reduce-historical/r34/xlog/rounded.log

Sat Jun 29 13:37:56 PDT 1991
REDUCE 3.4, 15-Jul-91 ...

1: 1: 
2: 2: 
3: 3: % 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;

4: 4: 
Quitting
Sat Jun 29 13:38:02 PDT 1991