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page ,132 subttl emfsqrt.asm - Square root;***;emfsqrt.asm - Square root;; Copyright (c) 1986-89, Microsoft Corporation;;Purpose:; Square root;; This Module contains Proprietary Information of Microsoft; Corporation and should be treated as Confidential.;;Revision History:; See emulator.hst;;*******************************************************************************
;-----------------------------------------;; ;; Square root ;; ;;-----------------------------------------;
ProfBegin FSQRT
pub eFSQRT MOV esi,[CURstk] CALL $FSQRT RET
;---------------------------------------------------; !; 8087 emulator square root !; !;---------------------------------------------------
; With 0<=x={TOS=[SI]}<infinity, $FSQRT performs {TOS=[SI]} <--; {TOS=[SI]}^.5. All registers except SI are destroyed. Roots; of negative numbers, infinities, and NAN's result in errors. The; square root of -0 is -0. Algorithm: x is initially adjusted; so that the exponent is even (when the exponent is odd the exponent; is incremented and the mantissa is shifted right one bit). The; exponent is then divided by two and resaved. A single word; estimate of y (the root of x) accurate to 5 bits is produced using; a wordlength implementation of a linear polynomial approximation; of sqrt x. Four Newton-Raphson iterations are then computed as; follows:;; 1) qa*ya+r1a=xa:0h,ya=(ya+qa)/2; 2) qa*ya+r1a=xa:xb,ya=(ya+qa)/2; 3) qa*ya+r1a=xa:xb,qb*ya+r2a=r1a:xc,ya:yb=(ya:yb+qa:qb)/2; *** iteration 4 implemented with standard divide ***; 4) qa*ya+r1a=xa:xb,p1a:p1b=qa*yb,; if p1a<r1a continue; if p1a=r1a; if p1b=xc continue else r1a=r1a+ya,qa=qa-1 endif,; else r1a=r1a+ya,qa=qa-1,p1a:p1b=p1a:p1b-yb endif,; r1a:r1b=r1a:xc-p1a:p1b,; qb:ya+r2a=r1a:r1b,p2a:p2b=qb*yb,; if p2a<r2a continue; if p2a=r2a; if p2b=xd continue else r2a=r2a+ya,qb=qb-1 endif,; else r2a=r2a+ya,qb=qb-1,p2a:p2b=p2a:p2b-yb endif,; r2a:r2b=r2a:xd-p2a:p2b,; qc*ya+r3a=r2a:r2b,p3a:p3b=qc*yb,; if p3a>=r3a then r3a=r3a+ya,qc=qc-1 endif,; r3a=r3a-p3a,qd*ya+r4a=r3a:0h,; ya:yb:yc:yd=(ya:yb:0h:0h+qa:qb:qc:qd)/2
pub SQRTSPECIAL RCR AH,1 ;if NAN JNC short SETFLAG ; set invalid flag and return RCL AL,1 ;if -infinity JC short SQRTERROR ; return real indefinite MOV AL,[CWcntl] ;get Infinity control TEST AL,ICaffine ;if affine closure JNZ short SQRTDONE ; return +infinity JMP SHORT SQRTERROR ;else return real indefinite
pub NOTPOSVALID TEST AH,2 ;if special JNZ SQRTSPECIAL ; process special RCR AH,1 ;if zero JC SHORT SQRTDONE ; return argument ;otherwise -ve, return NAN
pub SQRTERROR MOV edi,esi MOV esi,offset IEEEindefinite CALL csMOVRQQ MOV esi,edi ;return indefinite
pub SETFLAG OR [CURerr],Invalid+SquareRootNeg ;Set flag indicating invalid
pub SQRTDONE RET
pub $FSQRT MOV AX,[esi+Flag] ;get flags TEST AX,00380H ;if Sign, Invalid or Zero JNZ NOTPOSVALID ; perform special processing PUSH esi ;save ptr to x MOV edi,offset TEMP1 ;[DI]=y=temp MOV word ptr [edi+Flag],0 ;clear flags in y MOV AX,[esi+Expon] ;get exponent of x DEC AX ;adjust for shift divide by 2 MOV BX,[esi+6] MOV CX,[esi+4] MOV DX,[esi+2] ;get first three mantissa words of x TEST AL,1 ;if exponent is even JZ short EXPEVEN ; bypass adjust INC AX ;increment exponent SHR BX,1 RCR CX,1 RCR DX,1 ;divide mantissa by 2
pub EXPEVEN SAR AX,1 ;divide exponent by 2 MOV [edi+Expon],AX ;store exponent of y CMP BX,0FFFEH ;if mantissa < 0.FFFEh JB short NOTNEARONE1 ; perform main root routine STC ;otherwise x to become (1+x)/2 JMP SHORT SINGLEDONE ;single precision complete
pub NOTNEARONE1 PUSH edx ;save third mantissa word MOV AX,0B075H ;AX=.B075h MUL BX ;DX=.B075h*x MOV BP,057D8H ;BP=.57D8h ADD BP,DX ;BP=.B075h*x+.57D8h JNC short NORMEST ;if y is more than one MOV BP,0FFFFH ; replace y with .FFFFh
pub NORMEST MOV DX,BX XOR AX,AX ;load divide regs with xa:0h DIV BP ;qa*ya+r1a=xa:0h ADD BP,AX ;ya=ya+qa RCR BP,1 ;ya=ya/2 MOV DX,BX MOV AX,CX ;load divide regs with xa:xb DIV BP ;qa*ya+r1a=xa:xb STC ;add one to qa for better rounding ADC BP,AX ;ya=ya+qa RCR BP,1 ;ya=ya/2 MOV DX,BX MOV AX,CX ;load divide regs with xa:xb DIV BP ;qa*ya+r1a=xa:xb MOV SI,AX ;save qa POP eax ;load divide regs with r1a:xc DIV BP ;qb*ya+r2a=r1a:xc MOV BX,BP MOV CX,AX ;move qa:qb ADD CX,1 ;add one to qa:qb for better rounding ADC BX,SI ;ya:yb=ya:0h+qa:qb
pub SINGLEDONE RCR BX,1 RCR CX,1 ;ya:yb=(ya:0h+qa:qb)/2 MOV word ptr [edi+6],BX MOV word ptr [edi+4],CX MOV word ptr [edi+2],0 MOV word ptr [edi],0 ;save ya:yb:0h:0h MOV esi,edi ;[SI]=y POP edi ;[DI]=x MOV [RESULT],edi ;result=[DI] CALL DIDRQQ ;[DI]=x/y MOV esi,offset TEMP1 ;[SI]=y CALL ADDRQQ ;[DI]=y+x/y DEC word ptr [edi+Expon] ;[DI]=(y+x/y)/2=TOS MOV esi,edi ;[SI]=sqrt(x) RET
ProfEnd FSQRT
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