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adcroft merged 1 commit into from
Nov 18, 2015
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*Expanding integer powers to explicit multiplications #241

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70 changes: 34 additions & 36 deletions src/ALE/MOM_remapping.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -615,7 +615,6 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
real :: x0jRl, x0jRr ! Left/right position of cell jR
real :: hAct ! The distance actually used in the integration
! (notionally xR - xL) which differs due to roundoff.
integer :: n1,n2,n3,n4,n5

#ifdef __DO_SAFETY_CHECKS__
real :: h0Total
Expand All @@ -638,7 +637,6 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
! 'The target cell ends beyond the right edge of the source grid')
#endif

n1=1;n2=2;n3=3;n4=4;n5=5

q = -1.E30
x0jLl = -1.E30
Expand Down Expand Up @@ -704,14 +702,14 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
!uAve = evaluation_polynomial( ppoly0_coefficients(jL,:), 3, xi0 )
uAve = (ppoly0_coefficients(jL,1) &
+ ppoly0_coefficients(jL,2) * xi0) &
+ ppoly0_coefficients(jL,3) * xi0**2
+ ppoly0_coefficients(jL,3) * xi0*xi0
case ( INTEGRATION_PQM )
!uAve = evaluation_polynomial( ppoly0_coefficients(jL,:), 5, xi0 )
uAve = (((ppoly0_coefficients(jL,1) &
+ ppoly0_coefficients(jL,2) * xi0) &
+ ppoly0_coefficients(jL,3) * xi0**2) &
+ ppoly0_coefficients(jL,4) * xi0**3) &
+ ppoly0_coefficients(jL,5) * xi0**4
+ ppoly0_coefficients(jL,3) * xi0*xi0) &
+ ppoly0_coefficients(jL,4) * xi0*xi0*xi0) &
+ ppoly0_coefficients(jL,5) * xi0*xi0*xi0*xi0
case default
call MOM_error( FATAL,'The selected integration method is invalid' )
end select
Expand Down Expand Up @@ -777,22 +775,22 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
case ( INTEGRATION_PLM )
q = h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 1 )
(ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2) )
(ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0 )
case ( INTEGRATION_PPM )
q = h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 2 )
((ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jL,3)*(xi1**n3-xi0**n3)/real(n3))
((ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jL,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0)
case ( INTEGRATION_PQM )
q = h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 4 )
((((ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jL,3)*(xi1**n3-xi0**n3)/real(n3)) &
+ppoly0_coefficients(jL,4)*(xi1**n4-xi0**n4)/real(n4)) &
+ppoly0_coefficients(jL,5)*(xi1**n5-xi0**n5)/real(n5) )
((((ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jL,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0) &
+ppoly0_coefficients(jL,4)*(xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0)/4.0) &
+ppoly0_coefficients(jL,5)*(xi1*xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0*xi0)/5.0 )
case default
call MOM_error( FATAL,'The selected integration method is invalid' )
end select
Expand Down Expand Up @@ -836,22 +834,22 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
case ( INTEGRATION_PLM )
q = q + h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 1 )
(ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2) )
(ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0 )
case ( INTEGRATION_PPM )
q = q + h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 2 )
((ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jL,3)*(xi1**n3-xi0**n3)/real(n3))
((ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jL,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0)
case ( INTEGRATION_PQM )
q = q + h0(jL) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jL,:), 4 )
((((ppoly0_coefficients(jL,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jL,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jL,3)*(xi1**n3-xi0**n3)/real(n3)) &
+ppoly0_coefficients(jL,4)*(xi1**n4-xi0**n4)/real(n4)) &
+ppoly0_coefficients(jL,5)*(xi1**n5-xi0**n5)/real(n5) )
((((ppoly0_coefficients(jL,1)*(xi1-xi0) &
+ppoly0_coefficients(jL,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jL,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0) &
+ppoly0_coefficients(jL,4)*(xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0)/4.0) &
+ppoly0_coefficients(jL,5)*(xi1*xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0*xi0)/5.0 )
case default
call MOM_error( FATAL, 'The selected integration method is invalid' )
end select
Expand Down Expand Up @@ -895,22 +893,22 @@ subroutine integrateReconOnInterval( n0, h0, u0, ppoly0_E, ppoly0_coefficients,
case ( INTEGRATION_PLM )
q = q + h0(jR) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jR,:), 1 )
(ppoly0_coefficients(jR,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jR,2)*(xi1**n2-xi0**n2)/real(n2) )
(ppoly0_coefficients(jR,1)*(xi1-xi0) &
+ppoly0_coefficients(jR,2)*(xi1*xi1-xi0*xi0)/2.0 )
case ( INTEGRATION_PPM )
q = q + h0(jR) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jR,:), 2 )
((ppoly0_coefficients(jR,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jR,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jR,3)*(xi1**n3-xi0**n3)/real(n3))
((ppoly0_coefficients(jR,1)*(xi1-xi0) &
+ppoly0_coefficients(jR,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jR,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0)
case ( INTEGRATION_PQM )
q = q + h0(jR) * &
!integration_polynomial( xi0, xi1, ppoly0_coefficients(jR,:), 4 )
((((ppoly0_coefficients(jR,1)*(xi1-xi0)/real(n1) &
+ppoly0_coefficients(jR,2)*(xi1**n2-xi0**n2)/real(n2)) &
+ppoly0_coefficients(jR,3)*(xi1**n3-xi0**n3)/real(n3)) &
+ppoly0_coefficients(jR,4)*(xi1**n4-xi0**n4)/real(n4)) &
+ppoly0_coefficients(jR,5)*(xi1**n5-xi0**n5)/real(n5) )
((((ppoly0_coefficients(jR,1)*(xi1-xi0) &
+ppoly0_coefficients(jR,2)*(xi1*xi1-xi0*xi0)/2.0) &
+ppoly0_coefficients(jR,3)*(xi1*xi1*xi1-xi0*xi0*xi0)/3.0) &
+ppoly0_coefficients(jR,4)*(xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0)/4.0) &
+ppoly0_coefficients(jR,5)*(xi1*xi1*xi1*xi1*xi1-xi0*xi0*xi0*xi0*xi0)/5.0 )
case default
call MOM_error( FATAL,'The selected integration method is invalid' )
end select
Expand Down