ATN(B/A)+ATN(D/C)=ATN(((BC+AD)/AC)/((AC-BD)/AC))
ATN(B/A)-ATN(D/C)=ATN(((BC-AD)/AC)/((AC+BD)/AC))
FOR A=2 TO 100
FOR B=1 TO A
IF GCD(A,B)=1 THEN
FOR C=A+1 TO 100
FOR D=1 TO C
IF GCD(C,D)=1 THEN
LET XX=B*C+A*D
LET YY=A*C-B*D
LET P=ATN(B/A)+ATN(D/C)
LET L$="ATN(" & STR$(B) & "/" & STR$(A) & ")+ATN(" & STR$(D) & "/" & STR$(C) & ")"
IF XX=YY THEN PRINT "ATN(1)=";L$;P
IF XX=-YY THEN PRINT "ATN(-1)=";L$;P
IF XX>0 AND YY=0 THEN PRINT "ATN(0)=";L$;P
IF XX<0 AND YY=0 THEN PRINT "ATN(-0)=";L$;P
IF XX=0 AND YY>0 THEN PRINT "ATN(∞)=";L$;P
IF XX=0 AND YY<0 THEN PRINT "ATN(-∞)=";L$;P
LET XX=A*D-B*C
LET YY=A*C+B*D
LET P=-ATN(B/A)+ATN(D/C)
LET L$="-ATN(" & STR$(B) & "/" & STR$(A) & ")+ATN(" & STR$(D) & "/" & STR$(C) & ")"
IF XX=YY THEN PRINT "ATN(1)=";L$;P
IF XX=-YY THEN PRINT "ATN(-1)=";L$;P
IF XX>0 AND YY=0 THEN PRINT "ATN(0)=";L$;P
IF XX<0 AND YY=0 THEN PRINT "ATN(-0)=";L$;P
IF XX=0 AND YY>0 THEN PRINT "ATN(∞)=";L$;P
IF XX=0 AND YY<0 THEN PRINT "ATN(-∞)=";L$;P
LET XX=B*C-A*D
LET YY=A*C+B*D
LET P=ATN(B/A)-ATN(D/C)
LET L$="ATN(" & STR$(B) & "/" & STR$(A) & ")-ATN(" & STR$(D) & "/" & STR$(C) & ")"
IF XX=YY THEN PRINT "ATN(1)=";L$;P
IF XX=-YY THEN PRINT "ATN(-1)=";L$;P
IF XX>0 AND YY=0 THEN PRINT "ATN(0)=";L$;P
IF XX<0 AND YY=0 THEN PRINT "ATN(-0)=";L$;P
IF XX=0 AND YY>0 THEN PRINT "ATN(∞)=";L$;P
IF XX=0 AND YY<0 THEN PRINT "ATN(-∞)=";L$;P
END IF
NEXT D
NEXT C
END IF
NEXT B
NEXT A
END
EXTERNAL FUNCTION GCD(M,N)
DO WHILE N<>0
LET T=MOD(M,N)
LET M=N
LET N=T
LOOP
LET GCD=M
END FUNCTION
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