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unit matheunit;
{$mode objfpc}{$H+}
interface
uses
Classes, SysUtils, Gmp, Math;
type
tExtPoint = record
x,y: extended;
end;
tExtPointArray = array of tExtPoint;
pTExtPointArray = ^tExtPointArray;
tLongintArray = array of longint;
pTLongintArray = ^tLongintArray;
tExtendedArray = array of extended;
function plus(a,b: tExtPoint): tExtPoint;
function durch(a: tExtPoint; b: extended): tExtPoint;
function myFrac(x: extended): extended;
function mpfToStr(f: mpf_t): string;
function signSqr(x: extended): extended; inline;
function mpfMyRoot(rad: mpf_t; wzlExp: int64): extended;
function myTimeToStr(t: extended): string;
function cmpStr(s1,s2: string): longint;
function mitte(s1,s2: string): string;
function myFloatToStr(x: extended): string;
function myStrToFloat(s: string): extended;
implementation
function plus(a,b: tExtPoint): tExtPoint;
begin
result.x:=a.x+b.x;
result.y:=a.y+b.y;
end;
function durch(a: tExtPoint; b: extended): tExtPoint;
begin
result.x:=a.x/b;
result.y:=a.y/b;
end;
function myFrac(x: extended): extended;
begin
result:=frac(x);
while result<0 do
result:=result+1;
end;
function mpfToStr(f: mpf_t): string;
var
ex: int64;
off: byte;
begin
result:=mpf_get_str(nil,ex,10,0,f);
off:=1+byte(pos('-',result)=1);
if result='' then
result:='0'
else if ex=1 then
result:=copy(result,1,off)+','+copy(result,off+1,length(result)-off)
else
result:=copy(result,1,off)+','+copy(result,off+1,length(result)-off)+' * 10^'+inttostr(ex-1);
end;
function signSqr(x: extended): extended;
begin
result:=sign(x)*sqr(x);
end;
function mpfMyRoot(rad: mpf_t; wzlExp: int64): extended;
var
ex: int64;
begin
result:=power(mpf_get_d_2exp(ex,rad),1/wzlExp);
result:=result*power(2,ex/wzlExp);
end;
function myTimeToStr(t: extended): string;
var
tim: int64;
begin
tim:=floor(t*24*60*60);
result:=inttostr(tim mod 10)+'s';
tim:=tim div 10;
if tim=0 then exit;
result:=inttostr(tim mod 6)+result;
tim:=tim div 6;
if tim=0 then exit;
result:=inttostr(tim mod 10)+'min '+result;
tim:=tim div 10;
if tim=0 then exit;
result:=inttostr(tim mod 6)+result;
tim:=tim div 6;
if tim=0 then exit;
result:=inttostr(tim mod 24)+'h '+result;
tim:=tim div 24;
if tim=0 then exit;
result:=' '+result;
if (tim mod 7)<>1 then
result:='e'+result;
result:=inttostr(tim mod 7)+'Tag'+result;
tim:=tim div 7;
if tim=0 then exit;
result:=' '+result;
if tim<>1 then
result:='n'+result;
result:=inttostr(tim)+'Woche'+result;
end;
function cmpStr(s1,s2: string): longint;
var
i: longint;
begin
for i:=1 to min(length(s1),length(s2)) do
if s1[i]<>s2[i] then begin
result:=2*byte(s1[i]>s2[i])-1;
exit;
end;
if length(s1)<>length(s2) then begin
result:=2*byte(length(s1)>length(s2))-1;
exit;
end;
result:=0;
end;
function mitte(s1,s2: string): string;
var
i: longint;
w,nw: word;
begin
setlength(result,max(length(s1),length(s2)));
w:=0;
for i:=length(result) downto 1 do begin // result:= "s1+s2";
if i<=length(s1) then
w:=w+byte(s1[i]);
if i<=length(s2) then
w:=w+byte(s2[i]);
result[i]:=char(w and $ff);
w:=w shr 8;
end;
result:=char(w)+result;
w:=0;
for i:=1 to length(result) do begin
nw:=byte(odd(byte(result[i])+w));
result[i]:=char((byte(result[i])+w) div 2);
w:=nw shl 8;
end;
if w<>0 then
result:=result+char(w div 2);
if result[1]<>#0 then begin
writeln('Fehler bei der Mittenfindeung!');
halt;
end;
delete(result,1,1);
end;
function myFloatToStr(x: extended): string;
var
i,e: longint;
begin
e:=0;
if x<0 then begin
result:='-';
x:=-x;
end
else
result:='';
if x=0 then begin
result:='0';
exit;
end;
while x<1 do begin
dec(e);
x:=x*10;
end;
while x>=10 do begin
inc(e);
x:=x/10;
end;
result:=result+char(ord('0')+floor(x))+'.';
for i:=0 to 20 do begin
x:=(x-floor(x))*10;
result:=result+char(ord('0')+floor(x));
end;
if e<>0 then
result:=result+'E'+inttostr(e);
end;
function myStrToFloat(s: string): extended;
var
i,e: longint;
neg: boolean;
begin
if pos('E',s)>0 then begin
e:=strtoint(rightStr(s,length(s)-pos('E',s)));
delete(s,pos('E',s),length(s));
end
else e:=0;
if pos('.',s)=0 then begin
result:=strtoint(s)*power(10,e);
exit;
end;
neg:=leftStr(s,1)='-';
if neg then
delete(s,1,1);
if pos('.',s)=2 then begin
result:=0;
for i:=length(s) downto 3 do
result:=result/10 + ord(s[i])-ord('0');
result:=result/10 + ord(s[1])-ord('0');
end
else result:=strtofloat(s);
result:=result*power(10,e);
if neg then
result:=-result;
end;
end.
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