reduce-historical/r36/xlog/SCOPE.LOG

REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...


% Test SCOPE Package.
% ==================
% NOTE:  The SCOPE, GHORNER, GSTRUCTR and GENTRAN packages must be loaded
% to run these tests.

% Further reading: SCOPE 1.5 manual Section 3, example 1;

scope_switches$


 ON  :  evallhseqp  exp  ftch  nat  period  
 OFF :  acinfo  again  double  fort  gentranopt  inputc  intern  prefix
        priall  primat  roundbf  rounded  sidrel  vectorc  


% Further reading: SCOPE 1.5 manual Section 3.1, examples 2,3,4 and 5.

on priall$


optimize z:=a^2*b^2+10*a^2*m^6+a^2*m^2+2*a*b*m^4+2*b^2*m^6+b^2*m^2
           iname s;


      2  2       2  6    2  2          4      2  6    2  2
z := a *b  + 10*a *m  + a *m  + 2*a*b*m  + 2*b *m  + b *m

Sumscheme :

   || EC|Far
------------
  0||  1| z
------------



Productscheme :

   |  0  1  2| EC|Far
---------------------
  1|     2  2|  1| 0
  2|  6     2| 10| 0
  3|  2     2|  1| 0
  4|  4  1  1|  2| 0
  5|  6  2   |  2| 0
  6|  2  2   |  1| 0
---------------------
0  : m
1  : b
2  : a

Number of operations in the input is: 

Number of (+/-) operations      : 5
Number of unary - operations    : 0
Number of * operations          : 10
Number of integer ^ operations  : 11
Number of / operations          : 0
Number of function applications : 0


s0 := b*a
s4 := m*m
s1 := s4*b*b
s2 := s4*a*a
s3 := s4*s4
z := s1 + s2 + s0*(2*s3 + s0) + s3*(2*s1 + 10*s2)

Number of operations after optimization is:

Number of (+/-) operations      : 5
Number of unary - operations    : 0
Number of * operations          : 12
Number of integer ^ operations  : 0
Number of / operations          : 0
Number of function applications : 0


Sumscheme :

   |  0  3  4  5| EC|Far
------------------------
  0|        1  1|  1| z
 15|        2 10|  1| 14
 17|  2  1      |  1| 16
------------------------
0  : s3
3  : s0
4  : s1
5  : s2



Productscheme :

   |  8  9 10 11 17 18 19 20| EC|Far
------------------------------------
  7|                    1  1|  1| s0
  8|  1                 2   |  1| s1
  9|  1                    2|  1| s2
 10|  2                     |  1| s3
 11|                 2      |  1| s4
 14|     1                  |  1| 0
 16|              1         |  1| 0
------------------------------------
8  : s4
9  : s3
10 : s2
11 : s1
17 : s0
18 : m
19 : b
20 : a

off priall$


on primat,acinfo$


optimize
     ghorner <<z:=a^2*b^2+10*a^2*m^6+a^2*m^2+2*a*b*m^4+2*b^2*m^6+b^2*m^2>>
     vorder m
     iname s;


Sumscheme :

   || EC|Far
------------
  0||  1| z
  3||  1| 2
  7||  1| 6
 10||  1| 9
------------



Productscheme :

   |  0  1  2| EC|Far
---------------------
  1|     2  2|  1| 0
  2|  2      |  1| 0
  4|        2|  1| 3
  5|     2   |  1| 3
  6|  2      |  1| 3
  8|     1  1|  2| 7
  9|  2      |  1| 7
 11|        2| 10| 10
 12|     2   |  2| 10
---------------------
0  : m
1  : b
2  : a

Number of operations in the input is: 

Number of (+/-) operations      : 5
Number of unary - operations    : 0
Number of * operations          : 8
Number of integer ^ operations  : 9
Number of / operations          : 0
Number of function applications : 0


s0 := b*a
s1 := b*b
s2 := a*a
s3 := m*m
z := s0*s0 + s3*(s1 + s2 + s3*(2*s0 + s3*(2*s1 + 10*s2)))

Number of operations after optimization is:

Number of (+/-) operations      : 5
Number of unary - operations    : 0
Number of * operations          : 11
Number of integer ^ operations  : 0
Number of / operations          : 0
Number of function applications : 0


Sumscheme :

   |  0  1  2| EC|Far
---------------------
  0|         |  1| z
  3|     1  1|  1| 2
  7|  2      |  1| 6
 10|     2 10|  1| 9
---------------------
0  : s0
1  : s1
2  : s2



Productscheme :

   |  3  4  5  9 10 11 12| EC|Far
---------------------------------
  1|           2         |  1| 0
  2|  1                  |  1| 0
  6|  1                  |  1| 3
  9|  1                  |  1| 7
 13|                 1  1|  1| s0
 14|                 2   |  1| s1
 15|                    2|  1| s2
 16|              2      |  1| s3
---------------------------------
3  : s3
4  : s2
5  : s1
9  : s0
10 : m
11 : b
12 : a

off exp,primat,acinfo$

 
q:=a+b$


r:=q+a+b$


optimize x:=a+b,q:=:q^2,p(q)::=:r iname s;



x := a + b
q := x*x
p(x) := 2*x

on exp$


clear q,r$



% A similar example follows.
% operator a$% Not necessary. Some differences between REDUCE 3.5 and REDUCE 3.6
% when dealing with indices.

on inputc$


k:=j:=1$


u:=c*x+d$


v:=sin(u)$


optimize {a(k,j):=v*(v^2*cos(u)^2+u),
          a(k,j)::=:v*(v^2*cos(u)^2+u)} iname s;


              2       2
a(1,1) := v*(v *cos(u)  + u)

                      2             3
a(1,1) := cos(c*x + d) *sin(c*x + d)  + sin(c*x + d)*c*x + sin(c*x + d)*d


s9 := cos(u)*v
a(1,1) := v*(u + s9*s9)
s6 := x*c + d
s5 := sin(s6)
s10 := s5*cos(s6)
a(1,1) := s5*(s6 + s10*s10)

off exp$


optimize {a(k,j):=v*(v^2*cos(u)^2+u),
          a(k,j)::=:v*(v^2*cos(u)^2+u)} iname s;


              2       2
a(1,1) := v*(v *cos(u)  + u)

                                 2             2
a(1,1) := (c*x + d + cos(c*x + d) *sin(c*x + d) )*sin(c*x + d)


s9 := cos(u)*v
a(1,1) := v*(u + s9*s9)
s6 := x*c + d
s5 := sin(s6)
s10 := s5*cos(s6)
a(1,1) := s5*(s6 + s10*s10)

off inputc,period$


optlang fortran$


optimize z:=(6*a+18*b+9*c+3*d+6*j+18*f+6*g+5*h+5*k+3)^13 iname s;



      s0=5*(h+k)+3*(3*c+d+1+6*(b+f)+2*(a+j+g))
      s3=s0*s0*s0
      s2=s3*s3
      z=s0*s2*s2

off ftch$


optimize z:=(6*a+18*b+9*c+3*d+6*j+18*f+6*g+5*h+5*k+3)^13 iname s;


      z=(5*(h+k)+3*(3*c+d+1+6*(b+f)+2*(a+j+g)))**13

optlang c$


optimize z:=(6*a+18*b+9*c+3*d+6*j+18*f+6*g+5*h+5*k+3)^13 iname s;



{
    s0=5*(h+k)+3*(3*c+d+1+6*(b+f)+2*(a+j+g));
    s3=s0*s0*s0;
    s2=s3*s3;
    z=s0*s2*s2;
}


% Note: C code never contains exponentiations.

on ftch$


optimize {x:=3*a*p,y:=3*a*q,z:=6*a*r+2*b*p,u:=6*a*d+2*b*q,
v:=9*a*c+4*b*d,w:=4*b} iname s;



{
    s2=3*a;
    x=s2*p;
    y=s2*q;
    s0=2*b;
    s3=6*a;
    z=s0*p+s3*r;
    u=s0*q+s3*d;
    w=4*b;
    v=w*d+9*c*a;
}

off ftch$


optlang fortran$


optimize {x:=3*a*p,y:=3*a*q,z:=6*a*r+2*b*p,u:=6*a*d+2*b*q,
v:=9*a*c+4*b*d,w:=4*b} iname s;


      x=3*p*a
      y=3*q*a
      z=2*b*p+6*r*a
      u=2*b*q+6*d*a
      v=4*d*b+9*c*a
      w=4*b

on ftch$


setlength 2$


optimize {x:=3*a*p,y:=3*a*q,z:=6*a*r+2*b*p,u:=6*a*d+2*b*q,
v:=9*a*c+4*b*d,w:=4*b} iname s;


      x=3*p*a
      y=3*q*a
      z=2*b*p+6*r*a
      u=2*b*q+6*d*a
      v=4*d*b+9*c*a
      w=4*b

resetlength$


optlang nil$



% Further reading: SCOPE 1.5 manual section 3.1, example 9 and section 3.2.

u:=a*x+2*b$


v:=sin(u)$


w:=cos(u)$


f:=v^2*w;


                                  2
f := cos(a*x + 2*b)*sin(a*x + 2*b)

off exp$


optimize f:=:f,g:=:f^2+f iname s$



s3 := x*a + 2*b
s2 := sin(s3)
f := s2*s2*cos(s3)
g := f*(f + 1)

alst:=aresults;


alst := {s3=a*x + 2*b,

         s2=sin(s3),

                     2
         f=cos(s3)*s2 ,

         g=(f + 1)*f}

restorables;


{f}

f;


f

arestore f;


f;


                             2
cos(a*x + 2*b)*sin(a*x + 2*b)

alst;


{s3=a*x + 2*b,

 s2=sin(s3),

                              2           2
 cos(a*x + 2*b)*sin(a*x + 2*b) =cos(s3)*s2 ,

                                 2                                   2
 g=(cos(a*x + 2*b)*sin(a*x + 2*b)  + 1)*cos(a*x + 2*b)*sin(a*x + 2*b) }

optimize f:=:f,g:=:f^2+f iname s$



s3 := x*a + 2*b
s2 := sin(s3)
f := s2*s2*cos(s3)
g := f*(f + 1)

alst:=aresults$


optimize f:=:f,g:=:f^2+f iname s$



g := f*(f + 1)

restoreall$


f;


f


% Further reading: SCOPE 1.5 manual section 3.1, example 8. 
%                  See also section 5.
%                  Also recommended: section 9.

clear a$


matrix a(2,2)$


a(1,1):=x+y+z$


a(1,2):=x*y$


a(2,1):=(x+y)*x*y$


a(2,2):=(x+2*y+3)^3-x$


on exp$


off fort,nat$


optimize detexp:=:det(a) out "expfile" iname s$



off exp$


optimize detnexp:=:det(a) out "nexpfile" iname t$



in expfile$


in nexpfile$


on nat$


detexp-detnexp;


0

system "rm expfile nexpfile"$



% Further reading: SCOPE 1.5 manual section 4.2, example 15.
% Although the output is similar, it is in general equivalent and
% not identical when using REDUCE 3.6 in stead of REDUCE 3.5. This
% is due to improvements in the simplification strategy.

on acinfo$


optimize 
   gstructr<<a;aa:=(x+y)^2;b:=(x+y)*(y+z);c:=(x+2*y)*(y+z)*(z+x)^2>>
name v iname s;


Number of operations in the input is: 

Number of (+/-) operations      : 8
Number of unary - operations    : 0
Number of * operations          : 8
Number of integer ^ operations  : 3
Number of / operations          : 0
Number of function applications : 0


v1 := y + z
a(1,1) := v1 + x
a(1,2) := y*x
v3 := y + x
a(2,1) := a(1,2)*v3
s6 := 2*y + x
s4 := s6 + 3
a(2,2) := s4*s4*s4 - x
aa := v3*v3
b := v1*v3
s5 := z + x
c := s6*s5*s5*v1

Number of operations after optimization is:

Number of (+/-) operations      : 7
Number of unary - operations    : 0
Number of * operations          : 10
Number of integer ^ operations  : 0
Number of / operations          : 0
Number of function applications : 5


alst:=
  algopt(algstructr({a,b=(x+y)^2,c=(x+y)*(y+z),d=(x+2*y)*(y+z)*(z+x)^2},v),s);


Number of operations in the input is: 

Number of (+/-) operations      : 8
Number of unary - operations    : 0
Number of * operations          : 8
Number of integer ^ operations  : 3
Number of / operations          : 0
Number of function applications : 0



Number of operations after optimization is:

Number of (+/-) operations      : 7
Number of unary - operations    : 0
Number of * operations          : 10
Number of integer ^ operations  : 0
Number of / operations          : 0
Number of function applications : 5


*** a declared operator 

alst := {v1=y + z,

         a(1,1)=v1 + x,

         a(1,2)=x*y,

         v3=x + y,

         a(2,1)=a(1,2)*v3,

         s6=x + 2*y,

         s4=s6 + 3,

                  3
         a(2,2)=s4  - x,

             2
         b=v3 ,

         c=v1*v3,

         s5=x + z,

             2
         d=s5 *s6*v1}

off acinfo$



% Further reading: SCOPE 1.5 manual section 4.3, example 16.

clear a$


procedure taylor(fx,x,x0,n);
 sub(x=x0,fx)+(for k:=1:n sum(sub(x=x0,df(fx,x,k))*(x-x0)^k/factorial(k)))$


hlst:={f1=taylor(e^x,x,0,4),f2=taylor(cos x,x,0,6)}$


on rounded$


hlst:=hlst;


                              3      2
hlst := {f1=0.0416666666667*(x  + 4*x  + 12*x + 24)*x + 1,

                                  4       2         2
         f2= - 0.00138888888889*(x  - 30*x  + 360)*x  + 1}

optimize alghorner(hlst,{x}) iname g$



g1 := x*x
g0 := g1*x
f1 := 1 + x*(0.166666666667*g1 + 0.0416666666667*g0 + 1 + 0.5*x)
f2 := 1 + g1*(0.0416666666667*g1 - 0.5 - 0.00138888888889*g0*x)

off rounded$



% Further reading: SCOPE 1.5 manual section 3.1, examples 6 and 7.

optimize z:=:for j:=2:6 sum a^(1/j) iname s$



       1/60
s0 := a
s8 := s0*s0
s7 := s8*s0
s5 := s8*s7
s3 := s5*s5
s2 := s8*s3
s1 := s7*s2
s4 := s5*s1
z := s3 + s2 + s1 + s4 + s4*s3

optimize z1:=a+sqrt(sin(a^2+b^2)), z2:=b+sqrt(sin(a^2+b^2)), 
         z3:=a+b+(a^2+b^2)^(1/2),  z4:=sqroot(a^2+b^2)+(a^2+b^2)^3, 
         z5:=a^2+b^2+cos(a^2+b^2), z6:=(a^2+b^2)^(1/3)+(a^2+b^2)^(1/6)  
iname s;



s6 := b*b + a*a
s8 := sqrt(sin(s6))
z1 := s8 + a
z2 := s8 + b
        1/6
s7 := s6
s9 := s7*s7
z3 := a + b + s9*s7
z4 := sqroot(s6) + s6*s6*s6
z5 := s6 + cos(s6)
z6 := s7 + s9


% Further reading: SCOPE 1.5 manual section 6, examples 18 and 19.

optlang fortran$


optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s
         declare <<x(4),a(4,4),y(5):real;b(5):integer>>;



      integer b(5),i,s10,s9
      real a(4,4),x(4),y(5)
      s10=i+1
      s9=i-1
      x(s10,s9)=a(s10,s9)+b(i)
      y(s9)=a(s9,s10)-b(i)

optlang c$


optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s
         declare <<x(4),a(4,4),y(5):real;b(5):integer>>;



int b[6],i,s10,s9;
float a[5][5],x[5],y[6];
{
    s10=i+1;
    s9=i-1;
    x[s10][s9]=a[s10][s9]+b[i];
    y[s9]=a[s9][s10]-b[i];
}

optlang  pascal$


optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s
         declare <<x(4),a(4,4),y(5):real;b(5):integer>>;



var
    s9,s10,i: integer;
    b: array[0..5] of integer;
    y: array[0..5] of real;
    x: array[0..4] of real;
    a: array[0..4,0..4] of real;
begin
    s10:=i+1;
    s9:=i-1;
    x[s10,s9]:=a[s10,s9]+b[i];
    y[s9]:=a[s9,s10]-b[i]
end;

optlang ratfor$


optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s
         declare <<x(4),a(4,4),y(5):real;b(5):integer>>;



integer b(5),i,s10,s9
real a(4,4),x(4),y(5)
{
    s10=i+1
    s9=i-1
    x(s10,s9)=a(s10,s9)+b(i)
    y(s9)=a(s9,s10)-b(i)
}

precision 7$


on rounded, double$


optlang fortran$


optimize x1:=2         *a + 10        *b,
         x2:=2.00001   *a + 10        *b,
         x3:=2         *a + 10.00001  *b,
         x4:=6         *a + 10        *b,
         x5:=2.0000001 *a + 10.000001 *b
iname s
declare << x1,x2,x3,x4,x5,a,b:real>>$



      double precision a,b,s1,s2,x1,x2,x3,x4,x5
      s1=2*a
      s2=10*b
      x1=s2+s1
      x2=s2+2.00001d0*a
      x3=s1+1.000001d1*b
      x4=s2+6*a
      x5=x1


% Further reading: SCOPE 1.5 manual section 7, example 20.
% Notice the double role of e: In the lhs as identifier. In the rhs as
% exponential function.
% Further notice that a is expected to be declared operator. This is
% due to lower level scope activities.

optimize a(1,x+1)  := g + h*r^f,
         b(y+1)    := a(1,2*x+1)*(g+h*r^f),
         c1        := (h*r)/g*a(2,1+x),
         c2        := c1*a(1,x+1) + sin(d),
         a(1,x+1)  := c1^(5/2),
         d         := b(y+1)*a(1,x+1),
         a(1,1+2*x):= (a(1,x+1)*b(y+1)*c)/(d*g^2),
         b(y+1)    := a(1,1+x)+b(y+1) + sin(d),
         a(1,x+1)  := b(y+1)*c + h/(g + sin(d)),
         d         := k*e + d*(a(1,1+x) + 3),
         e         := d*(a(1,1+x) + 3) + sin(d),
         f         := d*(3 + a(1,1+x)) + sin(d),
         g         := d*(3 + a(1,1+x)) + f
iname s
declare << a(5,5),b(7),c,c1,d,e,f,g,h,r:real*8; x,y:integer>>$


*** a declared operator 


      integer x,y,s0,s2,s6
      double precision c,h,r,s34,s3,c1,c2,s4,s24,b(7),a(5,5),s29,k,d,s33
     . ,e,f,g
      s0=x+1
      s34=r**f*h+g
      s2=1+y
      s6=2*x+1
      s3=s34*a(1,s6)
      c1=a(2,s0)*((r*h)/g)
      c2=dsin(d)+s34*c1
      s4=dsqrt(c1)*c1*c1
      d=s4*s3
      a(1,s6)=(d*c)/(g*g*d)
      s24=dsin(d)
      b(s2)=s4+s3+s24
      a(1,s0)=h/(g+s24)+b(s2)*c
      s29=3+a(1,s0)
      d=s29*d+dexp(1.0d0)*k
      s33=s29*d
      e=s33+dsin(d)
      f=dexp(1.0d0)
      g=s33+f


% Further reading: SCOPE 1.5 manual section 8, examples 21 and 22.
%                  Also recommended: section 9.

optlang nil$


delaydecs$


 gentran declare <<a,b,c,d,q,w: real>>$


 gentran a:=b+c$


 gentran d:=b+c$


 gentran <<q:=b+c;w:=b+c>>$


makedecs$

      double precision a,b,c,d,q,w
      a=b+c
      d=b+c
      q=b+c
      w=b+c

on gentranopt$


delaydecs$


 gentran declare <<a,b,c,d,q,w: real>>$


 gentran a:=b+c$




 gentran d:=b+c$




 gentran <<q:=b+c;w:=b+c>>$




makedecs$

      double precision b,c,a,d,q,w
      a=b+c
      d=b+c
      q=b+c
      w=q

off gentranopt$


delayopts$


 gentran declare <<a,b,c,d,q,w: real>>$


 gentran a:=b+c$


 gentran d:=b+c$


 gentran <<q:=b+c;w:=b+c>>$


makeopts$



      a=b+c
      d=a
      q=a
      w=a

delaydecs$


 gentran declare <<a,b,c,d,q,w: real>>$


 delayopts$


  gentran a:=b+c$


  gentran d:=b+c$


  gentran <<q:=b+c;w:=b+c>>$


 makeopts$




makedecs$

      double precision b,c,a,d,q,w
      a=b+c
      d=a
      q=a
      w=a

clear a,b,c,d,q,w$


matrix a(2,2)$


a:=mat(((b+c)*(c+d),(b+c+2)*(c+d-3)),((c+b-3)*(d+b),(c+b)*(d+b+4)));


     [  (b + c)*(c + d)    (c + 2 + b)*(d - 3 + c)]
a := [                                            ]
     [(c - 3 + b)*(b + d)    (d + 4 + b)*(b + c)  ]


gentranlang!*:='c$


delayopts$


 gentran aa:=:a$


makeopts$



{
    {
        G17=b+c;
        G18=c+d;
        aa[1][1]=G18*G17;
        aa[1][2]=(G18-3)*(G17+2);
        G16=b+d;
        aa[2][1]=G16*(G17-3);
        aa[2][2]=G17*(G16+4);
    }
}

end;
(TIME:  scope 2110 2120)