Flexible precision in GEOS-Chem

Overview

Flexible precision was introduced in Fortran 90

In most Fortran codes (including GEOS-Chem) you will see declarations such as:

! Integers
INTEGER   :: I, J   ! 4-byte integer  
INTEGER*4 :: K, L   ! 4-byte integer
INTEGER*8 :: M, N   ! 8-byte integer

! Floating point
REAL      :: A, B   ! 4-byte floating point
REAL*4    :: C, D   ! 4-byte floating point
REAL*8    :: E, F   ! 8-byte floating point 

etc. Note that:

1. On most compilers, INTEGER refers to a 4-byte integer. You can make this default to an 8-byte integer by compiling with -i8. In most circumstances it is OK to use 4-byte integers, unless you need to point to a memory location or are reading an 8-byte integer from a netCDF file.
2. On most compilers, REAL refers to a 4-byte floating-point. You can make this default to an 8-byte floating point by compiling with -r8.
3. In some older Fortran codes, you will see the term DOUBLE PRECISION. This is the same as REAL*8 -- it is an 8-byte floating point.

Fortran 90 introduced a new precision concept. You can replace these fixed data type with declarations of arbitrary precision. This is done with the SELECTED_REAL_KIND and SELECTED_INT_KIND functions, which are described in more detail here.

--Bob Y. 15:01, 7 November 2014 (EST)

Why are we implementing flexible precision in GEOS-Chem

Long story short: we need to do this in order to interface GEOS-Chem into the NASA GEOS-5 GCM (and other GCM's) more efficiently.

Most of the floating-point variables in GEOS-Chem are declared as REAL*8. We wrote the GEOS-Chem code in this manner, starting many years ago, when we were running on coarser-resolution grids (i.e. 4° x 5°) where memory was not an issue.

Many GCMs—including the GEOS-5 GCM—declare floating-point variables as REAL*4. Because GCM's typically operate on very fine horizontal grids, conserving memory is of paramount concern.

When we connect GEOS-Chem to the GEOS-5 GCM, for example, we have to copy REAL*4 data from the GCM (such as the met fields, surface parameters, and relevant quantities) into GEOS-Chem's REAL*8 arrays. This copying operation is very costly, as it requires extra memory and CPU cycles. But if we can transform GEOS-Chem's REAL*8 arrays into REAL*4 arrays, then we could just use point GEOS-Chem's arrays to the GCM arrays without having to do the extra operations associated with the copying process.

Therefore, our goal is to recode GEOS-Chem so that you can select the floating-point precision that you want to use (either REAL*4 or REAL*8) at compile time. If you are going to connect GEOS-Chem to the GEOS-5 GCM, you can request all of the floating point variables to be declared as REAL*4, in order to match the variables in the GEOS-5 GCM. But if you are using the "traditional" serial GEOS-Chem, you can request that the floating point varaibles be declared as REAL*8, for backwards compatibility with prior code.

--Bob Y. 15:17, 7 November 2014 (EST)

Methodology

We followed this procedure in order to implement flexible precision into GEOS-Chem:

1. We defined module Headers/precision_mod.F90. This module defines a parameter that will be used to specify the precision of variables in other parts of the code.

MODULE PRECISION_MOD

  IMPLICIT NONE
  PRIVATE

#if defined( USE_REAL8 )

  ! Use 8-byte floating point precision when asked for it
  INTEGER, PARAMETER, PUBLIC :: fp = KIND( 0.d0 )

#else

  ! Use 4-byte floating point precision by default
  INTEGER, PARAMETER, PUBLIC :: fp = KIND( 0.0  )

#endif

END MODULE PRECISION_MOD

Instead of having to figure out the proper settings with SELECTED_REAL_KIND, we can just use the KIND command to return that for us.

• KIND( 0.d0 ) returns the proper "kind" value to define an 8-byte floating point
• KIND( 0.0 ) returns the proper "kind" value to define a 4-byte floating point

This value returned by the KIND function is saved in the constant named fp.

Note that we have used an #if defined block to define the value of FP. If we compile with -DUSE_REAL8, then the fp can be used to declare 8-byte floating-point variables. Otherwise, fp can be used to declare 4-byte variables by default.

3. Add precision_mod.F to the dependencies listing in the Headers/Makefile. Add this line:

precision_mod.o: precision_mod.F90

3. In the Makefille_header.mk, we added a new Makefile variable named PRECISION:

# %%%%% Default to 8-byte precision unless specified otherwise %%%%%
ifndef PRECISION
 PRECISION     :=8
endif

This variable is set to 8 by default (because for now, we want to compile the "traditional" serial GEOS-Chem with REAL*8 floating point precision, as it has always been compiled.

PRECISION is used again further down in the Makefile_header.mk to add a C-preprocessor switch:

# Add flexible precision declaration
ifeq ($(PRECISION),8)
USER_DEFS      += -DUSE_REAL8
endif

The -DUSE_REAL8 will define the USE_REAL8 C-preprocessor switch, which in turn will automatically pick 8-byte floating point precision.

4. At the top of each GEOS-Chem module or routine (typically in the !USES: comment section), you can place a reference to precision_mod.F90. For example, at the top of GeosCore/carbon_mod.F, you would add the line in RED:

!------------------------------------------------------------------------------
!                  GEOS-Chem Global Chemical Transport Model                  !
!------------------------------------------------------------------------------
!BOP
!     
! !MODULE: carbon_mod
!     
! !DESCRIPTION: Module CARBON\_MOD contains arrays and routines for performing
!  a carbonaceous aerosol simulation.  Original code taken from Mian Chin's 
!  GOCART model and modified accordingly. (rjp, bmy, 4/2/04, 6/30/10)
!\\   
!\\   
! !INTERFACE: 
!
      MODULE CARBON_MOD
!
! !USES:
!
!
      USE HCO_ERROR_MOD       ! For real precisions (hp)
      USE PRECISION_MOD       ! For GEOS-Chem precision (fp)

      IMPLICIT NONE
      PRIVATE

Note that HEMCO has its own precision parameters. We'll leave those alone, because HEMCO ships as a separate package as well.

5. Look for all variables in the module that are declared as REAL*8. Replace the REAL*8 text with REAL(fp) instead. So, in the above example, these lines:

      REAL*8, ALLOCATABLE :: ANTH_BLKC(:,:,:)
      REAL*8, ALLOCATABLE :: ANTH_ORGC(:,:,:)
      REAL*8, ALLOCATABLE :: BIOB_BLKC(:,:,:)

would become

      REAL(fp), ALLOCATABLE :: ANTH_BLKC(:,:,:)
      REAL(fp), ALLOCATABLE :: ANTH_ORGC(:,:,:)
      REAL(fp), ALLOCATABLE :: BIOB_BLKC(:,:,:)

6. IMPORTANT NOTE! Any literal constants in scientific notation made with the Fortran d exponents have to be changed to e. Also, the text _fp has to be appended to the exponent. This tells Fortran that we are using a customized precision definition. For example, the code:

      ! Molecules OH  per kg OH [molec/kg]
      REAL*8,  PARAMETER  :: XNUMOL_OH  = 6.022d23 / 17d-3
      REAL*8,  PARAMETER  :: CM3PERM3   = 1.d6

would become instead:

      ! Molecules OH  per kg OH [molec/kg]
      REAL(fp),  PARAMETER  :: XNUMOL_OH  = 6.022e+23_fp / 17e-3_fp
      REAL(fp),  PARAMETER  :: CM3PERM3   = 1.e+6_fp

7. We repeated the process in steps 4-6 for each GEOS-Chem source code file. We typically modify a file or two at a time, and then run a difference test. A difference test compares the code we are editing to a code with known behavior, such as the last accepted benchmarked version.

--Bob Y. 15:35, 7 November 2014 (EST)