#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  loss_of_significance
#
# Avoiding loss of significance in subtraction for the function
# f(x) = x - sin(x) near x = 0:

 y := sum((-1)^(k-1)*x^(2*k+1)/(2*k+1)!, k=1..10);
 Digits := 40;
 for x from 0.1 by 0.1 to 2.5 do
     x := evalf(x); 
     apx := evalf(y);
     cal := x - sin(x);
     err := abs(apx - cal);
 end do;