integer exponents: faster and shorter

src/grid/grid_mech_FEM.f90

@@ -697,9 +697,9 @@ subroutine formJacobian(da_local,x_local,Jac_pre,Jac,dummy,ierr)
 
 !--------------------------------------------------------------------------------------------------
 ! applying boundary conditions
-  diag = (C_volAvg(1,1,1,1)/delta(1)**2.0_pReal + &
+  diag = (C_volAvg(1,1,1,1)/delta(1)**2 + &
-          C_volAvg(2,2,2,2)/delta(2)**2.0_pReal + &
+          C_volAvg(2,2,2,2)/delta(2)**2 + &
-          C_volAvg(3,3,3,3)/delta(3)**2.0_pReal)*detJ
+          C_volAvg(3,3,3,3)/delta(3)**2)*detJ
   call MatZeroRowsColumns(Jac,size(rows),rows,diag,PETSC_NULL_VEC,PETSC_NULL_VEC,ierr)
   CHKERRQ(ierr)
   call DMGetGlobalVector(da_local,coordinates,ierr); CHKERRQ(ierr)

src/grid/spectral_utilities.f90

@@ -578,22 +578,22 @@ real(pReal) function utilities_divergenceRMS()
   do k = 1, grid3; do j = 1, grid(2)
     do i = 2, grid1Red -1                                                                           ! Has somewhere a conj. complex counterpart. Therefore count it twice.
       utilities_divergenceRMS = utilities_divergenceRMS &
-            + 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k),&                      ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
+            + 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k), &                     ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
-                                          conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal)&      ! --> sum squared L_2 norm of vector
+                                          conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2) &             ! --> sum squared L_2 norm of vector
                         +sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
-                                          conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal))
+                                          conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2))
     enddo
     utilities_divergenceRMS = utilities_divergenceRMS &                                             ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1)
                + sum( real(matmul(tensorField_fourier(1:3,1:3,1       ,j,k), &
-                                  conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
+                                  conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
                + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1       ,j,k), &
-                                  conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
+                                  conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2) &
                + sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
-                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) &
+                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2) &
                + sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
-                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal)
+                                  conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2)
   enddo; enddo
-  if (grid(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal                    ! counted twice in case of grid(1) == 1
+  if (grid(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal                   ! counted twice in case of grid(1) == 1
   call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr)
   if (ierr /=0) error stop 'MPI error'
   utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt                                     ! RMS in real space calculated with Parsevals theorem from Fourier space
@@ -630,7 +630,7 @@ real(pReal) function utilities_curlRMS()
                              -tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2))
       enddo
       utilities_curlRMS = utilities_curlRMS &
-                        +2.0_pReal*sum(curl_fourier%re**2.0_pReal+curl_fourier%im**2.0_pReal)       ! Has somewhere a conj. complex counterpart. Therefore count it twice.
+                        +2.0_pReal*sum(curl_fourier%re**2+curl_fourier%im**2)                       ! Has somewhere a conj. complex counterpart. Therefore count it twice.
     enddo
     do l = 1, 3
        curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) &
@@ -641,7 +641,7 @@ real(pReal) function utilities_curlRMS()
                        -tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2))
     enddo
     utilities_curlRMS = utilities_curlRMS &
-                      + sum(curl_fourier%re**2.0_pReal + curl_fourier%im**2.0_pReal)                ! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
+                      + sum(curl_fourier%re**2 + curl_fourier%im**2)                                ! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
     do l = 1, 3
       curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) &
                       -tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3))
@@ -651,13 +651,13 @@ real(pReal) function utilities_curlRMS()
                       -tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2))
     enddo
     utilities_curlRMS = utilities_curlRMS &
-                      + sum(curl_fourier%re**2.0_pReal + curl_fourier%im**2.0_pReal)                ! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
+                      + sum(curl_fourier%re**2 + curl_fourier%im**2)                                ! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
   enddo; enddo
 
   call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,ierr)
   if (ierr /=0) error stop 'MPI error'
   utilities_curlRMS = sqrt(utilities_curlRMS) * wgt
-  if (grid(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal                                ! counted twice in case of grid(1) == 1
+  if (grid(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal                               ! counted twice in case of grid(1) == 1
 
 end function utilities_curlRMS
 
@@ -836,13 +836,13 @@ subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,&
   dPdF_min = huge(1.0_pReal)
   dPdF_norm_min = huge(1.0_pReal)
   do i = 1, product(grid(1:2))*grid3
-    if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)) then
+    if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then
       dPdF_max = homogenization_dPdF(1:3,1:3,1:3,1:3,i)
-      dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)
+      dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)
     endif
-    if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)) then
+    if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then
       dPdF_min = homogenization_dPdF(1:3,1:3,1:3,1:3,i)
-      dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2.0_pReal)
+      dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)
     endif
   enddo
 

src/homogenization_mechanical_RGC.f90

@@ -546,7 +546,7 @@ module function RGC_updateState(P,F,avgF,dt,dPdF,ce) result(doneAndHappy)
          do k = 1,3; do l = 1,3
            nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_LeviCivita(j,k,l)                        ! compute the interface mismatch tensor from the jump of deformation gradient
          end do; end do
-         nDefNorm = nDefNorm + nDef(i,j)**2.0_pReal                                                 ! compute the norm of the mismatch tensor
+         nDefNorm = nDefNorm + nDef(i,j)**2                                                         ! compute the norm of the mismatch tensor
        end do; end do
        nDefNorm = max(nDefToler,sqrt(nDefNorm))                                                     ! approximation to zero mismatch if mismatch is zero (singularity)
        nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm                       ! total amount of mismatch experienced by the grain (at all six interfaces)

src/lattice.f90

@@ -473,13 +473,13 @@ function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(character
           p = sum(HEX_NTWINSYSTEM(1:f-1))+s
           select case(HEX_SHEARTWIN(p))                                                             ! from Christian & Mahajan 1995 p.29
             case (1)                                                                                ! <-10.1>{10.2}
-              characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA
+              characteristicShear(a) = (3.0_pReal-cOverA**2)/sqrt(3.0_pReal)/CoverA
             case (2)                                                                                ! <11.6>{-1-1.1}
               characteristicShear(a) = 1.0_pReal/cOverA
             case (3)                                                                                ! <10.-2>{10.1}
-              characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA
+              characteristicShear(a) = (4.0_pReal*cOverA**2-9.0_pReal)/sqrt(48.0_pReal)/cOverA
             case (4)                                                                                ! <11.-3>{11.2}
-              characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA
+              characteristicShear(a) = 2.0_pReal*(cOverA**2-2.0_pReal)/3.0_pReal/cOverA
           end select
         case default
           call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(lattice))
@@ -558,11 +558,11 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
     C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal))
 
     C_target_unrotated66 = 0.0_pReal
-    C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
+    C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2/C_bar66(4,4)
-    C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
+    C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2/C_bar66(4,4)
     C_target_unrotated66(1,3) = C_bar66(1,3)
     C_target_unrotated66(3,3) = C_bar66(3,3)
-    C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
+    C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
     C_target_unrotated66 = lattice_symmetrize_C66(C_target_unrotated66,'hP')
   elseif (lattice_target  == 'cI') then
     if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &

src/math.f90

@@ -924,7 +924,7 @@ real(pReal) function math_sampleGaussVar(mu, sigma, width)
     do
       call random_number(rnd)
       scatter = width_ * (2.0_pReal * rnd(1) - 1.0_pReal)
-      if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) exit                                    ! test if scattered value is drawn
+      if (rnd(2) <= exp(-0.5_pReal * scatter**2)) exit                                              ! test if scattered value is drawn
     enddo
 
     math_sampleGaussVar = scatter * sigma

src/phase_mechanical_eigen_thermalexpansion.f90

@@ -99,13 +99,13 @@ module subroutine thermalexpansion_LiAndItsTangent(Li, dLi_dTstar, ph,me)
   associate(prm => param(kinematics_thermal_expansion_instance(ph)))
     Li = dot_T * ( &
                   prm%A(1:3,1:3,1) &                                                                ! constant  coefficient
-                + prm%A(1:3,1:3,2)*(T - prm%T_ref)**1.0_pReal &                                     ! linear    coefficient
+                + prm%A(1:3,1:3,2)*(T - prm%T_ref)**1 &                                             ! linear    coefficient
-                + prm%A(1:3,1:3,3)*(T - prm%T_ref)**2.0_pReal &                                     ! quadratic coefficient
+                + prm%A(1:3,1:3,3)*(T - prm%T_ref)**2 &                                             ! quadratic coefficient
                 ) / &
          (1.0_pReal &
-               + prm%A(1:3,1:3,1)*(T - prm%T_ref)**1.0_pReal / 1.0_pReal &
+               + prm%A(1:3,1:3,1)*(T - prm%T_ref)**1 / 1.0_pReal &
-               + prm%A(1:3,1:3,2)*(T - prm%T_ref)**2.0_pReal / 2.0_pReal &
+               + prm%A(1:3,1:3,2)*(T - prm%T_ref)**2 / 2.0_pReal &
-               + prm%A(1:3,1:3,3)*(T - prm%T_ref)**3.0_pReal / 3.0_pReal &
+               + prm%A(1:3,1:3,3)*(T - prm%T_ref)**3 / 3.0_pReal &
          )
   end associate
   dLi_dTstar = 0.0_pReal

src/phase_mechanical_plastic_nonlocal.f90

@@ -620,7 +620,7 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
                         * spread((  1.0_pReal - prm%f_F &
                                    + prm%f_F &
                                    * log(0.35_pReal * prm%b_sl * sqrt(max(stt%rho_forest(:,en),prm%rho_significant))) &
-                                   / log(0.35_pReal * prm%b_sl * 1e6_pReal))** 2.0_pReal,2,prm%sum_N_sl)
+                                   / log(0.35_pReal * prm%b_sl * 1e6_pReal))**2,2,prm%sum_N_sl)
   else
     myInteractionMatrix = prm%h_sl_sl
   end if
@@ -646,7 +646,7 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
     rhoExcess(1,:) = rho_edg_delta
     rhoExcess(2,:) = rho_scr_delta
 
-    FVsize = geom(ph)%V_0(en) ** (1.0_pReal/3.0_pReal)
+    FVsize = geom(ph)%V_0(en)**(1.0_pReal/3.0_pReal)
 
     !* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities
 
@@ -1304,10 +1304,10 @@ function rhoDotFlux(timestep,ph,en,ip,el)
                          * math_inner(m(1:3,s,t), normal_neighbor2me) * area                        ! positive line length that wants to enter through this interface
               where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) &
                 rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) &
-                                + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal    ! transferring to equally signed mobile dislocation type
+                                + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2        ! transferring to equally signed mobile dislocation type
               where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) &
                 rhoDotFlux(:,topp) = rhoDotFlux(:,topp) &
-                                   + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to opposite signed mobile dislocation type
+                                   + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2     ! transferring to opposite signed mobile dislocation type
 
             end if
           end do
@@ -1336,7 +1336,7 @@ function rhoDotFlux(timestep,ph,en,ip,el)
             c = (t + 1) / 2
             if (v0(s,t) * math_inner(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then             ! flux from en to my neighbor == leaving flux for en (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
               if (v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal) then                                     ! no sign change in flux density
-                transmissivity = sum(compatibility(c,:,s,n,ip,el)**2.0_pReal)                       ! overall transmissivity from this slip system to my neighbor
+                transmissivity = sum(compatibility(c,:,s,n,ip,el)**2)                               ! overall transmissivity from this slip system to my neighbor
               else                                                                                  ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
                 transmissivity = 0.0_pReal
               end if
@@ -1663,7 +1663,7 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
       !* Peierls contribution
       tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s))
       lambda_P = prm%b_sl(s)
-      activationVolume_P = prm%w *prm%b_sl(s)**3.0_pReal
+      activationVolume_P = prm%w *prm%b_sl(s)**3
       criticalStress_P = prm%peierlsStress(s,c)
       activationEnergy_P = criticalStress_P * activationVolume_P
       tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
@@ -1678,7 +1678,7 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
       ! Contribution from solid solution strengthening
       tauEff = abs(tau(s)) - tauThreshold(s)
       lambda_S = prm%b_sl(s) / sqrt(prm%c_sol)
-      activationVolume_S = prm%f_sol * prm%b_sl(s)**3.0_pReal / sqrt(prm%c_sol)
+      activationVolume_S = prm%f_sol * prm%b_sl(s)**3 / sqrt(prm%c_sol)
       criticalStress_S = prm%Q_sol / activationVolume_S
       tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
       tSolidSolution = 1.0_pReal /  prm%nu_a &
@@ -1694,8 +1694,8 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
 
       v(s) = sign(1.0_pReal,tau(s)) &
            / (tPeierls / lambda_P + tSolidSolution / lambda_S + prm%B /(prm%b_sl(s) * tauEff))
-      dv_dtau(s)   = v(s)**2.0_pReal * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2.0_pReal))
+      dv_dtau(s)   = v(s)**2 * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2))
-      dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / lambda_P
+      dv_dtauNS(s) = v(s)**2 * dtPeierls_dtau / lambda_P
 
     end if
   end do

src/rotations.f90

@@ -1099,7 +1099,7 @@ pure function ho2ax(ho) result(ax)
             +0.000003953714684212874_pReal, -0.00000036555001439719544_pReal ]
 
   ! normalize h and store the magnitude
-  hmag_squared = sum(ho**2.0_pReal)
+  hmag_squared = sum(ho**2)
   if (dEq0(hmag_squared)) then
     ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ]
   else