⟦1072da152⟧

GIER Text (HTML)

begin
_____
   procedure Test(a);
   _________
   string a;
   ______
   begin
   _____
      writecr;
      writetext(a);
      outsp(50);
      outtext(|<
              <
Test |,a)
     >
   end;
   ___
   Test(|<10.127|);
        <       >
   begin
   _____
      integer i,j,j1;
      _______
      real ul,arg,a1,max,m1,maxarg,ma1,exlog,e1,r1,r11,r2,r21,h,h1,rm,ru;
      ____
      outtext(|<    double ln, double exp, exlog|, outcr,outcr,outcr,
              <                                 >
              |<arg1   ln(arg1)|,outsp(23),|<rel.error|,outcr);
              <                >           <          >
      for i:=100 step 50 until 300 do
      ___        ____    _____     __
      begin
      _____
         max:=m1:=0;
         j1:=0;
         for j:=i-50 step 1 until i do
         ___         ____   _____   __
         begin
         _____
            assign(arg,div(j,100));
            assign(exlog,doubleexp(doubleln(arg)));
            assign(h,sub(arg,exlog));
            if abs(h)>abs(max) then
            __                 ____
            begin
            _____
               assign(max,h);
               assign(maxarg,arg)
            end
            ___
         end;
         ___
         outcr; output(|d.dd|,maxarg,outsp(3));
                       <    >
         doubleoutput(20,doubleln(maxarg),outsp(3));
         output(|-d.d10+dd|,div(max,maxarg))
                <        >
      end;
      ___
      outcr; outcr;
      outtext(|<arg2|,outsp(29),|<ln(arg2)|,outsp(24),
              <     >           <         >
              |<abs.error2  rel.error2|,outcr);
              <                       >
      assign(r1,div(1,mult(power(10,64),power(10,76))));
      for j:=j while r1<10125 do
      ___      _____         __
      begin
      _____
         max:=m1:=0;
         ul:=21019⨯r1;
         assign(r2,r1);
         for j:=j while r2<ul do
         ___      _____       __
         begin
         _____
            assign(exlog,doubleexp(doubleln(r2)));
            assign(h,sub(r2,exlog));
            if sub(double abs(h),doubleabs(max))>0 then
            __                                     ____
            begin
            _____
               assign(max,h);
               assign(maxarg,r2)
            end;
            ___
            assign(r2,mult(10,r2))
         end;
         ___
         outcr;
         doubleoutput(20,maxarg, outsp(5),doubleln(maxarg),outsp(5));
         output(|-d.d10+dd|,div(max,maxarg),outsp(4),
                <        >
                           div(div(max,maxarg),doubleln(maxarg)));
         assign(r1,if 0.9<r1∧r1<1.1∧-,(r1=1∧r11=0) then 1 else
                   __                              ____   ____
                     mult(r1,power(10,20)))
      end;
      ___
      outchar(42)
   end;
   ___
   Test(|<10.128|);
        <       >
   begin
   _____
      integer q,q1,y,y1,upy,lowy,maxq,maxupy,maxlowy;
      _______
      real max,m1,up,u1,low,l1,log,l2,dif,d1,M,M1,e,e1,h,h1;
      ____
      procedure print(u,u1);
      _________
      value u,u1;
      _____
      real u,u1;
      ____
      begin
      _____
         real w,w1;
         ____
         assign(w,doubleln(u));
         outcr;
         output(|dd.dd|,u,outsp(2));
                <     >
         doubleoutput(20,w,outsp(2),mult(w,M))
      end;
      ___
      doubleinput(M,e);
      outtext(|<   double ln|,outcr,outcr,outcr);
              <             >
      max:=-1; m1:=0; q1:=y1:=0;
      for q:=11 step 1 until 19,20 step 10 until 90 do
      ___       ____   _____       ____    _____    __
      begin
      _____
         assign(up,sub(doubleln(div(q,10)),1)); assign(low,add(up,2));
         for y:=1 step 1 until 100 do
         ___      ____   _____     __
         begin
         _____
            assign(log,sub(doubleln(div(q⨯y,100)),doubleln(div(y,10))));
            if sub(log,up)>0 then
            __               ____
            begin
            _____
               upy:=y;
               assign(up,log)
            end;
            ___
            if sub(log,low)<0 then
            __                ____
            begin
            _____
               lowy:=y;
               assign(low,log)
            end
            ___
         end;
         ___
         assign(dif,sub(up,low));
         if sub(dif,max)>0 then
         __                ____
         begin
         _____
            maxq:=q;
            maxupy:=upy;
            maxlowy:=lowy;
            assign(max,dif)
         end
         ___
      end;
      ___
      outcr;
      output(|nd.d|,maxq/10);
             <    >
      outsp(4);
      output(|d.d10+dd|,max);
             <       >
      outcr;
      outcr;
      outtext(|<  x     ln(x)                         log10(x)|);
              <                                              >
      for y:=maxlowy,maxupy do
      ___                   __
      begin
      _____
         outcr;
         assign(h,div(maxq⨯y,100));
         print(h,h1);
         assign(h,div(y,10));
         print(h,h1)
      end;
      ___
      outcr;
      print(1,0);
      outcr;
      print(e,e1);
      outcr;
      print(10,0);
      outcr;
      outchar(42)
   end;
   ___
   Test(|<10.129|);
        <       >
   begin
   _____
      integer k;
      _______
      real arg,arg1,max,max1,maxarg,maxarg1,konst,konst1,hj,hj1,
      ____
           basearg,basearg1,relative error,relative error 1;
      outtext(|<    double sqrt|,outcr,outcr,outcr,|<arg|,outsp(28),
              <                >                   <    >
              |<sqrt(arg)|,outsp(22),|<rel.error|,outcr);
              <          >           <          >
      assign(konst,div(11,10));
      for k:=-100 step 50 until 150 do
      ___         ____    _____     __
      begin
      _____
         assign(basearg,if k<0 then div(1,power(10,-k)) else
                        __     ____                     ____
                        if k<150 then power(10,k) else
                        __       ____             ____
                        mult(power(10,64),power(10,86)));
         max := -1; max1 := 0;
         assign(arg,div(basearg,power(10,50)));
         for k:=k while sub(arg,basearg)<0 do
         ___      _____                    __
         begin
         _____
            assign(hj,doublesqrt(arg));
            assign(relative error,div(doubleabs(sub(mult(hj,hj),arg)),arg));
            if sub(relative error,max)>0 then
            __                           ____
            begin
            _____
               assign(max,relative error);
               assign(maxarg,arg)
            end;
            ___
            assign(arg,mult(arg,konst))
         end;
         ___
         doubleoutput(20,outcr,maxarg,outsp(3),doublesqrt(maxarg),outsp(3));
         output(|d.d10-dd|,max);
                <       >
      end;
      ___
      outchar(42)
   end;
   ___
   Test(|<10.130|);
        <       >
   begin
   _____
      real x,x1,h,h1;
      ____
      outtext(|<    double exp|,outcr,outcr,outcr,|<arg|,
              <               >                   <    >
              outsp(27),|<exp(arg)|,outcr,outcr);
                        <         >
      doubleoutput(20,0,outsp(2),doubleexp(0));
      x:=-1; x1:=0;
      for x:=2⨯x while x>-1050 do
      ___        _____        __
      begin
      _____
         assign(h,doubleexp(x));
         if h_0 then
         __  <  ____
         begin
         _____
            outcr;
            doubleoutput(20,x,outsp(2),h,outcr);
            assign(h,doubleexp(mult(3,x)/4));
            doubleoutput(20,mult(3,x)/4,outsp(2),h);
            x:=-1;
            x1:=0;
            goto B
            ____
         end
         ___
      end;
      ___
B:    for x:=x/2 while abs(x)>10-20 do
      ___        _____             __
      begin
      _____
         assign(h,doubleexp(x));
         if h=1∧h1=0 then
         __          ____
         begin
         _____
            outcr;
            doubleoutput(20,x,outsp(2),h,outcr,
                            mult(3,x)/2,outsp(2),
                            doubleexp(mult(3,x)/2));
            if x<0
            __
            then begin x:=1; goto B end
            ____ _____       ____   ___
            else goto A
            ____ ____
         end
         ___
      end;
      ___
A:    for x:=1,x⨯2 while x<512 do
      ___          _____       __
         doubleoutput(20,outcr,x,outsp(2),doubleexp(x));
      outchar(42)
   end;
   ___
   Test(|<10.131|);
        <       >
   begin
   _____
      integer n,n1,i,j,j1;
      _______
      real max,m1,arg,a1,plog,pl1,ppow,pp1,h,h1,maxarg,ma1;
      ____
      outtext(|<    double exp,double ln|,outcr,outcr,outcr,|<n|,outsp(4),
              <                         >                   <  >
              |<arg|,outsp(4),|<abs error|,outsp(3),|<rel error|,outcr);
              <    >          <          >          <          >
      n1:=0;
      for n:=2,3,5,10 do
      ___             __
      begin
      _____
         outcr;
         output(|nd|,n,outsp(3));
                <  >
         for i:=100 step 50 until 300 do
         ___        ____    _____     __
         begin
         _____
            max:=m1:=0; j1:=0;
            for j:=i-50 step 1 until i do
            ___         ____   _____   __
            begin
            _____
               assign(arg,div(j,100));
               assign(plog,doubleexp(mult(n,doubleln(arg))));
               assign(ppow,power(arg,n));
               assign(h,sub(plog,ppow));
               if abs(h)>abs(max) then
               __                 ____
               begin
               _____
                  assign(max,h);
                  assign(maxarg,arg)
               end
               ___
            end;
            ___
            output(|d.dd|,maxarg); outsp(3);
                   <    >
            assign(h,div(max,power(maxarg,n)));
            output(|-d.dd10+dd|,max,outsp(3),h,outcr,outsp(5))
                   <         >
         end;
         ___
         outcr
      end;
      ___
      doubleoutput(20,outcr,doubleln(doubleexp(1)),outcr,
                   doubleln(doubleln(doubleexp(doubleexp(div(1,100))))));
      outchar(42)
   end;
   ___
   Test(|<10.132|);
        <       >
   begin
   _____
      integer i,j,j1;
      _______
      real arg,a1,max,m1,maxarg,ma1,logex,e1,h,h1;
      ____
      outtext(|<    double ln, double exp, logex|,outcr,outcr,outcr,
              <                                 >
              |<arg    ln(exp(arg))|,outsp(18),|<rel.error|,outcr);
              <                    >           <          >
      for i:=100 step 50 until 300 do
      ___        ____    _____     __
      begin
      _____
         max:=m1:=0; j1:=0;
         for j:=i-50 step 1 until i do
         ___         ____   _____   __
         begin
         _____
            assign(arg,div(j,100));
            assign(logex,doubleln(doubleexp(arg)));
            assign(h,sub(arg,logex));
            if abs(h)>abs(max) then
            __                 ____
            begin
            _____
               assign(max,h);
               assign(maxarg,arg)
            end
            ___
         end;
         ___
         outcr;
         output(|d.dd|,maxarg,outsp(3));
                <    >
         doubleoutput(20,doubleln(doubleexp(maxarg))); outsp(3);
         output(|-d.d10+dd|, max/maxarg)
                <        >
      end;
      ___
      outchar(42)
   end;
   ___
   Test(|<10.133|);
        <       >
   begin
   _____
      integer i,i1,k,k1;
      _______
      real s,s1,x,x1,led,led1,de,de1;
      ____
      outtext(|<    double exp|,outcr,outcr,outcr,|<x|,outsp(6),
              <               >                   <  >
              |<exp(x) - Taylor|,outsp(14),|<exp(x)|,outsp(27),
              <                >           <       >
              |<abs.error   rel.error|,outcr);
              <                      >
      i1:=k1:=0;
      for i:=-50,-20,-15,-10 step 1 until 10, 15,20,50 do
      ___                    ____   _____              __
      begin
      _____
         assign(s,1);
         assign(led,s);
         assign(x,div(i,10));
         k:=2;
L:       k:=k+1;
         assign(led,div(mult(x,led),k));
         assign(s,add(s,led));
         if abs(led)>10-20 then goto L;
         __               ____ ____
         assign(s,add(1,add(x,mult(mult(x,x),div(s,2)))));
         output(|-d.d|,outcr,x,outsp(2));
                <    >
         assign(de,doubleexp(x));
         doubleoutput(20,s,outsp(2),de,outsp(4));
         output(|-d.d10-dd|,sub(s,de),outsp(4),div(sub(s,de),s));
                <        >
      end;
      ___
      outchar(42)
   end;
   ___
   Test(|<10.134|);
        <       >
   begin
   _____
      integer i,i1,k,k1,m,j;
      _______
      real pi,pi1,s,s1,x,x1,xh,xh1,xsq,xsq1,led,led1,max,max1,
      ____
      maxh,maxh1,maxi,maxs,maxs1,maxx,maxx1;
      outtext(|<    double sin|,outcr,outcr,outcr,|<pi|,
              <               >                   <   >
              outsp(26),|<degrees  sin(x) - Taylor|,
                        <                         >
              outsp(15),|<sin(x)|,outsp(23),|<abs.error  rel.error|,outcr);
                        <       >           <                     >
      i1:=k1:=0;
      for j:=1,2 do
      ___        __
      begin
      _____
         assign(pi,doubleinone);
         doubleoutput(20,outcr,outcr,pi);
         assign(xh,div(pi,1800));
         for m:=400 step 400 until 4000 do
         ___        ____     _____      __
         begin
         _____
            max:=max1:=0;
            for i:=m-400 step 5 until m do
            ___          ____   _____   __
            begin
            _____
               assign(x,mult(xh,i));
               assign(xsq,mult(x,x));
               assign(s,assign(led,div(xsq,20)));
               k:=4;
L:             k:=k+2;
               assign(led,div(div(mult(minus(xsq),led),k),k+1));
               assign(s,add(s,led));
               if abs(led)>mult(10-20,doubleabs(s)) then goto L;
               __                                  ____ ____
               assign(s,add(x,div(mult(sub(s,1),mult(xsq,x)),6)));
               assign(maxh,doubleabs(sub(s,doublesin(x))));
               if sub(maxh,max)>0 then
               __                 ____
               begin
               _____
                  assign(max,maxh);
                  maxi:=i;
                  assign(maxs,s);
                  assign(maxx,x)
               end
               ___
            end;
            ___
            output(|ndd.d|,maxi/10,outsp(4));
                   <     >
            assign(x,maxx);
            assign(s,doublesin(x));
            doubleoutput(20,maxs,outsp(2),s,outsp(3));
            output(|-d.d10-dd|,max,outsp(3),
                   <        >
                   div(max,add(doubleabs(s),doubleabs(mult(x,doublecos(x))))));
            outcr;
            outsp(28)
         end;
         ___
      end
      ___
      outchar(42)
   end;
   ___
   Test(|<10.135|);
        <       >
   begin
   _____
      integer i,i1,k,k1,m,j;
      _______
      real pi,pi1,s,s1,x,x1,xh,xh1,xsq,xsq1,led,led1,max,max1,
      ____
      maxh,maxh1,maxi,maxs,maxs1,maxx,maxx1;
      outtext(|<    double cos|,outcr,outcr,outcr,|<pi|,
              <               >                   <   >
              outsp(26),|<degrees  cos(x) - Taylor|,
                        <                         >
              outsp(15),|<cos(x)|,outsp(24),|<abs.error  rel.error|,outcr);
                        <       >           <                     >
      i1:=k1:=0;
      for j:=1,2 do
      ___        __
      begin
      _____
         assign(pi,doubleinone);
         doubleoutput(20,outcr,outcr,pi);
         assign(xh,div(pi,1800));
         for m:=400 step 400 until 4000 do
         ___        ____     _____      __
         begin
         _____
            max:=max1:=0;
            for i:=m-400 step 5 until m do
            ___          ____   _____   __
            begin
            _____
               assign(x,mult(xh,i));
               assign(xsq,mult(x,x));
               assign(s,assign(led,div(xsq,12)));
               k:=3;
L:             k:=k+2;
               assign(led,div(div(mult(minus(xsq),led),k),k+1));
               assign(s,add(s,led));
               if abs(led)>mult(10-20,doubleabs(s)) then goto L;
               __                                  ____ ____
               assign(s,add(1,div(mult(sub(s,1),xsq),2)));
               assign(maxh,doubleabs(sub(s,doublecos(x))));
               if sub(maxh,max)>0 then
               __                 ____
               begin
               _____
                  assign(max,maxh);
                  maxi:=i;
                  assign(maxs,s);
                  assign(maxx,x)
               end
               ___
            end;
            ___
            output(|ndd.d|,maxi/10,outsp(4));
                   <     >
            assign(x,maxx);
            assign(s,doublecos(x));
            doubleoutput(20,maxs,outsp(2),s,outsp(3));
            output(|-d.d10-dd|,max,outsp(3),
                   <        >
                   div(max,add(doubleabs(s),doubleabs(mult(x,doublesin(x))))));
            outcr; outsp(28)
         end;
         ___
      end;
      ___
      outchar(42)
   end;
   ___
   Test(|<10.136|);
        <       >
   begin
   _____
      integer m,i,i1,k,k1,maxi,j;
      _______
      real pi,pi1,max,max1,angle,angle1,arg,arg1,standard,standard1,led,led1,
      ____
      sum,sum1,pow,pow1,argsq,argsq1,maxarg,maxarg1,maxstd,maxstd1;
      outtext(|<    double arctan|,outcr,outcr,outcr);
              <                  >
      i1:=k1:=0;
      for j:=1,2 do
      ___        __
      begin
      _____
         assign(pi,doubleinone);
         outcr;
         doubleoutput(20,outtext(|<pi = |),pi,outcr);
                                 <      >
         outtext(outcr,|<degr.  x|,outsp(27),|<arctan(x)|,outsp(20),
                       <         >           <          >
             |<arctan(x) - Taylor|,outsp(11),|<arctan/pi⨯180|,
             <                   >           <              >
             outsp(16),|<rel.error|,outcr);
                       <          >
         for m:=100 step if m<200 then 100 else 500 until 5200 do
         ___        ____ __       ____     ____     _____      __
         begin
         _____
            assign(max,-1);
            for i:=m-(if m_200 then 100 else 500) step
            ___       __  <    ____     ____      ____
                 if m_200 then 1 else 10 until m do
                 __  <    ____   ____    _____   __
            begin
            _____
               assign(angle,mult(pi,div(i,18000)));
               assign(arg,div(doublesin(angle),doublecos(angle)));
               if i<2700 then
               __        ____
               begin
               _____
                  assign(pow,minus(power(arg,3)));
                  assign(argsq,minus(mult(arg,arg)));
                  k:=3;
                  assign(sum,0);
L:                assign(pow,mult(pow,argsq));
                  k:=k+2;
                  assign(led,div(pow,k));
                  assign(sum,add(sum,led));
                  if sub(doubleabs(led),mult(10-20,doubleabs(sum)))>0
                  __
                    then goto L;
                    ____ ____
                  assign(standard,add(mult(argsq,div(arg,3)),add(sum,arg)));
               end
               ___
               else assign(standard,angle);
               ____
               assign(angle,doublearctan(arg));
               if sub(doubleabs(sub(standard,angle)),max)>0 then
               __                                           ____
               begin
               _____
                  maxi:=i;
                  assign(maxarg,arg);
                  assign(maxstd,standard);
                  assign(max,doubleabs(sub(standard,angle)))
               end
               ___
            end;
            ___
            output(|nd.dd|,outcr,maxi/100,outsp(1));
                   <     >
            assign(angle,doublearctan(maxarg));
            doubleoutput(20,maxarg,outsp(1),angle,outsp(1),maxstd,outsp(1),
                            mult(180,div(angle,pi)));
            output(|-d.d10-dd|,outsp(1),div(max,add(angle,10-21)))
                   <        >
         end;
         ___
      end;
      ___
      outchar(42)
   end
   ___
end;
___
data double ln:     0.43429 44819 03251 82765, 2.71828 18284 59045 23536
data double sin:    3.14159 26535 89793 23835, 3.14159 26535 89793 23855
data double cos:    3.14159 26535 89793 23835, 3.14159 26535 89793 23855
data double arctan: 3.14159 26535 89793 23835, 3.14159 26535 89793 23855
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