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252 lines
6.2 KiB
252 lines
6.2 KiB
page ,132
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subttl emfdiv.asm - Division
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;***
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;emfdiv.asm - Division
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;
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; Copyright (c) 1986-89, Microsoft Corporation
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;
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;Purpose:
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; Division
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;
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; This Module contains Proprietary Information of Microsoft
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; Corporation and should be treated as Confidential.
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;
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;Revision History:
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; See emulator.hst
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;
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;*******************************************************************************
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;-----------------------------------------;
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; ;
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; Division ;
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; ;
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;-----------------------------------------;
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ProfBegin FDIV
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RDBRQQ: ; Routine Div Both must see if we have two singles.
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if fastSP
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MOV BX,DX
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XOR BX,Single + 256*Single
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TEST BX,Single + 256*Single
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JNZ RDDRQQ
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MOV bx,offset TDSRQQ
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JMP [bx]
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endif ;fastSP
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pub RDDRQQ ; Routine Division Double
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; Now we have
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; SI --> numerator , AX - Expon , DL - Sign
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; DI --> denominator , CX - Expon , DH - Sign
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if fastSP
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CALL CoerceToDouble ; insure that both args are double
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endif ;fastSP
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STC ; exponent will be difference - 1
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SBB AX,CX ; compute result exponent
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; AH has the (tentative) true exponent of the result. It is correct if the
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; result does not need normalizing. If normalizing is required, then this
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; must be incremented to give the correct result exponent
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XOR DH,DL ; Compute sign
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PUSH ebp
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PUSH edx ; Save sign
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PUSH esi
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PUSH edi
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ADD esi,6
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ADD edi,6
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MOV ecx,4
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STD
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REP CMPS word ptr [esi],word ptr [edi] ; compare numerator mantissa
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CLD ; with denominator mantissa
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POP edi
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POP esi
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PUSHF ; save the flags from the compare
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MOV BP,AX ; save the exponent
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LODS word ptr [esi] ; Load up numerator
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MOV CX,AX
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LODS word ptr [esi]
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MOV BX,AX
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LODS word ptr [esi]
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MOV DX,AX
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LODS word ptr [esi]
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XCHG AX,DX
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; Move divisor to DAC so we can get at it easily.
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MOV esi,edi ; Move divisor to DAC
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MOV edi,offset DAC
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ifdef i386
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MOVSD
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MOVSD
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else
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MOVSW
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MOVSW
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MOVSW
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MOVSW
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endif
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; Now we're all set:
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; DX:AX:BX:CX has dividend
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; DAC has divisor (in normal format)
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; Both are 64 bits with zeros and have implied bit set.
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; Top of stack has sign and tentative exponent.
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XOR DI,DI
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POPF ; numerator mantissa < denominator?
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; 80286 errata for POPF shouldn't
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; apply because interrupts should be
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; turned on in this context
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JB short DivNoShift ; if so bypass numerator shift
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SHR DX,1 ; Make sure dividend is smaller than divisor
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RCR AX,1 ; by dividing it by two
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RCR BX,1
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RCR CX,1
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RCR DI,1
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INC BP ; increment result exponent
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pub DivNoShift
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PUSH ebp ; save result exponent
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MOV [REMLSW],DI ; Save lsb of remainder
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CALL DIV16 ; Get a quotient digit
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PUSH edi
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MOV [REMLSW],0 ; Turn off the shifted bit
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CALL DIV16
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PUSH edi
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CALL DIV16
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PUSH edi
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CALL DIV16
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MOV BP,8001H ; turn round and sticky on
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SHL CX,1
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RCL BX,1
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RCL AX,1
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RCL DX,1 ; multiply remainder by 2
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JC short BPset ; if overflow, then round,sticky valid
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MOV esi,offset DAC
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CMP DX,[esi+6]
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JNE short RemainderNotHalf
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CMP AX,[esi+4]
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JNE short RemainderNotHalf
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CMP BX,[esi+2]
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JNE short RemainderNotHalf
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CMP CX,[esi] ; compare 2*remainder with denominator
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;Observe, oh wondering one, how you can assume the result of this last
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;compare is not equality. Use the following notation: n=numerator,
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;d=denominator,q=quotient,r=remainder,b=base(2^64 here). If
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;initially we had n < d then there was no shift and we will find q and r
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;so that q*d+r=n*b, if initially we had n >= d then there was a shift and
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;we will find q and r so that q*d+r=n*b/2. If we have equality here
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;then r=d/2 ==> n={possibly 2*}(2*q+1)*d/(2*b), since this can only
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;be integral if d is a multiple of b, but by definition b/2 <= d < b, we
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;have a contradiction. Equality is thus impossible at this point.
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pub RemainderNotHalf ; if 2*remainder > denominator
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JAE short BPset ; then round and sticky are valid
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OR AX,DX
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OR AX,CX
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OR AX,BX
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OR AL,AH ; otherwise or sticky bits into AL
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XOR AH,AH ; clear round bit
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MOV BP,AX ; move round and sticky into BP
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pub BPset
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MOV DX,DI ; get low 16 bits into proper location
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POP ecx
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POP ebx
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POP edi
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POP esi ; Now restore exponent
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JMP ROUND ; Result is normalized, round it
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; Remainder in DX:AX:BX:CX:REMLSW
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pub DIV16
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MOV SI,[DAC+6] ; Get high word of divisor
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XOR DI,DI ; Initialize quotient digit to zero
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CMP DX,SI ; Will we overflow?
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JAE MAXQUO ; If so, go handle special
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OR DX,DX ; Is dividend small?
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JNZ short DDIV
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CMP SI,AX ; Will divisor fit at all?
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JA short ZERQUO ; No - quotient is zero
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pub DDIV
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DIV SI ; AX is our digit "guess"
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PUSH edx ; Save remainder -
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PUSH ebx ; top 32 bits
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XCHG AX,DI ; Quotient digit in DI
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XOR BP,BP ; Initialize quotient * divisor
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MOV SI,BP
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MOV AX,[DAC]
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OR AX,AX ; If zero, save multiply time
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JZ short REM2
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MUL DI ; Begin computing quotient * divisor
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MOV SI,DX
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pub REM2
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PUSH eax ; Save lowest word of quotient * divisor
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MOV AX,[DAC+2]
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OR AX,AX
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JZ short REM3
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MUL DI
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ADD SI,AX
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ADC BP,DX
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pub REM3
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MOV AX,[DAC+4]
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OR AX,AX
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JZ short REM4
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MUL DI
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ADD BP,AX
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ADC DX,0
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XCHG AX,DX
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; Remainder - Quotient * divisor
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; [SP+4]:[SP+2]:CX:REMLSW - AX:BP:SI:[SP]
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pub REM4
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MOV DX,[REMLSW] ; Low word of remainder
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POP ebx ; Recover lowest word of quotient * divisor
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SUB DX,BX
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SBB CX,SI
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POP ebx
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SBB BX,BP
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POP ebp ; Remainder from DIV
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SBB BP,AX
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XCHG AX,BP
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pub ZERQUO ; Remainder in AX:BX:CX:DX
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XCHG AX,DX
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XCHG AX,CX
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XCHG AX,BX
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JNC short DRET ; Remainder in DX:AX:BX:CX
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pub RESTORE
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DEC DI ; Drop quotient since it didn't fit
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ADD CX,[DAC] ; Add divisor back in until remainder goes +
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ADC BX,[DAC+2]
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ADC AX,[DAC+4]
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ADC DX,[DAC+6]
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JNC RESTORE ; Loop is performed at most twice
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pub DRET
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RET
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pub MAXQUO
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DEC DI ; DI=FFFF=2**16-1, DX:AX:BX:CX is remainder,
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SUB CX,[DAC] ; DX = [DAC+6], d = divisor = [DAC]
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SBB BX,[DAC+2]
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SBB AX,[DAC+4] ; subtract 2^16*d from DX:AX:BX:CX:0000H
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ADD CX,[DAC+2] ; (DX-[DAC+6] = 0 is implied)
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ADC BX,[DAC+4]
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ADC AX,DX ; add high 48 bits of d to AX:BX:CX:0000H
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MOV DX,[DAC] ; add low 16 bits of d to zero giving DX
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CMC ; DI should be FFFEH if no carry from add
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JMP ZERQUO
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ProfEnd FDIV
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