REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
% Tests in the exact mode.
x := 1/2;
1
x := ---
2
y := x + 0.7;
6
y := ---
5
% Tests in approximate mode.
on rounded;
y;
1.2
% as expected not converted to approximate form.
z := y+1.2;
z := 2.4
z/3;
0.8
% Let's raise this to a high power.
ws^24;
0.00472236648287
% Now a high exponent value.
% 10.2^821;
% Elementary function evaluation.
cos(pi);
- 1
symbolic ws;
(!*sq ((!:rd!: . -1.0) . 1) t)
z := sin(pi);
z := 1.22460635382e-16
symbolic ws;
(!*sq ((!:rd!: . 1.2246063538224e-016) . 1) t)
% Handling very small quantities.
% With normal defaults, underflows are converted to 0.
exp(-100000.1**2);
0
% However, if you really want that small number, roundbf can be used.
on roundbf;
exp(-100000.1**2);
1.18441281937e-4342953505
off roundbf;
% Now let us evaluate pi.
pi;
3.14159265359
% Let us try a higher precision.
precision 50;
12
pi;
3.1415926535897932384626433832795028841971693993751
% Now find the cosine of pi/6.
cos(ws/6);
0.86602540378443864676372317075293618347140262690519
% This should be the sqrt(3)/2.
ws**2;
0.75
%Here are some well known examples which show the power of this system.
precision 10;
50
% This should give the usual default again.
let xx=e**(pi*sqrt(163));
let yy=1-2*cos((6*log(2)+log(10005))/sqrt(163));
% First notice that xx looks like an integer.
xx;
2.625374126e+17
% and that yy looks like zero.
yy;
0
% but of course it's an illusion.
precision 50;
10
xx;
2.6253741264076874399999999999925007259719818568888e+17
yy;
- 1.2815256559456092775159749532170513334408547400481e-16
%now let's look at an unusual way of finding an old friend;
precision 50;
50
procedure agm;
<<a := 1$ b := 1/sqrt 2$ u:= 1/4$ x := 1$ pn := 4$ repeat
<<p := pn;
y := a; a := (a+b)/2; b := sqrt(y*b); % Arith-geom mean.
u := u-x*(a-y)**2; x := 2*x; pn := a**2/u;
write "pn=",pn>> until pn>=p; p>>;
agm
let ag=agm();
ag;
pn=3.1876726427121086272019299705253692326510535718594
pn=3.1416802932976532939180704245600093827957194388154
pn=3.1415926538954464960029147588180434861088792372613
pn=3.1415926535897932384663606027066313217577024113424
pn=3.1415926535897932384626433832795028841971699491647
pn=3.1415926535897932384626433832795028841971693993751
pn=3.1415926535897932384626433832795028841971693993751
3.1415926535897932384626433832795028841971693993751
% The limit is obviously.
pi;
3.1415926535897932384626433832795028841971693993751
end;
(TIME: rounded 190 190)