From Documentation
Jump to: navigation, search
(→‎Set Nsz=37 (fails))
 
(57 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
{{Template:CCDelete}}
 +
{{Template:LegacyPage}}
 
{{Software
 
{{Software
 
|package_name=MPFUN90
 
|package_name=MPFUN90
Line 9: Line 11:
 
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.
 
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=
+
=Versions=
  
 
==20060123==
 
==20060123==
  
 
<pre>
 
<pre>
−
module purge; module load ldwrapper; module load intel/12.1.3; module load mpfun90/20060123  
+
module load intel/12.1.3
 +
module load mpfun90/20060123  
 
</pre>
 
</pre>
  
Line 20: Line 23:
  
 
<pre>
 
<pre>
−
module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
+
module load intel/15.0.3
 +
module load mpfun90/intel1503/20100825
 
</pre>
 
</pre>
  
−
=Job Submission=
+
=Usage=
  
 +
==Cluster==
 
To submit a job to the serial queue use:
 
To submit a job to the serial queue use:
  
 
   sqsub -r 10m --mpp=2G -o ofile.%J ./a.out
 
   sqsub -r 10m --mpp=2G -o ofile.%J ./a.out
  
−
=Sample Problems=
+
==Interactive==
  
−
==1) testmp90==
+
===testmp90===
  
 
This example shows how to compile and run <i>testmp90.f90</i> and <i>testmp90.f</i> using the 2006 and 2010 sharcnet mpfun90 modules:
 
This example shows how to compile and run <i>testmp90.f90</i> and <i>testmp90.f</i> using the 2006 and 2010 sharcnet mpfun90 modules:
  
−
===20060123===
+
====20060123====
  
−
  [roberpj@orc-login2:~] module purge; module load ldwrapper; module load intel/12.1.3; module load mpfun90/20060123
+
  [roberpj@orc-login2:~] 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] 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] ifort testmp90.f90 $CPPFLAGS $LDFLAGS -lmp
Line 47: Line 52:
 
  Completed Test 62
 
  Completed Test 62
  
−
===20100825===
+
====20100825====
  
−
  [roberpj@orc-login2:~] module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
+
  [roberpj@orc-login2:~] module unload intel mkl mpfun90
 +
[roberpj@orc-login2:~] 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] 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] ifort -free testmp90.f $MPFUN90_ROOT/toolkit/mpfun90.o  -I$MPFUN90_ROOT/toolkit
Line 59: Line 65:
 
  Completed Test 62
 
  Completed Test 62
  
−
==2) factorial_100==
+
o Note that when using the mpfun90/20100825 (or newer sharcnet modules) when the main program contains "use mpmodule" its necessary to include "$MPFUN90_ROOT/toolkit/mpmod90.o" when compiling otherwise error messages such as <i>"undefined reference to mpdefmod_mp_mpinit_"</i> will occur.  Also note this is not required with the legacy mpfun90/20060123 module since the custom built static mp library (which is no longer being provided by sharcnet) contains all mpfun objects.
 +
 
 +
===factorial_100.f90===
  
 
This example shows how to compile and run the program <i>factorial_100.f90</i> using the 2010 sharcnet mpfun90 module only:
 
This example shows how to compile and run the program <i>factorial_100.f90</i> using the 2010 sharcnet mpfun90 module only:
Line 93: Line 101:
 
       end
 
       end
 
   
 
   
−
===Compile===
+
====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  
+
  [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===  
+
====Execute====
  
 
  [roberpj@orc-login2:~/samples/mpfun90/factorial_100_pgm] ./a.out
 
  [roberpj@orc-login2:~/samples/mpfun90/factorial_100_pgm] ./a.out
Line 105: Line 114:
 
  DONE
 
  DONE
  
−
=General Notes=
+
==Graphical==
 +
 
 +
There is no graphical usage component for this software package.
 +
 
 +
=Notes=
  
−
==OpenMP with MPFUN and QD==
+
==OpenMP==
  
−
The Multi Precision packages MPFUN90 and QD use "user defined data type" for their variables.
+
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
 
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.
 
with OpenMP the reduction must be done manually in a PARALLEL OpenMP region.
Line 118: Line 131:
 
https://www.sharcnet.ca/help/index.php/OpenMP_Reduction_for_User_Defined_Data_Types
 
https://www.sharcnet.ca/help/index.php/OpenMP_Reduction_for_User_Defined_Data_Types
  
−
==Handling large arrays in an MPFUN program ==
+
==Large Arrays==
  
 
Declaring large arrays in an MPFUN program often leads to compile
 
Declaring large arrays in an MPFUN program often leads to compile
Line 214: Line 227:
 
</pre>
 
</pre>
  
−
====Set Nsz=12 (works)====
+
====Nsz=12 (works)====
  
 
<pre>
 
<pre>
Line 266: Line 279:
 
</pre>
 
</pre>
  
−
====Set Nsz=37 (fails)====
+
====Nsz=37 (fails)====
  
 
<pre>
 
<pre>
Line 292: Line 305:
  
 
===betay.f90===
 
===betay.f90===
 +
 +
Copy betay.f90 from betax.f90 and modify as follows:
  
 
<pre>
 
<pre>
Line 328: Line 343:
 
       return
 
       return
 
       END
 
       END
−
</pre>
 
−
 
−
! ----------------------------------------------------------------------
 
 
   
 
   
 
       program BETAY
 
       program BETAY
Line 374: Line 386:
 
       stop
 
       stop
 
       end
 
       end
 +
</pre>
  
−
# Edit betax.f90 to set Nsz=12 then compile and execute (should work)
+
====Run Interactive====
−
# Edit betax.f90 to set Nsz=40 then compile and execute (should work)
+
  
−
============================================================================
+
<pre>
−
+
[roberpj@orc-login2:~/samples/mpfun90/betax] ssh orc-dev1
−
# File betay.f90 was copied from betax.f90 and modified as described earlier.
+
[roberpj@orc129:~] module purge; module load ldwrapper; module load intel/15.0.3; module load mpfun90/intel1503/20100825
−
+
[roberpj@orc129:~] cd ~/samples/mpfun90/betax
−
# Compile betay.f90
+
[roberpj@orc129:~/samples/mpfun90/betay] ifort betay.f90 -mcmodel medium -shared-intel $MPFUN90_ROOT/toolkit/mpmod90.o $MPFUN90_ROOT/toolkit/mpfun90.o -I$MPFUN90_ROOT/toolkit
−
+
[roberpj@orc129:~/samples/mpfun90/betay] ./a.out
−
ifort betay.f90 -mcmodel medium -shared-intel \
+
  Done with allocations
−
-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
+
−
+
−
============================================================================
+
  
 +
I,J,K,L =  24 23 22 21
  
−
<br>
+
fac(024) =10 ^        23 x  6.2044840173323943936,
  
−
==MPFUN's TOOLKIT==
+
BETA2(024,023) =
 +
10 ^      -14 x  6.2020112243197155666795543346647015590753323586760996092750
 +
322219057797634187521971369584938063040803657153278083912027225083805532623694
 +
253019502124309149392729129350380917947755526197968886374824625487894350759012
 +
041810328483619840297565282378760232413828873982152911730876431238573292437598
 +
662321548481235961397432074855738879756265023434311148398287293760405994587153
 +
193913843867324131168164219803469468792765957446870530750541069496092327458240
 +
264036867349068267612059922537556261610989123549224099029159406148147186635876
 +
682339231176161254018298581141061530140422181489818261044243997939224351270878
 +
819950204611859530447542248373743937988058087925403948261102164487732977810152
 +
365677688323239749,
  
 +
BETA3(024,023,022) =
 +
10 ^      -49 x  5.8275670518268372535457693390802431850085211093628371195552
 +
665374004872800254829089878748169551314149473682136937787061527746060528126189
 +
766201816798822863047397630953393452298952922317427385387709426414471466082503
 +
710520168054747139227447182197529542668023453841447481072362595230792080104688
 +
990118018686670752770192225324208683555045454680275731685429800649187636704457
 +
682218863512356150460390146982645823361128943131689947031597399022247950302452
 +
330798644776819869632357497968409458052013048605853804143958746701285425073948
 +
635138571530969417104049554300550153503104110125327389142504664160736472211972
 +
376564769573352356164657421339817982321431569247028739128974299782191260982443
 +
302487480103263037,
 +
 +
BETA4(024,023,022,021) =
 +
10 ^      -82 x  4.9281568290835382164029311372592682488032902612395816340121
 +
089418282192742634150386978468714226783345875673304699950206823277002261928996
 +
900244023525594363488176338336719985617691508208486288075631383295355204178844
 +
640181812076780791059441681639997667611161419120033906970044689546074997396047
 +
324233844363558571961437990937177293607133483649131082039969185440365241880338
 +
469876039008981574675398716901015661349359043742699044662693828465598208328182
 +
649393881845546476915223922569122221086448855100004979240419350679011848465439
 +
752707160104858505636971713317247147406784939008134376861978582533070195429961
 +
381129842064351212761591279694768634684602143478580742025860111467351736320562
 +
750016997598905712,
 +
 +
DONE
 +
</pre>
 +
 +
====Run In Queue====
 +
 +
The executable requires 4G or more. Setting mpp=8G should work (logout then in again to reset to default environment):
 +
 +
<pre>
 +
sqsub -r 5m --mpp=8.0G -o ofile.%J ./a.out
 +
</pre>
 +
 +
==Math Toolkit==
 +
 +
===Running Mathinit===
 
This toolkit provides and extensive example of how the mpfun package can be used.  Read the header of files  
 
This toolkit provides and extensive example of how the mpfun package can be used.  Read the header of files  
 
  mathinit.f90  
 
  mathinit.f90  
Line 415: Line 460:
 
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.
 
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  
 
To run Mathtool you must first generate following two input files  
 
  const.dat  
 
  const.dat  
Line 424: Line 468:
  
 
<pre>
 
<pre>
−
[roberpj@bal34:~/samples/mpfun] /opt/sharcnet/mpfun90/version/[flavor]/toolkit/mathinit
+
[roberpj@orc-login1:~/samples/mpfun90/math] cp /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mathinit .
 +
[roberpj@orc-login1:~/samples/mpfun90/math] chmod 700 mathinit
 +
[roberpj@orc-login1:~/samples/mpfun90/math] ./mathinit
 
  mathinit: start
 
  mathinit: start
 
  const complete
 
  const complete
 
  file const.dat written
 
  file const.dat written
−
  cpu time = 0.E+0
+
  cpu time =   2.57360911369324   
 
initqts: Tanh-sinh quadrature initialization
 
initqts: Tanh-sinh quadrature initialization
−
0 18632
+
          0       18632
−
1000 18632
+
        1000       18632
−
2000 18632
+
        2000       18632
−
3000 18632
+
        3000       18632
−
4000 18632
+
        4000       18632
−
5000 18632
+
        5000       18632
−
6000 18632
+
        6000       18632
−
7000 18632
+
        7000       18632
−
8000 18632
+
        8000       18632
 
initqts: Table spaced used =    8177
 
initqts: Table spaced used =    8177
 
  initqts complete
 
  initqts complete
 
  file quadts.dat written
 
  file quadts.dat written
−
  cpu time = 0.E+0
+
  cpu time =   90.4362528324127   
−
  total cpu time = 0.E+0
+
  total cpu time =   93.0098619461060
−
 
+
[roberpj@orc-login1:~/samples/mpfun90/mathinit] ls
−
[roberpj@bal34:~/samples/mpfun] ls
+
const.dat mathinit quadts.dat
−
const.dat  quadts.dat
+
 
</pre>
 
</pre>
  
−
====Running Mathtool====
+
===Running Mathtool===
 
Use the files created in the previous section to run mathtool as follows:
 
Use the files created in the previous section to run mathtool as follows:
  
 
<pre>
 
<pre>
−
[roberpj@bal34:~/samples/mpfun] /opt/sharcnet/mpfun90/version/[flavor]/toolkit/mathtool
+
[roberpj@orc-login1:~/samples/mpfun90/math] cp /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mathtool .
 +
[roberpj@orc-login1:~/samples/mpfun90/math] chmod 700 mathtool
 +
[roberpj@orc-login1:~/samples/mpfun90/math] ./mathtool  
 
Welcome to the Experimental Mathematician's Toolkit
 
Welcome to the Experimental Mathematician's Toolkit
 
Initializing...
 
Initializing...
Line 467: Line 514:
 
Quadrature level =  6
 
Quadrature level =  6
 
Quadrature type =  3  (Tanh-Sinh)
 
Quadrature type =  3  (Tanh-Sinh)
−
-- snip --
 
  
−
TYPE: integrate[1/(1+x^2), {x, 0, 1}]   (hit enter)
+
Sample expressions (case insensitive):
 +
e + pi + log2 + log10 + catalan  Adds these pre-defined constants.
 +
result[1] + result[2]            Adds result #1 to result #2.
 +
alpha = arctan[3] - 3*log[2]    Defines or sets user variable alpha.
 +
fun1[x,y] = 2*sqrt[x]*erf[y]    Defines user function fun1.
 +
clear[nam1]                      Clears definition of variable or function.
 +
integrate[1/(1+x^2), {x, 0, 1}]  Integrates 1/(1+x^2) from x=0 to 1.
 +
sum[1/2^k, {k, 0, infinity}]    Sums 1/2^k from k=0 to infinity.
 +
binomial[20,10]*factorial[10]    Evaluates binomial coeff and factorial.
 +
zeta[3] + zetaz[1,1,2]          Evaluates zeta and multi-zeta functions.
 +
table[x^k, {k, 1, 4}]            Forms the list [x^1, x^2, x^3, x^4].
 +
pslq[table[x^k, {k, 0, n}]]      Finds coeffs of degree-n poly for x.
 +
polyroot[1,-1,-1,{0.618}]        Finds real root of 1-x-x^2=0 near 0.618.
 +
polyroot[1,2,3,{-0.33, 0.47}]    Complex root of 1+2x+3x^2 near -0.33+0.47i.
 +
digits = 200                    Sets working precision to 200 digits.
 +
epsilon = -190                  Sets epsilon level to 10^(-190).
 +
eformat[190,180]                Display using E format with 180 digits.
 +
fformat[60,50]                  Display using F format with 50 digits.
 +
input file.dat                  Inputs commands from file file.dat.
 +
output file.dat                  Outputs user vars and funs to file.dat.
 +
help polyroot                    Displays a brief explanation of polyroot.
 +
functions                        Displays a list of all defined functions.
 +
variables                        Displays a list of all defined variables.
 +
prompt                          Displays this message.
 +
exit                            Exits this program.
 +
Expressions may be continued on next line by typing \ at end of line.
 +
 
 +
integrate[1/(1+x^2), {x, 0, 1}] (hit enter)
 
quadts: Iteration  1 of  6; est error = 10^    0; approx value =
 
quadts: Iteration  1 of  6; est error = 10^    0; approx value =
 
       7.853157298876894309110693190063938396203990510665917998384243e-1
 
       7.853157298876894309110693190063938396203990510665917998384243e-1
Line 484: Line 557:
 
Result[  1] =
 
Result[  1] =
 
     7.85398163397448309615660845819875721049292349843776455243736148076954e-1
 
     7.85398163397448309615660845819875721049292349843776455243736148076954e-1
−
CPU time =      0.0000
+
CPU time =      0.1730
  
−
TYPE: functions (hit enter)
+
functions   (hit enter)
 
Abs              Arccos          Arcsin          Arctan           
 
Abs              Arccos          Arcsin          Arctan           
 
Arctan2          Bessel          Besselexp        Binomial         
 
Arctan2          Bessel          Besselexp        Binomial         
Line 495: Line 568:
 
Tan              Zeta            Zetap            Zetaz           
 
Tan              Zeta            Zetap            Zetaz           
  
−
TYPE: variables (hit enter)
+
variables   (hit enter)
 
E                Log2            Log10            Pi               
 
E                Log2            Log10            Pi               
 
Catalan          Eulergamma      Infinity        Arg1             
 
Catalan          Eulergamma      Infinity        Arg1             
Line 504: Line 577:
 
Quadtype        x                 
 
Quadtype        x                 
  
−
TYPE: Pi (hit enter)
+
Pi         (hit enter)    
 
Result[  2] =
 
Result[  2] =
 
       3.14159265358979323846264338327950288419716939937510582097494459230781e0
 
       3.14159265358979323846264338327950288419716939937510582097494459230781e0
 
CPU time =      0.0000
 
CPU time =      0.0000
−
</pre>
 
  
−
==More Mathtool commands==
+
sqrt[1600]    (hit enter)  
−
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:
+
Result[  1] =
−
+
      4.00000000000000000000000000000000000000000000000000000000000000000000e1
−
/opt/sharcnet/mpfun/current/toolkit/mathtool
+
CPU time =      0.0000
−
 
+
−
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]
+
help  Binomial  (hit enter)  
−
Result[ 2] =
+
Binomial[m,n] computes the binomial coefficient of integers (m,n).        
−
      4.00000000000000000000000000000000000000000000000000000000000000000000e1
+
−
CPU time =      0.0000
+
  
−
help  Binomial
+
Binomial[3,2]   (hit enter)   
−
Binomial[m,n] computes the binomial coefficient of integers (m,n).
+
Result[  2] =
−
 
+
−
  Binomial[3,2]
+
−
Result[  3] =
+
 
       3.00000000000000000000000000000000000000000000000000000000000000000000e0
 
       3.00000000000000000000000000000000000000000000000000000000000000000000e0
−
CPU time =      0.0000
+
CPU time =      0.0000
  
−
hypo[x,y] = sqrt[x^2+y^2]
+
hypo[x,y] = sqrt[x^2+y^2]   (hit enter)  
−
  parse: new function name = hypo
+
parse: new function name = hypo          
−
CPU time =      0.0000
+
CPU time =      0.0000
  
−
z=hypo[3,4]
+
z=hypo[3,4]                 (hit enter) 
−
parse: new variable name = z
+
parse: new variable name = z              
−
CPU time =      0.0000
+
CPU time =      0.0000
  
−
z
+
z                           (hit enter) 
−
Result[  4] =
+
Result[  3] =
−
      5.00000000000000000000000000000000000000000000000000000000000000000000e0
+
      5.00000000000000000000000000000000000000000000000000000000000000000000e0
−
CPU time =      0.0000
+
CPU time =      0.0000
−
 
+
</pre>
−
exit
+
  
 
=References=
 
=References=

Latest revision as of 10:30, 6 June 2019

This page is scheduled for deletion because it is either redundant with information available on the CC wiki, or the software is no longer supported.
Note: This page's content only applies to the SHARCNET's legacy systems; it does not apply to Graham.


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.

Versions

20060123

module load intel/12.1.3
module load mpfun90/20060123

20100825

module load intel/15.0.3
module load mpfun90/intel1503/20100825

Usage

Cluster

To submit a job to the serial queue use: 

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

Interactive

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 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 unload intel mkl mpfun90
[roberpj@orc-login2:~] 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

o Note that when using the mpfun90/20100825 (or newer sharcnet modules) when the main program contains "use mpmodule" its necessary to include "$MPFUN90_ROOT/toolkit/mpmod90.o" when compiling otherwise error messages such as "undefined reference to mpdefmod_mp_mpinit_" will occur. Also note this is not required with the legacy mpfun90/20060123 module since the custom built static mp library (which is no longer being provided by sharcnet) contains all mpfun objects.

factorial_100.f90

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

Graphical

There is no graphical usage component for this software package.

Notes

OpenMP

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

Large Arrays

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:

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

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

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

Copy betay.f90 from betax.f90 and modify as follows: 

       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

Run Interactive

[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/betay] ifort betay.f90 -mcmodel medium -shared-intel $MPFUN90_ROOT/toolkit/mpmod90.o $MPFUN90_ROOT/toolkit/mpfun90.o -I$MPFUN90_ROOT/toolkit
[roberpj@orc129:~/samples/mpfun90/betay] ./a.out
 Done with allocations

I,J,K,L =  24 23 22 21

fac(024) =10 ^        23 x  6.2044840173323943936,

BETA2(024,023) =
10 ^       -14 x  6.2020112243197155666795543346647015590753323586760996092750
322219057797634187521971369584938063040803657153278083912027225083805532623694
253019502124309149392729129350380917947755526197968886374824625487894350759012
041810328483619840297565282378760232413828873982152911730876431238573292437598
662321548481235961397432074855738879756265023434311148398287293760405994587153
193913843867324131168164219803469468792765957446870530750541069496092327458240
264036867349068267612059922537556261610989123549224099029159406148147186635876
682339231176161254018298581141061530140422181489818261044243997939224351270878
819950204611859530447542248373743937988058087925403948261102164487732977810152
365677688323239749,

BETA3(024,023,022) =
10 ^       -49 x  5.8275670518268372535457693390802431850085211093628371195552
665374004872800254829089878748169551314149473682136937787061527746060528126189
766201816798822863047397630953393452298952922317427385387709426414471466082503
710520168054747139227447182197529542668023453841447481072362595230792080104688
990118018686670752770192225324208683555045454680275731685429800649187636704457
682218863512356150460390146982645823361128943131689947031597399022247950302452
330798644776819869632357497968409458052013048605853804143958746701285425073948
635138571530969417104049554300550153503104110125327389142504664160736472211972
376564769573352356164657421339817982321431569247028739128974299782191260982443
302487480103263037,

BETA4(024,023,022,021) =
10 ^       -82 x  4.9281568290835382164029311372592682488032902612395816340121
089418282192742634150386978468714226783345875673304699950206823277002261928996
900244023525594363488176338336719985617691508208486288075631383295355204178844
640181812076780791059441681639997667611161419120033906970044689546074997396047
324233844363558571961437990937177293607133483649131082039969185440365241880338
469876039008981574675398716901015661349359043742699044662693828465598208328182
649393881845546476915223922569122221086448855100004979240419350679011848465439
752707160104858505636971713317247147406784939008134376861978582533070195429961
381129842064351212761591279694768634684602143478580742025860111467351736320562
750016997598905712,

DONE

Run In Queue

The executable requires 4G or more. Setting mpp=8G should work (logout then in again to reset to default environment): 

sqsub -r 5m --mpp=8.0G -o ofile.%J ./a.out

Math Toolkit

Running Mathinit

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.

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@orc-login1:~/samples/mpfun90/math] cp /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mathinit .
[roberpj@orc-login1:~/samples/mpfun90/math] chmod 700 mathinit 
[roberpj@orc-login1:~/samples/mpfun90/math] ./mathinit
 mathinit: start
 const complete
 file const.dat written
 cpu time =   2.57360911369324     
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 =   90.4362528324127     
 total cpu time =   93.0098619461060
[roberpj@orc-login1:~/samples/mpfun90/mathinit] ls
const.dat  mathinit  quadts.dat

Running Mathtool

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

[roberpj@orc-login1:~/samples/mpfun90/math] cp /opt/sharcnet/mpfun90/20100825/intel1503/toolkit/mathtool .
[roberpj@orc-login1:~/samples/mpfun90/math] chmod 700 mathtool 
[roberpj@orc-login1:~/samples/mpfun90/math] ./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)

Sample expressions (case insensitive):
e + pi + log2 + log10 + catalan  Adds these pre-defined constants.
result[1] + result[2]            Adds result #1 to result #2.
alpha = arctan[3] - 3*log[2]     Defines or sets user variable alpha.
fun1[x,y] = 2*sqrt[x]*erf[y]     Defines user function fun1.
clear[nam1]                      Clears definition of variable or function.
integrate[1/(1+x^2), {x, 0, 1}]  Integrates 1/(1+x^2) from x=0 to 1.
sum[1/2^k, {k, 0, infinity}]     Sums 1/2^k from k=0 to infinity.
binomial[20,10]*factorial[10]    Evaluates binomial coeff and factorial.
zeta[3] + zetaz[1,1,2]           Evaluates zeta and multi-zeta functions.
table[x^k, {k, 1, 4}]            Forms the list [x^1, x^2, x^3, x^4].
pslq[table[x^k, {k, 0, n}]]      Finds coeffs of degree-n poly for x.
polyroot[1,-1,-1,{0.618}]        Finds real root of 1-x-x^2=0 near 0.618.
polyroot[1,2,3,{-0.33, 0.47}]    Complex root of 1+2x+3x^2 near -0.33+0.47i.
digits = 200                     Sets working precision to 200 digits.
epsilon = -190                   Sets epsilon level to 10^(-190).
eformat[190,180]                 Display using E format with 180 digits.
fformat[60,50]                   Display using F format with 50 digits.
input file.dat                   Inputs commands from file file.dat.
output file.dat                  Outputs user vars and funs to file.dat.
help polyroot                    Displays a brief explanation of polyroot.
functions                        Displays a list of all defined functions.
variables                        Displays a list of all defined variables.
prompt                           Displays this message.
exit                             Exits this program.
Expressions may be continued on next line by typing \ at end of line.

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 =      0.1730

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           

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                

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

sqrt[1600]    (hit enter)  
Result[  1] =
      4.00000000000000000000000000000000000000000000000000000000000000000000e1
CPU time =      0.0000

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

Binomial[3,2]    (hit enter)  
Result[  2] =
      3.00000000000000000000000000000000000000000000000000000000000000000000e0
CPU time =      0.0000

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

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

z                            (hit enter)  
Result[  3] =
      5.00000000000000000000000000000000000000000000000000000000000000000000e0
CPU time =      0.0000

References

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

Retrieved from "https://www.sharcnet.ca/help/index.php?title=MPFUN90&oldid=17956"