Sat May 30 16:09:14 PDT 1992
REDUCE 3.4.1, 15-Jul-92 ...
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Time: 0 ms
4: 4: % 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 := 0
symbolic ws;
0
% 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);
1.18440746497E-4342953505
off roundbf;
% Now let us evaluate pi.
pi;
3.14159265359
% Let us try a higher precision.
precision 50;
12
pi;
3.141 59265 35897 93238 46264 33832 79502 88419 71693 99375 1
% Now find the cosine of pi/6.
cos(ws/6);
0.866 02540 37844 38646 76372 31707 52936 18347 14026 26905 19
% 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;
26253 74126 40768 743.9 99999 99999 92500 72597 19818 56888 8
yy;
- 1.281 52565 59456 09277 51597 49532 17051 34 E -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=3.187 67264 27121 08627 20192 99705 25369 23265 10535 71859 4
pn=3.141 68029 32976 53293 91807 04245 60009 38279 57194 38815 4
pn=3.141 59265 38954 46496 00291 47588 18043 48610 88792 37261 3
pn=3.141 59265 35897 93238 46636 06027 06631 32175 77024 11342 4
pn=3.141 59265 35897 93238 46264 33832 79502 88419 71699 49164 7
pn=3.141 59265 35897 93238 46264 33832 79502 88419 71693 99375 1
pn=3.141 59265 35897 93238 46264 33832 79502 88419 71693 99375 1
3.141 59265 35897 93238 46264 33832 79502 88419 71693 99375 1
% The limit is obviously.
pi;
3.141 59265 35897 93238 46264 33832 79502 88419 71693 99375 1
end;
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Time: 1904 ms
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Quitting
Sat May 30 16:09:16 PDT 1992