@@ -1,256 +1,256 @@
-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)
+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)