Revision as of 18:48, 5 January 2016

MPFUN90
Description: A Fortran-90 arbitrary precision package
SHARCNET Package information: see MPFUN90 software page in web portal
Full list of SHARCNET supported software

Introduction

MPFUN90 is a Fortran-90 arbitrary precision package (i.e. user specifies the desired precision)written by David H. Bailey et. al from the Lawrence Berkeley National Laboratory. If 64 digits of precision are sufficient for an application then users should use QD instead of MPFUN which would run much faster.

Version Selection

20060123

module purge; module load ldwrapper; module load intel/12.1.3; module load mpfun90/20060123

20100825

module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825

Job Submission

To submit a job to the serial queue use:

 sqsub -r 10m --mpp=2G -o ofile.%J ./a.out

Sample Problems

1) testmp90

This example shows how to compile and run testmp90.f90 and testmp90.f using the 2006 and 2010 sharcnet mpfun90 modules:

20060123

[roberpj@orc-login2:~] module purge; module load ldwrapper; module load intel/12.1.3; module load mpfun90/20060123
[roberpj@orc-login2:~/samples/mpfun90/20060123] cp /opt/sharcnet/mpfun90/20060123/f90/src/testmp90.f90 .
[roberpj@orc-login2:~/samples/mpfun90/20060123] ifort testmp90.f90 $CPPFLAGS $LDFLAGS -lmp
[roberpj@orc-login2:~/samples/mpfun90/20060123] ./a.out
Completed Test  1
Completed Test  2
Completed Test  3
.................
Completed Test 62

20100825

[roberpj@orc-login2:~] module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
[roberpj@orc-login2:~/samples/mpfun90/20100825] cp $MPFUN90_ROOT/f90/testmp90.f .
[roberpj@orc-login2:~/samples/mpfun90/20100825] ifort -free testmp90.f $MPFUN90_ROOT/toolkit/mpfun90.o  -I$MPFUN90_ROOT/toolkit
[roberpj@orc-login2:~/samples/mpfun90/20100825] ./a.out
Completed Test  1
Completed Test  2
Completed Test  3
.................
Completed Test 62

2) factorial_100

This example shows how to compile and run the program factorial_100.f90 using the 2010 sharcnet mpfun90 module only:

      program factorial_100_pgm
      use mpmodule
      implicit none
      integer, parameter :: Nmx = 100
      integer            :: AllocateStatus
      integer            :: J
      type(mp_real) zero, one
      type(mp_real), dimension (:), allocatable        :: fac
      call mpinit(800)
      call mpsetprec(800)
      call mpsetoutputprec(700)
      zero='0.'
      one ='1.'
      allocate(fac(0:Nmx),STAT=AllocateStatus)
      IF (AllocateStatus /= 0) STOP "Not enough memory for fac "
      fac(0)=one
      do J=1,Nmx
        fac(J)=fac(J-1)*J
      end do
      J=4
      write(6,1001) J
 1001 format(/"fac(",i3.3,") =",$)
      call mpwrite(6,fac(J))
      J=100
      write(6,1001) J
      call mpwrite(6,fac(J))
      write(6,1005)
 1005 format(/"DONE"//)
      end

Compile

[roberpj@orc-login2:~/samples/mpfun90/factorial_100_pgm] ifort factorial_100.f90 $MPFUN90_ROOT/toolkit/mpmod90.o $MPFUN90_ROOT/toolkit/mpfun90.o -I$MPFUN90_ROOT/toolkit

Execute

[roberpj@orc-login2:~/samples/mpfun90/factorial_100_pgm] ./a.out
fac(004) =10 ^         1 x  2.4,
fac(100) =10 ^       157 x  9.3326215443944152681699238856266700490715968264381621468592
 963895217599993229915608941463976156518286253697920827223758251185210916864,
DONE

General Notes

OpenMP with MPFUN and QD

The Multi Precision packages MPFUN90 and QD use "user defined data type" for their variables. Since the OpenMP reduction clause cannot be used for "user defined data types" to run MPFUN90 or QD with OpenMP the reduction must be done manually in a PARALLEL OpenMP region.

Detailed documentation on how to use OpenMP with MPFUN90 and QD are presented in the following document:

https://www.sharcnet.ca/help/index.php/OpenMP_Reduction_for_User_Defined_Data_Types

Handling large arrays in an MPFUN program

Declaring large arrays in an MPFUN program often leads to compile errors like:

 "relocation truncated to fit r_x86_64_pc32 against .bss"

Even with the flag '-mcmodel large' in the compile command the error will persist, because there is a limit to the amount of data you can have allocated in static arrays for x86_64 architecture. This data segment is limited to 2GB. The data in COMMON plus any other statically declared arrays PLUS your code must fit in 2GB.

In order to overcome this problem use allocatable arrays declared in a module together with a short subroutine which allocates the arrays.

We illustrate these concepts by starting with a program 'betax.f90' which work fine for values of parameter 'Nsz' less than 37. Thus, if you compile it with

      integer, parameter :: Nsz=36

it works, but for any higher values it fails with error message:

 "relocation truncated to fit: R_X86_64_PC32 against symbol '...'"

To overcome this problem, we first copy program betax.f90 into a new file, say, betay.f90, and write a module called 'mp_data' and a subroutine called 'allocate_arrays' at the top of the new file. We move all the declarations of large arrays into the module, and declare them as 'allocatable'.

In the subroutine 'allocate_arrays' we do the allocations and in the main program we add the statements:

     USE mp_data
     ...
     call allocate_arrays
     ...

Below you will find the listings for the files 'betax.f90', 'betay.f90' and the 'HIST' file containing the commands to compile these files and submit jobs:

1) betax.f90

       program BETAX
       use mpmodule
       implicit none
 !     integer, parameter :: Nsz=12   ! compilation fails for 37
       integer, parameter :: Nsz=37
       INTEGER :: I,J,K,L
       type(mp_real) zero, one
       type(mp_real) fac(0:Nsz),fci(0:Nsz)
       type(mp_real) BETA2(Nsz,Nsz)
       type(mp_real) BETA3(Nsz,Nsz,Nsz)
       type(mp_real) BETA4(Nsz,Nsz,Nsz,Nsz)
       call mpinit(800)
       call mpsetprec(800)
       call mpsetoutputprec(700)
       zero='0.'
       one ='1.'
       fac(0)=one
       fci(0)=one
       do j=1,Nsz
         fac(j)=fac(j-1)*j
         fci(j)=one/fac(j)
       end do
       I=Nsz/2
       J=I-1
       K=J-1
       L=K-1
       write(6,1000) I,J,K,L
  1000 format(/"I,J,K,L = ",4i3)
       write(6,1001) I
  1001 format(/"fac(",i3.3,") =",$)
       call mpwrite(6,fac(I))
       BETA2(I,J)      =fac(I)*fac(J)*fci(I+J)
       BETA3(I,J,K)    =fac(I)*fac(J)*fac(K)*fci(I+J)*fci(J+K)
       BETA4(I,J,K,L)  =fac(I)*fac(J)*fac(K)*fac(L)*                     &
      &                 fci(I+J)*fci(J+K)*fci(K+L)
       write(6,1002) I,J
  1002 format(/"BETA2(",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA2(I,J))
       write(6,1003) I,J,K
  1003 format(/"BETA3(",i3.3,",",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA3(I,J,K))
       write(6,1004) I,J,K,L
  1004 format(/"BETA4(",i3.3,",",i3.3,",",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA4(I,J,K,L))
       write(6,1005)
  1005 format(/"DONE"//)
       stop
       end

Set Nsz=12 (works)

[roberpj@orc-login2:~] ssh orc-dev1
[roberpj@orc129:~] module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
[roberpj@orc129:~] cd ~/samples/mpfun90/betax
[roberpj@orc129:~/samples/mpfun90/betax] ifort betax.f90 $MPFUN90_ROOT/toolkit/mpmod90.o $MPFUN90_ROOT/toolkit/mpfun90.o -I$MPFUN90_ROOT/toolkit
[roberpj@orc129:~/samples/mpfun90/betax] ./a.out

I,J,K,L =   6  5  4  3

fac(006) =10 ^         2 x  7.2,

BETA2(006,005) =
10 ^        -3 x  2.1645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645021645021645021645021645021645021645021645021645021645021645
021645021645021645,

BETA3(006,005,004) =
10 ^        -7 x  1.4315490505966696442886919077395267871458347648823839300029
776220252410728601204791680982157172633363109553585744061934538125014315490505
966696442886919077395267871458347648823839300029776220252410728601204791680982
157172633363109553585744061934538125014315490505966696442886919077395267871458
347648823839300029776220252410728601204791680982157172633363109553585744061934
538125014315490505966696442886919077395267871458347648823839300029776220252410
728601204791680982157172633363109553585744061934538125014315490505966696442886
919077395267871458347648823839300029776220252410728601204791680982157172633363
109553585744061934538125014315490505966696442886919077395267871458347648823839
300029776220252410,

BETA4(006,005,004,003) =
10 ^       -10 x  1.7042250602341305289151094139756271275545651962885522976225
924071729060391191910466286883520443611146558992363981026112545386921804155364
246067193912998901661033180307556724790284880987828833633822295953815228191645
425205515908463754268742930874450148826566060126150829098674903663565795085069
461486695046785749733595538584200715719990096407329967420670368516173504835636
354910731327964888055591003436808425470556989831366248599808690511638357443346
105477624752001169234729325432273278078266740398259672636089869649960352908198
713187375318894593271010504570595273543119348108010239529513905931139491230194
178039983028645160164434540851774411865114812960617949280080799355175772409332
500035447881252869,

DONE

Set Nsz=37 (fails)

[roberpj@orc-login2:~/samples/mpfun90/betax] ssh orc-dev1
[roberpj@orc129:~] module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
[roberpj@orc129:~] cd ~/samples/mpfun90/betax
[roberpj@orc129:~/samples/mpfun90/betax] ifort betax.f90 $MPFUN90_ROOT/toolkit/mpmod90.o $MPFUN90_ROOT/toolkit/mpfun90.o -I$MPFUN90_ROOT/toolkit
/opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o: In function `mpdefmod_mp_mpsetprec_':
mpmod90.f:(.text+0x1b): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_new_mpipl_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0xa0): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_new_mpwds_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0xa6): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0xcf): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
/opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o: In function `mpdefmod_mp_mpgetprec_':
mpmod90.f:(.text+0xe6): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
/opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o: In function `mpdefmod_mp_mpsetprecwords_':
mpmod90.f:(.text+0x109): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_new_mpwds_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0x18c): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0x198): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
/opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o: In function `mpdefmod_mp_mpgetprecwords_':
mpmod90.f:(.text+0x1b2): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_mpnwx_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
/opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o: In function `mpdefmod_mp_mpsetoutputprec_':
mpmod90.f:(.text+0x1c9): relocation truncated to fit: R_X86_64_PC32 against symbol `mpdefmod_mp_new_mpipl_' defined in COMMON section in /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mpmod90.o
mpmod90.f:(.text+0x24c): additional relocation overflows omitted from the output

betay.f90

       module mp_data
       use mpmodule
       use mpfunmod
       implicit none
       integer, parameter :: Nsz =48
       integer            :: AllocateStatus
 !     type(mp_real) zero, one
 !
 !     type(mp_real) fac(0:Nsz),fci(0:Nsz)
 !     type(mp_real) BETA2(Nsz,Nsz)
 !     type(mp_real) BETA3(Nsz,Nsz,Nsz)
 !     type(mp_real) BETA4(Nsz,Nsz,Nsz,Nsz)
       type(mp_real) zero, one
       type(mp_real), dimension (:), allocatable        :: fac,fci
       type(mp_real), dimension (:,:), allocatable      :: BETA2
       type(mp_real), dimension (:,:,:), allocatable    :: BETA3
       type(mp_real), dimension (:,:,:,:), allocatable  :: BETA4
       end module mp_data
       subroutine allocate_arrays
       USE mp_data
       implicit none
       allocate(fac(0:Nsz),STAT=AllocateStatus)
       IF (AllocateStatus /= 0) STOP "Not enough memory for fac "
       allocate(fci(0:Nsz),STAT=AllocateStatus)
       IF (AllocateStatus /= 0) STOP "Not enough memory for fci "
       allocate(BETA2(Nsz,Nsz),STAT=AllocateStatus)
       IF (AllocateStatus /= 0) STOP "Not enough memory for BETA2"
       allocate(BETA3(Nsz,Nsz,Nsz),STAT=AllocateStatus)
       IF (AllocateStatus /= 0) STOP "Not enough memory for BETA3"
       allocate(BETA4(Nsz,Nsz,Nsz,Nsz),STAT=AllocateStatus)
       IF (AllocateStatus /= 0) STOP "Not enough memory for BETA4"
       print *,"Done with allocations"
       return
       END
 
       program BETAY
       USE mp_data
       implicit none
       INTEGER :: I,J,K,L
       call mpinit(800)
       call mpsetprec(800)
       call mpsetoutputprec(700)
       zero='0.'
       one ='1.'
       call allocate_arrays
       fac(0)=one
       fci(0)=one
       do j=1,Nsz
         fac(j)=fac(j-1)*j
         fci(j)=one/fac(j)
       end do
       I=Nsz/2
       J=I-1
       K=J-1
       L=K-1
       write(6,1000) I,J,K,L
  1000 format(/"I,J,K,L = ",4i3)
       write(6,1001) I
  1001 format(/"fac(",i3.3,") =",$)
       call mpwrite(6,fac(I))
       BETA2(I,J)      =fac(I)*fac(J)*fci(I+J)
       BETA3(I,J,K)    =fac(I)*fac(J)*fac(K)*fci(I+J)*fci(J+K)
       BETA4(I,J,K,L)  =fac(I)*fac(J)*fac(K)*fac(L)*                     &
      &                 fci(I+J)*fci(J+K)*fci(K+L)
       write(6,1002) I,J
  1002 format(/"BETA2(",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA2(I,J))
       write(6,1003) I,J,K
  1003 format(/"BETA3(",i3.3,",",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA3(I,J,K))
       write(6,1004) I,J,K,L
  1004 format(/"BETA4(",i3.3,",",i3.3,",",i3.3,",",i3.3,") =")
       call mpwrite(6,BETA4(I,J,K,L))
       write(6,1005)
  1005 format(/"DONE"//)
       stop
       end

============================================================================

# File betay.f90 was copied from betax.f90 and modified as described earlier.

# Compile betay.f90

ifort betay.f90 -mcmodel medium -shared-intel \
-I/opt/sharcnet/mpfun/6.1.23/f90/include          \
-L/opt/sharcnet/mpfun/6.1.23/f90/lib -lmp >& AOUT2

============================================================================

# The executable might require more than 2.0G of memory: 

# This will pruduce an error: 

sqsub -r 5m  --mpp=4.0G  -o OUTPUTFILE4 ./a.out

# This should work:

sqsub -r 5m  --mpp=8.0G  -o OUTPUTFILE8 ./a.out

============================================================================

MPFUN's TOOLKIT

This toolkit provides and extensive example of how the mpfun package can be used. Read the header of files

mathinit.f90 
    and 
mathtool.f90

found under

/opt/sharcnet/mpfun90/version/[flavor]/toolkit

for an explanation what the package does. The Makefile in this directory shows how the mpfun libraries were linked to compile this sample program pair. The following steps shows the first initialization step followed by actually running the mathtool program to perform some examples such as performing an integration and displaying the value of pie. Note that the displayed zero cputimes are due to a bug in the mpfun current build which will be fixed in future updates on the clusters.

Initializing Mathtool

To run Mathtool you must first generate following two input files

const.dat 
  and 
quadts.dat

which can be accomplished by running following command:

[roberpj@bal34:~/samples/mpfun] /opt/sharcnet/mpfun90/version/[flavor]/toolkit/mathinit
 mathinit: start
 const complete
 file const.dat written
 cpu time = 0.E+0
initqts: Tanh-sinh quadrature initialization
 0 18632
 1000 18632
 2000 18632
 3000 18632
 4000 18632
 5000 18632
 6000 18632
 7000 18632
 8000 18632
initqts: Table spaced used =    8177
 initqts complete
 file quadts.dat written
 cpu time = 0.E+0
 total cpu time = 0.E+0

[roberpj@bal34:~/samples/mpfun] ls
const.dat  quadts.dat

Running Mathtool

Use the files created in the previous section to run mathtool as follows:

[roberpj@bal34:~/samples/mpfun] /opt/sharcnet/mpfun90/version/[flavor]/toolkit/mathtool
Welcome to the Experimental Mathematician's Toolkit
Initializing...

Current settings:
Debug level =   2
Primary precision level =   100 digits
Secondary precision level =   200 digits
Primary epsilon = 10^  -100
Secondary epsilon = 10^  -200
PSLQ bound = 100
PSLQ level =   1
Quadrature level =   6
Quadrature type =   3  (Tanh-Sinh)
-- snip --

TYPE: integrate[1/(1+x^2), {x, 0, 1}]   (hit enter)
quadts: Iteration  1 of  6; est error = 10^    0; approx value =
       7.853157298876894309110693190063938396203990510665917998384243e-1
quadts: Iteration  2 of  6; est error = 10^    0; approx value =
       7.853981605125528448099840689980111720633592558858121242731082e-1
quadts: Iteration  3 of  6; est error = 10^  -17; approx value =
       7.853981633974483082028533923930157568609007576776270726821597e-1
quadts: Iteration  4 of  6; est error = 10^  -36; approx value =
       7.853981633974483096156608458198757190586422063114153956005278e-1
quadts: Iteration  5 of  6; est error = 10^  -71; approx value =
       7.853981633974483096156608458198757210492923498437764552437361e-1
quadts: Iteration  6 of  6; est error = 10^ -101; approx value =
       7.853981633974483096156608458198757210492923498437764552437361e-1
Result[  1] =
     7.85398163397448309615660845819875721049292349843776455243736148076954e-1
CPU time =      0.0000

TYPE: functions  (hit enter)
Abs              Arccos           Arcsin           Arctan          
Arctan2          Bessel           Besselexp        Binomial        
Cos              Erf              Exp              Factorial       
Gamma            Integrate        Log              Max             
Min              Polyroot         Pslq             Result          
Sin              Sqrt             Sum              Table           
Tan              Zeta             Zetap            Zetaz           

TYPE: variables  (hit enter)
E                Log2             Log10            Pi              
Catalan          Eulergamma       Infinity         Arg1            
Arg2             Arg3             Arg4             Arg5            
Arg6             Arg7             Arg8             Arg9            
Debug            Digits           Digits2          Epsilon         
Epsilon2         Pslqbound        Pslqlevel        Quadlevel       
Quadtype         x                

TYPE: Pi  (hit enter)
Result[  2] =
      3.14159265358979323846264338327950288419716939937510582097494459230781e0
CPU time =      0.0000

More Mathtool commands

To start mathtool (assuming you have issued the command /opt/sharcnet/mpfun/current/toolkit/mathinit and have these two files: const.dat HIST quadts.dat - you type:

/opt/sharcnet/mpfun/current/toolkit/mathtool

Then try following commands:

integrate[2*x,{x,0,1}]
sqrt[1600]
help  Binomial
Binomial[3,2]
hypo[x,y] = sqrt[x^2+y^2]
z=hypo[3,4]
z
exit

This is what you should get from above commands:

integrate[2*x,{x,0,1}]
quadts: Iteration  1 of  6; est error = 10^    0; approx  value =
        1.000003359570811224742398159504692881030640064061042259417294e0
quadts: Iteration  2 of  6; est error = 10^    0; approx value =
         1.000000000000036584185557611216071731517571134591404403031033e0
quadts: Iteration  3 of  6; est error = 10^  -27; approx  value =
        1.000000000000000000000000000001046972220803162709182580101627e0
quadts: Iteration  4 of  6; est error = 10^  -60; approx value =
         1.000000000000000000000000000000000000000000000000000000000000e0
quadts: Iteration  5 of  6; est error = 10^ -101; approx  value =
      9.999999999999999999999999999999999999999999999999999999999999e-1
Result[  1] =
    9.99999999999999999999999999999999999999999999999999999999999999999999e-1
CPU time =      0.0000

sqrt[1600]
Result[  2] =
      4.00000000000000000000000000000000000000000000000000000000000000000000e1
CPU time =      0.0000

help  Binomial
Binomial[m,n] computes the binomial coefficient of integers (m,n).

Binomial[3,2]
Result[  3] =
     3.00000000000000000000000000000000000000000000000000000000000000000000e0
CPU time =      0.0000

hypo[x,y] = sqrt[x^2+y^2]
parse: new function name = hypo
CPU time =      0.0000

z=hypo[3,4]
parse: new variable name = z
CPU time =      0.0000

z
Result[  4] =
      5.00000000000000000000000000000000000000000000000000000000000000000000e0
CPU time =      0.0000

exit

References

o High-Precision Software Directory
http://crd.lbl.gov/~dhbailey/mpdist/index.html

@@ Line 161: / Line 161: @@
 jobs:
-===betax.f90===
+===1) betax.f90===
 <pre>

Difference between revisions of "MPFUN90"

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Revision as of 18:48, 5 January 2016

Contents

Introduction

Version Selection

20060123

20100825

Job Submission

Sample Problems

1) testmp90

20060123

20100825

2) factorial_100

Compile

Execute

General Notes

OpenMP with MPFUN and QD

Handling large arrays in an MPFUN program

1) betax.f90

Set Nsz=12 (works)

Set Nsz=37 (fails)

betay.f90

MPFUN's TOOLKIT

Initializing Mathtool

Running Mathtool

More Mathtool commands

References

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