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-rw-r--r--dist/Math-BigRat/t/bigfltpm.inc1673
1 files changed, 1673 insertions, 0 deletions
diff --git a/dist/Math-BigRat/t/bigfltpm.inc b/dist/Math-BigRat/t/bigfltpm.inc
new file mode 100644
index 0000000000..fcc09c75be
--- /dev/null
+++ b/dist/Math-BigRat/t/bigfltpm.inc
@@ -0,0 +1,1673 @@
+#include this file into another test for subclass testing...
+
+ok ($class->config()->{lib},$CL);
+
+use strict;
+
+my $z;
+
+while (<DATA>)
+ {
+ chomp;
+ $_ =~ s/#.*$//; # remove comments
+ $_ =~ s/\s+$//; # trailing spaces
+ next if /^$/; # skip empty lines & comments
+ if (s/^&//)
+ {
+ $f = $_;
+ }
+ elsif (/^\$/)
+ {
+ $setup = $_; $setup =~ s/\$/\$${class}::/g; # round_mode, div_scale
+ #print "\$setup== $setup\n";
+ }
+ else
+ {
+ if (m|^(.*?):(/.+)$|)
+ {
+ $ans = $2;
+ @args = split(/:/,$1,99);
+ }
+ else
+ {
+ @args = split(/:/,$_,99); $ans = pop(@args);
+ }
+ $try = "\$x = $class->new(\"$args[0]\");";
+ if ($f eq "fnorm")
+ {
+ $try .= "\$x;";
+ } elsif ($f eq "finf") {
+ $try .= "\$x->finf('$args[1]');";
+ } elsif ($f eq "is_inf") {
+ $try .= "\$x->is_inf('$args[1]');";
+ } elsif ($f eq "fone") {
+ $try .= "\$x->bone('$args[1]');";
+ } elsif ($f eq "fstr") {
+ $try .= "\$x->accuracy($args[1]); \$x->precision($args[2]);";
+ $try .= '$x->fstr();';
+ } elsif ($f eq "parts") {
+ # ->bstr() to see if an object is returned
+ $try .= '($a,$b) = $x->parts(); $a = $a->bstr(); $b = $b->bstr();';
+ $try .= '"$a $b";';
+ } elsif ($f eq "exponent") {
+ # ->bstr() to see if an object is returned
+ $try .= '$x->exponent()->bstr();';
+ } elsif ($f eq "mantissa") {
+ # ->bstr() to see if an object is returned
+ $try .= '$x->mantissa()->bstr();';
+ } elsif ($f =~ /^(numify|length|as_number|as_hex|as_bin)$/) {
+ $try .= "\$x->$f();";
+ # some unary ops (test the fxxx form, since that is done by AUTOLOAD)
+ } elsif ($f =~ /^f(nan|sstr|neg|floor|ceil|abs)$/) {
+ $try .= "\$x->f$1();";
+ # some is_xxx test function
+ } elsif ($f =~ /^is_(zero|one|negative|positive|odd|even|nan|int)$/) {
+ $try .= "\$x->$f();";
+ } elsif ($f eq "finc") {
+ $try .= '++$x;';
+ } elsif ($f eq "fdec") {
+ $try .= '--$x;';
+ }elsif ($f eq "fround") {
+ $try .= "$setup; \$x->fround($args[1]);";
+ } elsif ($f eq "ffround") {
+ $try .= "$setup; \$x->ffround($args[1]);";
+ } elsif ($f eq "fsqrt") {
+ $try .= "$setup; \$x->fsqrt();";
+ } elsif ($f eq "ffac") {
+ $try .= "$setup; \$x->ffac();";
+ } elsif ($f eq "flog") {
+ if (defined $args[1] && $args[1] ne '')
+ {
+ $try .= "\$y = $class->new($args[1]);";
+ $try .= "$setup; \$x->flog(\$y);";
+ }
+ else
+ {
+ $try .= "$setup; \$x->flog();";
+ }
+ }
+ else
+ {
+ $try .= "\$y = $class->new(\"$args[1]\");";
+
+ if ($f eq "bgcd")
+ {
+ if (defined $args[2])
+ {
+ $try .= " \$z = $class->new(\"$args[2]\"); ";
+ }
+ $try .= "$class\::bgcd(\$x, \$y";
+ $try .= ", \$z" if (defined $args[2]);
+ $try .= " );";
+ }
+ elsif ($f eq "blcm")
+ {
+ if (defined $args[2])
+ {
+ $try .= " \$z = $class->new(\"$args[2]\"); ";
+ }
+ $try .= "$class\::blcm(\$x, \$y";
+ $try .= ", \$z" if (defined $args[2]);
+ $try .= " );";
+ } elsif ($f eq "fcmp") {
+ $try .= '$x->fcmp($y);';
+ } elsif ($f eq "facmp") {
+ $try .= '$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") {
+ $try .= '$x + $y;';
+ } elsif ($f eq "fsub") {
+ $try .= '$x - $y;';
+ } elsif ($f eq "fmul") {
+ $try .= '$x * $y;';
+ } elsif ($f eq "fdiv") {
+ $try .= "$setup; \$x / \$y;";
+ } elsif ($f eq "fdiv-list") {
+ $try .= "$setup; join(',',\$x->fdiv(\$y));";
+ } elsif ($f eq "frsft") {
+ $try .= '$x >> $y;';
+ } elsif ($f eq "flsft") {
+ $try .= '$x << $y;';
+ } elsif ($f eq "fmod") {
+ $try .= '$x % $y;';
+ } else { warn "Unknown op '$f'"; }
+ }
+ # print "# Trying: '$try'\n";
+ $ans1 = eval $try;
+ print "# Error: $@\n" if $@;
+ if ($ans =~ m|^/(.*)$|)
+ {
+ my $pat = $1;
+ if ($ans1 =~ /$pat/)
+ {
+ ok (1,1);
+ }
+ else
+ {
+ print "# '$try' expected: /$pat/ got: '$ans1'\n" if !ok(1,0);
+ }
+ }
+ else
+ {
+ if ($ans eq "")
+ {
+ ok_undef ($ans1);
+ }
+ else
+ {
+ print "# Tried: '$try'\n" if !ok ($ans1, $ans);
+ if (ref($ans1) eq "$class")
+ {
+ # float numbers are normalized (for now), so mantissa shouldn't have
+ # trailing zeros
+ #print $ans1->_trailing_zeros(),"\n";
+ print "# Has trailing zeros after '$try'\n"
+ if !ok ($CL->_zeros( $ans1->{_m}), 0);
+ }
+ }
+ } # end pattern or string
+ }
+ } # end while
+
+# check whether $class->new( Math::BigInt->new()) destroys it
+# ($y == 12 in this case)
+$x = Math::BigInt->new(1200); $y = $class->new($x);
+ok ($y,1200); ok ($x,1200);
+
+###############################################################################
+# Really huge, big, ultra-mega-biggy-monster exponents
+# Technically, the exponents should not be limited (they are BigInts), but
+# practically there are a few places were they are limited to a Perl scalar.
+# This is sometimes for speed, sometimes because otherwise the number wouldn't
+# fit into your memory (just think of 1e123456789012345678901234567890 + 1!)
+# anyway. We don't test everything here, but let's make sure it just basically
+# works.
+
+my $monster = '1e1234567890123456789012345678901234567890';
+
+# new and exponent
+ok ($class->new($monster)->bsstr(),
+ '1e+1234567890123456789012345678901234567890');
+ok ($class->new($monster)->exponent(),
+ '1234567890123456789012345678901234567890');
+# cmp
+ok ($class->new($monster) > 0,1);
+
+# sub/mul
+ok ($class->new($monster)->bsub( $monster),0);
+ok ($class->new($monster)->bmul(2)->bsstr(),
+ '2e+1234567890123456789012345678901234567890');
+
+# mantissa
+$monster = '1234567890123456789012345678901234567890e2';
+ok ($class->new($monster)->mantissa(),
+ '123456789012345678901234567890123456789');
+
+###############################################################################
+# zero,inf,one,nan
+
+$x = $class->new(2); $x->fzero(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->finf(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->fone(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->fnan(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+
+###############################################################################
+# bone/binf etc as plain calls (Lite failed them)
+
+ok ($class->fzero(),0);
+ok ($class->fone(),1);
+ok ($class->fone('+'),1);
+ok ($class->fone('-'),-1);
+ok ($class->fnan(),'NaN');
+ok ($class->finf(),'inf');
+ok ($class->finf('+'),'inf');
+ok ($class->finf('-'),'-inf');
+ok ($class->finf('-inf'),'-inf');
+
+$class->accuracy(undef); $class->precision(undef); # reset
+
+###############################################################################
+# bug in bsstr()/numify() showed up in after-rounding in bdiv()
+
+$x = $class->new('0.008'); $y = $class->new(2);
+$x->bdiv(3,$y);
+ok ($x,'0.0027');
+
+###############################################################################
+# fsqrt() with set global A/P or A/P enabled on $x, also a test whether fsqrt()
+# correctly modifies $x
+
+
+$x = $class->new(12); $class->precision(-2); $x->fsqrt(); ok ($x,'3.46');
+
+$class->precision(undef);
+$x = $class->new(12); $class->precision(0); $x->fsqrt(); ok ($x,'3');
+
+$class->precision(-3); $x = $class->new(12); $x->fsqrt(); ok ($x,'3.464');
+
+{
+ no strict 'refs';
+ # A and P set => NaN
+ ${${class}.'::accuracy'} = 4; $x = $class->new(12);
+ $x->fsqrt(3); ok ($x,'NaN');
+ # supplied arg overrides set global
+ $class->precision(undef); $x = $class->new(12); $x->fsqrt(3); ok ($x,'3.46');
+ $class->accuracy(undef); $class->precision(undef); # reset for further tests
+}
+
+#############################################################################
+# can we call objectify (broken until v1.52)
+
+{
+ no strict;
+ $try =
+ '@args' . " = $class" . "::objectify(2,$class,4,5);".'join(" ",@args);';
+ $ans = eval $try;
+ ok ($ans,"$class 4 5");
+}
+
+#############################################################################
+# is_one('-') (broken until v1.64)
+
+ok ($class->new(-1)->is_one(),0);
+ok ($class->new(-1)->is_one('-'),1);
+
+#############################################################################
+# bug 1/0.5 leaving 2e-0 instead of 2e0
+
+ok ($class->new(1)->fdiv('0.5')->bsstr(),'2e+0');
+
+###############################################################################
+# [perl #30609] bug with $x -= $x not being 0, but 2*$x
+
+$x = $class->new(3); $x -= $x; ok ($x, 0);
+$x = $class->new(-3); $x -= $x; ok ($x, 0);
+$x = $class->new(3); $x += $x; ok ($x, 6);
+$x = $class->new(-3); $x += $x; ok ($x, -6);
+
+$x = $class->new('NaN'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('-inf'); $x -= $x; ok ($x->is_nan(), 1);
+
+$x = $class->new('NaN'); $x += $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x += $x; ok ($x->is_inf(), 1);
+$x = $class->new('-inf'); $x += $x; ok ($x->is_inf('-'), 1);
+
+$x = $class->new('3.14'); $x -= $x; ok ($x, 0);
+$x = $class->new('-3.14'); $x -= $x; ok ($x, 0);
+$x = $class->new('3.14'); $x += $x; ok ($x, '6.28');
+$x = $class->new('-3.14'); $x += $x; ok ($x, '-6.28');
+
+$x = $class->new('3.14'); $x *= $x; ok ($x, '9.8596');
+$x = $class->new('-3.14'); $x *= $x; ok ($x, '9.8596');
+$x = $class->new('3.14'); $x /= $x; ok ($x, '1');
+$x = $class->new('-3.14'); $x /= $x; ok ($x, '1');
+$x = $class->new('3.14'); $x %= $x; ok ($x, '0');
+$x = $class->new('-3.14'); $x %= $x; ok ($x, '0');
+
+###############################################################################
+# the following two were reported by "kenny" via hotmail.com:
+
+#perl -MMath::BigFloat -wle 'print Math::BigFloat->new(0)->bpow(".1")'
+#Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851.
+
+$x = $class->new(0); $y = $class->new('0.1');
+ok ($x ** $y, 0, 'no warnings and zero result');
+
+#perl -MMath::BigFloat -lwe 'print Math::BigFloat->new(".222222222222222222222222222222222222222222")->bceil()'
+#Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851.
+
+$x = $class->new(".222222222222222222222222222222222222222222");
+ok ($x->bceil(), 1, 'no warnings and one as result');
+
+###############################################################################
+# test **=, <<=, >>=
+
+# ((2^148)-1)/17
+$x = $class->new(2); $x **= 148; $x++; $x->bdiv(17, 60)->bfloor(); $x->accuracy(undef);
+ok ($x,"20988936657440586486151264256610222593863921");
+ok ($x->length(),length "20988936657440586486151264256610222593863921");
+
+$x = $class->new('2');
+my $y = $class->new('18');
+ok ($x <<= $y, 2 << 18);
+ok ($x, 2 << 18);
+ok ($x >>= $y, 2);
+ok ($x, 2);
+
+$x = $class->new('2');
+$y = $class->new('18.2');
+$x <<= $y; # 2 * (2 ** 18.2);
+
+ok ($x->copy()->bfround(-9), '602248.763144685');
+ok ($x >>= $y, 2); # 2 * (2 ** 18.2) / (2 ** 18.2) => 2
+ok ($x, 2);
+
+1; # all done
+
+###############################################################################
+# Perl 5.005 does not like ok ($x,undef)
+
+sub ok_undef
+ {
+ my $x = shift;
+
+ ok (1,1) and return if !defined $x;
+ ok ($x,'undef');
+ }
+
+__DATA__
+&bgcd
+inf:12:NaN
+-inf:12:NaN
+12:inf:NaN
+12:-inf:NaN
+inf:inf:NaN
+inf:-inf:NaN
+-inf:-inf:NaN
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:0
++0:+1:1
++1:+0:1
++1:+1:1
++2:+3:1
++3:+2:1
+-3:+2:1
+-3:-2:1
+-144:-60:12
+144:-60:12
+144:60:12
+100:625:25
+4096:81:1
+1034:804:2
+27:90:56:1
+27:90:54:9
+&blcm
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:NaN
++1:+0:0
++0:+1:0
++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
+-2::NaN
+# base > 0, base != 1
+2:-1:NaN
+2:0:NaN
+2:1:NaN
+# log(1) is always 1, regardless of $base
+1::0
+1:1:0
+1:2:0
+2::0.6931471805599453094172321214581765680755
+2.718281828::0.9999999998311266953289851340574956564911
+$div_scale = 20;
+2.718281828::0.99999999983112669533
+$div_scale = 15;
+123::4.81218435537242
+10::2.30258509299405
+1000::6.90775527898214
+100::4.60517018598809
+2::0.693147180559945
+3.1415::1.14470039286086
+12345::9.42100640177928
+0.001::-6.90775527898214
+# bug until v1.71:
+10:10:1
+100:100:1
+# reset for further tests
+$div_scale = 40;
+1::0
+&frsft
+NaNfrsft:2:NaN
+0:2:0
+1:1:0.5
+2:1:1
+4:1:2
+123:1:61.5
+32:3:4
+&flsft
+NaNflsft:0:NaN
+2:1:4
+4:3:32
+5:3:40
+1:2:4
+0:5:0
+&fnorm
+1:1
+-0:0
+fnormNaN:NaN
++inf:inf
+-inf:-inf
+123:123
+-123.4567:-123.4567
+# invalid inputs
+1__2:NaN
+1E1__2:NaN
+11__2E2:NaN
+.2E-3.:NaN
+1e3e4:NaN
+# strange, but valid
+.2E2:20
+1.E3:1000
+# some inputs that result in zero
+0e0:0
++0e0:0
++0e+0:0
+-0e+0:0
+0e-0:0
+-0e-0:0
++0e-0:0
+000:0
+00e2:0
+00e02:0
+000e002:0
+000e1230:0
+00e-3:0
+00e+3:0
+00e-03:0
+00e+03:0
+-000:0
+-00e2:0
+-00e02:0
+-000e002:0
+-000e1230:0
+-00e-3:0
+-00e+3:0
+-00e-03:0
+-00e+03:0
+&as_number
+0:0
+1:1
+1.2:1
+2.345:2
+-2:-2
+-123.456:-123
+-200:-200
+# test for bug in brsft() not handling cases that return 0
+0.000641:0
+0.0006412:0
+0.00064123:0
+0.000641234:0
+0.0006412345:0
+0.00064123456:0
+0.000641234567:0
+0.0006412345678:0
+0.00064123456789:0
+0.1:0
+0.01:0
+0.001:0
+0.0001:0
+0.00001:0
+0.000001:0
+0.0000001:0
+0.00000001:0
+0.000000001:0
+0.0000000001:0
+0.00000000001:0
+0.12345:0
+0.123456:0
+0.1234567:0
+0.12345678:0
+0.123456789:0
+&finf
+1:+:inf
+2:-:-inf
+3:abc:inf
+&as_hex
++inf:inf
+-inf:-inf
+hexNaN:NaN
+0:0x0
+5:0x5
+-5:-0x5
+&as_bin
++inf:inf
+-inf:-inf
+hexNaN:NaN
+0:0b0
+5:0b101
+-5:-0b101
+&numify
+# uses bsstr() so 5 => 5e+0 to be compatible w/ Perls output
+0:0e+1
++1:1e+0
+1234:1234e+0
+NaN:NaN
++inf:inf
+-inf:-inf
+-5:-5e+0
+100:1e+2
+-100:-1e+2
+&fnan
+abc:NaN
+2:NaN
+-2:NaN
+0:NaN
+&fone
+2:+:1
+-2:-:-1
+-2:+:1
+2:-:-1
+0::1
+-2::1
+abc::1
+2:abc:1
+&fsstr
++inf:inf
+-inf:-inf
+abcfsstr:NaN
+-abcfsstr:NaN
+1234.567:1234567e-3
+123:123e+0
+-5:-5e+0
+-100:-1e+2
+&fstr
++inf:::inf
+-inf:::-inf
+abcfstr:::NaN
+1234.567:9::1234.56700
+1234.567::-6:1234.567000
+12345:5::12345
+0.001234:6::0.00123400
+0.001234::-8:0.00123400
+0:4::0
+0::-4:0.0000
+&fnorm
+inf:inf
++inf:inf
+-inf:-inf
++infinity:NaN
++-inf:NaN
+abc:NaN
+ 1 a:NaN
+1bcd2:NaN
+11111b:NaN
++1z:NaN
+-1z:NaN
+0e999:0
+0e-999:0
+-0e999:0
+-0e-999:0
+0:0
++0:0
++00:0
++0_0_0:0
+000000_0000000_00000:0
+-0:0
+-0000:0
++1:1
++01:1
++001:1
++00000100000:100000
+123456789:123456789
+-1:-1
+-01:-1
+-001:-1
+-123456789:-123456789
+-00000100000:-100000
+123.456a:NaN
+123.456:123.456
+0.01:0.01
+.002:0.002
++.2:0.2
+-0.0003:-0.0003
+-.0000000004:-0.0000000004
+123456E2:12345600
+123456E-2:1234.56
+-123456E2:-12345600
+-123456E-2:-1234.56
+1e1:10
+2e-11:0.00000000002
+# excercise _split
+ .02e-1:0.002
+ 000001:1
+ -00001:-1
+ -1:-1
+ 000.01:0.01
+ -000.0023:-0.0023
+ 1.1e1:11
+-3e111:-3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+-4e-1111:-0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004
+&fpow
+NaN:1:NaN
+1:NaN:NaN
+NaN:-1:NaN
+-1:NaN:NaN
+NaN:-21:NaN
+-21:NaN:NaN
+NaN:21:NaN
+21:NaN:NaN
+0:0:1
+0:1:0
+0:9:0
+0:-2:inf
+2:2:4
+1:2:1
+1:3:1
+-1:2:1
+-1:3:-1
+123.456:2:15241.383936
+2:-2:0.25
+2:-3:0.125
+128:-2:0.00006103515625
+abc:123.456:NaN
+123.456:abc:NaN
++inf:123.45:inf
+-inf:123.45:-inf
++inf:-123.45:inf
+-inf:-123.45:-inf
+-2:2:4
+-2:3:-8
+-2:4:16
+-2:5:-32
+-3:2:9
+-3:3:-27
+-3:4:81
+-3:5:-243
+# 2 ** 0.5 == sqrt(2)
+# 1.41..7 and not 1.4170 since fallback (bsqrt(9) is '3', not 3.0...0)
+2:0.5:1.41421356237309504880168872420969807857
+#2:0.2:1.148698354997035006798626946777927589444
+#6:1.5:14.6969384566990685891837044482353483518
+$div_scale = 20;
+#62.5:12.5:26447206647554886213592.3959144
+$div_scale = 40;
+&fneg
+fnegNaN:NaN
++inf:-inf
+-inf:inf
++0:0
++1:-1
+-1:1
++123456789:-123456789
+-123456789:123456789
++123.456789:-123.456789
+-123456.789:123456.789
+&fabs
+fabsNaN:NaN
++inf:inf
+-inf:inf
++0:0
++1:1
+-1:1
++123456789:123456789
+-123456789:123456789
++123.456789:123.456789
+-123456.789:123456.789
+&fround
+$round_mode = "trunc"
++inf:5:inf
+-inf:5:-inf
+0:5:0
+NaNfround:5:NaN
++10123456789:5:10123000000
+-10123456789:5:-10123000000
++10123456789.123:5:10123000000
+-10123456789.123:5:-10123000000
++10123456789:9:10123456700
+-10123456789:9:-10123456700
++101234500:6:101234000
+-101234500:6:-101234000
+$round_mode = "zero"
++20123456789:5:20123000000
+-20123456789:5:-20123000000
++20123456789.123:5:20123000000
+-20123456789.123:5:-20123000000
++20123456789:9:20123456800
+-20123456789:9:-20123456800
++201234500:6:201234000
+-201234500:6:-201234000
+$round_mode = "+inf"
++30123456789:5:30123000000
+-30123456789:5:-30123000000
++30123456789.123:5:30123000000
+-30123456789.123:5:-30123000000
++30123456789:9:30123456800
+-30123456789:9:-30123456800
++301234500:6:301235000
+-301234500:6:-301234000
+$round_mode = "-inf"
++40123456789:5:40123000000
+-40123456789:5:-40123000000
++40123456789.123:5:40123000000
+-40123456789.123:5:-40123000000
++40123456789:9:40123456800
+-40123456789:9:-40123456800
++401234500:6:401234000
+-401234500:6:-401235000
+$round_mode = "odd"
++50123456789:5:50123000000
+-50123456789:5:-50123000000
++50123456789.123:5:50123000000
+-50123456789.123:5:-50123000000
++50123456789:9:50123456800
+-50123456789:9:-50123456800
++501234500:6:501235000
+-501234500:6:-501235000
+$round_mode = "even"
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601234000
+-601234500:6:-601234000
++60123456789.0123:5:60123000000
+-60123456789.0123:5:-60123000000
+$round_mode = "common"
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:6:60123500000
+-60123456789:6:-60123500000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601235000
+-601234500:6:-601235000
++601234400:6:601234000
+-601234400:6:-601234000
++601234600:6:601235000
+-601234600:6:-601235000
++601234300:6:601234000
++60123456789.0123:5:60123000000
+-60123456789.0123:5:-60123000000
+&ffround
+$round_mode = "trunc"
++inf:5:inf
+-inf:5:-inf
+0:5:0
+NaNffround:5:NaN
++1.23:-1:1.2
++1.234:-1:1.2
++1.2345:-1:1.2
++1.23:-2:1.23
++1.234:-2:1.23
++1.2345:-2:1.23
++1.23:-3:1.230
++1.234:-3:1.234
++1.2345:-3:1.234
+-1.23:-1:-1.2
++1.27:-1:1.2
+-1.27:-1:-1.2
++1.25:-1:1.2
+-1.25:-1:-1.2
++1.35:-1:1.3
+-1.35:-1:-1.3
+-0.0061234567890:-1:0.0
+-0.0061:-1:0.0
+-0.00612:-1:0.0
+-0.00612:-2:0.00
+-0.006:-1:0.0
+-0.006:-2:0.00
+-0.0006:-2:0.00
+-0.0006:-3:0.000
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:0
+0.41:0:0
+$round_mode = "zero"
++2.23:-1:/2.2(?:0{5}\d+)?
+-2.23:-1:/-2.2(?:0{5}\d+)?
++2.27:-1:/2.(?:3|29{5}\d+)
+-2.27:-1:/-2.(?:3|29{5}\d+)
++2.25:-1:/2.2(?:0{5}\d+)?
+-2.25:-1:/-2.2(?:0{5}\d+)?
++2.35:-1:/2.(?:3|29{5}\d+)
+-2.35:-1:/-2.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+$round_mode = "+inf"
++3.23:-1:/3.2(?:0{5}\d+)?
+-3.23:-1:/-3.2(?:0{5}\d+)?
++3.27:-1:/3.(?:3|29{5}\d+)
+-3.27:-1:/-3.(?:3|29{5}\d+)
++3.25:-1:/3.(?:3|29{5}\d+)
+-3.25:-1:/-3.2(?:0{5}\d+)?
++3.35:-1:/3.(?:4|39{5}\d+)
+-3.35:-1:/-3.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:1
+0.51:0:1
+0.41:0:0
+$round_mode = "-inf"
++4.23:-1:/4.2(?:0{5}\d+)?
+-4.23:-1:/-4.2(?:0{5}\d+)?
++4.27:-1:/4.(?:3|29{5}\d+)
+-4.27:-1:/-4.(?:3|29{5}\d+)
++4.25:-1:/4.2(?:0{5}\d+)?
+-4.25:-1:/-4.(?:3|29{5}\d+)
++4.35:-1:/4.(?:3|29{5}\d+)
+-4.35:-1:/-4.(?:4|39{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.007|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+$round_mode = "odd"
++5.23:-1:/5.2(?:0{5}\d+)?
+-5.23:-1:/-5.2(?:0{5}\d+)?
++5.27:-1:/5.(?:3|29{5}\d+)
+-5.27:-1:/-5.(?:3|29{5}\d+)
++5.25:-1:/5.(?:3|29{5}\d+)
+-5.25:-1:/-5.(?:3|29{5}\d+)
++5.35:-1:/5.(?:3|29{5}\d+)
+-5.35:-1:/-5.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.007|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:1
+0.51:0:1
+0.41:0:0
+$round_mode = "even"
++6.23:-1:/6.2(?:0{5}\d+)?
+-6.23:-1:/-6.2(?:0{5}\d+)?
++6.27:-1:/6.(?:3|29{5}\d+)
+-6.27:-1:/-6.(?:3|29{5}\d+)
++6.25:-1:/6.(?:2(?:0{5}\d+)?|29{5}\d+)
+-6.25:-1:/-6.(?:2(?:0{5}\d+)?|29{5}\d+)
++6.35:-1:/6.(?:4|39{5}\d+|29{8}\d+)
+-6.35:-1:/-6.(?:4|39{5}\d+|29{8}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+0.01234567:-3:0.012
+0.01234567:-4:0.0123
+0.01234567:-5:0.01235
+0.01234567:-6:0.012346
+0.01234567:-7:0.0123457
+0.01234567:-8:0.01234567
+0.01234567:-9:0.012345670
+0.01234567:-12:0.012345670000
+&fcmp
+fcmpNaN:fcmpNaN:
+fcmpNaN:+0:
++0:fcmpNaN:
++0:+0:0
+-1:+0:-1
++0:-1:1
++1:+0:1
++0:+1:-1
+-1:+1:-1
++1:-1:1
+-1:-1:0
++1:+1:0
+-1.1:0:-1
++0:-1.1:1
++1.1:+0:1
++0:+1.1:-1
++123:+123:0
++123:+12:1
++12:+123:-1
+-123:-123:0
+-123:-12:-1
+-12:-123:1
++123:+124:-1
++124:+123:1
+-123:-124:1
+-124:-123:-1
+0:0.01:-1
+0:0.0001:-1
+0:-0.0001:1
+0:-0.1:1
+0.1:0:1
+0.00001:0:1
+-0.0001:0:-1
+-0.1:0:-1
+0:0.0001234:-1
+0:-0.0001234:1
+0.0001234:0:1
+-0.0001234:0:-1
+0.0001:0.0005:-1
+0.0005:0.0001:1
+0.005:0.0001:1
+0.001:0.0005:1
+0.000001:0.0005:-1
+0.00000123:0.0005:-1
+0.00512:0.0001:1
+0.005:0.000112:1
+0.00123:0.0005:1
+1.5:2:-1
+2:1.5:1
+1.54321:234:-1
+234:1.54321:1
+# infinity
+-inf:5432112345:-1
++inf:5432112345:1
+-inf:-5432112345:-1
++inf:-5432112345:1
+-inf:54321.12345:-1
++inf:54321.12345:1
+-inf:-54321.12345:-1
++inf:-54321.12345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:1
+-inf:+inf:-1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&facmp
+fcmpNaN:fcmpNaN:
+fcmpNaN:+0:
++0:fcmpNaN:
++0:+0:0
+-1:+0:1
++0:-1:-1
++1:+0:1
++0:+1:-1
+-1:+1:0
++1:-1:0
+-1:-1:0
++1:+1:0
+-1.1:0:1
++0:-1.1:-1
++1.1:+0:1
++0:+1.1:-1
++123:+123:0
++123:+12:1
++12:+123:-1
+-123:-123:0
+-123:-12:1
+-12:-123:-1
++123:+124:-1
++124:+123:1
+-123:-124:-1
+-124:-123:1
+0:0.01:-1
+0:0.0001:-1
+0:-0.0001:-1
+0:-0.1:-1
+0.1:0:1
+0.00001:0:1
+-0.0001:0:1
+-0.1:0:1
+0:0.0001234:-1
+0:-0.0001234:-1
+0.0001234:0:1
+-0.0001234:0:1
+0.0001:0.0005:-1
+0.0005:0.0001:1
+0.005:0.0001:1
+0.001:0.0005:1
+0.000001:0.0005:-1
+0.00000123:0.0005:-1
+0.00512:0.0001:1
+0.005:0.000112:1
+0.00123:0.0005:1
+1.5:2:-1
+2:1.5:1
+1.54321:234:-1
+234:1.54321:1
+# infinity
+-inf:5432112345:1
++inf:5432112345:1
+-inf:-5432112345:1
++inf:-5432112345:1
+-inf:54321.12345:1
++inf:54321.12345:1
+-inf:-54321.12345:1
++inf:-54321.12345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:0
+-inf:+inf:0
+5:inf:-1
+-1:inf:-1
+5:-inf:-1
+-1:-inf:-1
+# return undef
++inf:facmpNaN:
+facmpNaN:inf:
+-inf:facmpNaN:
+facmpNaN:-inf:
+&fdec
+fdecNaN:NaN
++inf:inf
+-inf:-inf
++0:-1
++1:0
+-1:-2
+1.23:0.23
+-1.23:-2.23
+100:99
+101:100
+-100:-101
+-99:-100
+-98:-99
+99:98
+&finc
+fincNaN:NaN
++inf:inf
+-inf:-inf
++0:1
++1:2
+-1:0
+1.23:2.23
+-1.23:-0.23
+100:101
+-100:-99
+-99:-98
+-101:-100
+99:100
+&fadd
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:NaN
+-inf:+inf:NaN
++inf:+inf:inf
+-inf:-inf:-inf
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
++0:+0:0
++1:+0:1
++0:+1:1
++1:+1:2
+-1:+0:-1
++0:-1:-1
+-1:-1:-2
+-1:+1:0
++1:-1:0
++9:+1:10
++99:+1:100
++999:+1:1000
++9999:+1:10000
++99999:+1:100000
++999999:+1:1000000
++9999999:+1:10000000
++99999999:+1:100000000
++999999999:+1:1000000000
++9999999999:+1:10000000000
++99999999999:+1:100000000000
++10:-1:9
++100:-1:99
++1000:-1:999
++10000:-1:9999
++100000:-1:99999
++1000000:-1:999999
++10000000:-1:9999999
++100000000:-1:99999999
++1000000000:-1:999999999
++10000000000:-1:9999999999
++123456789:+987654321:1111111110
+-123456789:+987654321:864197532
+-123456789:-987654321:-1111111110
++123456789:-987654321:-864197532
+0.001234:0.0001234:0.0013574
+&fsub
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:inf
+-inf:+inf:-inf
++inf:+inf:NaN
+-inf:-inf:NaN
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
++0:+0:0
++1:+0:1
++0:+1:-1
++1:+1:0
+-1:+0:-1
++0:-1:1
+-1:-1:0
+-1:+1:-2
++1:-1:2
++9:+1:8
++99:+1:98
++999:+1:998
++9999:+1:9998
++99999:+1:99998
++999999:+1:999998
++9999999:+1:9999998
++99999999:+1:99999998
++999999999:+1:999999998
++9999999999:+1:9999999998
++99999999999:+1:99999999998
++10:-1:11
++100:-1:101
++1000:-1:1001
++10000:-1:10001
++100000:-1:100001
++1000000:-1:1000001
++10000000:-1:10000001
++100000000:-1:100000001
++1000000000:-1:1000000001
++10000000000:-1:10000000001
++123456789:+987654321:-864197532
+-123456789:+987654321:-1111111110
+-123456789:-987654321:864197532
++123456789:-987654321:1111111110
+&fmul
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:NaNmul:NaN
++inf:NaNmul:NaN
+NaNmul:+inf:NaN
+NaNmul:-inf:NaN
++inf:+inf:inf
++inf:-inf:-inf
++inf:-inf:-inf
++inf:+inf:inf
++inf:123.34:inf
++inf:-123.34:-inf
+-inf:123.34:-inf
+-inf:-123.34:inf
+123.34:+inf:inf
+-123.34:+inf:-inf
+123.34:-inf:-inf
+-123.34:-inf:inf
++0:+0:0
++0:+1:0
++1:+0:0
++0:-1:0
+-1:+0:0
++123456789123456789:+0:0
++0:+123456789123456789:0
+-1:-1:1
+-1:+1:-1
++1:-1:-1
++1:+1:1
++2:+3:6
+-2:+3:-6
++2:-3:-6
+-2:-3:6
++111:+111:12321
++10101:+10101:102030201
++1001001:+1001001:1002003002001
++100010001:+100010001:10002000300020001
++10000100001:+10000100001:100002000030000200001
++11111111111:+9:99999999999
++22222222222:+9:199999999998
++33333333333:+9:299999999997
++44444444444:+9:399999999996
++55555555555:+9:499999999995
++66666666666:+9:599999999994
++77777777777:+9:699999999993
++88888888888:+9:799999999992
++99999999999:+9:899999999991
+6:120:720
+10:10000:100000
+&fdiv-list
+0:0:NaN,NaN
+0:1:0,0
+9:4:2.25,1
+9:5:1.8,4
+# bug in v1.74 with bdiv in list context, when $y is 1 or -1
+2.1:-1:-2.1,0
+2.1:1:2.1,0
+-2.1:-1:2.1,0
+-2.1:1:-2.1,0
+&fdiv
+$div_scale = 40; $round_mode = 'even'
+abc:abc:NaN
+abc:+1:abc:NaN
++1:abc:NaN
+-1:abc:NaN
+0:abc:NaN
++0:+0:NaN
++0:+1:0
++1:+0:inf
++3214:+0:inf
++0:-1:0
+-1:+0:-inf
+-3214:+0:-inf
++1:+1:1
+-1:-1:1
++1:-1:-1
+-1:+1:-1
++1:+2:0.5
++2:+1:2
+123:+inf:0
+123:-inf:0
++10:+5:2
++100:+4:25
++1000:+8:125
++10000:+16:625
++10000:-16:-625
++999999999999:+9:111111111111
++999999999999:+99:10101010101
++999999999999:+999:1001001001
++999999999999:+9999:100010001
++999999999999999:+99999:10000100001
++1000000000:+9:111111111.1111111111111111111111111111111
++2000000000:+9:222222222.2222222222222222222222222222222
++3000000000:+9:333333333.3333333333333333333333333333333
++4000000000:+9:444444444.4444444444444444444444444444444
++5000000000:+9:555555555.5555555555555555555555555555556
++6000000000:+9:666666666.6666666666666666666666666666667
++7000000000:+9:777777777.7777777777777777777777777777778
++8000000000:+9:888888888.8888888888888888888888888888889
++9000000000:+9:1000000000
++35500000:+113:314159.2920353982300884955752212389380531
++71000000:+226:314159.2920353982300884955752212389380531
++106500000:+339:314159.2920353982300884955752212389380531
++1000000000:+3:333333333.3333333333333333333333333333333
+2:25.024996000799840031993601279744051189762:0.07992009269196593320152084692285869265447
+123456:1:123456
+$div_scale = 20
++1000000000:+9:111111111.11111111111
++2000000000:+9:222222222.22222222222
++3000000000:+9:333333333.33333333333
++4000000000:+9:444444444.44444444444
++5000000000:+9:555555555.55555555556
++6000000000:+9:666666666.66666666667
++7000000000:+9:777777777.77777777778
++8000000000:+9:888888888.88888888889
++9000000000:+9:1000000000
+1:10:0.1
+1:100:0.01
+1:1000:0.001
+1:10000:0.0001
+1:504:0.001984126984126984127
+2:1.987654321:1.0062111801179738436
+123456789.123456789123456789123456789:1:123456789.12345678912
+# the next two cases are the "old" behaviour, but are now (>v0.01) different
+#+35500000:+113:314159.292035398230088
+#+71000000:+226:314159.292035398230088
++35500000:+113:314159.29203539823009
++71000000:+226:314159.29203539823009
++106500000:+339:314159.29203539823009
++1000000000:+3:333333333.33333333333
+$div_scale = 1
+# round to accuracy 1 after bdiv
++124:+3:40
+123456789.1234:1:100000000
+# reset scale for further tests
+$div_scale = 40
+&fmod
++9:4:1
++9:5:4
++9000:56:40
++56:9000:56
+# inf handling, see table in doc
+0:inf:0
+0:-inf:0
+5:inf:5
+5:-inf:5
+-5:inf:-5
+-5:-inf:-5
+inf:5:0
+-inf:5:0
+inf:-5:0
+-inf:-5:0
+5:5:0
+-5:-5:0
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:8
+inf:0:inf
+# exceptions to reminder rule
+-inf:0:-inf
+-8:0:-8
+0:0:NaN
+abc:abc:NaN
+abc:1:abc:NaN
+1:abc:NaN
+0:0:NaN
+0:1:0
+1:0:1
+0:-1:0
+-1:0:-1
+1:1:0
+-1:-1:0
+1:-1:0
+-1:1:0
+1:2:1
+2:1:0
+1000000000:9:1
+2000000000:9:2
+3000000000:9:3
+4000000000:9:4
+5000000000:9:5
+6000000000:9:6
+7000000000:9:7
+8000000000:9:8
+9000000000:9:0
+35500000:113:33
+71000000:226:66
+106500000:339:99
+1000000000:3:1
+10:5:0
+100:4:0
+1000:8:0
+10000:16:0
+999999999999:9:0
+999999999999:99:0
+999999999999:999:0
+999999999999:9999:0
+999999999999999:99999:0
+-9:+5:1
++9:-5:-1
+-9:-5:-4
+-5:3:1
+-2:3:1
+4:3:1
+1:3:1
+-5:-3:-2
+-2:-3:-2
+4:-3:-2
+1:-3:-2
+4095:4095:0
+100041000510123:3:0
+152403346:12345:4321
+87654321:87654321:0
+# now some floating point tests
+123:2.5:0.5
+1230:2.5:0
+123.4:2.5:0.9
+123e1:25:5
+-2.1:1:0.9
+2.1:1:0.1
+-2.1:-1:-0.1
+2.1:-1:-0.9
+-3:1:0
+3:1:0
+-3:-1:0
+3:-1:0
+&ffac
+Nanfac:NaN
+-1:NaN
++inf:inf
+-inf:NaN
+0:1
+1:1
+2:2
+3:6
+4:24
+5:120
+6:720
+10:3628800
+11:39916800
+12:479001600
+&froot
+# sqrt()
++0:2:0
++1:2:1
+-1:2:NaN
+# -$x ** (1/2) => -$y, but not in froot()
+-123.456:2:NaN
++inf:2:inf
+-inf:2:NaN
+2:2:1.41421356237309504880168872420969807857
+-2:2:NaN
+4:2:2
+9:2:3
+16:2:4
+100:2:10
+123.456:2:11.11107555549866648462149404118219234119
+15241.38393:2:123.4559999756998444766131352122991626468
+1.44:2:1.2
+12:2:3.464101615137754587054892683011744733886
+0.49:2:0.7
+0.0049:2:0.07
+# invalid ones
+1:NaN:NaN
+-1:NaN:NaN
+0:NaN:NaN
+-inf:NaN:NaN
++inf:NaN:NaN
+NaN:0:NaN
+NaN:2:NaN
+NaN:inf:NaN
+NaN:inf:NaN
+12:-inf:NaN
+12:inf:NaN
++0:0:NaN
++1:0:NaN
+-1:0:NaN
+-2:0:NaN
+-123.45:0:NaN
++inf:0:NaN
+12:1:12
+-12:1:NaN
+8:-1:NaN
+-8:-1:NaN
+# cubic root
+8:3:2
+-8:3:NaN
+# fourths root
+16:4:2
+81:4:3
+# see t/bigroot() for more tests
+&fsqrt
++0:0
+-1:NaN
+-2:NaN
+-16:NaN
+-123.45:NaN
+nanfsqrt:NaN
++inf:inf
+-inf:NaN
+1:1
+2:1.41421356237309504880168872420969807857
+4:2
+9:3
+16:4
+100:10
+123.456:11.11107555549866648462149404118219234119
+15241.38393:123.4559999756998444766131352122991626468
+1.44:1.2
+# sqrt(1.44) = 1.2, sqrt(e10) = e5 => 12e4
+1.44E10:120000
+2e10:141421.356237309504880168872420969807857
+144e20:120000000000
+# proved to be an endless loop under 7-9
+12:3.464101615137754587054892683011744733886
+0.49:0.7
+0.0049:0.07
+&is_nan
+123:0
+abc:1
+NaN:1
+-123:0
+&is_inf
++inf::1
+-inf::1
+abc::0
+1::0
+NaN::0
+-1::0
++inf:-:0
++inf:+:1
+-inf:-:1
+-inf:+:0
+# it must be exactly /^[+-]inf$/
++infinity::0
+-infinity::0
+&is_odd
+abc:0
+0:0
+-1:1
+-3:1
+1:1
+3:1
+1000001:1
+1000002:0
++inf:0
+-inf:0
+123.45:0
+-123.45:0
+2:0
+&is_int
+NaNis_int:0
+0:1
+1:1
+2:1
+-2:1
+-1:1
+-inf:0
++inf:0
+123.4567:0
+-0.1:0
+-0.002:0
+&is_even
+abc:0
+0:1
+-1:0
+-3:0
+1:0
+3:0
+1000001:0
+1000002:1
+2:1
++inf:0
+-inf:0
+123.456:0
+-123.456:0
+0.01:0
+-0.01:0
+120:1
+1200:1
+-1200:1
+&is_positive
+0:0
+1:1
+-1:0
+-123:0
+NaN:0
+-inf:0
++inf:1
+&is_negative
+0:0
+1:0
+-1:1
+-123:1
+NaN:0
+-inf:1
++inf:0
+&parts
+0:0 1
+1:1 0
+123:123 0
+-123:-123 0
+-1200:-12 2
+NaNparts:NaN NaN
++inf:inf inf
+-inf:-inf inf
+&exponent
+0:1
+1:0
+123:0
+-123:0
+-1200:2
++inf:inf
+-inf:inf
+NaNexponent:NaN
+&mantissa
+0:0
+1:1
+123:123
+-123:-123
+-1200:-12
++inf:inf
+-inf:-inf
+NaNmantissa:NaN
+&length
+123:3
+-123:3
+0:1
+1:1
+12345678901234567890:20
+&is_zero
+NaNzero:0
++inf:0
+-inf:0
+0:1
+-1:0
+1:0
+&is_one
+NaNone:0
++inf:0
+-inf:0
+0:0
+2:0
+1:1
+-1:0
+-2:0
+&ffloor
+0:0
+abc:NaN
++inf:inf
+-inf:-inf
+1:1
+-51:-51
+-51.2:-52
+12.2:12
+0.12345:0
+0.123456:0
+0.1234567:0
+0.12345678:0
+0.123456789:0
+&fceil
+0:0
+abc:NaN
++inf:inf
+-inf:-inf
+1:1
+-51:-51
+-51.2:-51
+12.2:13
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