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)