Pathological floating point problems: Difference between revisions

=={{header|Perl}}==

All three tasks can be solved by using either the <code>bigrat</code> or <code>bignum</code> core modules.

Both approaches are used, as demonstration.

==== Convergent series ====

The constants in the equation must be represented with a decimal point (even just <code>111.</code>) so that

they are treated as rationals, not integers.

<lang perl>use bigrat;

@s = qw(2, -4);

for my $n (2..99) {

$s[$n]= 111.0 - 1130.0/$s[-1] + 3000.0/($s[-1]*$s[-2]);

}

for $n (3..8, 20, 30, 35, 50, 100) {

($nu,$de) = $s[$n-1] =~ m#^(\d+)/(\d+)#;;

printf "n = %3d %18.15f\n", $n, $nu/$de;

}</lang>

{{out}}

<pre>n = 3 18.500000000000000

n = 4 9.378378378378379

n = 5 7.801152737752162

n = 6 7.154414480975249

n = 7 6.806784736923633

n = 8 6.592632768704439

n = 20 6.043552110189269

n = 30 6.006786093031206

n = 35 6.002716153954351

n = 50 6.000175846627188

n = 100 6.000000019319478</pre>

==== Chaotic bank society ====

The value of 𝑒 is imported from a module, but could also be calculated, as is done in

[[Calculating_the_value_of_e#Perl|Calculating the value of e]]

<lang perl>use bignum qw(bexp);

$e = bexp(1,43);

$years = 25;

$balance = $e - 1;

print "Starting balance, \$(e-1): \$$balance\n";

for $i (1..$years) { $balance = $i * $balance - 1 }

printf "After year %d, you will have \$%1.15g in your account.\n", $years, $balance;</lang>

{{out}}

<pre>Starting balance, $(e-1): $1.718281828459045235360287471352662497757247

After year 25, you will have $0.0399387296732302 in your account.</pre>

==== Rump's example ====

<lang perl>use bignum;

$a = 77617;

$b = 33096;

printf "%0.16f\n", 333.75*$b**6 + $a**2 * ( 11*$a**2 * $b**2 - $b**6 - 121*$b**4 - 2) + 5.5*$b**8 + $a/(2*$b);</lang>

{{out}}

<pre>-0.8273960599468214</pre>