[P5P] RFC: BigInt and overloading of sin/cos

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Moin,
AFAICS, the only methods in question are cos() and sin(), and they are only
triggered via overload. (e.g., there is currently no bcos() routine in
Big(Int|Float)).

However, for completeness, bcos() and bsin() should be added - probably alone
because the code for the overload section would get to big and clunky.

Actually, sin() and cos() in Math::Big are selfcontained, so we would only
need to copy/import these and the rest can stay happily in Math::Big. Which
makes the "let's copy it over and have Math::Big::cos() just call
Math::BigFLoat::bcos()" argument look even better.

There is also another reason to copy the code over apart from beeing less
hairy:

Math::Big uses BigFloat to calculate the result. So Math::BigInt::bcos() would
suddenly pull in Math::Big and Math::BigFloat. Ugh.

I lean towards to include an all-integer method of calculating sin() and cos()
in Calc, and then use it in BigInt and BigFloat, whith BigInt retunring 0 or
1 alway (truncated to integer) or upgrading to BigFloat if wanted.

However, thats some more work..

Best wishes,

Tels

PS: Here is the code from Math::Big, cos() is very similiar:

sub sin
{
# calculate sinus
# first argument is x, so that result is sin(x)
# Second argument is accuracy (number of significant digits), it
# stops when at least so much plus one digits are 'stable' and then
# rounds it. Default is 42.
my $x = shift || 0;
my $d = abs(shift || 42); $d = abs($d)+1;

$x = Math::BigFloat->new($x) if ref($x) ne 'Math::BigFloat';
my $diff = Math::BigFloat->new('1e-'.$d);

# taylor: x^3 x^5 x^7 x^9
# sin = x - --- + --- - --- + --- ...
# 3! 5! 7! 9!

# difference for each term is thus x^2 and 1,2

my $sin = $x->copy(); my $last = 0;
my $x2 = $x*$x;
my $over = $x2 * $x; my $below = 6; my $factorial = Math::BigInt->new(4);
my $sign = 1;
while ($sin ne $last) # no $x-$last > $diff because bdiv() limit on accuracy
{
$last = $sin->copy();
if ($sign == 0)
{
$sin += $over->copy()->bdiv($below,$d);
}
else
{
$sin -= $over->copy()->bdiv($below,$d);
}
$sign = 1-$sign; # alternate
$over *= $x2; # $x*$x
$below *= $factorial; $factorial++; # n*(n+1)
$below *= $factorial; $factorial++;
}
return $sin->round($d-1);
}

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Signed on Sun Oct 26 13:23:42 2003 with key 0x93B84C15.
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Moin,
I opted no to the following plan:

* Add an option ':fallback' to BigInt, which tricks overload to make
cos(Math::BigInt->new(1)) equivalent to cos(1)
* add option to Math::Big to overload cos(), sin(), atan2() and exp() so that
they produce BigFloats.

So:

* default BigInt dies with "no method found.
* use BigInt ':fallback'; is equivalent to no BigInt at all AFA
cos/sin/atan/exp are concerned (e.g. cos(1) returns 0.54etc to 10 digits
approcimately)
* use BigInt ':fallback'; use Math::Big qw/:cos :sin :atan2 :exp/; will
produce BigFloats (selectively)

There is only one snag:

te@null:~> cat cos.pl
#!/usr/bin/perl -w

package Test;

# without the "''" nomethod is never called
use overload
'""' => sub { $$_[0]} ;

sub new
{
my $a = $_[0];
bless \$a, 'Test';
}

sub import
{
overload->import (
nomethod => sub {
&{'sCORE::' . $_[3]}( $_[0], $_[1], $_[2] );
print "nomethod ", join(":", @_), "\n";
},
);
}

package main;

use Test;

print CORE::cos(1),"\n";
print cos(Test->new(1)),"\n";

te@null:~> perl cos.pl
0.54030230586814
Undefined subroutine &sCORE::cos called at cos.pl line 18.

I tried UNIVERSAL::cos, main::cos etc, but they all come back as "undefined".
However, a plain "CORE::cos" works just fine. What do I do wrong? *puzzled*

Best wishes,

Tels

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Signed on Sat Nov 1 17:31:45 2003 with key 0x93B84C15.
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PGP key on http://bloodgate.com/tels.asc or per email.

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Moin,
FYI: Note the typo here ("sCORE"), but it still doesn't work if you fix it to
"correct" 'CORE::' . $_[3]...

Using somple $_[3] does also not work, since it then dies with "Undefined
Test::cos called"...

Best wishes,

Tels

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Signed on Sat Nov 1 18:46:52 2003 with key 0x93B84C15.
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