'*************************************************
'* Test elementary operations on complex numbers *
'* --------------------------------------------- *
'*                                               *
'* SAMPLE RUN:                                   *
'*                                               *
'* Z1=( 1.0000,-2.0000)                          *
'* Z2=( 2.5000, 5.7500)                          *
'* Z1+Z2=( 3.5000, 3.7500)                       *
'* Z1+Z2 with modulus and phase:                 *
'* ( 5.1296, 0.8199)                             *
'* Z1 with modulus and phase:                    *
'* ( 2.2361,-1.1071)                             *
'* Z2 with modulus and phase:                    *
'* ( 6.2700, 1.1607)                             *
'* Z1*Z2=(14.0000, 0.7500)                       *
'* Z1*Z2 with modulus and phase:                 *
'* (14.0201, 0.0535)                             *
'* Z1/Z2 with modulus and phase:                 *
'* ( 0.3566,-2.2678)                             *
'* Exp(Z1)=(-1.1312,-2.4717)                     *
'* Exp(Z1) with modulus and phase:               *
'* ( 2.7183,-2.0000)                             *
'* ArgSh(Z2)=( 2.5246, 1.1560)                   *
'*                                               *
'*           BASIC version by J-P Moreau, Paris. *
'*                    (www.jpmoreau.fr)          *
'*************************************************
DEFINT I-N
DEFDBL A-H, O-Z

'a complex number z is represented as a table with 4 locations:
' z(1), z(2) for algebraic form  x+iy
' z(3), z(4) for polar form  r*exp(i*t)

DIM ZZ(4), Z(4), Z1(4), Z2(4)    'Complex numbers
DIM temp(4), u(4)                'Complex numbers

  XINF = 1.2E+16          'big number
  TINY = 1E-16            'small number
  PI = 4# * ATN(1)
  F$ = "##.####"

  CLS
  x = 1#: y = -2#
  GOSUB 500 'AssignXY(ZZ,x,y)
  FOR i = 1 TO 4
    Z1(i) = ZZ(i)
  NEXT
  x = 2.5#: y = 5.75#
  GOSUB 500 'AssignXY(ZZ,x,y)
  FOR i = 1 TO 4
    Z2(i) = ZZ(i)
  NEXT
  GOSUB 1000 'AddComplex(ZZ,Z1,Z2)
  FOR i = 1 TO 4
    Z(i) = ZZ(i)
  NEXT
  PRINT
  PRINT " Z1=";
  FOR i = 1 TO 4
    ZZ(i) = Z1(i)
  NEXT
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT " Z2=";
  FOR i = 1 TO 4
    ZZ(i) = Z2(i)
  NEXT
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT " Z1+Z2=";
  FOR i = 1 TO 4
    ZZ(i) = Z(i)
  NEXT
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT " Z1+Z2 with modulus and phase:"
  GOSUB 900  'DisplayComplexR(ZZ)
  PRINT " Z1 with modulus and phase:"
  FOR i = 1 TO 4
    ZZ(i) = Z1(i)
  NEXT
  GOSUB 900  'DisplayComplexR(ZZ)
  PRINT " Z2 with modulus and phase:"
  FOR i = 1 TO 4
    ZZ(i) = Z2(i)
  NEXT
  GOSUB 900  'DisplayComplexR(ZZ)
  GOSUB 1300 'MulComplex(ZZ,Z1,Z2)
  PRINT " Z1*Z2=";
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT " Z1*Z2 with modulus and phase:"
  GOSUB 900  'DisplayComplexR(ZZ)
  GOSUB 1400 'DivComplex(ZZ,Z1,Z2)
  PRINT " Z1/Z2 with modulus and Phase:"
  GOSUB 900  'DisplayComplexR(ZZ)
  GOSUB 1500 'ExpComplex(ZZ,Z1)
  PRINT " Exp(Z1)=";
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT " Exp(Z1) with modulus and Phase:"
  GOSUB 900  'DisplayComplexR(ZZ)
  'put Z2 in Z1
  x = 2.5#: y = 5.75#
  GOSUB 500 'AssignXY(ZZ,x,y)
  FOR i = 1 TO 4
    Z1(i) = ZZ(i)
  NEXT
  GOSUB 2800 'ArgShComplex(ZZ,Z1)
  PRINT " ArgSh(Z2)=";
  GOSUB 800  'DisplayComplex(ZZ)
  PRINT
END

'define complex number ZZ by x and y
500 ZZ(1) = x: ZZ(2) = y
    ZZ(3) = SQR(x * x + y * y)
    IF x = 0 THEN
      IF y > 0 THEN
        ZZ(4) = PI / 2
      ELSEIF y = 0 THEN
        ZZ(4) = -PI / 2
      ELSE
        ZZ(4) = 0#
      END IF
    ELSE
      ZZ(4) = ATN(y / x)
      IF x < 0 THEN
        IF y >= 0 THEN
          ZZ(4) = ZZ(4) + PI
        ELSE
          ZZ(4) = ZZ(4) - PI
        END IF
      END IF
      IF ZZ(4) > PI THEN ZZ(4) = ZZ(4) - 2 * PI
      IF ZZ(4) < -PI THEN ZZ(4) = ZZ(4) + 2 * PI
    END IF
RETURN

'define complex number by r and t in radians
600 ZZ(3) = r: ZZ(4) = t
    IF ZZ(4) > PI THEN ZZ(4) = ZZ(4) - 2 * PI
    IF ZZ(4) < -PI THEN ZZ(4) = ZZ(4) + 2 * PI
    ZZ(1) = r * COS(t): ZZ(2) = r * SIN(t)
RETURN

'display complex number with x and y
800 PRINT "("; : PRINT USING F$; ZZ(1);
    PRINT ","; : PRINT USING F$; ZZ(2);
    PRINT ")"
RETURN

'display complex number with radius and phase in radians
900 PRINT " ("; : PRINT USING F$; ZZ(3);
    PRINT ","; : PRINT USING F$; ZZ(4);
    PRINT ")"
RETURN

'add two complex numbers: ZZ=Z1+Z2
1000 ZZ(1) = Z1(1) + Z2(1): ZZ(2) = Z1(2) + Z2(2)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

'substract two complex numbers: ZZ=Z1-Z2
1100 ZZ(1) = Z1(1) - Z2(1): ZZ(2) = Z1(2) - Z2(2)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

'change sign of a complex number: ZZ=-ZZ
1200 ZZ(1) = -ZZ(1): ZZ(2) = -ZZ(2)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

'multiply two complex numbers: ZZ=Z1*Z2
1300 ZZ(3) = Z1(3) * Z2(3): ZZ(4) = Z1(4) + Z2(4)
     r = ZZ(3): t = ZZ(4)
     GOSUB 600  'AssignRT(ZZ,r,t)
RETURN

'divide two complex numbers: ZZ=Z1/Z2
1400 IF Z2(3) < TINY THEN
       ZZ(3) = XINF
     ELSE
       ZZ(3) = Z1(3) / Z2(3)
     END IF
     ZZ(4) = Z1(4) - Z2(4)
     r = ZZ(3): t = ZZ(4)
     GOSUB 600  'AssignRT(ZZ,r,t)
RETURN

'exponential complex function: ZZ=Exp(Z1)
1500 IF EXP(Z1(1)) > XINF THEN
       tmp = XINF
     ELSE
       tmp = EXP(Z1(1))
     END IF
     ZZ(1) = tmp * COS(Z1(2)): ZZ(2) = tmp * SIN(Z1(2))
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=LN(Z1)
1600 IF Z1(3) <= 0 THEN
       ZZ(1) = -XINF
     ELSE
       ZZ(1) = LOG(Z1(3))
     END IF
     ZZ(2) = Z1(4)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

'Complex power ZZ=Z1^Z2
1700 GOSUB 1600  'LnComplex(temp,Z1)
     FOR i = 1 TO 4
       Z1(i) = Z2(i)
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1300  'MulComplex(temp,Z1,temp)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1500  'ExpComplex(ZZ,Z1)
RETURN

' ZZ=COS(Z1)
1800 ZZ(1) = (EXP(-Z1(2)) * COS(Z1(1)) + EXP(Z1(2)) * COS(-Z1(1))) / 2#
     ZZ(2) = (EXP(-Z1(2)) * SIN(Z1(1)) + EXP(Z1(2)) * SIN(-Z1(1))) / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=SIN(Z1)
1900 ZZ(1) = (EXP(-Z1(2)) * SIN(Z1(1)) - EXP(Z1(2)) * SIN(-Z(1))) / 2#
     ZZ(2) = -(EXP(-Z1(2)) * COS(Z1(1)) - EXP(Z1(2)) * COS(-Z(1))) / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=TAN(Z1)
2000 GOSUB 1900  'SinComplex(ZZ,Z1)
     FOR i = 1 TO 4
       temp(i) = ZZ(i)
     NEXT
     GOSUB 1800  'CosComplex(ZZ,Z1)
     FOR i = 1 TO 4
       Z1(i) = temp(i)
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1400  'DivComplex(ZZ,Z1,Z2)
RETURN

' ZZ=CH(Z1)
2100 ZZ(1) = (EXP(Z1(1)) * COS(Z1(2)) + EXP(-Z1(1)) * COS(-Z1(2))) / 2#
     ZZ(2) = (EXP(Z1(1)) * SIN(Z1(2)) + EXP(-Z1(1)) * SIN(-Z1(2))) / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=SH(Z1)
2200 ZZ(1) = (EXP(Z1(1)) * COS(Z1(2)) - EXP(-Z1(1)) * COS(-Z1(2))) / 2#
     ZZ(2) = -(EXP(Z1(1)) * SIN(Z1(2)) - EXP(-Z1(1)) * SIN(-Z1(2))) / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=TH(Z1)
2300 GOSUB 2200  'ShComplex(ZZ,Z1)
     FOR i = 1 TO 4
       temp(i) = ZZ(i)
     NEXT
     GOSUB 2100  'ChComplex(ZZ,Z1)
     FOR i = 1 TO 4
       Z1(i) = temp(i)
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1400  'DivComplex(ZZ,Z1,Z2)
RETURN

' ZZ=ARCCOS(Z1)
2400 FOR i = 1 TO 4
       Z(i) = Z1(i)
     NEXT
     temp(1) = 1# - Z1(1) * Z1(1) + Z1(2) * Z1(2)
     temp(2) = -2# * Z1(1) * Z1(2)
     x = temp(1): y = temp(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = .5#: y = 0#
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1700 'PowerComplex(ZZ,Z1,Z2)
     tmp = ZZ(1)
     ZZ(1) = Z(1) - ZZ(2)
     ZZ(2) = Z(2) + tmp
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
     tmp = ZZ(1)
     ZZ(1) = ZZ(2): ZZ(2) = -tmp
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=ARCSIN(Z1)
2500 FOR i = 1 TO 4
       Z(i) = Z1(i)
     NEXT
     temp(1) = 1# - Z1(1) * Z1(1) + Z1(2) * Z1(2)
     temp.b = -2# * Z1(1) * Z1(2)
     x = temp(1): y = temp(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = .5#: y = 0#
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1700 'PowerComplex(ZZ,Z1,Z2)
     ZZ(1) = ZZ(1) - Z(2)
     ZZ(2) = ZZ(2) + Z(1)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
     tmp = ZZ(1)
     ZZ(1) = ZZ(2): ZZ(2) = -tmp
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=ARCTAN(Z1)
2600 temp(1) = -Z1(1): temp(2) = 1# - Z1(2)
     u(1) = Z1(1): u(2) = 1# + Z1(2)
     x = temp(1): y = temp(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = u(1): y = u(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1400 'DivComplex(ZZ,Z1,Z2)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
     tmp = ZZ(1)
     ZZ(1) = ZZ(2) / 2#: ZZ(2) = -tmp / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN

' ZZ=ARGCH(Z1)
2700 FOR i = 1 TO 4
       Z(i) = Z1(i)
     NEXT
     temp(1) = -1# + Z1(1) * Z1(1) + Z1(2) * Z1(2)
     temp(2) = 2# * Z1(1) * Z1(2)
     x = temp(1): y = temp(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = .5#: y = 0#
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1700 'PowerComplex(ZZ,Z1,Z2)
     ZZ(1) = ZZ(1) + Z(1)
     ZZ(2) = ZZ(2) + Z(2)
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
RETURN

' ZZ=ARGSH(Z1)
2800 FOR i = 1 TO 4
       Z(i) = Z1(i)
     NEXT
     temp(1) = 1# + Z1(1) * Z1(1) - Z1(2) * Z1(2)
     temp(2) = 2# * Z1(1) * Z1(2)
     x = temp(1): y = temp(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = .5#: y = 0#
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1700 'PowerComplex(ZZ,Z1,Z2)
     x = ZZ(1) + Z(1)
     y = ZZ(2) + Z(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
RETURN

' ZZ=ARGTH(Z1)
2900 FOR i = 1 TO 4
       Z(i) = Z1(i)
     NEXT
     Z1(1) = 1# + Z(1): Z1(2) = Z(2)
     Z2(1) = 1# - Z(1): Z2(2) = -Z(2)
     x = Z1(1): y = Z1(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     x = Z2(1): y = Z2(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
     FOR i = 1 TO 4
       Z2(i) = ZZ(i)
     NEXT
     GOSUB 1400 'DivComplex(ZZ,Z1,Z2)
     FOR i = 1 TO 4
       Z1(i) = ZZ(i)
     NEXT
     GOSUB 1600 'LnComplex(ZZ,Z1)
     ZZ(1) = ZZ(1) / 2#: ZZ(2) = ZZ(2) / 2#
     x = ZZ(1): y = ZZ(2)
     GOSUB 500  'AssignXY(ZZ,x,y)
RETURN


'end of file tcomplex.bas