Bug #57148 for Math-Algebra-Symbols: Re: Bug#578941: libmath-algebra-symbols-perl: FTBFS with perl 5.12.0-1: long doubles

On many systems with long doubles a bug is detected that goes unnoticed elswhere. The problem is a wrong optimization when calculating square roots. In order to detect whether a square root can be numerically evaluated or should rather be kept as a symbolic operation, Math::Algebra::Symbols::Term checks whether a number is equal to the square of its square root, assuming that this will be true only for precise results, like 2.5 == sqrt(6.25). This assumption, however, is too optimistic. Rounding effects can create false positives. The check should be replaced by something that is rather too pessimistic, as false negatives will not introduce mathematical errors. I have added a patch with a suggestion for such a check. It also fixes two minor issues triggering warnings when the test suite is run under perl5.16.1. -Martin

diff -rup Math-Algebra-Symbols-1.21.orig/lib/Math/Algebra/Symbols/Sum.pm Math-Algebra-Symbols-1.21/lib/Math/Algebra/Symbols/Sum.pm --- Math-Algebra-Symbols-1.21.orig/lib/Math/Algebra/Symbols/Sum.pm 2004-06-15 00:25:54.000000000 +0200 +++ Math-Algebra-Symbols-1.21/lib/Math/Algebra/Symbols/Sum.pm 2012-08-28 15:47:50.000000000 +0200 @@ -1713,7 +1713,6 @@ use overload 'sqrt' =>\&sqrt3, 'exp' =>\&exp3, 'log' =>\&log3, - 'tan' =>\&tan3, 'sin' =>\&sin3, 'cos' =>\&cos3, '""' =>\&print3, diff -rup Math-Algebra-Symbols-1.21.orig/lib/Math/Algebra/Symbols/Term.pm Math-Algebra-Symbols-1.21/lib/Math/Algebra/Symbols/Term.pm --- Math-Algebra-Symbols-1.21.orig/lib/Math/Algebra/Symbols/Term.pm 2004-06-15 00:25:54.000000000 +0200 +++ Math-Algebra-Symbols-1.21/lib/Math/Algebra/Symbols/Term.pm 2012-08-28 18:35:28.000000000 +0200 @@ -813,6 +813,16 @@ sub power($$) } +# return a square root guaranteed to be precise, or undef +sub _safe_sqrt + {my ($a) = @_; + return undef if $a >= 65536 || $a < 0; + my $s = int(sqrt($a)*256)/256; # $s now has at most 8+8 bits + return undef if $s*$s != $a; + return $s; + } + + =head3 sqrt2 Square root of a term @@ -836,8 +846,8 @@ sub sqrt2($) my ($c, $d, $i) = ($t->{c}, $t->{d}, 0); $c = -$c, $i = 1 if $c < 0; - my $c2 = sqrt($c); return undef unless $c2*$c2 == $c; - my $d2 = sqrt($d); return undef unless $d2*$d2 == $d; + my $c2 = _safe_sqrt($c); return undef if !defined $c2; + my $d2 = _safe_sqrt($d); return undef if !defined $d2; my $z = clone($t)->c($c2)->d($d2)->i($i); @@ -1093,7 +1103,7 @@ sub print($) $s .= '*$'.$_.'**'. $v->{$_} for grep {$v->{$_} > 1} @k; $s .= '/$'.$_.'**'.-$v->{$_} for grep {$v->{$_} < -1} @k; $s .= '/('. $t->{divide} .')' if $t->{divide}; - $s .= '*sqrt('. $t->{sqrt} .')' if $t->{sqrt}; + $s .= '*sqrt('. $t->{sqrt} .')' if defined $t->{sqrt}; $s .= '*exp('. $t->{exp} .')' if $t->{exp}; $s .= '*log('. $t->{log} .')' if $t->{log}; $s; diff -rup Math-Algebra-Symbols-1.21.orig/t/bug_2004_6_5.t Math-Algebra-Symbols-1.21/t/bug_2004_6_5.t --- Math-Algebra-Symbols-1.21.orig/t/bug_2004_6_5.t 2004-06-15 00:25:53.000000000 +0200 +++ Math-Algebra-Symbols-1.21/t/bug_2004_6_5.t 2012-08-28 15:47:50.000000000 +0200 @@ -25,5 +25,7 @@ print $y, "\n"; use Math::Complex; # Need complex arithmetic $x = 2; -my $sx = eval $y; +my $qy = "$y"; +$qy =~ s/-/ - /g; +my $sx = eval $qy; ok($sx>0.90 and $sx<0.91);

HI Martin: This is very kind of you. Do I apply the patches you have supplied or is this all taken care of in CPAN for me? Thanks, Phil Philip R Brenan On Wed, Sep 5, 2012 at 4:31 PM, Martin Becker via RT < bug-Math-Algebra-Symbols@rt.cpan.org> wrote: Show quoted text