!  Solving a quadratic equation with the famous formula
 !  ----------------------------------------------------
 !  Note that we are using structure constructors to build the
 !  "2" and "4" constants that appear in the formula. This is a
 !  better practice than extending the definition of all the
 !  basic operations to include real/sea_abs pairs (however,
 !  most basic operations support precise/sea_abs pairs).
 !
 !  Automatic extension will necessarily assume some fixed
 !  associated error range, a messy assumption.  Note that
 !  physical constants have an associated non-zero error range
 !  and even mathematical ones may be computed only to finite
 !  accuracy.  Automatic extension would tempt programmers by
 !  making program porting quick and easy but less correct.
 !
 !  In this example there is actually no such problem.
 !  The mathematical constants "2" and "4" are exact and have
 !  zero error.

 program test
   use sea_arithmetic                        !  Error analytic module
   type(sea_abs) :: a, b, c, x               !  Declare our vars

   call sea_check_precise()                  !  Verify PRECISE reals exists

   call sea_write_txt_nl(fout, "ax^2 + bx +c = 0")  !  Write a line of text

   call sea_read_abs(fin, a, "Enter |a,e|: ")       !  Input a
   call sea_read_abs(fin, b, "Enter |b,e|: ")       !  Input b
   call sea_read_abs(fin, c, "Enter |c,e|: ")       !  Input c
   call sea_write_nl(fout)                          !  Write a newline

   ! method I: Convert real constants to precise constants.
   !           Partly supported and bad programming practice!
   !
   ! x = (-b + sqrt(b**2 - 4.0_precise * a * c)) / (2.0_precise * a)

   ! method II: Use a structure constructor to build a
   !            sea_abs constant.  Recommended!
   !
   x = (-b + sqrt(b**2 - sea_abs(4.0,0.0) * a * c)) / (sea_abs(2.0,0.0) * a)

   call sea_write_entry(fout, "x = ", x, 5)         !  Write result
   call sea_write_nl(fout)                          !  Write a newline

 end program test