Thiele's interpolation formula: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
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3.14159265358979
3.1415926535898</pre>
=={{header|Phix}}==
Line 1,317 ⟶ 1,257:
3.1415926535897953
</lang>
=={{header|Raku}}==
(formerly Perl 6)
{{Works with|rakudo|2018.09}}<br>
Implemented to parallel the generalized formula, making for clearer, but slower, code. Offsetting that, the use of <code>Promise</code> allows concurrent calculations, so running all three types of interpolation should not take any longer than running just one (presuming available cores).
<lang perl6># reciprocal difference:
multi sub ρ(&f, @x where * < 1) { 0 } # Identity
multi sub ρ(&f, @x where * == 1) { &f(@x[0]) }
multi sub ρ(&f, @x where * > 1) {
( @x[0] - @x[* - 1] ) # ( x - x[n] )
/ (ρ(&f, @x[^(@x - 1)]) # / ( ρ[n-1](x[0], ..., x[n-1])
- ρ(&f, @x[1..^@x]) ) # - ρ[n-1](x[1], ..., x[n]) )
+ ρ(&f, @x[1..^(@x - 1)]); # + ρ[n-2](x[1], ..., x[n-1])
}
# Thiele:
multi sub thiele($x, %f, $ord where { $ord == +%f }) { 1 } # Identity
multi sub thiele($x, %f, $ord) {
my &f = {%f{$^a}}; # f(x) as a table lookup
# must sort hash keys to maintain order between invocations
my $a = ρ(&f, %f.keys.sort[^($ord +1)]);
my $b = ρ(&f, %f.keys.sort[^($ord -1)]);
my $num = $x - %f.keys.sort[$ord];
my $cont = thiele($x, %f, $ord +1);
# Thiele always takes this form:
return $a - $b + ( $num / $cont );
}
## Demo
sub mk-inv(&fn, $d, $lim) {
my %h;
for 0..$lim { %h{ &fn($_ * $d) } = $_ * $d }
return %h;
}
sub MAIN($tblsz = 12) {
my ($sin_pi, $cos_pi, $tan_pi);
my $p1 = Promise.start( { my %invsin = mk-inv(&sin, 0.05, $tblsz); $sin_pi = 6 * thiele(0.5, %invsin, 0) } );
my $p2 = Promise.start( { my %invcos = mk-inv(&cos, 0.05, $tblsz); $cos_pi = 3 * thiele(0.5, %invcos, 0) } );
my $p3 = Promise.start( { my %invtan = mk-inv(&tan, 0.05, $tblsz); $tan_pi = 4 * thiele(1.0, %invtan, 0) } );
await $p1, $p2, $p3;
say "pi = {pi}";
say "estimations using a table of $tblsz elements:";
say "sin interpolation: $sin_pi";
say "cos interpolation: $cos_pi";
say "tan interpolation: $tan_pi";
}</lang>
Output:
<pre>pi = 3.14159265358979
estimations using a table of 12 elements:
sin interpolation: 3.14159265358961
cos interpolation: 3.1387286696692
tan interpolation: 3.14159090545243</pre>
=={{header|Sidef}}==
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