; ************* 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,Float2H Fix2Float: 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, Float2H Float2Fix: 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 # 0 Float2eq0: clr Float2L clr Float2H ret ; Change sign of floating point number Float2=-Float2 ; Input - Float2 ; Output - Float2 ; registers used - Float2O,Float2L,Float2H FNeg: 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 Float2O eor Float1L,Float2L ; push Float1L eor Float2L,Float1L ; mov Float1L,Float2L eor Float1L,Float2L ; pop Float2L eor 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, Float2H FAdd: 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, Float2H FSub: 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_J ror 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 - return FMul_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, FCnt FDiv: 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