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Potential issues in M7 for Single Precision #2

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307ecdf
Add remark from Xuemei regarding test on volume in M&N
plesager May 29, 2026
afe4d71
Use the standard erf implementation to compute CDF
plesager May 29, 2026
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198 changes: 11 additions & 187 deletions ifs-source/arpifs/m7/module/mo_ham_m7.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -59,16 +59,15 @@

MODULE mo_ham_m7

USE mo_kind, ONLY: dp
USE mo_kind, ONLY: dp

IMPLICIT NONE

PRIVATE
IMPLICIT NONE

PUBLIC :: m7, m7_cumulative_normal
PRIVATE
PUBLIC :: m7, m7_cumulative_normal

!REAL(dp), PUBLIC, ALLOCATABLE :: rwet_m7(:,:,:), rdry_m7(:,:,:)
!REAL(dp), PUBLIC, ALLOCATABLE :: densaer_m7(:,:,:), aerwat_m7(:,:,:)
!REAL(dp), PUBLIC, ALLOCATABLE :: rwet_m7(:,:,:), rdry_m7(:,:,:)
!REAL(dp), PUBLIC, ALLOCATABLE :: densaer_m7(:,:,:), aerwat_m7(:,:,:)

CONTAINS

Expand Down Expand Up @@ -143,192 +142,17 @@ SUBROUTINE m7_cumulative_normal ( arg, presult, ccum )
! functions, and proper selection of the machine-dependent
! constants.
!
! Explanation of machine-dependent constants.
!
! MIN = smallest machine representable number.
!
! EPS = argument below which anorm(x) may be represented by
! 0.5 and above which x*x will not underflow.
! A conservative value is the largest machine number X
! such that 1.0 + X = 1.0 to machine precision.
!
! Error returns
!
! The program returns ANORM = 0 for ARG .LE. XLOW.
!
! Author:
!
! W. J. Cody
! Mathematics and Computer Science Division
! Argonne National Laboratory
! Argonne, IL 60439
!
! Latest modification: March 15, 1992
!
USE mo_kind, ONLY: dp
!
IMPLICIT NONE
!
REAL(dp), PARAMETER, DIMENSION ( 5 ) :: a = (/ &
2.2352520354606839287e00_dp, &
1.6102823106855587881e02_dp, &
1.0676894854603709582e03_dp, &
1.8154981253343561249e04_dp, &
6.5682337918207449113e-2_dp /)
REAL(dp) :: arg
REAL(dp), PARAMETER, DIMENSION ( 4 ) :: b = (/ &
4.7202581904688241870e01_dp, &
9.7609855173777669322e02_dp, &
1.0260932208618978205e04_dp, &
4.5507789335026729956e04_dp /)
REAL(dp), PARAMETER, DIMENSION ( 9 ) :: c = (/ &
3.9894151208813466764e-1_dp, &
8.8831497943883759412e00_dp, &
9.3506656132177855979e01_dp, &
5.9727027639480026226e02_dp, &
2.4945375852903726711e03_dp, &
6.8481904505362823326e03_dp, &
1.1602651437647350124e04_dp, &
9.8427148383839780218e03_dp, &
1.0765576773720192317e-8_dp /)
REAL(dp) :: ccum
REAL(dp), PARAMETER, DIMENSION ( 8 ) :: d = (/ &
2.2266688044328115691e01_dp, &
2.3538790178262499861e02_dp, &
1.5193775994075548050e03_dp, &
6.4855582982667607550e03_dp, &
1.8615571640885098091e04_dp, &
3.4900952721145977266e04_dp, &
3.8912003286093271411e04_dp, &
1.9685429676859990727e04_dp /)
REAL(dp) :: del
!@@@ REAL(dp) :: dpmpar
REAL(dp) :: eps
INTEGER :: i
REAL(dp) :: zmin
REAL(dp), PARAMETER, DIMENSION ( 6 ) :: p = (/ &
2.1589853405795699e-1_dp, &
1.274011611602473639e-1_dp, &
2.2235277870649807e-2_dp, &
1.421619193227893466e-3_dp, &
2.9112874951168792e-5_dp, &
2.307344176494017303e-2_dp /)
REAL(dp), PARAMETER, DIMENSION ( 5 ) :: q = (/ &
1.28426009614491121e00_dp, &
4.68238212480865118e-1_dp, &
6.59881378689285515e-2_dp, &
3.78239633202758244e-3_dp, &
7.29751555083966205e-5_dp /)
REAL(dp) :: presult
REAL(dp), PARAMETER :: root32 = 5.656854248_dp
REAL(dp), PARAMETER :: sixten = 16.0_dp
REAL(dp) :: temp
REAL(dp), PARAMETER :: sqrpi = 3.9894228040143267794e-1_dp
REAL(dp), PARAMETER :: thrsh = 0.66291_dp
REAL(dp) :: x
REAL(dp) :: xden
REAL(dp) :: xnum
REAL(dp) :: y
REAL(dp) :: xsq


!REAL(dp), ALLOCATABLE :: rwet_m7(:,:,:), rdry_m7(:,:,:)
!REAL(dp), ALLOCATABLE :: densaer_m7(:,:,:), aerwat_m7(:,:,:)
!
! Machine dependent constants
!
eps = EPSILON ( 1.0_dp ) * 0.5_dp
!
!@@@ Simplified calculation of the smallest machine representable number
! (Higher accuracy than needed!)
!
!@@@ min = dpmpar(2)

zmin = EPSILON ( 1.0_dp )

x = arg
y = ABS ( x )

IF ( y <= thrsh ) THEN
!
! Evaluate anorm for |X| <= 0.66291
!
IF ( y > eps ) THEN
xsq = x * x
ELSE
xsq = 0.0_dp
END IF
REAL(dp), INTENT(IN) :: arg
REAL(dp), INTENT(OUT) :: ccum
REAL(dp), INTENT(OUT) :: presult

xnum = a(5) * xsq
xden = xsq
DO i = 1, 3
xnum = ( xnum + a(i) ) * xsq
xden = ( xden + b(i) ) * xsq
END DO
presult = x * ( xnum + a(4) ) / ( xden + b(4) )
temp = presult
presult = 0.5_dp + temp
ccum = 0.5_dp - temp
!
! Evaluate ANORM for 0.66291 <= |X| <= sqrt(32)
!
ELSE IF ( y <= root32 ) THEN

xnum = c(9) * y
xden = y
!DIR$ UNROLL
!CDIR UNROLL=7
DO i = 1, 7
xnum = ( xnum + c(i) ) * y
xden = ( xden + d(i) ) * y
END DO
presult = ( xnum + c(8) ) / ( xden + d(8) )
xsq = AINT ( y * sixten ) / sixten
del = ( y - xsq ) * ( y + xsq )
presult = EXP(-xsq*xsq*0.5_dp) * EXP(-del*0.5_dp) * presult
ccum = 1.0_dp - presult

IF ( x > 0.0_dp ) THEN
temp = presult
presult = ccum
ccum = temp
END IF
!
! Evaluate anorm for |X| > sqrt(32).
!
ELSE

presult = 0.0_dp
xsq = 1.0_dp / ( x * x )
xnum = p(6) * xsq
xden = xsq
DO i = 1, 4
xnum = ( xnum + p(i) ) * xsq
xden = ( xden + q(i) ) * xsq
END DO

presult = xsq * ( xnum + p(5) ) / ( xden + q(5) )
presult = ( sqrpi - presult ) / y
xsq = AINT ( x * sixten ) / sixten
del = ( x - xsq ) * ( x + xsq )
presult = EXP ( - xsq * xsq * 0.5_dp ) * EXP ( - del * 0.5_dp ) * presult
ccum = 1.0_dp - presult

IF ( x > 0.0_dp ) THEN
temp = presult
presult = ccum
ccum = temp
END IF

END IF

IF ( presult < zmin ) THEN
presult = 0.0_dp
END IF

IF ( ccum < zmin ) THEN
ccum = 0.0_dp
END IF
presult = 0.5_dp * (1.0_dp + erf(arg / sqrt(2.0_dp)))
ccum = 1.0_dp - presult
Comment on lines +154 to +155
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@plesager plesager May 29, 2026

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The ERF function is default in Fortran 2003 and above. We could even use the MKL library with Intel, but that can be left for future improvement.
Using erf here removes all the tests on eps and zmin introduced in that subroutine.


END SUBROUTINE m7_cumulative_normal

Expand Down
6 changes: 6 additions & 0 deletions ifs-source/arpifs/m7/phys_ec/yoe_aer_activ.F90
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Expand Up @@ -527,6 +527,12 @@ SUBROUTINE AER_ACTIV_MORALES_NENES_FULL(KIDIA, KFDIA, KTDIA, KLON, KLEV, LCLOUD,
NCL(JL) = NNACL(JL)
NH2SO4(JL) = NSO4(JL) - NNA2SO4(JL)

! QUESTION: should we use a fixed lower value (e.g.
! 1e-30) to avoid ovestimating aerosol volume by SP.
!
! The argument is that we miss all value between
! EPS(SP)=~1e-7 and EPS(DP)=~2e-16 when running at SP
!
IF (ZVOL(JL) .GE. ZEPS) THEN !eehol: total volume per mode need to be above treshold to avoid div by zero
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@plesager plesager May 29, 2026

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An idea is to devise a the test independent from the precision, for example by using a fixed lower value of 1e-30 (or just 2e-16 so we are closer to what EPS in DP is currently using)

!---mode kappa = volume-weighted sum of component kappa's
ZKAPPA(JL,JK,JMOD) = ( (Kap_ss * NNACL(JL) * WNACL / (DNACL*1.E3_JPRB)) + &
Expand Down