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The calculator actually generates pseudo-random integer numbers in range 0-32767. The result is later multiplied by 0.30517578125E-4 (=1/32768) to return a real number in range 0-0.9999...
The BASIC program below calculates pseudo-random 15-bit integer numbers using the same algorithm as function RAN#. For comparison it also prints values returned by actual RAN# function.
10 S=32768*RAN# 20 S=12869*S+6925 30 S=S-32768*INT(S/32768) 40 PRINT S;32768*RAN# 50 GOTO 20
The BASIC program shown below illustrates the algorithm used by the MK-85. It calculates square roots of numbers in range 1 to 99.9999... with a precision of R digits.
The original procedure uses only simple and effective math operations: shift, add/subtract, compare and table lookup. The BASIC version thereof had to simulate shifts of BCD numbers with multiplications by powers of 10.
The detailed algorithm description of this and the following functions can be found in the article J.E. Meggitt, Pseudo Division and Pseudo Multiplication processes, IBM Journal, Res & Dev, April 1962.
5 R=7 10 INPUT "Radicand=",A 20 IF A<1 THEN 40 30 IF A<100 THEN 50 40 PRINT "Invalid!":GOTO 10 50 B=1:Q=0:J=0 200 IF J>=R THEN 600 210 IF A<B THEN 400 300 A=A-B 310 GOSUB 800 320 B=B+2*D 330 Q=Q+1 340 GOTO 200 400 A=10*A 410 B=B-D 420 Q=10*Q 430 J=J+1 440 GOSUB 800 450 B=B+D 460 GOTO 200 600 PRINT "SQR=";Q/10^R 610 GOTO 10 800 D=10^-J 810 RETURN
The following BASIC program calculates EXP(x) for numbers in range 0 to LN(10) with a precision of R digits. It uses the same algorithm as the original code in the MK-85 ROM.
10 R=7:IF R>6; DEFM(R-1) 20 FOR J=0 TO R-1 30 T(J)=LN(1+10^-J)*10^J 40 NEXT J 100 INPUT "Argument=",A 110 IF A<0 THEN 130 120 IF A<LN(10) THEN 140 130 PRINT "Invalid!":GOTO 100 140 Q=0:J=0 150 GOTO 500 200 IF J>=R THEN 600 210 IF A<B THEN 400 300 A=A-B 310 Q=Q+1 320 GOTO 200 400 A=A*10 410 Q=Q*10 420 J=J+1 500 B=T(J) 510 GOTO 200 600 A=0:B=10^R 700 IF FRAC(Q/10)<>0 THEN 800 710 IF Q<>0 THEN 900 720 GOTO 1000 800 M=INT(B/10^J) 810 A=A+B 820 B=B+M 830 Q=Q-1 840 GOTO 700 900 A=INT(A/10) 910 Q=INT(Q/10) 920 J=J-1 930 GOTO 700 1000 PRINT "EXP=";1+A/10^(R+J) 1010 GOTO 100
The following BASIC program calculates LN(x) for numbers in range 1 to 10 with a precision of R digits. It uses the same algorithm as the original code in the MK-85 ROM.
10 R=7:IF R>6; DEFM(R-1) 20 FOR J=0 TO R-1 30 T(J)=LN(1+10^-J)*10^J 40 NEXT J 100 INPUT "Argument=",A 110 IF A<1 THEN 130 120 IF A<10 THEN 140 130 PRINT "Invalid!":GOTO 100 140 Q=0:B=1:J=0 150 A=A-1 200 IF J>=R THEN 500 210 IF A<B THEN 400 300 M=B*10^-J 310 A=A-B 320 B=B+M 330 Q=Q+1 340 GOTO 200 400 A=A*10 410 Q=Q*10 420 J=J+1 430 GOTO 200 500 A=0 510 GOTO 900 600 IF 10*FRAC(Q/10)<>0 THEN 700 610 IF Q<>0 THEN 800 620 GOTO 1000 700 A=A+B 710 Q=Q-1 720 GOTO 600 800 A=INT(A/10) 810 Q=INT(Q/10) 820 J=J-1 900 B=T(J) 910 GOTO 600 1000 PRINT "LN=";A*10^-J 1010 GOTO 100
The following BASIC program calculates ATN(x) for arguments in range 0 to 1 with a precision of R digits. It uses the same algorithm as the original code in the MK-85 ROM.
10 R=7:IF R>6; DEFM(R-1) 20 FOR J=0 TO R-1 30 T(J)=ATN(10^-J)*10^J 40 NEXT J 100 INPUT "Argument=",A 110 IF A<0 THEN 130 120 IF A<1 THEN 140 130 PRINT "Invalid!":GOTO 100 140 Q=0:B=1:J=0 200 IF J>=R THEN 500 210 IF A<B THEN 400 300 M=A*10^(-2*J) 310 A=A-B 320 B=B+M 330 Q=Q+1 340 GOTO 200 400 A=A*10 410 Q=Q*10 420 J=J+1 430 GOTO 200 500 A=0 510 GOTO 900 600 IF 10*FRAC(Q/10)<>0 THEN 700 610 IF Q<>0 THEN 800 620 GOTO 1000 700 A=A+B 710 Q=Q-1 720 GOTO 600 800 A=INT(A/10) 810 Q=INT(Q/10) 820 J=J-1 900 B=T(J) 910 GOTO 600 1000 PRINT "ATN=";A*10^-J 1010 GOTO 100
The following BASIC program calculates TAN(x) for angles in range 0 to PI/2 radians with a precision of R digits. It uses the same algorithm as the original code in the MK-85 ROM.
10 MODE 5:R=7:IF R>6; DEFM(R-1) 20 FOR J=0 TO R-1 30 T(J)=ATN(10^-J)*10^J 40 NEXT J 100 INPUT "Argument=",A 110 IF A<0 THEN 130 120 IF A<PI/2 THEN 140 130 PRINT "Invalid!":GOTO 100 140 Q=0:J=0 150 GOTO 500 200 IF J>=R THEN 600 210 IF A<B THEN 400 300 A=A-B 310 Q=Q+1 320 GOTO 200 400 A=A*10 410 Q=Q*10 420 J=J+1 500 B=T(J) 510 GOTO 200 600 A=0:B=10^R 700 IF 10*FRAC(Q/10)<>0 THEN 800 710 IF Q<>0 THEN 900 720 GOTO 1000 800 M=INT(A*10^(-2*J)) 810 A=A+B 820 B=B-M 830 Q=Q-1 840 GOTO 700 900 A=INT(A/10) 910 Q=INT(Q/10) 920 J=J-1 930 GOTO 700 1000 PRINT "TAN=";A/B/10^J 1010 GOTO 100