The code generation (codegen) package contains tools for creating, manipulating, and translating Maple procedures into other languages. This includes tools for automatic differentiation of Maple procedures, code optimization, translation into C, Fortran and MathML, and an operation count of a Maple procedure.

Each command in the codegen package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

Important: The newer CodeGeneration package also offers translation of Maple code to other languages. The codegen[C] and codegen[fortran] commands have been deprecated, and the superseding commands CodeGeneration:-C and CodeGeneration:-Fortran should be used instead.  Additionally, codegen[maple2intrep] and codegen[intrep2maple] have been superseded by ToInert and FromInert.

The following is a list of available commands.

To display the help page for a particular codegen command, see Getting Help with a Command in a Package.

$\mathrm{with}\left(\mathrm{codegen}\right)\:$

$f≔1-\exp \left(-t\right)xy\:$

$g≔x-y\exp \left(-t\right)x^2\:$

$v≔\mathrm{vector}\left(\left[f\,g\right]\right)$

$v≔\left[\begin{array}{cc}1-{\ⅇ}^{-t}xy& x-y{\ⅇ}^{-t}{x}^2\end{array}\right]$

fg := makeproc(v,parameters=[t,x,y]);

$\mathrm{fg}≔\mathbf{proc}\left(t\,x\,y\right)\mathbf{local}v\;v≔\mathrm{array}\left(1..2\right)\;v\[1\]≔1-\exp \left(\−t\right)\*x\*y\;v\[2\]≔x-y\*\exp \left(\−t\right)\*x\^2\;v\mathbf{end\; proc}$

$\mathrm{fortran}\left(\mathrm{fg}\,\mathrm{optimized}\right)$

      subroutine fg(t,x,y,crea_par)
      doubleprecision t
      doubleprecision x
      doubleprecision y
      doubleprecision crea_par(2)

      doubleprecision t1
      doubleprecision t5
      doubleprecision v(2)

        t1 = exp(-t)
        v(1) = -y*x*t1+1
        t5 = x**2
        v(2) = -t5*t1*y+x
        crea_par(1) = v(1)
        crea_par(2) = v(2)
        return
        return
      end

f := proc(C,D,theta,x,y,h,k,r)
local s,c,xbar,ybar,d1,d2,d;
  s := sin(theta);
  c := cos(theta);
  xbar := (x+C)*c + (y+D)*s;
  ybar := (y+D)*c - (x+C)*s;
  d1 := (h-xbar)^2;
  d2 := (k-ybar)^2;
  d := sqrt( d1+d2 ) - r;
  d^2
end proc:

$G≔\mathrm{GRADIENT}\left(f\,\left[C\,\mathrm{D}\,\mathrm{\theta }\right]\,\mathrm{result\_type}=\mathrm{array}\right)$

$G≔\mathbf{proc}\left(C\,\mathrm{D}\,\mathrm{\θ}\,x\,y\,h\,k\,r\right)\mathbf{local}c\,d\,\mathrm{d1}\,\mathrm{d2}\,\mathrm{dfr0}\,\mathrm{grd}\,s\,\mathrm{xbar}\,\mathrm{ybar}\;s≔\sin \left(\mathrm{\θ}\right)\;c≔\cos \left(\mathrm{\θ}\right)\;\mathrm{xbar}≔\left(x\+C\right)\*c\+\left(y\+\mathrm{D}\right)\*s\;\mathrm{ybar}≔\left(y\+\mathrm{D}\right)\*c-\left(x\+C\right)\*s\;\mathrm{d1}≔\left(h-\mathrm{xbar}\right)\^2\;\mathrm{d2}≔\left(k-\mathrm{ybar}\right)\^2\;d≔\mathrm{sqrt}\left(\mathrm{d1}\+\mathrm{d2}\right)-r\;\mathrm{dfr0}≔\mathrm{array}\left(1..7\right)\;\mathrm{dfr0}\[7\]≔2\*d\;\mathrm{dfr0}\[6\]≔1\/2\*\mathrm{dfr0}\[7\]\/\left(\mathrm{d1}\+\mathrm{d2}\right)\^\left(1\/2\right)\;\mathrm{dfr0}\[5\]≔1\/2\*\mathrm{dfr0}\[7\]\/\left(\mathrm{d1}\+\mathrm{d2}\right)\^\left(1\/2\right)\;\mathrm{dfr0}\[4\]≔\mathrm{dfr0}\[6\]\*\left(\−2\*k\+2\*\mathrm{ybar}\right)\;\mathrm{dfr0}\[3\]≔\mathrm{dfr0}\[5\]\*\left(\−2\*h\+2\*\mathrm{xbar}\right)\;\mathrm{dfr0}\[2\]≔\mathrm{dfr0}\[4\]\*\left(y\+\mathrm{D}\right)\+\mathrm{dfr0}\[3\]\*\left(x\+C\right)\;\mathrm{dfr0}\[1\]≔\mathrm{dfr0}\[4\]\*\left(\−x-C\right)\+\mathrm{dfr0}\[3\]\*\left(y\+\mathrm{D}\right)\;\mathrm{grd}≔\mathrm{array}\left(1..3\right)\;\mathrm{grd}\[1\]≔0\;\mathrm{grd}\[2\]≔c\*\mathrm{dfr0}\[4\]\+s\*\mathrm{dfr0}\[3\]\;\mathrm{grd}\[3\]≔\−\mathrm{dfr0}\[2\]\*\sin \left(\mathrm{\θ}\right)\+\mathrm{dfr0}\[1\]\*\cos \left(\mathrm{\θ}\right)\;\mathbf{return}\mathrm{grd}\mathbf{end\; proc}$

$C\left(G\,\mathrm{optimized}\,\mathrm{precision}=\mathrm{single}\right)$

#include <math.h>
void G(C,D,theta,x,y,h,k,r,grd)
float C;
float D;
float theta;
float x;
float y;
float h;
float k;
float r;
float grd[3];
{
  float c;
  float d1;
  float d2;
  float dfr0[7];
  float s;
  float t1;
  float t10;
  float t12;
  float t20;
  float t22;
  float t3;
  float t7;
  float t8;
  float t9;
  {
    s = sin(theta);
    c = cos(theta);
    t1 = x+C;
    t3 = y+D;
    t7 = -c*t1-s*t3+h;
    d1 = t7*t7;
    t8 = -c*t3+s*t1+k;
    d2 = t8*t8;
    t9 = d1+d2;
    t10 = sqrt(t9);
    dfr0[6] = 2.0*t10-2.0*r;
    t12 = sqrt(t9);
    dfr0[5] = 1/t12*dfr0[6]/2.0;
    dfr0[4] = dfr0[5];
    dfr0[3] = -2.0*t8*dfr0[4];
    dfr0[2] = -2.0*t7*dfr0[4];
    t20 = dfr0[3];
    t22 = dfr0[2];
    dfr0[1] = t1*t22+t3*t20;
    dfr0[0] = -t1*t20+t3*t22;
    grd[0] = 0.0;
    grd[1] = c*t20+s*t22;
    grd[2] = c*dfr0[0]-s*dfr0[1];
    return;
  }
}

$\mathrm{cost}\left(\mathrm{optimize}\left(G\right)\right)$

$23\mathrm{storage}+25\mathrm{assignments}+5\mathrm{functions}+12\mathrm{additions}+22\mathrm{multiplications}+18\mathrm{subscripts}+\mathrm{divisions}$

$f≔\mathrm{Sum}\left(\frac{x^i}{i!}\&comma;i=0..n\right)$

$f≔\sum _{i=0}^n\frac{x^i}{i!}$

F := makeproc(f,parameters=[n,x],locals=[i]);

$F≔\mathbf{proc}\left(n\&comma;x\right)\mathbf{local}i\&semi;\mathrm{Sum}\left(x\&Hat;i\&sol;\mathrm{factorial}\left(i\right)\&comma;i\&equals;0..n\right)\mathbf{end\; proc}$

$F≔\mathrm{prep2trans}\left(F\right)$

$F≔\mathbf{proc}\left(n\&comma;x\right)\mathbf{local}i\&comma;\mathrm{i1}\&comma;\mathrm{s1}\&comma;\mathrm{t1}\&semi;\mathbf{if}0<\&minus;n\mathbf{then}\mathrm{s1}≔0\mathbf{else}\mathrm{t1}≔1\&semi;\mathrm{s1}≔1\&semi;\mathbf{for}\mathrm{i1}\mathbf{to}n\mathbf{do}\mathrm{t1}≔x\&ast;\mathrm{t1}\&sol;\mathrm{i1}\&semi;\mathrm{s1}≔\mathrm{s1}\&plus;\mathrm{t1}\mathbf{end\; do}\mathbf{end\; if}\&semi;\mathrm{s1}\mathbf{end\; proc}$

$F≔\mathrm{declare}\left(n::\mathrm{integer}\&comma;F\right)$

$F≔\mathbf{proc}\left(n::\mathrm{integer}\&comma;x\right)\mathbf{local}i\&comma;\mathrm{i1}\&comma;\mathrm{s1}\&comma;\mathrm{t1}\&semi;\mathbf{if}0<\&minus;n\mathbf{then}\mathrm{s1}≔0\mathbf{else}\mathrm{t1}≔1\&semi;\mathrm{s1}≔1\&semi;\mathbf{for}\mathrm{i1}\mathbf{to}n\mathbf{do}\mathrm{t1}≔x\&ast;\mathrm{t1}\&sol;\mathrm{i1}\&semi;\mathrm{s1}≔\mathrm{s1}\&plus;\mathrm{t1}\mathbf{end\; do}\mathbf{end\; if}\&semi;\mathrm{s1}\mathbf{end\; proc}$

$C\left(F\right)$

double F(n,x)
int n;
double x;
{
  double i;
  int i1;
  double s1;
  double t1;
  {
    if( 0.0 < -n )
      s1 = 0.0;
    else
      {
        t1 = 1.0;
        s1 = 1.0;
        for(i1 = 1;i1 <= n;i1++)
        {
          t1 = x/i1*t1;
          s1 += t1;
        }
      }
    return(s1);
  }
}

$f≔\mathrm{Proc}\left(\mathrm{Parameters}\left(n::\mathrm{integer}\&comma;x::\mathrm{float}\right)\&comma;\mathrm{Locals}\left(i\&comma;s\&comma;t\right)\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(s\&comma;1.0\right)\&comma;\mathrm{Assign}\left(t\&comma;1.0\right)\&comma;\mathrm{For}\left(i\&comma;1\&comma;1\&comma;n\&comma;\mathrm{true}\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(t\&comma;\frac{xt}{i}\right)\&comma;\mathrm{Assign}\left(s\&comma;s+t\right)\right)\&comma;\mathrm{false}\right)\&comma;s\right)\right)$

$f≔\mathrm{Proc}\left(\mathrm{Parameters}\left(n::\mathbb{Z}\&comma;x::\mathrm{float}\right)\&comma;\mathrm{Locals}\left(i\&comma;s\&comma;t\right)\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(s\&comma;1.0\right)\&comma;\mathrm{Assign}\left(t\&comma;1.0\right)\&comma;\mathrm{For}\left(i\&comma;1\&comma;1\&comma;n\&comma;\mathrm{true}\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(t\&comma;\frac{xt}{i}\right)\&comma;\mathrm{Assign}\left(s\&comma;s+t\right)\right)\&comma;\mathrm{false}\right)\&comma;s\right)\right)$

$F≔\mathrm{intrep2maple}\left(f\right)$

$F≔\mathbf{proc}\left(n::\mathrm{integer}\&comma;x::\mathrm{float}\right)\mathbf{local}i\&comma;s\&comma;t\&semi;s≔1.0\&semi;t≔1.0\&semi;\mathbf{for}i\mathbf{to}n\mathbf{do}t≔x\&ast;t\&sol;i\&semi;s≔s\&plus;t\mathbf{end\; do}\&semi;s\mathbf{end\; proc}$

$f≔1-\exp \left(-t\right)xy$

$f≔1-{\&ExponentialE;}^{-t}xy$

F := makeproc(f,[x,y,t]);

$F≔\mathbf{proc}\left(x\&comma;y\&comma;t\right)1-\exp \left(\&minus;t\right)\&ast;x\&ast;y\mathbf{end\; proc}$

$G≔\mathrm{GRADIENT}\left(F\&comma;\left[x\&comma;y\right]\&comma;\mathrm{result\_type}=\mathrm{array}\right)$

$G≔\mathbf{proc}\left(x\&comma;y\&comma;t\right)\mathbf{local}\mathrm{grd}\&semi;\mathrm{grd}≔\mathrm{array}\left(1..2\right)\&semi;\mathrm{grd}\&lsqb;1\&rsqb;≔\&minus;\exp \left(\&minus;t\right)\&ast;y\&semi;\mathrm{grd}\&lsqb;2\&rsqb;≔\&minus;\exp \left(\&minus;t\right)\&ast;x\&semi;\mathbf{return}\mathrm{grd}\mathbf{end\; proc}$

$G≔\mathrm{dontreturn}\left(\mathrm{grd}\&comma;\mathrm{makeparam}\left(\mathrm{grd}\&comma;G\right)\right)$

$G≔\mathbf{proc}\left(x\&comma;y\&comma;t\&comma;\mathrm{grd}::\left(\mathrm{array}\left(1..2\right)\right)\right)\mathrm{grd}\&lsqb;1\&rsqb;≔\&minus;\exp \left(\&minus;t\right)\&ast;y\&semi;\mathrm{grd}\&lsqb;2\&rsqb;≔\&minus;\exp \left(\&minus;t\right)\&ast;x\&semi;\mathbf{return}\mathbf{end\; proc}$

$H≔\mathrm{HESSIAN}\left(F\&comma;\left[x\&comma;y\right]\&comma;\mathrm{result\_type}=\mathrm{array}\right)\&colon;$

$H≔\mathrm{renamevar}\left(\mathrm{grd}=\mathrm{hes}\&comma;\mathrm{dontreturn}\left(\mathrm{grd}\&comma;\mathrm{makeparam}\left(\mathrm{grd}\&comma;H\right)\right)\right)$

$H≔\mathbf{proc}\left(x\&comma;y\&comma;t\&comma;\mathrm{hes}::\left(\mathrm{array}\left(1..2\&comma;1..2\right)\right)\right)\mathbf{local}\mathrm{df}\&comma;\mathrm{dfr0}\&comma;\mathrm{grd1}\&comma;\mathrm{grd2}\&comma;\mathrm{t1}\&semi;\mathrm{t1}≔\exp \left(\&minus;t\right)\&semi;\mathrm{grd1}≔\&minus;y\&ast;\mathrm{t1}\&semi;\mathrm{grd2}≔\&minus;x\&ast;\mathrm{t1}\&semi;\mathrm{df}≔\mathrm{array}\left(1..2\right)\&semi;\mathrm{dfr0}≔\mathrm{array}\left(1..2\right)\&semi;\mathrm{df}\&lsqb;1\&rsqb;≔1\&semi;\mathrm{dfr0}\&lsqb;2\&rsqb;≔1\&semi;\mathrm{hes}\&lsqb;1\&comma;1\&rsqb;≔0\&semi;\mathrm{hes}\&lsqb;1\&comma;2\&rsqb;≔\&minus;\mathrm{df}\&lsqb;1\&rsqb;\&ast;\mathrm{t1}\&semi;\mathrm{hes}\&lsqb;2\&comma;1\&rsqb;≔\&minus;\mathrm{dfr0}\&lsqb;2\&rsqb;\&ast;\mathrm{t1}\&semi;\mathrm{hes}\&lsqb;2\&comma;2\&rsqb;≔0\&semi;\mathbf{return}\mathbf{end\; proc}$

$\mathrm{GH}≔\mathrm{optimize}\left(\mathrm{joinprocs}\left(\left[G\&comma;H\right]\right)\right)$

$\mathrm{GH}≔\mathbf{proc}\left(x\&comma;y\&comma;t\&comma;\mathrm{grd}\&comma;\mathrm{hes}::\left(\mathrm{array}\left(1..2\&comma;1..2\right)\right)\right)\mathbf{local}\mathrm{t1}\&comma;\mathrm{t2}\&semi;\mathrm{t2}≔\exp \left(\&minus;t\right)\&semi;\mathrm{grd}\&lsqb;1\&rsqb;≔\&minus;y\&ast;\mathrm{t2}\&semi;\mathrm{grd}\&lsqb;2\&rsqb;≔\&minus;x\&ast;\mathrm{t2}\&semi;\mathrm{t1}≔\mathrm{t2}\&semi;\mathrm{hes}\&lsqb;1\&comma;1\&rsqb;≔0\&semi;\mathrm{hes}\&lsqb;1\&comma;2\&rsqb;≔\&minus;\mathrm{t1}\&semi;\mathrm{hes}\&lsqb;2\&comma;1\&rsqb;≔\mathrm{hes}\&lsqb;1\&comma;2\&rsqb;\&semi;\mathrm{hes}\&lsqb;2\&comma;2\&rsqb;≔0\&semi;\mathbf{return}\mathbf{end\; proc}$

f := proc(x,n) local A,i;
  A := Array(0..n);
  A[0] := 1;
  for i to n do A[i] := x*A[i-1] end do;
  A
end proc:

$\mathrm{IR}≔\mathrm{maple2intrep}\left(f\right)$

$\mathrm{IR}≔\mathrm{Proc}\left(\mathrm{Name}\left(f..\mathrm{List}\left(0..n\&comma;\mathrm{float}\right)\right)\&comma;\mathrm{Parameters}\left(x..\mathrm{float}\&comma;n..\mathrm{integer}\right)\&comma;\mathrm{Options}\left(\right)\&comma;\mathrm{Description}\left(\right)\&comma;\mathrm{Locals}\left(A..\mathrm{List}\left(0..n\&comma;\mathrm{float}\right)\&comma;i..\mathrm{integer}\right)\&comma;\mathrm{Globals}\left(\right)\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(A\&comma;\mathrm{Array}\left(0..n\right)\right)\&comma;\mathrm{Assign}\left(A_0\&comma;1\right)\&comma;\mathrm{For}\left(i\&comma;1\&comma;1\&comma;n\&comma;\mathrm{true}\&comma;\mathrm{StatSeq}\left(\mathrm{Assign}\left(A_i\&comma;x{A}_{-1+i}\right)\right)\&comma;\mathrm{false}\right)\&comma;A\right)\right)$

$\mathrm{intrep2maple}\left(\mathrm{IR}\right)$

Error, integer dimensions required

$\mathrm{intrep2maple}\left(\mathrm{eval}\left(\mathrm{IR}\&comma;1\right)\right)$

$\mathbf{proc}\left(x\&comma;n\right)\mathbf{local}A\&comma;i\&semi;A≔\mathrm{Array}\left(0..n\right)\&semi;A\&lsqb;0\&rsqb;≔1\&semi;\mathbf{for}i\mathbf{to}n\mathbf{do}A\&lsqb;i\&rsqb;≔x\&ast;A\&lsqb;i-1\&rsqb;\mathbf{end\; do}\&semi;A\mathbf{end\; proc}$