You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
469 lines
13 KiB
469 lines
13 KiB
page ,132
|
|
subttl emftran.asm - Transcendentals
|
|
;***
|
|
;emftran.asm - Transcendentals
|
|
;
|
|
; Copyright (c) 1986-89, Microsoft Corporation
|
|
;
|
|
;Purpose:
|
|
; Transcendentals
|
|
;
|
|
; This Module contains Proprietary Information of Microsoft
|
|
; Corporation and should be treated as Confidential.
|
|
;
|
|
;Revision History:
|
|
; See emulator.hst
|
|
;
|
|
;*******************************************************************************
|
|
|
|
|
|
;-----------------------------------------;
|
|
; ;
|
|
; Transcendentals ;
|
|
; ;
|
|
;-----------------------------------------;
|
|
|
|
ProfBegin FTRAN
|
|
|
|
|
|
pub MoveCodeSItoDataSI
|
|
PUSH edi
|
|
MOV edi,offset COEFFICIENT
|
|
ifdef i386
|
|
rept Reg87Len/4
|
|
MOVS dword ptr es:[edi],dword ptr cs:[esi]
|
|
endm
|
|
else
|
|
rept Reg87Len/2
|
|
MOVS word ptr es:[edi],word ptr cs:[esi]
|
|
endm
|
|
endif
|
|
MOV esi,offset COEFFICIENT
|
|
POP edi
|
|
RET
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator transcendental utilities !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; COMPcsSIDI is analogous to the 8086 CMP instruction with operands
|
|
; cs:[SI],[DI]. All registers except CX and DX are left unaltered.
|
|
; Zero and negative zero are determined to be unequal. NAN's and
|
|
; infinities may not be compared with this routine.
|
|
;
|
|
; FRAT2X performs {TOS=[DI]} <-- {TOS=[SI]}*PNUM({TOS=[SI]}^2),
|
|
; and program created {temp=[SI]} <-- PDEN({TOS=[SI]}^2). On input,
|
|
; [BX] must contain the degree of PNUM, the coefficients of PNUM
|
|
; in descending order, the degree-1 of PDEN and the coefficients
|
|
; of PDEN in descending order. PDEN is evaluated assuming an implied
|
|
; highest coefficient of one. [BX] is left unaltered, ARG2 is loaded
|
|
; with {TOS}^2, DENORX is used, all registers are destroyed with
|
|
; DI returning the value input in SI.
|
|
|
|
pub BOTHZERO
|
|
CMP CH,CH ;set flags to equal
|
|
JMP short COMPDONE ;compare finished
|
|
|
|
pub COMPcsSIDI
|
|
MOV CX,CS
|
|
MOV DS,CX
|
|
MOV CX,[esi+Flag] ;get sign byte of [SI]
|
|
AND CL,Sign ;mask for sign
|
|
MOV DX,ES:[edi+Flag] ;get sign byte of [DI]
|
|
AND DL,Sign ;mask for sign
|
|
CMP DL,CL ;compare signs
|
|
JNE short SIGNDIFF
|
|
PUSH ES
|
|
PUSH esi
|
|
PUSH edi ;save pointers
|
|
OR CL,CL ;if signs are +
|
|
JNS short BOTHPOS ; don't exchange pointers
|
|
PUSH DS
|
|
PUSH ES
|
|
POP DS
|
|
POP ES
|
|
XCHG esi,edi ;exchange pointers
|
|
XCHG CX,DX ;exchange flags
|
|
|
|
pub BOTHPOS
|
|
AND CH,ZROorINF ;mask for zero
|
|
AND DH,ZROorINF ;mask for zero
|
|
CMP DH,CH ;if exactly one zero
|
|
JNE short COMPDONE ; then finished
|
|
OR CH,CH ;if both zero
|
|
JA BOTHZERO ; then done after flags set
|
|
MOV CX,[esi+Expon] ;get exponent of [SI]
|
|
ADD CX,IexpBias ;make it unbiased
|
|
MOV DX,ES:[edi+Expon] ;get exponent of [DI]
|
|
ADD DX,IexpBias ;make it unbiased
|
|
CMP CX,DX
|
|
JNE short COMPDONE ;compare exponents
|
|
ADD esi,MB6
|
|
ADD edi,MB6
|
|
STD
|
|
CMPS word ptr [edi],word ptr [esi]
|
|
JNE short COMPDONE
|
|
CMPS word ptr [edi],word ptr [esi]
|
|
JNE short COMPDONE
|
|
CMPS word ptr [edi],word ptr [esi]
|
|
JNE short COMPDONE
|
|
CMPS word ptr [edi],word ptr [esi] ;compare mantissas
|
|
|
|
pub COMPDONE
|
|
CLD
|
|
POP edi
|
|
POP esi
|
|
POP ES
|
|
|
|
pub SIGNDIFF
|
|
MOV CX,ES
|
|
MOV DS,CX
|
|
RET
|
|
|
|
pub FRAT2X
|
|
MOV edi,offset DENORX ;[DI]=temp
|
|
CALL MOVRQQ ;[DI]=x=temp
|
|
PUSH edi ;save ptr to x=temp
|
|
PUSH esi ;save ptr to TOS
|
|
PUSH ebx ;save ptr to polynomials
|
|
MOV edi,offset ARG2 ;get ptr to space for x^2
|
|
CALL MOVRQQ ;copy x to space for x^2
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL MUDRQQ ;ARG2 gets x^2
|
|
POP esi ;get ptr to numerator poly
|
|
ifdef i386
|
|
xor ecx,ecx
|
|
endif
|
|
LODS word ptr CS:[esi]
|
|
XCHG CX,AX ;CX=denominator degree-1
|
|
POP edi ;[DI]=TOS
|
|
CALL csMOVRQQ ;[DI]=first coeff=TOS
|
|
MOV [RESULT],edi ;result=[DI]
|
|
|
|
pub POLYLOOPA
|
|
PUSH ecx ;save no. of terms left
|
|
PUSH esi ;save ptr to next coeff
|
|
MOV esi,offset ARG2 ;get ptr to x^2
|
|
CALL MUDRQQ ;multiply TOS by x^2
|
|
POP esi ;get pointer to coeff
|
|
ADD esi,Reg87Len ;point to next coeff
|
|
PUSH esi ;save pointer to coeff
|
|
CALL MoveCodeSItoDataSI
|
|
CALL ADDRQQ ;add coeff to TOS
|
|
POP esi ;get ptr to coeff
|
|
POP ecx ;get no. of terms remaining
|
|
LOOP POLYLOOPA ;loop until no terms left
|
|
|
|
MOV ebx,esi ;move poly ptr
|
|
POP esi ;[SI]=x=temp
|
|
PUSH esi ;save ptr to x
|
|
PUSH ebx ;save poly ptr
|
|
CALL MUDRQQ ;multiply poly by x
|
|
POP esi ;get ptr to poly
|
|
ADD esi,12 ;[SI]=denominator degree-1
|
|
ifdef i386
|
|
xor ecx,ecx
|
|
endif
|
|
LODS word ptr CS:[esi]
|
|
XCHG CX,AX ;CX=denominator degree-1
|
|
POP ebx ;[BX]=temp
|
|
PUSH edi ;save denominator ptr
|
|
MOV edi,ebx ;[DI]=temp
|
|
CALL csMOVRQQ ;move second coeff to temp
|
|
PUSH ecx ;save poly degree-1
|
|
PUSH esi ;save ptr to denominator poly
|
|
MOV esi,offset ARG2 ;get ptr to x^2
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL ADDRQQ ;add x^2 to temp
|
|
POP esi ;get ptr to second coeff
|
|
POP ecx ;get poly degree-1
|
|
|
|
pub POLYLOOPB
|
|
PUSH ecx ;save no. of terms left
|
|
ADD esi,Reg87Len ;point to next coeff
|
|
PUSH esi ;save ptr to next coeff
|
|
MOV esi,offset ARG2 ;get ptr to x^2
|
|
CALL MUDRQQ ;multiply temp by x^2
|
|
POP esi ;get pointer to coeff
|
|
PUSH esi ;save pointer to coeff
|
|
CALL MoveCodeSItoDataSI
|
|
CALL ADDRQQ ;add coeff to temp
|
|
POP esi ;get ptr to coeff
|
|
POP ecx ;get no. of terms remaining
|
|
LOOP POLYLOOPB ;loop until no terms left
|
|
|
|
MOV esi,edi ;[SI]=denominator=temp
|
|
POP edi ;[DI]=numerator=TOS
|
|
RET
|
|
;-------------------------------------------------------------------------------
|
|
|
|
pub eFPTAN
|
|
MOV esi,[CURstk]
|
|
CALL $FPTAN
|
|
PUSH esi
|
|
PUSHST
|
|
MOV edi,[CURstk]
|
|
POP esi
|
|
CALL MOVRQQ
|
|
RET
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator partial tangent !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; When 0<=x={TOS=[SI]}<=pi/4 then $FPTAN performs {TOS=[DI]} <--
|
|
; numerator tangent ({TOS=[SI]}), system created {temp=[SI]} <--
|
|
; denominator tangent ({TOS=[SI]). Every register except DI is
|
|
; destroyed.
|
|
|
|
pub $FPTAN
|
|
MOV ebx,offset TANRAT ;[BX]=rational function
|
|
CALL FRAT2X ;[DI]=numerator=TOS,
|
|
RET ; [SI]=denominator=temp
|
|
;-------------------------------------------------------------------------------
|
|
|
|
pub eFPATAN
|
|
MOV edi,[CURstk]
|
|
MOV esi,edi
|
|
MOV AX,Flag[esi]
|
|
SUB edi,Reg87Len
|
|
|
|
pub CALLFPATAN
|
|
CALL $FPATAN
|
|
MOV esi,[CURstk]
|
|
POPST
|
|
RET
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator arctangent !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; When 0<y={[DI]=NOS}<=x={[SI]=TOS}<infinity then $FPATAN performs
|
|
; {NOS=[DI]} <-- arctangent({NOS=[DI]}/{TOS=[SI]}), TOS is left
|
|
; unaltered. All registers except DI are destroyed.
|
|
|
|
pub $FPATAN
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL DIDRQQ ;NOS=[DI] <-- [DI]/[SI]=x
|
|
MOV AL,0 ;flag reset
|
|
MOV esi,offset TWOMRT3 ;[SI]=2-3^.5
|
|
CALL COMPcsSIDI ;if 2-3^.5 >= x
|
|
JNB short ATNREDUCED ; then bypass arg reduction
|
|
MOV esi,edi ;[SI]=x=NOS
|
|
MOV edi,offset TEMP1 ;[DI]=temp
|
|
CALL MOVRQQ ;[DI]=x=temp
|
|
PUSH esi ;save NOS
|
|
MOV esi,offset RT3 ;[SI]=3^.5
|
|
CALL MoveCodeSItoDataSI
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL MUDRQQ ;[DI]=3^.5*x=temp
|
|
MOV esi,offset cFLD1 ;[SI]=1
|
|
CALL MoveCodeSItoDataSI
|
|
CALL SUDRQQ ;[DI]=3^.5*x-1
|
|
POP esi ;get NOS
|
|
PUSH edi ;save ptr to 3^.5*x-1
|
|
MOV edi,esi ;DI gets NOS
|
|
MOV esi,offset RT3 ;[SI]=3^.5
|
|
CALL MoveCodeSItoDataSI
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL ADDRQQ ;[DI]=x+3^.5=NOS
|
|
POP esi ;[SI]=3^.5*x-1
|
|
CALL DRDRQQ ;[DI]=(3^.5*x-1)/(x+3^.5)=NOS
|
|
MOV AL,1 ;flag set
|
|
|
|
pub ATNREDUCED
|
|
PUSH eax ;save flag
|
|
MOV esi,edi ;[SI]=reduced x=NOS
|
|
MOV ebx,offset ATNRAT ;[BX]=rational function
|
|
CALL FRAT2X ;[DI]=numerator=NOS,
|
|
; [SI]=denominator=temp
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL DIDRQQ ;[DI]=arctan(reduced x)=NOS
|
|
POP eax ;get flag
|
|
OR AL,AL ;if flag=0
|
|
JZ short ATNCOMPLETE ; bypass adjust
|
|
MOV esi,offset PIBY6 ;[SI]=pi/6
|
|
CALL MoveCodeSItoDataSI
|
|
CALL ADDRQQ ;[DI]=arctan(x)=NOS
|
|
|
|
pub ATNCOMPLETE
|
|
RET
|
|
;-------------------------------------------------------------------------------
|
|
|
|
pub eF2XM1
|
|
MOV esi,[CURstk]
|
|
CALL $F2XM1
|
|
RET
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator exponential !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; When 0<=x={TOS=[SI]}<=.5 then $F2XM1 performs {TOS=[SI]} <--
|
|
; 2^{TOS=[SI]}-1. All registers except SI are destroyed.
|
|
|
|
pub $F2XM1
|
|
MOV ebx,offset EXPRAT ;[BX]=rational function
|
|
CALL FRAT2X ;[DI]=numerator=TOS
|
|
PUSH edi ;save numerator=TOS
|
|
XCHG esi,edi ;[SI]=numerator, [DI]=denominator
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL SUDRQQ ;[DI]=denominator-numerator
|
|
MOV esi,edi ;[SI]=denominator-numerator
|
|
POP edi ;[DI]=numerator=TOS
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL DIDRQQ ;[DI]=(2^x-1)/2
|
|
INC word ptr [edi+Expon] ;[DI]=2^x-1
|
|
MOV esi,edi ;[SI]=2^x-1
|
|
RET
|
|
;-------------------------------------------------------------------------------
|
|
|
|
pub eFYL2X
|
|
MOV edi,[CURstk]
|
|
MOV esi,edi
|
|
MOV AX,Flag[esi]
|
|
SUB edi,Reg87Len
|
|
|
|
pub CALLFYL2X
|
|
CALL $FYL2X
|
|
MOV esi,[CURstk]
|
|
POPST
|
|
RET
|
|
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator multiple of logarithm !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; When -infinity<y={NOS=[DI]}<infinity and 0<x={TOS=[SI]}<infinity
|
|
; then $FYL2X performs {NOS=[DI]} <-- {NOS=[DI]}*log2({TOS=[SI]}).
|
|
; TOS is left unaltered, all registers except DI are destroyed.
|
|
|
|
pub $FYL2X
|
|
PUSH esi ;save ptr to x=TOS
|
|
MOV esi,edi ;[SI]=y=NOS
|
|
MOV edi,offset TEMP2 ;[DI]=temp2
|
|
CALL MOVRQQ ;[DI]=y=temp2
|
|
MOV edi,esi ;[DI]=y=NOS
|
|
POP esi ;[SI]=x=TOS
|
|
PUSH edi ;save ptr to y=NOS
|
|
MOV edi,offset TEMP3 ;[DI]=temp3
|
|
CALL MOVRQQ ;[DI]=x=temp3
|
|
MOV BX,[edi+Expon] ;BX=exponent of x
|
|
MOV word ptr [edi+Expon],0 ;set exponent of x to 0
|
|
MOV esi,offset RT2 ;[SI]=2^.5
|
|
CALL COMPcsSIDI ;if reduced x < 2^.5
|
|
JA short LOGREDUCED ; then bypass normalization
|
|
DEC word ptr [edi+Expon] ;otherwise make x < 2^.5
|
|
INC BX ;adjust exponent
|
|
|
|
pub LOGREDUCED
|
|
PUSH ebx ;save exponent of x
|
|
MOV esi,offset cFLD1 ;[SI]=1
|
|
CALL MoveCodeSItoDataSI
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL SUDRQQ ;[DI]=(reduced x)-1=temp3
|
|
MOV esi,edi ;[SI]=(reduced x)-1=temp3
|
|
POP ebx ;get exponent of x
|
|
POP edi ;[DI]=y=NOS
|
|
PUSH ebx ;save exponent of x
|
|
CALL $FYL2XP1 ;[DI]=y*log2(reduced x)=NOS
|
|
POP ebx ;get exponent of x
|
|
XOR AX,AX ;zero AX
|
|
OR BX,BX ;if exponent is zero
|
|
JZ short LOGRETURN ; then done
|
|
MOV DX,AX ;make sign +
|
|
JNS short EXPPOSITIVE ;if + then bypass adjust
|
|
MOV DL,Sign ;make sign -
|
|
NEG BX ;negate exponent
|
|
|
|
pub EXPPOSITIVE
|
|
MOV CX,16 ;initialize bit count
|
|
|
|
pub LOGLOOP
|
|
DEC CX ;decrement shift count
|
|
SHL BX,1 ;and shift exponent of x left
|
|
JNC LOGLOOP ;until carry detected
|
|
PUSH edi ;save ptr to y*log2(reduced x)=NOS
|
|
RCR BX,1 ;normalize exponent of x
|
|
MOV edi,offset TEMP3 ;[DI]=temp3
|
|
STOS word ptr es:[edi]
|
|
STOS word ptr es:[edi]
|
|
STOS word ptr es:[edi]
|
|
MOV AX,BX
|
|
STOS word ptr es:[edi]
|
|
MOV AX,CX
|
|
STOS word ptr es:[edi]
|
|
MOV AX,DX
|
|
STOS word ptr es:[edi] ;store exponent of x in temp3
|
|
MOV edi,offset TEMP2 ;[DI]=y=temp2
|
|
MOV esi,offset TEMP3 ;[SI]=exponent of x=temp3
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL MUDRQQ ;[DI]=y*exponent of x=temp2
|
|
MOV esi,edi ;[SI]=y*exponent of x=temp2
|
|
POP edi ;[DI]=y*log2(reduced x)=NOS
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL ADDRQQ ;[DI]=y*log2(x)=NOS
|
|
|
|
pub LOGRETURN
|
|
RET
|
|
;-------------------------------------------------------------------------------
|
|
|
|
pub eFYL2XP1
|
|
MOV edi,[CURstk]
|
|
MOV esi,edi
|
|
MOV AX,Flag[esi]
|
|
SUB edi,Reg87Len
|
|
|
|
pub CALLFYL2XP1
|
|
CALL $FYL2XP1
|
|
MOV esi,[CURstk]
|
|
POPST
|
|
RET
|
|
|
|
;---------------------------------------------------
|
|
; !
|
|
; 8087 emulator add 1 multiple of logarithm !
|
|
; !
|
|
;---------------------------------------------------
|
|
|
|
; When -infinity<y={[DI]=NOS}<infinity and
|
|
; 2^-.5-1<=x={[SI]=TOS}<2^.5-1 then $FYL2XP1 performs {NOS=[DI]}
|
|
; <-- {NOS=[DI]}*log2({TOS=[SI]}+1). TOS is left unaltered, all
|
|
; registers except DI are destroyed.
|
|
|
|
pub $FYL2XP1
|
|
PUSH edi ;save ptr to y
|
|
MOV edi,offset TEMP1 ;[DI]=temp
|
|
CALL MOVRQQ ;[DI]=x=temp
|
|
PUSH esi ;save ptr to x
|
|
MOV esi,offset TWO ;[SI]=2
|
|
CALL MoveCodeSItoDataSI
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL ADDRQQ ;[DI]=x+2=temp
|
|
POP esi ;[SI]=x=TOS
|
|
CALL DRDRQQ ;[DI]=x/(x+2)=temp
|
|
INC word ptr [edi+Expon] ;[DI]=2x/(x+2)=temp
|
|
MOV esi,edi ;[SI]=2x/(x+2)=temp
|
|
MOV ebx,offset LOGRAT ;[BX]=rational function
|
|
CALL FRAT2X ;[DI]=numerator=temp,
|
|
; [SI]=denominator=temp
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL DIDRQQ ;[DI]=log2(x+1)=temp
|
|
MOV esi,edi ;[SI]=log2(x+1)=temp
|
|
POP edi ;get ptr to y=NOS
|
|
MOV [RESULT],edi ;result=[DI]
|
|
CALL MUDRQQ ;[DI]=y*log2(x+1)=NOS
|
|
RET
|
|
|
|
ProfEnd FTRAN
|