Change 31364 by [EMAIL PROTECTED] on 2007/06/11 15:18:27
Subject: pidigits benchmark and bpi() method in
Math::BigFloat/Math::BigInt, take 7 [PATCH]
From: Tels <[EMAIL PROTECTED]>
Date: Fri, 8 Jun 2007 19:29:41 +0200
Message-Id: <[EMAIL PROTECTED]>
Affected files ...
... //depot/perl/lib/Math/BigFloat.pm#73 edit
... //depot/perl/lib/Math/BigInt.pm#81 edit
... //depot/perl/lib/Math/BigInt/t/bare_mbf.t#24 edit
... //depot/perl/lib/Math/BigInt/t/bare_mbi.t#27 edit
... //depot/perl/lib/Math/BigInt/t/bigfltpm.inc#32 edit
... //depot/perl/lib/Math/BigInt/t/bigfltpm.t#35 edit
... //depot/perl/lib/Math/BigInt/t/bigintpm.inc#32 edit
... //depot/perl/lib/Math/BigInt/t/bigintpm.t#42 edit
... //depot/perl/lib/Math/BigInt/t/sub_mbf.t#28 edit
... //depot/perl/lib/Math/BigInt/t/sub_mbi.t#32 edit
... //depot/perl/lib/Math/BigInt/t/with_sub.t#18 edit
Differences ...
==== //depot/perl/lib/Math/BigFloat.pm#73 (text) ====
Index: perl/lib/Math/BigFloat.pm
--- perl/lib/Math/BigFloat.pm#72~31330~ 2007-06-03 09:23:03.000000000 -0700
+++ perl/lib/Math/BigFloat.pm 2007-06-11 08:18:27.000000000 -0700
@@ -16,7 +16,8 @@
require 5.006002;
require Exporter;
[EMAIL PROTECTED] = qw(Math::BigInt);
[EMAIL PROTECTED] = qw/Math::BigInt/;
[EMAIL PROTECTED] = qw/bpi/;
use strict;
# $_trap_inf/$_trap_nan are internal and should never be accessed from outside
@@ -2324,6 +2325,137 @@
}
###############################################################################
+# trigonometric functions
+
+# helper function for bpi()
+
+sub _signed_sub
+ {
+ my ($a, $s, $b) = @_;
+
+ if ($s == 0)
+ {
+ # $a and $b are negativ: -> add
+ $MBI->_add($a, $b);
+ }
+ else
+ {
+ my $c = $MBI->_acmp($a,$b);
+ # $a positiv, $b negativ
+ if ($c >= 0)
+ {
+ $MBI->_sub($a,$b);
+ }
+ else
+ {
+ # make negativ
+ $a = $MBI->_sub( $MBI->_copy($b), $a);
+ $s = 0;
+ }
+ }
+
+ ($a,$s);
+ }
+
+sub _signed_add
+ {
+ my ($a, $s, $b) = @_;
+
+ if ($s == 1)
+ {
+ # $a and $b are positiv: -> add
+ $MBI->_add($a, $b);
+ }
+ else
+ {
+ my $c = $MBI->_acmp($a,$b);
+ # $a positiv, $b negativ
+ if ($c >= 0)
+ {
+ $MBI->_sub($a,$b);
+ }
+ else
+ {
+ # make positiv
+ $a = $MBI->_sub( $MBI->_copy($b), $a);
+ $s = 1;
+ }
+ }
+
+ ($a,$s);
+ }
+
+sub bpi
+ {
+ # Calculate PI to N digits (including the 3 before the dot).
+
+ # The basic algorithm is the one implemented in:
+
+ # The Computer Language Shootout
+ # http://shootout.alioth.debian.org/
+ #
+ # contributed by Robert Bradshaw
+ # modified by Ruud H.G.van Tol
+ # modified by Emanuele Zeppieri
+
+ # We re-implement it here by using the low-level library directly. Also,
+ # the functions consume() and extract_digit() were inlined and some
+ # rendundand operations ( like *= 1 ) were removed.
+
+ my ($self,$n) = @_;
+ if (@_ == 1)
+ {
+ # called like Math::BigFloat::bpi(10);
+ $n = $self; $self = $class;
+ }
+ $self = ref($self) if ref($self);
+ $n = 40 if !defined $n || $n < 1;
+
+ my $z0 = $MBI->_one();
+ my $z1 = $MBI->_zero();
+ my $z2 = $MBI->_one();
+ my $ten = $MBI->_ten();
+ my $three = $MBI->_new(3);
+ my ($s, $d, $e, $r); my $k = 0; my $z1_sign = 0;
+
+ # main loop
+ for (1..$n)
+ {
+ while ( 1 < 3 )
+ {
+ if ($MBI->_acmp($z0,$z2) != 1)
+ {
+ # my $o = $z0 * 3 + $z1;
+ my $o = $MBI->_mul( $MBI->_copy($z0), $three);
+ $z1_sign == 0 ? $MBI->_sub( $o, $z1) : $MBI->_add( $o, $z1);
+ ($d,$r) = $MBI->_div( $MBI->_copy($o), $z2 );
+ $d = $MBI->_num($d);
+ $e = $MBI->_num( scalar $MBI->_div( $MBI->_add($o, $z0), $z2 ) );
+ last if $d == $e;
+ }
+ $k++;
+ my $k2 = $MBI->_new( 2*$k+1 );
+ # mul works regardless of the sign of $z1 since $k is always positive
+ $MBI->_mul( $z1, $k2 );
+ ($z1, $z1_sign) = _signed_add($z1, $z1_sign, $MBI->_mul(
$MBI->_new(4*$k+2), $z0 ) );
+ $MBI->_mul( $z0, $MBI->_new($k) );
+ $MBI->_mul( $z2, $k2 );
+ }
+ $MBI->_mul( $z1, $ten );
+ ($z1, $z1_sign) = _signed_sub($z1, $z1_sign, $MBI->_mul(
$MBI->_new(10*$d), $z2 ) );
+ $MBI->_mul( $z0, $ten );
+ $s .= $d;
+ }
+
+ my $x = $self->new(0);
+ $x->{_es} = '-';
+ $x->{_e} = $MBI->_new(length($s)-1);
+ $x->{_m} = $MBI->_new($s);
+
+ $x;
+ }
+
+###############################################################################
# rounding functions
sub bfround
@@ -2728,11 +2860,8 @@
# register us with MBI to get notified of future lib changes
Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } );
-
- # any non :constant stuff is handled by our parent, Exporter
- # even if @_ is empty, to give it a chance
- $self->SUPER::import(@a); # for subclasses
- $self->export_to_level(1,$self,@a); # need this, too
+
+ $self->export_to_level(1,$self,@a); # export wanted functions
}
sub bnorm
@@ -2887,13 +3016,16 @@
use Math::BigFloat;
# Number creation
- $x = Math::BigFloat->new($str); # defaults to 0
- $nan = Math::BigFloat->bnan(); # create a NotANumber
- $zero = Math::BigFloat->bzero(); # create a +0
- $inf = Math::BigFloat->binf(); # create a +inf
- $inf = Math::BigFloat->binf('-'); # create a -inf
- $one = Math::BigFloat->bone(); # create a +1
- $one = Math::BigFloat->bone('-'); # create a -1
+ my $x = Math::BigFloat->new($str); # defaults to 0
+ my $y = $x->copy(); # make a true copy
+ my $nan = Math::BigFloat->bnan(); # create a NotANumber
+ my $zero = Math::BigFloat->bzero(); # create a +0
+ my $inf = Math::BigFloat->binf(); # create a +inf
+ my $inf = Math::BigFloat->binf('-'); # create a -inf
+ my $one = Math::BigFloat->bone(); # create a +1
+ my $mone = Math::BigFloat->bone('-'); # create a -1
+
+ my $pi = Math::BigFloat->bpi(100); # PI to 100 digits
# Testing
$x->is_zero(); # true if arg is +0
@@ -3253,6 +3385,14 @@
This method was added in v1.84 of Math::BigInt (April 2007).
+=head2 bpi()
+
+ print Math::BigFloat->bpi(100), "\n";
+
+Calculate PI to N digits (including the 3 before the dot).
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
=head1 Autocreating constants
After C<use Math::BigFloat ':constant'> all the floating point constants
@@ -3329,6 +3469,14 @@
However, this request is ignored, as the current code now uses the low-level
math libary for directly storing the number parts.
+=head1 EXPORTS
+
+C<Math::BigFloat> exports nothing by default, but can export the C<bpi()>
method:
+
+ use Math::BigFloat qw/bpi/;
+
+ print bpi(10), "\n";
+
=head1 BUGS
Please see the file BUGS in the CPAN distribution Math::BigInt for known bugs.
==== //depot/perl/lib/Math/BigInt.pm#81 (text) ====
Index: perl/lib/Math/BigInt.pm
--- perl/lib/Math/BigInt.pm#80~31330~ 2007-06-03 09:23:03.000000000 -0700
+++ perl/lib/Math/BigInt.pm 2007-06-11 08:18:27.000000000 -0700
@@ -2831,6 +2831,27 @@
}
###############################################################################
+# trigonometric functions
+
+sub bpi
+ {
+ # Calculate PI to N digits. Unless upgrading is in effect, returns the
+ # result truncated to an integer, that is, always returns '3'.
+ my ($self,$n) = @_;
+ if (@_ == 1)
+ {
+ # called like Math::BigInt::bpi(10);
+ $n = $self; $self = $class;
+ }
+ $self = ref($self) if ref($self);
+
+ return $upgrade->new($n) if defined $upgrade;
+
+ # hard-wired to "3"
+ $self->new(3);
+ }
+
+###############################################################################
# this method returns 0 if the object can be modified, or 1 if not.
# We use a fast constant sub() here, to avoid costly calls. Subclasses
# may override it with special code (f.i. Math::BigInt::Constant does so)
@@ -2865,14 +2886,17 @@
my $n = 1; my $sign = '-';
# Number creation
- $x = Math::BigInt->new($str); # defaults to 0
- $y = $x->copy(); # make a true copy
- $nan = Math::BigInt->bnan(); # create a NotANumber
- $zero = Math::BigInt->bzero(); # create a +0
- $inf = Math::BigInt->binf(); # create a +inf
- $inf = Math::BigInt->binf('-'); # create a -inf
- $one = Math::BigInt->bone(); # create a +1
- $one = Math::BigInt->bone('-'); # create a -1
+ my $x = Math::BigInt->new($str); # defaults to 0
+ my $y = $x->copy(); # make a true copy
+ my $nan = Math::BigInt->bnan(); # create a NotANumber
+ my $zero = Math::BigInt->bzero(); # create a +0
+ my $inf = Math::BigInt->binf(); # create a +inf
+ my $inf = Math::BigInt->binf('-'); # create a -inf
+ my $one = Math::BigInt->bone(); # create a +1
+ my $mone = Math::BigInt->bone('-'); # create a -1
+
+ my $pi = Math::BigInt->bpi(); # returns '3'
+ # see Math::BigFloat::bpi()
$h = Math::BigInt->new('0x123'); # from hexadecimal
$b = Math::BigInt->new('0b101'); # from binary
@@ -3497,6 +3521,23 @@
This method was added in v1.84 of Math::BigInt (April 2007).
+=head2 bpi()
+
+ print Math::BigInt->bpi(100), "\n"; # 3
+
+Returns PI truncated to an integer, with the argument being ignored. that
+is it always returns C<3>.
+
+If upgrading is in effect, returns PI to N digits (including the "3"
+before the dot):
+
+ use Math::BigFloat;
+ use Math::BigInt upgrade => Math::BigFloat;
+ print Math::BigInt->bpi(3), "\n"; # 3.14
+ print Math::BigInt->bpi(100), "\n"; # 3.1415....
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
=head2 blsft()
$x->blsft($y); # left shift in base 2
@@ -4385,6 +4426,13 @@
arguments are of the class mentioned in $upgrade (This might change in later
versions to a more sophisticated scheme):
+=head1 EXPORTS
+
+C<Math::BigInt> exports nothing by default, but can export the following
methods:
+
+ bgcd
+ blcm
+
=head1 BUGS
=over 2
==== //depot/perl/lib/Math/BigInt/t/bare_mbf.t#24 (text) ====
Index: perl/lib/Math/BigInt/t/bare_mbf.t
--- perl/lib/Math/BigInt/t/bare_mbf.t#23~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/bare_mbf.t 2007-06-11 08:18:27.000000000 -0700
@@ -27,7 +27,7 @@
}
print "# INC = @INC\n";
- plan tests => 2064;
+ plan tests => 2070;
}
use Math::BigFloat lib => 'BareCalc';
==== //depot/perl/lib/Math/BigInt/t/bare_mbi.t#27 (text) ====
Index: perl/lib/Math/BigInt/t/bare_mbi.t
--- perl/lib/Math/BigInt/t/bare_mbi.t#26~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/bare_mbi.t 2007-06-11 08:18:27.000000000 -0700
@@ -26,7 +26,7 @@
}
print "# INC = @INC\n";
- plan tests => 3093;
+ plan tests => 3099;
}
use Math::BigInt lib => 'BareCalc';
==== //depot/perl/lib/Math/BigInt/t/bigfltpm.inc#32 (text) ====
Index: perl/lib/Math/BigInt/t/bigfltpm.inc
--- perl/lib/Math/BigInt/t/bigfltpm.inc#31~31159~ 2007-05-07
02:47:00.000000000 -0700
+++ perl/lib/Math/BigInt/t/bigfltpm.inc 2007-06-11 08:18:27.000000000 -0700
@@ -63,6 +63,8 @@
# some is_xxx test function
} elsif ($f =~ /^is_(zero|one|negative|positive|odd|even|nan|int)$/) {
$try .= "\$x->$f();";
+ } elsif ($f eq "bpi") {
+ $try .= '$class->bpi($x);';
} elsif ($f eq "finc") {
$try .= '++$x;';
} elsif ($f eq "fdec") {
@@ -399,6 +401,10 @@
+27:+90:270
+1034:+804:415668
$div_scale = 40;
+&bpi
+77:3.1415926535897932384626433832795028841971693993751058209749445923078164062862
++0:3.141592653589793238462643383279502884197
+11:3.1415926535
&bnok
+inf:10:inf
NaN:NaN:NaN
==== //depot/perl/lib/Math/BigInt/t/bigfltpm.t#35 (xtext) ====
Index: perl/lib/Math/BigInt/t/bigfltpm.t
--- perl/lib/Math/BigInt/t/bigfltpm.t#34~31285~ 2007-05-28 03:17:22.000000000
-0700
+++ perl/lib/Math/BigInt/t/bigfltpm.t 2007-06-11 08:18:27.000000000 -0700
@@ -26,7 +26,7 @@
}
print "# INC = @INC\n";
- plan tests => 2064
+ plan tests => 2070
+ 5; # own tests
}
==== //depot/perl/lib/Math/BigInt/t/bigintpm.inc#32 (text) ====
Index: perl/lib/Math/BigInt/t/bigintpm.inc
--- perl/lib/Math/BigInt/t/bigintpm.inc#31~31159~ 2007-05-07
02:47:00.000000000 -0700
+++ perl/lib/Math/BigInt/t/bigintpm.inc 2007-06-11 08:18:27.000000000 -0700
@@ -91,6 +91,8 @@
$try .= '"$m,$e";';
}elsif ($f eq "bexp"){
$try .= "\$x->bexp();";
+ } elsif ($f eq "bpi"){
+ $try .= "$class\->bpi(\$x);";
} else {
# binary ops
$try .= "\$y = $class->new('$args[1]');";
@@ -2232,6 +2234,10 @@
inf:inf
1:2
2:7
+&bpi
+77:3
++0:3
+11:3
# see t/bignok.t for more tests
&bnok
+inf:10:inf
==== //depot/perl/lib/Math/BigInt/t/bigintpm.t#42 (xtext) ====
Index: perl/lib/Math/BigInt/t/bigintpm.t
--- perl/lib/Math/BigInt/t/bigintpm.t#41~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/bigintpm.t 2007-06-11 08:18:27.000000000 -0700
@@ -10,7 +10,7 @@
my $location = $0; $location =~ s/bigintpm.t//;
unshift @INC, $location; # to locate the testing files
chdir 't' if -d 't';
- plan tests => 3093;
+ plan tests => 3099;
}
use Math::BigInt lib => 'Calc';
==== //depot/perl/lib/Math/BigInt/t/sub_mbf.t#28 (xtext) ====
Index: perl/lib/Math/BigInt/t/sub_mbf.t
--- perl/lib/Math/BigInt/t/sub_mbf.t#27~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/sub_mbf.t 2007-06-11 08:18:27.000000000 -0700
@@ -26,7 +26,7 @@
}
print "# INC = @INC\n";
- plan tests => 2064
+ plan tests => 2070
+ 6; # + our own tests
}
==== //depot/perl/lib/Math/BigInt/t/sub_mbi.t#32 (xtext) ====
Index: perl/lib/Math/BigInt/t/sub_mbi.t
--- perl/lib/Math/BigInt/t/sub_mbi.t#31~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/sub_mbi.t 2007-06-11 08:18:27.000000000 -0700
@@ -26,7 +26,7 @@
}
print "# INC = @INC\n";
- plan tests => 3093
+ plan tests => 3099
+ 5; # +5 own tests
}
==== //depot/perl/lib/Math/BigInt/t/with_sub.t#18 (text) ====
Index: perl/lib/Math/BigInt/t/with_sub.t
--- perl/lib/Math/BigInt/t/with_sub.t#17~31159~ 2007-05-07 02:47:00.000000000
-0700
+++ perl/lib/Math/BigInt/t/with_sub.t 2007-06-11 08:18:27.000000000 -0700
@@ -28,7 +28,7 @@
}
print "# INC = @INC\n";
- plan tests => 2064
+ plan tests => 2070
+ 1;
}
End of Patch.
