Pathological floating point problems: Difference between revisions
Pathological floating point problems (view source)
Revision as of 21:44, 24 March 2021
, 3 years agoAdded Delphi example
m (Renamed "decimal" to "nim-decimal".) |
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</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{libheader| Velthuis.BigIntegers}}
{{libheader| Velthuis.BigRationals}}
{{libheader| Velthuis.BigDecimals}}
{{Trans|Go}}
<lang Delphi>
program Pathological_floating_point_problems;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
Velthuis.BigIntegers,
Velthuis.BigRationals,
Velthuis.BigDecimals;
type
TBalance = record
e, d: BigInteger;
end;
procedure Sequence(Precision: Integer);
var
v, v1, c111, c1130, c3000, t2, t3: BigRational;
n: integer;
begin
BigDecimal.DefaultPrecision := Precision;
v1 := 2;
v := -4;
n := 2;
c111 := BigRational(111);
c1130 := BigRational(1130);
c3000 := BigRational(3000);
var r :=
function(): BigRational
begin
t3 := v * v1;
t3 := BigRational.Create(BigDecimal.Divide(c3000, t3));
t2 := BigRational.Create(BigDecimal.Divide(c1130, v));
result := c111 - t2;
result := result + t3;
end;
writeln(' n sequence value');
for var x in [3, 4, 5, 6, 7, 8, 20, 30, 50, 100] do
begin
while n < x do
begin
var tmp := BigRational.Create(v);
v := BigRational.Create(r());
v1 := BigRational.Create(tmp);
inc(n);
end;
var f := double(v);
writeln(format('%3d %19.16f', [n, f]));
end;
end;
procedure Bank();
var
balance: TBalance;
m, one, ef, df: BigInteger;
e, b: BigDecimal;
begin
balance.e := 1;
balance.d := -1;
one := BigInteger.One;
for var y := 1 to 25 do
begin
m := y;
balance.e := m * balance.e;
balance.d := m * balance.d;
balance.d := balance.d - one;
end;
e := BigDecimal.Create('2.71828182845904523536028747135');
ef := balance.e;
df := balance.d;
b := e * ef;
b := b + df;
writeln(format('Bank balance after 25 years: $%.2f', [b.AsDouble]));
end;
function f(a, b: Double): Double;
var
a1, a2, b1, b2, b4, b6, b8, two, t1, t21, t2, t3, t4, t23: BigDecimal;
begin
var fp :=
function(x: double): BigDecimal
begin
Result := BigDecimal.Create(x);
end;
a1 := fp(a);
b1 := fp(b);
a2 := a1 * a1;
b2 := b1 * b1;
b4 := b2 * b2;
b6 := b2 * b4;
b8 := b4 * b4;
two := fp(2);
t1 := fp(333.75);
t1 := t1 * b6;
t21 := fp(11);
t21 := t21 * a2 * b2;
t23 := fp(121);
t23 := t23 * b4;
t2 := t21 - b6;
t2 := (t2 - t23) - two;
t2 := a2 * t2;
t3 := fp(5.5);
t3 := t3 * b8;
t4 := two * b1;
t4 := a1 / t4;
var s := t1 + t2;
s := s + t3;
s := s + t4;
result := s.AsDouble;
end;
procedure Rump();
var
a, b: Double;
begin
a := 77617;
b := 33096;
writeln(format('Rump f(%g, %g): %g', [a, b, f(a, b)]));
end;
{ TBigRationalHelper }
begin
for var Precision in [100, 200] do
begin
writeln(#10'Precision: ', Precision);
sequence(Precision);
bank();
rump();
end;
readln;
end.</lang>
{{out}}
<pre>Precision: 100
n sequence value
3 18,5000000000000000
4 9,3783783783783790
5 7,8011527377521617
6 7,1544144809752490
7 6,8067847369236327
8 6,5926327687044388
20 6,0435521101892693
30 6,0067860930312058
50 6,0001758466271866
100 100,0000000000000000
Bank balance after 25 years: $0,04
Rump f(77617, 33096): -0,827396059946821
Precision: 200
n sequence value
3 18,5000000000000000
4 9,3783783783783772
5 7,8011527377521617
6 7,1544144809752499
7 6,8067847369236336
8 6,5926327687044388
20 6,0435521101892693
30 6,0067860930312067
50 6,0001758466271875
100 6,0000000193194776
Bank balance after 25 years: $0,04
Rump f(77617, 33096): -0,827396059946821</pre>
=={{header|Excel}}==
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