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- Apple II Reference Manual (Red Book), January 1978, pages 94-95.
- ***********************
- * *
- * APPLE-II FLOATING *
- * POINT ROUTINES *
- * *
- * COPYRIGHT 1977 BY *
- * APPLE COMPUTER INC. *
- * *
- * ALL RIGHTS RESERVED *
- * *
- * S. WOZNIAK *
- * *
- ***********************
- TITLE "FLOATING POINT ROUTINES"
- SIGN EPZ $F3
- X2 EPZ $F4
- M2 EPZ $F5
- X1 EPZ $F8
- M1 EPZ $F9
- E EPZ $FC
- OVLOC EQU $3F5
- ORG $F425
- F425: 18 ADD CLC CLEAR CARRY
- F426: A2 02 LDX #$2 INDEX FOR 3-BYTE ADD.
- F428: B5 F9 ADD1 LDA M1,X
- F42A: 75 F5 ADC M2,X ADD A BYTE OF MANT2 TO MANT1
- F42C: 95 F9 STA M1,X
- F42E: CA DEX INDEX TO NEXT MORE SIGNIF. BYTE.
- F42F: 10 F7 BPL ADD1 LOOP UNTIL DONE.
- F431: 60 RTS RETURN
- F432: 06 F3 MD1 ASL SIGN CLEAR LSB OF SIGN.
- F434: 20 37 F4 JSR ABSWAP ABS VAL OF M1, THEN SWAP WITH M2
- F437: 24 F9 ABSWAP BIT M1 MANT1 NEGATIVE?
- F439: 10 05 BPL ABSWAP1 NO, SWAP WITH MANT2 AND RETURN.
- F43B: 20 A4 F4 JSR FCOMPL YES, COMPLEMENT IT.
- F43E: E6 F3 INC SIGN INCR SIGN, COMPLEMENTING LSB.
- F440: 38 ABSWAP1 SEC SET CARRY FOR RETURN TO MUL/DIV.
- F441: A2 04 SWAP LDX #$4 INDEX FOR 4 BYTE SWAP.
- F443: 94 FB SWAP1 STY E-1,X
- F445: B5 F7 LDA X1-1,X SWAP A BYTE OF EXP/MANT1 WITH
- F447: B4 F3 LDY X2-1,X EXP/MANT2 AND LEAVE A COPY OF
- F449: 94 F7 STY X1-1,X MANT1 IN E (3 BYTES). E+3 USED
- F44B: 95 F3 STA X2-1,X
- F44D: CA DEX ADVANCE INDEX TO NEXT BYTE
- F44E: D0 F3 BNE SWAP1 LOOP UNTIL DONE.
- F450: 60 RTS RETURN
- F451: A9 8E FLOAT LDA #$8E INIT EXP1 TO 14,
- F453: 85 F8 STA X1 THEN NORMALIZE TO FLOAT.
- F455: A5 F9 NORM1 LDA M1 HIGH-ORDER MANT1 BYTE.
- F457: C9 C0 CMP #$C0 UPPER TWO BITS UNEQUAL?
- F459: 30 0C BMI RTS1 YES, RETURN WITH MANT1 NORMALIZED
- F45B: C6 F8 DEC X1 DECREMENT EXP1.
- F45D: 06 FB ASL M1+2
- F45F: 26 FA ROL M1+1 SHIFT MANT1 (3 BYTES) LEFT.
- F461: 26 F9 ROL M1
- F463: A5 F8 NORM LDA X1 EXP1 ZERO?
- F465: D0 EE BNE NORM1 NO, CONTINUE NORMALIZING.
- F467: 60 RTS1 RTS RETURN.
- F468: 20 A4 F4 FSUB JSR FCOMPL CMPL MANT1,CLEARS CARRY UNLESS 0
- F46B: 20 7B F4 SWPALGN JSR ALGNSWP RIGHT SHIFT MANT1 OR SWAP WITH
- F46E: A5 F4 FADD LDA X2
- F470: C5 F8 CMP X1 COMPARE EXP1 WITH EXP2.
- F472: D0 F7 BNE SWPALGN IF #,SWAP ADDENDS OR ALIGN MANTS.
- F474: 20 25 F4 JSR ADD ADD ALIGNED MANTISSAS.
- F477: 50 EA ADDEND BVC NORM NO OVERFLOW, NORMALIZE RESULT.
- F479: 70 05 BVS RTLOG OV: SHIFT M1 RIGHT, CARRY INTO SIGN
- F47B: 90 C4 ALGNSWP BCC SWAP SWAP IF CARRY CLEAR,
- * ELSE SHIFT RIGHT ARITH.
- F47D: A5 F9 RTAR LDA M1 SIGN OF MANT1 INTO CARRY FOR
- F47F: 0A ASL RIGHT ARITH SHIFT.
- F480: E6 F8 RTLOG INC X1 INCR X1 TO ADJUST FOR RIGHT SHIFT
- F482: F0 75 BEQ OVFL EXP1 OUT OF RANGE.
- F484: A2 FA RTLOG1 LDX #$FA INDEX FOR 6:BYTE RIGHT SHIFT.
- F486: 76 FF ROR1 ROR E+3,X
- F488: E8 INX NEXT BYTE OF SHIFT.
- F489: D0 FB BNE ROR1 LOOP UNTIL DONE.
- F48B: 60 RTS RETURN.
- F48C: 20 32 F4 FMUL JSR MD1 ABS VAL OF MANT1, MANT2
- F48F: 65 F8 ADC X1 ADD EXP1 TO EXP2 FOR PRODUCT EXP
- F491: 20 E2 F4 JSR MD2 CHECK PROD. EXP AND PREP. FOR MUL
- F494: 18 CLC CLEAR CARRY FOR FIRST BIT.
- F495: 20 84 F4 MUL1 JSR RTLOG1 M1 AND E RIGHT (PROD AND MPLIER)
- F498: 90 03 BCC MUL2 IF CARRY CLEAR, SKIP PARTIAL PROD
- F49A: 20 25 F4 JSR ADD ADD MULTIPLICAND TO PRODUCT.
- F49D: 88 MUL2 DEY NEXT MUL ITERATION.
- F49E: 10 F5 BPL MUL1 LOOP UNTIL DONE.
- F4A0: 46 F3 MDEND LSR SIGN TEST SIGN LSB.
- F4A2: 90 BF NORMX BCC NORM IF EVEN,NORMALIZE PROD,ELSE COMP
- F4A4: 38 FCOMPL SEC SET CARRY FOR SUBTRACT.
- F4A5: A2 03 LDX #$3 INDEX FOR 3 BYTE SUBTRACT.
- F4A7: A9 00 COMPL1 LDA #$0 CLEAR A.
- F4A9: F5 F8 SBC X1,X SUBTRACT BYTE OF EXP1.
- F4AB: 95 F8 STA X1,X RESTORE IT.
- F4AD: CA DEX NEXT MORE SIGNIFICANT BYTE.
- F4AE: D0 F7 BNE COMPL1 LOOP UNTIL DONE.
- F4B0: F0 C5 BEQ ADDEND NORMALIZE (OR SHIFT RT IF OVFL).
- F4B2: 20 32 F4 FDIV JSR MD1 TAKE ABS VAL OF MANT1, MANT2.
- F4B5: E5 F8 SBC X1 SUBTRACT EXP1 FROM EXP2.
- F4B7: 20 E2 F4 JSR MD2 SAVE AS QUOTIENT EXP.
- F4BA: 38 DIV1 SEC SET CARRY FOR SUBTRACT.
- F4BB: A2 02 LDX #$2 INDEX FOR 3-BYTE SUBTRACTION.
- F4BD: B5 F5 DIV2 LDA M2,X
- F4BF: F5 FC SBC E,X SUBTRACT A BYTE OF E FROM MANT2.
- F4C1: 48 PHA SAVE ON STACK.
- F4C2: CA DEX NEXT MORE SIGNIFICANT BYTE.
- F4C3: 10 F8 BPL DIV2 LOOP UNTIL DONE.
- F4C5: A2 FD LDX #$FD INDEX FOR 3-BYTE CONDITIONAL MOVE
- F4C7: 68 DIV3 PLA PULL BYTE OF DIFFERENCE OFF STACK
- F4C8: 90 02 BCC DIV4 IF M2<E THEN DON'T RESTORE M2.
- F4CA: 95 F8 STA M2+3,X
- F4CC: E8 DIV4 INX NEXT LESS SIGNIFICANT BYTE.
- F4CD: D0 F8 BNE DIV3 LOOP UNTIL DONE.
- F4CF: 26 FB ROL M1+2
- F4D1: 26 FA ROL M1+1 ROLL QUOTIENT LEFT, CARRY INTO LSB
- F4D3: 26 F9 ROL M1
- F4D5: 06 F7 ASL M2+2
- F4D7: 26 F6 ROL M2+1 SHIFT DIVIDEND LEFT
- F4D9: 26 F5 ROL M2
- F4DB: B0 1C BCS OVFL OVFL IS DUE TO UNNORMED DIVISOR
- F4DD: 88 DEY NEXT DIVIDE ITERATION.
- F4DE: D0 DA BNE DIV1 LOOP UNTIL DONE 23 ITERATIONS.
- F4E0: F0 BE BEQ MDEND NORM. QUOTIENT AND CORRECT SIGN.
- F4E2: 86 FB MD2 STX M1+2
- F4E4: 86 FA STX M1+1 CLEAR MANT1 (3 BYTES) FOR MUL/DIV.
- F4E6: 86 F9 STX M1
- F4E8: B0 0D BCS OVCHK IF CALC. SET CARRY,CHECK FOR OVFL
- F4EA: 30 04 BMI MD3 IF NEG THEN NO UNDERFLOW.
- F4EC: 68 PLA POP ONE RETURN LEVEL.
- F4ED: 68 PLA
- F4EE: 90 B2 BCC NORMX CLEAR X1 AND RETURN.
- F4F0: 49 80 MD3 EOR #$80 COMPLEMENT SIGN BIT OF EXPONENT.
- F4F2: 85 F8 STA X1 STORE IT.
- F4F4: A0 17 LDY #$17 COUNT 24 MUL/23 DIV ITERATIONS.
- F4F6: 60 RTS RETURN.
- F4F7: 10 F7 OVCHK BPL MD3 IF POSITIVE EXP THEN NO OVFL.
- F4F9: 4C F5 03 OVFL JMP OVLOC
- ORG $F63D
- F63D: 20 7D F4 FIX1 JSR RTAR
- F640: A5 F8 FIX LDA X1
- F642: 10 13 BPL UNDFL
- F644: C9 8E CMP #$8E
- F646: D0 F5 BNE FIX1
- F648: 24 F9 BIT M1
- F64A: 10 0A BPL FIXRTS
- F64C: A5 FB LDA M1+2
- F64E: F0 06 BEQ FIXRTS
- F650: E6 FA INC M1+1
- F652: D0 02 BNE FIXRTS
- F654: E6 F9 INC M1
- F656: 60 FIXRTS RTS
- F657: A9 00 UNDFL LDA #$0
- F659: 85 F9 STA M1
- F65B: 85 FA STA M1+1
- F65D: 60 RTS
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