;*********************************************** ; Complex number magnitude calculation ; using CORDIC algorithm described at ; www.dspguru.com\info\faqs\cordic.htm ; ; Input: ; ReH:ReL, ImH:ImL - complex number (16 bit signed) ; ; Output: ; ReH:ReL - magnitude (16 bit unsigned) ; ImH:ImL - garbage ; ; Temporaries: ; RekH:RekL - Re multipled by k (k=2^-L, L=0,1,2,...15) ; Counter - loop counter ; Temp ; ; Instructions: 147 ; Execution time(worst case including return): ; 18+18+15*(8+2+20+5+7.5*10-2)+60 ~= 1700 instruction cycles ; Notes: ; 1) Precision is 0.028%, depends on how exact ; the division by CORDIC gain is implemented: ; (0.60725293510314) ; a) 1/2+1/8-1/64-1/512 -> 0.028% ; b) 1/2+1/8-1/64-1/512-1/4096 -> 0.012384% ; c) 1/2+1/8-1/64-1/512-1/4096+1/16384 -> 0.002333% ; 2) Range of input data should be restricted so ; that M=sqrt(Re*Re+Im*Im) is less than 65536*0.60725293510314~=39760 ; to prevent overflow in magnitude during calculation ; 3) To reduce execution time, the number of loops can be ; reduced to 8. The angle after rotation the initial ; vector 8 times is less then 0.22381 deg, which is good ; enough precision. Besides, the gain at 8 rotations is smaller ; and closer to the approximated gain, which is used in this code. ; Reduced execution time will be ~850 cycles! ; ; 6 Aug 2000 by Nikolai Golovchenko ;*********************************************** Magnitude16 ;Find absolute value of the vector components sb ReH.7 ;Re = abs(Re) jmp Magnitude16a not ReL not ReH inc ReL snb Z inc ReH Magnitude16a sb ImH.7 ;Im = abs(Im) jmp Magnitude16b not ImL not ImH inc ImL snb Z inc ImH Magnitude16b ;Test imaginary part for zero and if yes, quit mov W, ImL or W, ImH snb Z ret ;quit if zero imaginary part ;Perform first iteration mov W, ImL ;Imk = Im mov ImkL, W mov W, ImH mov ImkH, W mov W, ReL ;Im' = Im - Re sub ImL, W mov W, ReH sb C movsz W, ++ReH sub ImH, W mov W, ImkL ;Re' = Re + Im = Re + Imk add ReL, W mov W, ImkH snb C movsz W, ++ImkH add ReH, W ;Begin loop mov W, #1 mov Counter, W Magnitude16loop ;load scaled values mov W, ImL ;Imk = Im mov ImkL, W mov W, ImH mov ImkH, W mov W, ReL ;Rek = Re mov RekL, W mov W, ReH mov RekH, W ;scale them (1 to 15 right shifts) mov W, Counter ;load counter value to Temp mov Temp, W Magnitude16loop2 clrb C ;unsigned right shift for Rek rr RekH rr RekL mov W, <<ImkH ;signed right shift for Imk rr ImkH rr ImkL decsz Temp jmp Magnitude16loop2 ;update current values mov W, ImkL snb ImH.7 ;if Im < 0 add a phase, if Im >= 0 substract a phase jmp Magnitude16AddPhase ;substract a phase add ReL, W ;Re' = Re + Imk mov W, ImkH snb C movsz W, ++ImkH add ReH, W mov W, RekL ;Im' = Im - Rek sub ImL, W mov W, RekH sb C movsz W, ++RekH sub ImH, W jmp Magnitude16loopend Magnitude16AddPhase ;add a phase snb C ;correct Imk, because shifts of negative movsz W, ++ImkL ;values like (-1 >> 1 = -1) can dec ImkH ;accumulate error. With this correction, inc ImkH ;shifts of negative values will work like ;shifts of positive values (i.e. round to zero) sub ReL, W ;Re' = Re - Imk mov W, ImkH sb C movsz W, ++ImkH sub ReH, W mov W, RekL ;Im' = Im + Rek add ImL, W mov W, RekH snb C movsz W, ++RekH add ImH, W Magnitude16loopend inc Counter sb Counter.4 ;repeat untill counter reaches 16 ;or uncomment this for better performance ; sb Counter.3 ;repeat untill counter reaches 8 jmp Magnitude16loop ;Optional: ;Divide result by 1.64676025786545 (CORDIC gain) ;or multiply by 0.60725293510314 = 1/2+1/8-1/64-1/512 - 0.028% mov W, ReH mov RekH, W mov W, ReL mov RekL, W clrb C rr ReH rr ReL clrb C rr ReH rr ReL clrb C rr ReH rr ReL not ReL not ReH inc ReL snb Z inc ReH clr Temp snb ReH.7 not Temp sub ReL, W mov W, RekH sb C movsz W, ++RekH sub ReH, W sb C dec Temp rr Temp rr ReH rr ReL rr Temp rr ReH rr ReL mov W, <<ReH rr ReH rr ReL mov W, RekL add ReL, W mov W, RekH snb C movsz W, ++RekH add ReH, W clrb C rr ReH rr ReL clrb C rr ReH rr ReL mov W, RekL add ReL, W mov W, RekH snb C movsz W, ++RekH add ReH, W rr ReH rr ReL ;Done! ret ;***********************************************
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