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; ************* Floating point library for AVR microprocessors *************
;
; Assembler AVRASM v. 1.21
; Processor AT90S2313, AT90S8515
; Code Size 256 words (512 bytes)
; **************************************************************************
; Author Y.Andrienko
; Phone (057-2) 44-85-40, 98-07-58
; FIDO 2:461/44.14
; E-mail yurik@aqua.kharkov.ua, aya@apexmail.com
;
; Last modification - 28.09.1999
; **************************************************************************
; Floating point number format: 3-bytes
; 1st - order - bit 7 - number sign (1 - negative number)
; 6 - order sign (1 - positive order)
; 0..5 - order value
; 2nd - mantissa low byte
; 3d - mantissa high byte; !!! This variables must be defined in main programm !!!
;.def Float1O =r16
;.def Float1L =r17
;.def Float1H =r18
;
;.def Float2O =r19
;.def Float2L =r20
;.def Float2H =r21;.def FTempO =r22
;.def FTempL =r23
;.def FTempH =r24
;.def FCnt =r25
; ************************************************************************
; Fix2Float - translate fixed format number to floating point format
; Float2Fix - translate floating point number to fixed format
; FNeg - negate floating point number
; SwapFl - exchange Float1 and Float2
; FAdd - floating point addition Float2=Float2+Float1
; FSub - floating point substraction Float2=Float2-Float1
; FMul - floating point multiplication Float2=Float2*Float1
; FDiv - floating point division Float2=Float1/Float2
;*************************************************************************; translate number from fix to floating point format
; Input - 2-byte number in Float2L,Float2H
; Output - 3-byte floating point number in Float2
;
; high registers used - Float2O,Float2L,Float2HFix2Float:
clc ; clear carry
tst Float2L ; check number for 0
brne Fx2Fl_A
tst Float2H
brne Fx2Fl_A
ldi Float2O,$40 ; if Float2L=Float2H=0 set number to 0
ret
Fx2Fl_A:
ldi Float2O,$50 ; if fixed num # 0 set order to 50H
Fx2Fl_B:
sbrc Float2H,7 ; skip if bit 7#0
ret ; else return
rol FLoat2L ; shift number left
rol Float2H
dec Float2O ; and decrement order
rjmp Fx2Fl_B ; continue while bit 7#1; translate floating point number to fixed format
; Input - Float2
; Output - Float2L, Float2H
; carry=1 if overflow
;
; registers used - Float2O, Float2L, Float2HFloat2Fix:
sbrc Float2O,7 ; check number sign
rjmp SetOverflow ; for negative number set overflow and return
sbrs Float2O,6 ; check order sign
rjmp Float2eq0 ; for neg.order set number to 0
andi Float2O,$3f ; mask sign bits
cpi Float2O,$11 ; check maximal order
brlo Fl2Fx_A ; jump if order<11H
rjmp SetOverflow ; else set overflow and return
Fl2Fx_A:
subi Float2O,$10
neg Float2O ; Float2O=10H-Float2O
Fl2Fx_C:
clc ; clear carry
tst Float2O ; check order
brne Fl2Fx_B
ret ; return if order 0
Fl2Fx_B:
ror Float2H ; shift right
ror Float2L
dec Float2O ; decrement order
rjmp Fl2Fx_C ; repeat while order # 0Float2eq0:
clr Float2L
clr Float2H
ret; Change sign of floating point number Float2=-Float2
; Input - Float2
; Output - Float2
; registers used - Float2O,Float2L,Float2HFNeg:
neg Float2O
subi Float2O,$80
neg Float2O
clc
ret; Swap Float1 and Float2 numbers
; (Thanks for A.Redchhuk)
SwapFl:
; it is it was
eor Float1O,Float2O ; push Float1O
eor Float2O,Float1O ; mov Float1O,Float2O
eor Float1O,Float2O ; pop Float2Oeor Float1L,Float2L ; push Float1L
eor Float2L,Float1L ; mov Float1L,Float2L
eor Float1L,Float2L ; pop Float2Leor Float1H,Float2H ; push Float1H
eor Float2H,Float1H ; mov Float1H,Float2H
eor Float1H,Float2H ; pop Float2H
ret; Floating point addition Float2=Float1+Float2
; Input - Float1, Float2
; Output - Float2
; registers used - Float1O, Float1L, Float1H, Float2O, Float2L, Float2HFAdd:
sbrc Float1O,7 ; skip if Float1>0
rjmp FAdd_A ; jump if Float1<0
sbrs Float2O,7 ; skip if Float2<0
rjmp FAdd_B ; jump if FLoat1 and Float2 < 0; if numbers signs not equal (Float1>0,Float2<0 or Float1<0, Float2>0)
; if Float1>0 Float2<0 result = Float1-Float2
FAdd_C:
rcall FNeg ; change Float2 sign
rcall SwapFl
rjmp FSub ; and continue in substraction programm
; If Float1<0,Float2>0 result = Float2-Float1
FAdd_X:
rcall SwapFl ; Change Float1 sign
rcall FNeg
rcall SwapFl
rjmp FSub
FAdd_A:
sbrs Float2O,7 ; skip if Float1<0 and Float2<0
rjmp FAdd_X
; if numbers signs are equal
FAdd_B:
tst Float1H ; check Float1 for 0
brne FAdd_D
tst Float1L
brne FAdd_D
ret ; if Float1=0 result =Float2
FAdd_D:
tst Float2H ; check Float2 for 0
brne FAdd_E
tst Float2L
brne FAdd_E
rjmp Fl1toFl2 ; if Float2=0 copy Float1 as result and return
FAdd_E:
cp Float2O,Float1O ; compare orders
breq FAdd_G ; if orders are equal
brlo FAdd_F ; if Float2O<Float1O
rcall SwapFl ; else swap numbers
FAdd_F:
sub Float2O,Float1O
neg Float2O ; Float2O=Float1O-Float2O
cpi Float2O,$10
brlo FAdd_H ; if Float1O-Float2O<16
rjmp Fl1toFl2 ; else copy Float1 as result and return
FAdd_H:
clc ; clear carry
ror Float2H ; shift Float2 right
ror Float2L
dec Float2O ; decrement order
brne FAdd_H ; repeat while orders not equal
; if orders are equal
FAdd_G:
add Float2L,Float1L ; add numbers
adc Float2H,Float1H
brcs FAdd_I ; jump if carry set
FAdd_J:
mov Float2O,Float1O ; copy order value
ret ; and return
FAdd_I:
ror FLoat2H ; shift number
ror Float2L
inc Float1O ; increment order
rjmp FAdd_J; Floating point numbers substraction Float2=Float1-Float2
; Input - Float1, Float2
; Output - Float2
; registers used - Float1O, Float1L, Float1H, Float2O, Float2L, Float2HFSub:
sbrc Float1O,7 ; skip if Float1>0
rjmp FSub_A ; jump if Float1<0
sbrs Float2O,7 ; skip if Float2<0
rjmp FSub_B ; jump if Float1>0 and Float2>0; if numbers signs not equal
FSub_C:
rcall SwapFl
rcall FNeg ; change sign of 2nd number
rcall SwapFl
rjmp FAdd ; and continue in substraction programm
FSub_A:
sbrs Float2O,7 ; skip if Float2<0 and Float1<0
rjmp FSub_C ; jump if Float2>0 (Float1<0); if signs of numbers are equal
FSub_B:
tst Float1H ; check Float1 for 0
brne FSub_D
tst Float1L
brne FSub_D
ret ; if Float1=0 result = Float2 - return
FSub_D:
tst Float2H ; check Float2 for 0
brne FSub_E
tst Float2L
brne FSub_E
rcall Fl1toFl2 ; if FLoat2=0, result = -Float1, copy an return
rjmp FNeg ; change sign and return
FSub_E:
clt
cp Float1O,Float2O ; compare orders
breq FSub_G ; if orders are equal
brlo FSub_F ; if Float1O<Float2O
set ; set flag
rcall SwapFl ; swap numbers if Float1O>Float2O
FSub_F:
sub Float1O,Float2O
neg Float1O ; Float1O=Float2O-Float1O
cpi Float1O,$10
brlo FSub_H ; if Float2O-Float1O<16
ret ; else result=Float2; equalize orders
FSub_H:
clc
ror Float1H ; shift Float right
ror Float1L
dec Float1O
brne FSub_H ; repeat before orders not equal
brtc FSub_G ;
rcall SwapFl ; swap again
clt
FSub_G:
cp Float2L,Float1L
cpc Float2H,Float1H
brlo FSub_I
FSub_J:
sub Float2L,Float1L ; add numbers
sbc Float2H,Float1H
sbrc Float2H,7 ; skip if MSB=0
ret ; else return
rjmp Fx2Fl_B ; normalise result
FSub_I:
rcall SwapFl ; swap numbers
rcall FNeg ; change result sign
rjmp FSub_Jror FLoat2H ; shift number
ror Float2L
inc Float2O ; increment order
rcall FNeg ; and change sign
ret ; else return
; Floating point multiplication Float2 = Float1 * Float2
; Input - Float1, Float2
; Output - Float2
; registers used - Float1O, Float1L, Float1H, Float2O, Float2L, Float2H
; FTempO, FTempL, FCnt
;
FMul:
tst Float1H ; check Float1 for 0
brne FMul_A
tst Float1L
brne FMul_A
rjmp SetRes0 ; if Float1=0, set Float2=0 and return
FMul_A:
tst Float2H ; check Float2 for 0
brne FMul_B
tst Float2L
brne FMul_B
ret ; if Float2=0 - returnFMul_B:
mov FTempO,Float1O ; Find result sign
eor FTempO,Float2O ; FTempO bit 7 equal result sign
cbr Float1O,$80 ; reset numbers signs
cbr Float2O,$80
bst FTempO,7 ; save result sign in T
add Float2O,Float1O ; add orders
ldi Float1O,$40 ;
add Float2O,Float1O
bld Float2O,7; 16x16 bits unsigned multiplication from ****AVR200**** application note
FMul_D:
clr FTempO ;clear 2 highest bytes of result
clr FTempL
ldi FCnt,16 ;init loop counter
lsr Float2H
ror Float2L
FMul_E:
brcc FMul_F ;if bit 0 of multiplier set
add FTempO,Float1L ;add multiplicand Low to byte 2 of res
adc FTempL,Float1H ;add multiplicand high to byte 3 of res
FMul_F:
ror FTempL ;shift right result byte 3
ror FTempO ;rotate right result byte 2
ror Float2H ;rotate result byte 1 and multiplier High
ror Float2L ;rotate result byte 0 and multiplier Low
dec FCnt ;decrement loop counter
brne FMul_E ;if not done, loop more
; after multiplication - normalise result
FMul_H:
sbrc FTempL,7
rjmp FMul_G ; jump if result is normalised
rol Float2L ; shift number left
rol Float2H
rol FTempO
rol FTempL
dec Float2O ; decrement result order
rjmp FMul_H
FMul_G:
bld Float2O,7 ; restore result sign from T
mov Float2L,FTempO ; copy mantissa to result
mov Float2H,FTempL
ret; Floating point division Float2 = Float1/Float2
; Input - Float1, Float2
; Output - Float2
; registers used - Float1O, Float1L, Float1H, Float2O, Float2L, Float2H
; FTempO, FTempL, FTempH, FCntFDiv:
mov FTempO,Float1L ; Check Float1 for 0
or FTempO,Float1H
tst FTempO
brne FDiv_A
rjmp SetRes0 ; if Float1=0 - result = 0
FDiv_A:
sbrs Float2H,7
rjmp SetOverflow ; if Float2 not normalized or 0 - overflow
ldi FCnt,$10 ; bits counter
mov FTempO,Float1O
andi FTempO,$80 ; select sign bit
add FTempO,Float2O ;
bst FTempO,7 ; store result sign in T
mov FTempO,Float1O ; read 1st number order
sub FTempO,Float2O ; substract orders
subi FTempO,-$41 ; add 41H
bld FTempO,7 ; restore result sign
clr Float1O ; clear orders
clr Float2O
clr FTempH
ldi FTempL,1
; main division cykle
FDiv_C:
sbrs FTempL,0
rjmp FDiv_D
sub Float1L,Float2L
sbc Float1H,Float2H
sbc Float1O,Float2O ; set carry
rjmp FDiv_E
FDiv_D:
add Float1L,Float2L
adc Float1H,Float2H
adc Float1O,Float2O
FDiv_E:
andi Float1O,$01
push Float1O ; save order
clc
eor Float1O,Float2O
brne FDiv_F
sec
FDiv_F:
pop Float1O ; restore order
rol FTempL
rol FTempH
clc ; clear carry
rol Float1L
rol Float1H
mov Float1O,FTempH
rol Float1O
dec FCnt ; decremet counter
brne FDiv_C ; repeate while FCnt#0
mov Float2L,FTempL ; copy result
mov Float2H,FTempH
mov Float2O,FTempO
rjmp Fx2Fl_B ; normalise result; Common subroutines
; Set overflow flag and return
SetOverflow:
sec
ret; Copy Float1 to Float2
Fl1toFl2:
mov Float2O,Float1O
mov Float2H,Float1H
mov Float2L,Float1L
ret; Set result to 0 (Float2=0)
SetRes0:
clr Float2L ; set result=0
clr Float2H
ldi Float2O,$40
ret
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