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Re: [OT] Function to do x**y for |y|<1 w/o ** operator.

by salva (Monsignor)
on Feb 20, 2013 at 11:37 UTC ( #1019768=note: print w/ replies, xml ) Need Help??

in reply to [OT] Function to do x**y for |y|<1 w/o ** operator.

Another solution based on the fact that a floating point number is actually a sum of powers of 2.

For 0 <= y <= 0, it holds that y = b0*20 + b1*2-1 + b2*2-2 + b3*2-3 + ...

And so, xy = xb0*20 + b1*2-1 + b2*2-2 + b3*2-3 + ... = xb0*20 * xb1*2-1 * xb2*2-2 * xb3*2-3 * ... = Πi, bi≠0 x2-i

Which in Perl becomes...

#!/usr/bin/perl use strict; use warnings; my ($X, $Y, $n) = @ARGV; $n ||= 20; my $Z = $X ** $Y; my ($neg, $y) = ($Y < 0 ? (1, -$Y) : (0, $Y)); $y > 1 and die "Y is out of range"; my $bit = 1; my $x = $X; my $z = 1; while ($y) { if ($y >= $bit) { $y -= $bit; $z *= $x; } $bit /= 2; $x = sqrt($x); } $z = 1/$z if $neg; my $e = abs($z - $X ** $Y); print "z=$z, e=$e\n";

sqrt is also an expensive operation. If you have to calculate xy for different values of y while x stays constant, you may be able to speed up the process creating a table with the values of x2-i.

Alternatively, you can write a function to calculate ex (using a table with the values of e2i), and then calculate xy as elog(x)*y.

update: there are also several implementations of exp(x) freely available, for instance, the one in OpenBSD is here.

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