slwi r6,r6,16 endr bdnz Division6_loop2 Division6_end popgpr popctr blr ;;/ ;// Div64 ****************************************************************************** * r5,r6 = Div64 (r4,r5,r6) * * Performs the 64 bit division on PPC systems * this emulation is not 100% (no OV, no DIV0, unsigned ...)! * r8/r10 are trashed! * * r6 [.L] = high word of dividend * r5 [.L] = low word of dividend * r4 [.L] = divisor * * r5 [.L] = quotient * r6 [.L] = remainder ****************************************************************************** DivCore macro bge .cont\@ addc r5,r5,r5 adde r6,r6,r6 add r8,r8,r8 b .cont1\@ .cont\@ addc r5,r5,r5 adde r6,r6,r6 add r8,r8,r8 cmplw r4,r6 bgt .cont2\@ .cont1\@ subf. r6,r4,r6 addi r8,r8,1 .cont2\@ endm Div64 push r4 li r8,0 tstw r6 rept 32 DivCore endr mr r5,r8 pop r4 blr ;;/