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This queue is for tickets about the Math-BigFloat CPAN distribution.

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The Basics
Id: 43460
Status: open
Priority: 0/
Queue: Math-BigFloat

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Owner: Nobody in particular
Requestors: nir.nussbaum [...] gmail.com
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AdminCc:

Bug Information
Severity: Important
Broken in: (no value)
Fixed in: (no value)



Subject: Bug in Math::BigFloat - gives wrong results for bpow and bexp
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Hello, I'm working with Perl 5.10 and tried it on Ubuntu and Feodora. bexp gives wrong result for high numbers (negative) and takes ages to calculate, if it is a real negative number such as -394.84010945716266885 (or even -394.8). bpow gave also wrong result for power -394.8 of e. For numbers like -394 it would give the right result. The code: my $i=Math::BigFloat->new(-394.84010945715266885, 20)->bexp(); print ("exp: ".exp(-394.84010945715266885).", BigFloat exp: $i\n"); I'd expect it to give the same results, no? The output: exp: 3.33517962278651e-172, BigFloat exp: 19871330168979164802000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000 Would be happy to hear from you. Best regards, Nir.
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Attached is a patch to fix. This is caused by needing far more precision in the intermediate calculations. The easy fix is shown in "Fast Algorithms for High-Precision Computations of Elementary Functions" by Brent, 2006. When x < 0, use exp(x) = 1/exp(-x). For example: perl -Mbignum -E 'say 45.6**-28.4' before: -295.151342321403826190692606470102755169 after: 0.000000000000000000000000000000000000000000000007680658721702948549500271947332317125487 I will point out that that paper also shows methods to speed up the calculation by substantial amounts. A simple demonstration is calculating -8000.8->bexp() with the current code, then with line 1201 in bexp changed from: $x->bpow($x_org, @params); to: $x->bpow(scalar $x_org->bdiv(16,$scale+5),$scale+5)->bpow(16, @params); which runs over 400x faster for me (and passes the test suite, and agrees with PARI/GP). A real patch would be dynamic and also consider things like expm1 or other methods.
Subject: bigfloat-bpow-fix.patch
--- lib/Math/BigFloat.pm.orig 2013-10-30 13:55:42.426664527 -0700 +++ lib/Math/BigFloat.pm 2013-10-30 13:55:47.262664515 -0700 @@ -2342,6 +2342,15 @@ $HALF = $self->new($HALF) unless ref($HALF); return $x->bsqrt(@r,$y) if $y->bcmp($HALF) == 0; + # if y < 0, use: exp(x) = 1/exp(-x) + if ($y->{sign} eq '-') + { + my $neg_y = $y->copy()->bneg(); + my $xpow = $x->copy->_pow($neg_y, @r); + $x->bone->bdiv($xpow); + return $x; + } + # Using: # a ** x == e ** (x * ln a)
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Here is an alternate patch that fixes the original issue as well as the related issue: perl -Iblib/lib -Iblib/arch -Mbignum -E 'say .01**28.4' before: 648531815674.9002481119466764195627749488 after: 0.000000000000000000000000000000000000000000000000000000001584893192461113485202101373391507013269 .01 ** 23.5: before: -124.4365830026889488973983751515276488572 after: 0.00000000000000000000000000000000000000000000001 The previous patch looked at the sign of y for x^y. This one looks at the sign of u where u = y*ln(x). The should cover both cases.
Subject: bigfloat-bpow-fix.patch
--- lib/Math/BigFloat.pm.orig 2013-10-30 13:55:42.426664527 -0700 +++ lib/Math/BigFloat.pm 2013-10-30 15:55:08.406646654 -0700 @@ -2389,6 +2389,13 @@ my ($limit,$v,$u,$below,$factor,$next,$over); $u = $x->copy()->blog(undef,$scale)->bmul($y); + # if u < 0, use: exp(x) = 1/exp(-x) + my $do_invert = 0; + if ($u->{sign} eq '-') + { + $do_invert = 1; + $u->bneg(); + } $v = $self->bone(); # 1 $factor = $self->new(2); # 2 $x->bone(); # first term: 1 @@ -2413,6 +2420,8 @@ #$steps++; } + + $x = $x->copy->bone->bdiv($x, $scale) if $do_invert; # shortcut to not run through _find_round_parameters again if (defined $params[0])
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It looks like the last line of the last patch needs to be modified to make sure $x is modified in place: if ($do_invert) { my $x_copy = $x->copy; $x->bone->bdiv($x_copy, $scale); } perl -Iblib/lib -Iblib/arch -Mbignum -E 'say 0+(-112.5)->bexp' should print something like: 0.0000000000000000000000000000000000000000000000001386343293641170635024487001056748670217 (perl 5.8.9 through 5.19.5 all print 1650.xxx)
Subject: Re: [rt.cpan.org #43460] Bug in Math::BigFloat - gives wrong results for bpow and bexp
Date: Thu, 31 Oct 2013 15:55:49 -0400
To: bug-Math-BigFloat [...] rt.cpan.org
From: "Tels" <nospam-abuse [...] bloodgate.com>
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On Wed, October 30, 2013 8:45 pm, Dana Jacobsen via RT wrote: Show quoted text
> Queue: Math-BigFloat > Ticket <URL: https://rt.cpan.org/Ticket/Display.html?id=43460 > > > It looks like the last line of the last patch needs to be modified to make > sure $x is modified in place: > > if ($do_invert) > { > my $x_copy = $x->copy; > $x->bone->bdiv($x_copy, $scale); > }
Might also make sense to add a method to compute 1/x in place like $x->reciprocal()? Regards, Tels PS: Please keep up the good work, it's good to see that the Math modules are still improved. (And I can't say mea culpa oten enough for the problems I left behind :) -- http://bloodgate.com/galleries/
RT-Send-CC: nospam-abuse [...] bloodgate.com
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I have no permission to close this ticket. MARKB or TELS are the only two with permission to do that. This issue fixed in Math-BigInt1.999715.


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