1 dop = ###; % Specify the number of digits of precision. a = 2; b = ###; 5 C-5; 6 7 % Compute the quadratic solutions x1 and x2 using double precision. 8 x1 (b+ sqrt(b^2-4*a*c))/###; 9 x2 (-b sqrt(b^2-4*a*c))/###; 10 fprintf('Using double precision, x1 = %f and x2 = %f\n',x1,###) 11 12 % Test if parts of the quadratic solutions might be sensitive to 13 % catastrophic cancellations. 14 if abs(-b+sqrt(b^2-4*a*c)) < 0.1*b 15 trust flag = 1; %% possible issue with x1 % b>0 16 elseif abs(-b-sqrt(b^2-4*a*c)) < abs(0.1*###) % b<0 17 18 else 19 20 end 21 trustflag = 2; %% possible issue with x2 trustflag = 0; %% no issue 22 % Redo the calculations using the specified digits if precision. 23 % The numdop function is defined at the bottom. 24 a numdop(a, dop); 25 bnumdop (b,dop); 26 c = numdop(###); 27 % Every operation must be done with the specified digits of precision. 28 bsq numdop(b^2, dop); 29 fac numdop (numdop (4*a, dop) *c, dop); 30 bsqmfac = numdop (bsq-fac, dop); 31 sqrtterm = numdop(sqrt(###), dop); 32 numer1 = numdop(-b+sqrtterm, dop); 33 numer2numdop(-b-sqrtterm, dop); 34 denom numdop (2*a, dop); 35 36 x1dop numdop (###, dop); 37 x2dop numdop (###, dop); 38 fprintf('Using %d digits of precision, x1 = %f and x2 = %f\n', dop, x1dop,x2dop) 39 40 if trustflag == 1 41 42 43 x1m numdop (numdop (c/a, dop)/x2dop, dop); fprintf(['However, x1 is susceptible to catastrophic cancellations' ... and the modified solution x1 = %f should be taken.\n'],x1m) 44 elseif trustflag == 2 45 46 47 48 else 49 50 end x2m = numdop (numdop (c/a, dop) ###, dop); fprintf(['However, x2 is susceptible to catastrophic cancellations' ... and the modified solution x2 = %f should be taken.\n'], ###) disp('No modification of x1 or x2 is required') 51 52 53 % The numdop function rewrites num as 0.#####e# which is equivalent to 54 % dec x 10^pow. With dop holding the specified number of digits of 55 % precision, dec is multiplied by 10^dop, rounded, then mutiplied by 56 % 10^-dop to return it its original format. This new number is expressed 57 % with the appropriate digits of precision. 58 % To find the correctly formatted version of num, it is multiplied by a 59 % vector of powers of ten. The resultant vector of products is then 60 % searched to find the last entry less than 1. This gives the decimal part 61 % and its location in the vector gives the power. 62 function newnum = numdop (num, dop) 63 p = -8:8; 64 tempnum num * 10.^p; 65 ind find (abs (tempnum)<1); 66 dec = tempnum(ind (end)); 67 pow = -p(ind(end)); 68 newnum = round(dec*10^(dop))/10^(dop-pow); 69 end 70 ► Run Script ?