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178 lines
5.0 KiB
178 lines
5.0 KiB
page ,132
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subttl emfsqrt.asm - Square root
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;***
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;emfsqrt.asm - Square root
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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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; Square root
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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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; Square root ;
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; ;
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;-----------------------------------------;
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ProfBegin FSQRT
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pub eFSQRT
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MOV esi,[CURstk]
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CALL $FSQRT
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RET
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;---------------------------------------------------
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; !
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; 8087 emulator square root !
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; !
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;---------------------------------------------------
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; With 0<=x={TOS=[SI]}<infinity, $FSQRT performs {TOS=[SI]} <--
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; {TOS=[SI]}^.5. All registers except SI are destroyed. Roots
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; of negative numbers, infinities, and NAN's result in errors. The
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; square root of -0 is -0. Algorithm: x is initially adjusted
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; so that the exponent is even (when the exponent is odd the exponent
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; is incremented and the mantissa is shifted right one bit). The
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; exponent is then divided by two and resaved. A single word
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; estimate of y (the root of x) accurate to 5 bits is produced using
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; a wordlength implementation of a linear polynomial approximation
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; of sqrt x. Four Newton-Raphson iterations are then computed as
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; follows:
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;
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; 1) qa*ya+r1a=xa:0h,ya=(ya+qa)/2
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; 2) qa*ya+r1a=xa:xb,ya=(ya+qa)/2
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; 3) qa*ya+r1a=xa:xb,qb*ya+r2a=r1a:xc,ya:yb=(ya:yb+qa:qb)/2
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; *** iteration 4 implemented with standard divide ***
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; 4) qa*ya+r1a=xa:xb,p1a:p1b=qa*yb,
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; if p1a<r1a continue
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; if p1a=r1a
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; if p1b=xc continue else r1a=r1a+ya,qa=qa-1 endif,
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; else r1a=r1a+ya,qa=qa-1,p1a:p1b=p1a:p1b-yb endif,
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; r1a:r1b=r1a:xc-p1a:p1b,
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; qb:ya+r2a=r1a:r1b,p2a:p2b=qb*yb,
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; if p2a<r2a continue
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; if p2a=r2a
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; if p2b=xd continue else r2a=r2a+ya,qb=qb-1 endif,
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; else r2a=r2a+ya,qb=qb-1,p2a:p2b=p2a:p2b-yb endif,
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; r2a:r2b=r2a:xd-p2a:p2b,
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; qc*ya+r3a=r2a:r2b,p3a:p3b=qc*yb,
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; if p3a>=r3a then r3a=r3a+ya,qc=qc-1 endif,
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; r3a=r3a-p3a,qd*ya+r4a=r3a:0h,
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; ya:yb:yc:yd=(ya:yb:0h:0h+qa:qb:qc:qd)/2
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pub SQRTSPECIAL
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RCR AH,1 ;if NAN
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JNC short SETFLAG ; set invalid flag and return
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RCL AL,1 ;if -infinity
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JC short SQRTERROR ; return real indefinite
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MOV AL,[CWcntl] ;get Infinity control
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TEST AL,ICaffine ;if affine closure
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JNZ short SQRTDONE ; return +infinity
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JMP SHORT SQRTERROR ;else return real indefinite
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pub NOTPOSVALID
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TEST AH,2 ;if special
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JNZ SQRTSPECIAL ; process special
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RCR AH,1 ;if zero
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JC SHORT SQRTDONE ; return argument
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;otherwise -ve, return NAN
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pub SQRTERROR
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MOV edi,esi
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MOV esi,offset IEEEindefinite
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CALL csMOVRQQ
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MOV esi,edi ;return indefinite
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pub SETFLAG
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OR [CURerr],Invalid+SquareRootNeg ;Set flag indicating invalid
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pub SQRTDONE
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RET
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pub $FSQRT
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MOV AX,[esi+Flag] ;get flags
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TEST AX,00380H ;if Sign, Invalid or Zero
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JNZ NOTPOSVALID ; perform special processing
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PUSH esi ;save ptr to x
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MOV edi,offset TEMP1 ;[DI]=y=temp
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MOV word ptr [edi+Flag],0 ;clear flags in y
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MOV AX,[esi+Expon] ;get exponent of x
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DEC AX ;adjust for shift divide by 2
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MOV BX,[esi+6]
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MOV CX,[esi+4]
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MOV DX,[esi+2] ;get first three mantissa words of x
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TEST AL,1 ;if exponent is even
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JZ short EXPEVEN ; bypass adjust
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INC AX ;increment exponent
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SHR BX,1
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RCR CX,1
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RCR DX,1 ;divide mantissa by 2
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pub EXPEVEN
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SAR AX,1 ;divide exponent by 2
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MOV [edi+Expon],AX ;store exponent of y
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CMP BX,0FFFEH ;if mantissa < 0.FFFEh
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JB short NOTNEARONE1 ; perform main root routine
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STC ;otherwise x to become (1+x)/2
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JMP SHORT SINGLEDONE ;single precision complete
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pub NOTNEARONE1
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PUSH edx ;save third mantissa word
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MOV AX,0B075H ;AX=.B075h
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MUL BX ;DX=.B075h*x
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MOV BP,057D8H ;BP=.57D8h
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ADD BP,DX ;BP=.B075h*x+.57D8h
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JNC short NORMEST ;if y is more than one
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MOV BP,0FFFFH ; replace y with .FFFFh
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pub NORMEST
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MOV DX,BX
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XOR AX,AX ;load divide regs with xa:0h
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DIV BP ;qa*ya+r1a=xa:0h
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ADD BP,AX ;ya=ya+qa
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RCR BP,1 ;ya=ya/2
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MOV DX,BX
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MOV AX,CX ;load divide regs with xa:xb
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DIV BP ;qa*ya+r1a=xa:xb
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STC ;add one to qa for better rounding
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ADC BP,AX ;ya=ya+qa
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RCR BP,1 ;ya=ya/2
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MOV DX,BX
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MOV AX,CX ;load divide regs with xa:xb
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DIV BP ;qa*ya+r1a=xa:xb
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MOV SI,AX ;save qa
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POP eax ;load divide regs with r1a:xc
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DIV BP ;qb*ya+r2a=r1a:xc
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MOV BX,BP
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MOV CX,AX ;move qa:qb
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ADD CX,1 ;add one to qa:qb for better rounding
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ADC BX,SI ;ya:yb=ya:0h+qa:qb
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pub SINGLEDONE
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RCR BX,1
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RCR CX,1 ;ya:yb=(ya:0h+qa:qb)/2
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MOV word ptr [edi+6],BX
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MOV word ptr [edi+4],CX
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MOV word ptr [edi+2],0
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MOV word ptr [edi],0 ;save ya:yb:0h:0h
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MOV esi,edi ;[SI]=y
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POP edi ;[DI]=x
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MOV [RESULT],edi ;result=[DI]
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CALL DIDRQQ ;[DI]=x/y
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MOV esi,offset TEMP1 ;[SI]=y
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CALL ADDRQQ ;[DI]=y+x/y
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DEC word ptr [edi+Expon] ;[DI]=(y+x/y)/2=TOS
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MOV esi,edi ;[SI]=sqrt(x)
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RET
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ProfEnd FSQRT
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