lib/Math/BigRat/t/big_ap.t Math::BigRat test
lib/Math/BigRat/t/bigfltpm.inc Math::BigRat test
lib/Math/BigRat/t/bigfltrt.t Math::BigRat test
+lib/Math/BigRat/t/biglog.t Math::BigRat test
lib/Math/BigRat/t/bigratpm.inc Math::BigRat test
lib/Math/BigRat/t/bigratpm.t Math::BigRat test
lib/Math/BigRat/t/bigrat.t Math::BigRat test
lib/Math/BigRat/t/bigratup.t test under $Math::BigInt::upgrade
+lib/Math/BigRat/t/bigroot.t Math::BigRat test
lib/Math/BigRat/t/requirer.t see if require works properly
lib/Math/BigRat/t/trap.t see if trap_nan and trap_inf work
lib/Math/Complex.pm A Complex package
@ISA = qw(Math::BigFloat);
-$VERSION = '0.19';
+$VERSION = '0.20';
use overload; # inherit overload from Math::BigFloat
# return (later set?) configuration data as hash ref
my $class = shift || 'Math::BigRat';
+ if (@_ == 1 && ref($_[0]) ne 'HASH')
+ {
+ my $cfg = $class->SUPER::config();
+ return $cfg->{$_[0]};
+ }
+
my $cfg = $class->SUPER::config(@_);
# now we need only to override the ones that are different from our parent
$x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) );
}
+sub bexp
+ {
+ # set up parameters
+ my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$a,$p,$r) = objectify(2,$class,@_);
+ }
+
+ return $x->binf() if $x->{sign} eq '+inf';
+ return $x->bzero() if $x->{sign} eq '-inf';
+
+ # we need to limit the accuracy to protect against overflow
+ my $fallback = 0;
+ my ($scale,@params);
+ ($x,@params) = $x->_find_round_parameters($a,$p,$r);
+
+ # also takes care of the "error in _find_round_parameters?" case
+ return $x if $x->{sign} eq 'NaN';
+
+ # no rounding at all, so must use fallback
+ if (scalar @params == 0)
+ {
+ # simulate old behaviour
+ $params[0] = $self->div_scale(); # and round to it as accuracy
+ $params[1] = undef; # P = undef
+ $scale = $params[0]+4; # at least four more for proper round
+ $params[2] = $r; # round mode by caller or undef
+ $fallback = 1; # to clear a/p afterwards
+ }
+ else
+ {
+ # the 4 below is empirical, and there might be cases where it's not enough...
+ $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+ }
+
+ return $x->bone(@params) if $x->is_zero();
+
+ # See the comments in Math::BigFloat on how this algorithm works.
+ # Basically we calculate A and B (where B is faculty(N)) so that A/B = e
+
+ my $x_org = $x->copy();
+ if ($scale <= 75)
+ {
+ # set $x directly from a cached string form
+ $x->{_n} = $MBI->_new("90933395208605785401971970164779391644753259799242");
+ $x->{_d} = $MBI->_new("33452526613163807108170062053440751665152000000000");
+ $x->{sign} = '+';
+ }
+ else
+ {
+ # compute A and B so that e = A / B.
+
+ # After some terms we end up with this, so we use it as a starting point:
+ my $A = $MBI->_new("90933395208605785401971970164779391644753259799242");
+ my $F = $MBI->_new(42); my $step = 42;
+
+ # Compute how many steps we need to take to get $A and $B sufficiently big
+ my $steps = Math::BigFloat::_len_to_steps($scale - 4);
+# print STDERR "# Doing $steps steps for ", $scale-4, " digits\n";
+ while ($step++ <= $steps)
+ {
+ # calculate $a * $f + 1
+ $A = $MBI->_mul($A, $F);
+ $A = $MBI->_inc($A);
+ # increment f
+ $F = $MBI->_inc($F);
+ }
+ # compute $B as factorial of $steps (this is faster than doing it manually)
+ my $B = $MBI->_fac($MBI->_new($steps));
+
+# print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n";
+
+ $x->{_n} = $A;
+ $x->{_d} = $B;
+ $x->{sign} = '+';
+ }
+
+ # $x contains now an estimate of e, with some surplus digits, so we can round
+ if (!$x_org->is_one())
+ {
+ # raise $x to the wanted power and round it in one step:
+ $x->bpow($x_org, @params);
+ }
+ else
+ {
+ # else just round the already computed result
+ delete $x->{_a}; delete $x->{_p};
+ # shortcut to not run through _find_round_parameters again
+ if (defined $params[0])
+ {
+ $x->bround($params[0],$params[2]); # then round accordingly
+ }
+ else
+ {
+ $x->bfround($params[1],$params[2]); # then round accordingly
+ }
+ }
+ if ($fallback)
+ {
+ # clear a/p after round, since user did not request it
+ delete $x->{_a}; delete $x->{_p};
+ }
+
+ $x;
+ }
+
+sub bnok
+ {
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,$class,@_);
+ }
+
+ # do it with floats
+ $x->_new_from_float( $x->_as_float()->bnok(Math::BigFloat->new("$y"),@r) );
+ }
+
sub _float_from_part
{
my $x = shift;
Works currently only for integers.
-=head2 blog()
-
-Is not yet implemented.
-
=head2 bround()/round()/bfround()
Are not yet implemented.
Please see the documentation in L<Math::BigInt> for further details.
+=head2 bexp()
+
+ $x->bexp($accuracy); # calculate e ** X
+
+Calculates two integers A and B so that A/B is equal to C<e ** $x>, where C<e> is
+Euler's number.
+
+This method was added in v0.20 of Math::BigRat (May 2007).
+
+See also L<blog()>.
+
+=head2 bnok()
+
+ $x->bnok($y); # x over y (binomial coefficient n over k)
+
+Calculates the binomial coefficient n over k, also called the "choose"
+function. The result is equivalent to:
+
+ ( n ) n!
+ | - | = -------
+ ( k ) k!(n-k)!
+
+This method was added in v0.20 of Math::BigRat (May 2007).
+
=head2 config()
use Data::Dumper;
$try .= '$x->facmp($y);';
} elsif ($f eq "fpow") {
$try .= '$x ** $y;';
+ } elsif ($f eq "bnok") {
+ $try .= '$x->bnok($y);';
} elsif ($f eq "froot") {
$try .= "$setup; \$x->froot(\$y);";
} elsif ($f eq "fadd") {
+27:+90:270
+1034:+804:415668
$div_scale = 40;
+&bnok
++inf:10:inf
+NaN:NaN:NaN
+NaN:1:NaN
+1:NaN:NaN
+1:1:1
+# k > n
+1:2:0
+2:3:0
+# k < 0
+1:-2:0
+# 7 over 3 = 35
+7:3:35
+7:6:1
+100:90:17310309456440
&flog
0::NaN
-1::NaN
plan tests => 1;
}
-use Math::BigRat::Test; # test via this Subclass
+use Math::BigRat::Test lib => 'Calc'; # test via this Subclass
use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
$class = "Math::BigRat::Test";
ok (1,1);
-# fails stil 185 tests
+# fails still too many tests
#require 'bigfltpm.inc'; # all tests here for sharing
--- /dev/null
+#!/usr/bin/perl -w
+
+# Test blog function (and bpow, since it uses blog), as well as bexp().
+
+use Test::More;
+use strict;
+
+BEGIN
+ {
+ $| = 1;
+ # to locate the testing files
+ my $location = $0; $location =~ s/biglog.t//i;
+ if ($ENV{PERL_CORE})
+ {
+ # testing with the core distribution
+ @INC = qw(../lib);
+ }
+ unshift @INC, '../lib';
+ if (-d 't')
+ {
+ chdir 't';
+ require File::Spec;
+ unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+ }
+ else
+ {
+ unshift @INC, $location;
+ }
+ print "# INC = @INC\n";
+
+ plan tests => 14;
+ }
+
+use Math::BigRat;
+
+my $cl = "Math::BigRat";
+
+#############################################################################
+# test log($n)
+
+# does not work yet
+#is ($cl->new(2)->blog(), '0', "blog(2)");
+#is ($cl->new(288)->blog(), '5',"blog(288)");
+#is ($cl->new(2000)->blog(), '7', "blog(2000)");
+
+#############################################################################
+# test exp($n)
+
+is ($cl->new(1)->bexp()->as_int(), '2', "bexp(1)");
+is ($cl->new(2)->bexp()->as_int(), '7',"bexp(2)");
+is ($cl->new(3)->bexp()->as_int(), '20', "bexp(3)");
+
+# rounding not implemented yet
+#is ($cl->new(3)->bexp(10), '20', "bexp(3,10)");
+
+# $x < 0 => NaN
+ok ($cl->new(-2)->blog(), 'NaN');
+ok ($cl->new(-1)->blog(), 'NaN');
+ok ($cl->new(-10)->blog(), 'NaN');
+ok ($cl->new(-2,2)->blog(), 'NaN');
+
+#############################################################################
+# test bexp() with cached results
+
+is ($cl->new(1)->bexp(),
+ '90933395208605785401971970164779391644753259799242' . '/' .
+ '33452526613163807108170062053440751665152000000000',
+ 'bexp(1)');
+#is ($cl->new(2)->bexp(40), $cl->new(1)->bexp(45)->bpow(2,40), 'bexp(2)');
+
+#is ($cl->new("12.5")->bexp(61), $cl->new(1)->bexp(65)->bpow(12.5,61), 'bexp(12.5)');
+
+#############################################################################
+# test bexp() with big values (non-cached)
+
+#is ($cl->new(1)->bexp(100),
+# '2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427',
+# 'bexp(100)');
+
+is ($cl->new("12.5")->bexp(91), $cl->new(1)->bexp(95)->bpow(12.5,91),
+ 'bexp(12.5) to 91 digits');
+
+#############################################################################
+# some integer results
+is ($cl->new(2)->bpow(32)->blog(2), '32', "2 ** 32");
+is ($cl->new(3)->bpow(32)->blog(3), '32', "3 ** 32");
+is ($cl->new(2)->bpow(65)->blog(2), '65', "2 ** 65");
+
+my $x = Math::BigInt->new( '777' ) ** 256;
+my $base = Math::BigInt->new( '12345678901234' );
+is ($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
+
+$x = Math::BigInt->new( '777' ) ** 777;
+$base = Math::BigInt->new( '777' );
+is ($x->copy()->blog($base), 777, 'blog(777**777, 777)');
+
+# all done
+1;
+
--- /dev/null
+#!/usr/bin/perl -w
+
+# Test broot function (and bsqrt() function, since it is used by broot()).
+
+# It is too slow to be simple included in bigfltpm.inc, where it would get
+# executed 3 times.
+
+# But it is better to test the numerical functionality, instead of not testing
+# it at all.
+
+use Test::More;
+use strict;
+
+BEGIN
+ {
+ $| = 1;
+ # to locate the testing files
+ my $location = $0; $location =~ s/bigroot.t//i;
+ if ($ENV{PERL_CORE})
+ {
+ # testing with the core distribution
+ @INC = qw(../lib);
+ }
+ unshift @INC, '../lib';
+ if (-d 't')
+ {
+ chdir 't';
+ require File::Spec;
+ unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+ }
+ else
+ {
+ unshift @INC, $location;
+ }
+ print "# INC = @INC\n";
+
+ plan tests => 4 * 2;
+ }
+
+use Math::BigFloat;
+use Math::BigInt;
+
+my $cl = "Math::BigFloat";
+my $c = "Math::BigInt";
+
+# 2 ** 240 =
+# 1766847064778384329583297500742918515827483896875618958121606201292619776
+
+# takes way too long
+#test_broot ('2','240', 8, undef, '1073741824');
+#test_broot ('2','240', 9, undef, '106528681.3099908308759836475139583940127');
+#test_broot ('2','120', 9, undef, '10321.27324073880096577298929482324664787');
+#test_broot ('2','120', 17, undef, '133.3268493632747279600707813049418888729');
+
+test_broot ('2','120', 8, undef, '32768');
+test_broot ('2','60', 8, undef, '181.0193359837561662466161566988413540569');
+test_broot ('2','60', 9, undef, '101.5936673259647663841091609134277286651');
+test_broot ('2','60', 17, undef, '11.54672461623965153271017217302844672562');
+
+sub test_broot
+ {
+ my ($x,$n,$y,$scale,$result) = @_;
+
+ my $s = $scale || 'undef';
+ is ($cl->new($x)->bpow($n)->broot($y,$scale),$result, "Try: $cl $x->bpow($n)->broot($y,$s) == $result");
+ $result =~ s/\..*//;
+ is ($c->new($x)->bpow($n)->broot($y,$scale),$result, "Try: $c $x->bpow($n)->broot($y,$s) == $result");
+ }
+
projects / p5sagit/p5-mst-13.2.git / commitdiff