EQUATIONS: Rewrite nr_iterate_srhd_adi_1dw().

Make sure all cases are considered. Also, in the case of profiling, the
subroutine counts timing correctly.

Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>

src/equations.F90

@@ -3835,6 +3835,10 @@ module equations
 !
   subroutine nr_iterate_srhd_adi_1dw(mm, bb, mb, en, dn, w, vv, info)
 
+! include external procedures
+!
+    use error, only : print_warning
+
 ! local variables are not implicit by default
 !
     implicit none
@@ -3852,6 +3856,10 @@ module equations
     real(kind=8) :: wl, wu, fl, fu
     real(kind=8) :: f, df, dw
     real(kind=8) :: err
+
+! local parameters
+!
+    character(len=*), parameter :: loc = 'EQUATIONS::nr_iterate_srhd_adi_1dw()'
 !
 !-------------------------------------------------------------------------------
 !
@@ -3866,54 +3874,38 @@ module equations
     wl   = sqrt(mm + dn * dn) + gammaxi * pmin
     wu   = en + pmin
 
-! make sure that the upper bracket is larger than the lower one
+! calculate the value of function for the lower bracket
 !
-    keep = wl >= wu
-    it   = nrmax
-    do while(keep)
-      wu   = 2.0d+00 * wu
-      it   = it - 1
-      keep = (wl >= wu) .and. it > 0
-    end do
-    if (it <= 0) then
-      write(*,*)
-      write(*,"(a,1x,a)") "ERROR in"                                           &
-                        , "EQUATIONS::nr_iterate_srhd_adi_1dw()"
-      write(*,"(a)"     ) "Could not find the upper limit for enthalpy!"
-      info = .false.
-      return
-    end if
+    call nr_function_srhd_adi_1d(mm, en, dn, wl, fl)
+
+! the lower bracket gives negative function, so there is chance it bounds
+! the root
+!
+    if (fl < 0.0d+00) then
+
+! make sure that the upper bracket is larger than the lower one and
+! the function has positive value
+!
+      if (wu <= wl) wu = 2.0d+00 * wl
 
 ! check if the brackets bound the root region, if not proceed until
 ! opposite function signs are found for the brackets
 !
-    call nr_function_srhd_adi_1d(mm, en, dn, wl, fl)
       call nr_function_srhd_adi_1d(mm, en, dn, wu, fu)
-
-    keep = (fl * fu > 0.0d+00)
       it   = nrmax
-
+      keep = fl * fu > 0.0d+00
       do while (keep)
-
+        it = it - 1
         wl = wu
         fl = fu
         wu = 2.0d+00 * wu
-
         call nr_function_srhd_adi_1d(mm, en, dn, wu, fu)
-
-      it   = it - 1
-
         keep = (fl * fu > 0.0d+00) .and. it > 0
-
       end do
-    if (it <= 0) then
-      write(*,*)
-      write(*,"(a,1x,a)") "ERROR in"                                           &
-                        , "EQUATIONS::nr_iterate_srhd_adi_1dw()"
-      write(*,"(a)"     ) "No initial brackets found!"
-      info = .false.
-      return
-    end if
+
+! the upper bracket was found, so proceed with determining the root
+!
+      if (it > 0 .and. fu >= 0.0d+00) then
 
 ! estimate the value of enthalpy close to the root and corresponding v²
 !
@@ -3946,16 +3938,10 @@ module equations
             fu = f
           end if
 
-! calculate the increment dW
+! calculate the increment dW, update the solution, and estimate the error
 !
           dw  = f / df
-
-! update the solution
-!
           w   = w - dw
-
-! calculate the error
-!
           err = abs(dw / w)
 
 ! check the convergence, if the convergence is not reached, iterate until
@@ -3968,30 +3954,40 @@ module equations
             keep = it > 0
           end if
 
-! if new W lays out of the brackets, use the bisection method to estimate
+! if new W leaves the brackets, use the bisection method to estimate
 ! the new guess
 !
           if (w < wl .or. w > wu) then
             w = 0.5d+00 * (wl + wu)
           end if
 
-! decrease the number of remaining iterations
-!
           it = it - 1
-
         end do ! NR iterations
 
+! print information about failed convergence or unphysical variables
+!
+        if (err >= tol) then
+          call print_warning(loc, "Convergence not reached!")
+          write(*,"(a,1x,1e24.16e3)") "Error: ", err
+        end if
+
 ! calculate |V|² from W
 !
         vv  = mm / (w * w)
 
-! print information about failed convergence or unphysical variables
-!
-    if (err >= tol) then
-      write(*,*)
-      write(*,"(a,1x,a)"        ) "WARNING in"                                 &
-                                , "EQUATIONS::nr_iterate_srhd_adi_1dw()"
-      write(*,"(a,1x,1e24.16e3)") "Convergence not reached: ", err
+      else ! the upper brack not found
+        call print_warning(loc, "Could not find the upper bracket!")
+        info = .false.
+
+      end if
+
+    else if (fl == 0.0d+00) then ! the lower bracket is a root, so return it
+      w    = wl
+      info = .true.
+
+    else ! the root cannot be found, since it is below the lower bracket
+      call print_warning(loc, "Positive function for lower bracket!")
+      info = .false.
     end if
 
 #ifdef PROFILE