#include this file into another test for subclass testing... is ($class->config()->{lib},$CL); use strict; my $z; while () { $_ =~ s/[\n\r]//g; # remove newlines $_ =~ s/#.*$//; # 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 "bpi") { $try .= '$class->bpi($x);'; } elsif ($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 "bcos") { $try .= '$x->bcos($y);'; } elsif ($f eq "bsin") { $try .= '$x->bsin($y);'; } elsif ($f eq "batan") { $try .= '$x->batan($y);'; } elsif ($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 { # Functions with three arguments $try .= "\$z = $class->new(\"$args[2]\");"; if( $f eq "bmodpow") { $try .= '$x->bmodpow($y,$z);'; } elsif ($f eq "bmuladd"){ $try .= '$x->bmuladd($y,$z);'; } elsif ($f eq "batan2"){ $try .= '$x->batan2($y,$z);'; } else { warn "Unknown op '$f'"; } } } # print "# Trying: '$try'\n"; $ans1 = eval $try; print "# Error: $@\n" if $@; if ($ans =~ m|^/(.*)$|) { my $pat = $1; if ($ans1 =~ /$pat/) { is (1,1); } else { print "# '$try' expected: /$pat/ got: '$ans1'\n" if !is (1,0); } } else { if ($ans eq "") { is ($ans1, undef); } else { print "# Tried: '$try'\n" if !is ($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 !is ($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); is ($y,1200); is ($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 $monster = '1e1234567890123456789012345678901234567890'; # new and exponent is ($class->new($monster)->bsstr(), '1e+1234567890123456789012345678901234567890'); is ($class->new($monster)->exponent(), '1234567890123456789012345678901234567890'); # cmp is ($class->new($monster) > 0,1); # sub/mul is ($class->new($monster)->bsub( $monster),0); is ($class->new($monster)->bmul(2)->bsstr(), '2e+1234567890123456789012345678901234567890'); # mantissa $monster = '1234567890123456789012345678901234567890e2'; is ($class->new($monster)->mantissa(), '123456789012345678901234567890123456789'); ############################################################################### # zero,inf,one,nan $x = $class->new(2); $x->fzero(); is ($x->{_a}, undef); is ($x->{_p}, undef); $x = $class->new(2); $x->finf(); is ($x->{_a}, undef); is ($x->{_p}, undef); $x = $class->new(2); $x->fone(); is ($x->{_a}, undef); is ($x->{_p}, undef); $x = $class->new(2); $x->fnan(); is ($x->{_a}, undef); is ($x->{_p}, undef); ############################################################################### # bone/binf etc as plain calls (Lite failed them) is ($class->fzero(),0); is ($class->fone(),1); is ($class->fone('+'),1); is ($class->fone('-'),-1); is ($class->fnan(),'NaN'); is ($class->finf(),'inf'); is ($class->finf('+'),'inf'); is ($class->finf('-'),'-inf'); is ($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); is ($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); $x->fsqrt(); is ($x,'3.46'); $class->precision(undef); $x = $class->new(12); $class->precision(0); $x->fsqrt(); is ($x,'3'); $class->precision(-3); $x = $class->new(12); $x->fsqrt(); is ($x,'3.464'); { no strict 'refs'; # A and P set => NaN ${${class}.'::accuracy'} = 4; $x = $class->new(12); $x->fsqrt(3); is ($x,'NaN'); # supplied arg overrides set global $class->precision(undef); $x = $class->new(12); $x->fsqrt(3); is ($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 $try; is ($ans,"$class 4 5"); } ############################################################################# # is_one('-') (broken until v1.64) is ($class->new(-1)->is_one(),0); is ($class->new(-1)->is_one('-'),1); ############################################################################# # bug 1/0.5 leaving 2e-0 instead of 2e0 is ($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 -= $x; is ($x, 0); $x = $class->new(-3); $x -= $x; is ($x, 0); $x = $class->new(3); $x += $x; is ($x, 6); $x = $class->new(-3); $x += $x; is ($x, -6); $x = $class->new('NaN'); $x -= $x; is ($x->is_nan(), 1); $x = $class->new('inf'); $x -= $x; is ($x->is_nan(), 1); $x = $class->new('-inf'); $x -= $x; is ($x->is_nan(), 1); $x = $class->new('NaN'); $x += $x; is ($x->is_nan(), 1); $x = $class->new('inf'); $x += $x; is ($x->is_inf(), 1); $x = $class->new('-inf'); $x += $x; is ($x->is_inf('-'), 1); $x = $class->new('3.14'); $x -= $x; is ($x, 0); $x = $class->new('-3.14'); $x -= $x; is ($x, 0); $x = $class->new('3.14'); $x += $x; is ($x, '6.28'); $x = $class->new('-3.14'); $x += $x; is ($x, '-6.28'); $x = $class->new('3.14'); $x *= $x; is ($x, '9.8596'); $x = $class->new('-3.14'); $x *= $x; is ($x, '9.8596'); $x = $class->new('3.14'); $x /= $x; is ($x, '1'); $x = $class->new('-3.14'); $x /= $x; is ($x, '1'); $x = $class->new('3.14'); $x %= $x; is ($x, '0'); $x = $class->new('-3.14'); $x %= $x; is ($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 = $class->new('0.1'); is ($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 = $class->new(".222222222222222222222222222222222222222222"); is ($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(); $x->accuracy(undef); is ($x,"20988936657440586486151264256610222593863921"); is ($x->length(),length "20988936657440586486151264256610222593863921"); $x = $class->new('2'); my $y = $class->new('18'); is ($x <<= $y, 2 << 18); is ($x, 2 << 18); is ($x >>= $y, 2); is ($x, 2); $x = $class->new('2'); $y = $class->new('18.2'); $x <<= $y; # 2 * (2 ** 18.2); is ($x->copy()->bfround(-9), '602248.763144685'); is ($x >>= $y, 2); # 2 * (2 ** 18.2) / (2 ** 18.2) => 2 is ($x, 2); 1; # all done __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; &bcos 1.2:10:0.3623577545 2.4:12:-0.737393715541 0:10:1 0:20:1 1:10:0.5403023059 1:12:0.540302305868 &bsin 1:10:0.8414709848 0:10:0 0:20:0 2.1:12:0.863209366649 1.2:13:0.9320390859672 0.2:13:0.1986693307951 3.2:12:-0.0583741434276 &batan NaN:10:NaN inf:14:1.5707963267949 -inf:14:-1.5707963267949 0.2:13:0.1973955598499 0.2:14:0.19739555984988 0:10:0 1:14:0.78539816339744 -1:14:-0.78539816339744 # test an argument X > 1 2:14:1.1071487177941 &batan2 NaN:1:10:NaN NaN:NaN:10:NaN 1:NaN:10:NaN inf:1:14:1.5707963267949 -inf:1:14:-1.5707963267949 0:-inf:14:3.1415926535898 -1:-inf:14:-3.1415926535898 1:-inf:14:3.1415926535898 0:inf:14:0 inf:-inf:14:2.3561944901923 -inf:-inf:14:-2.3561944901923 inf:+inf:14:0.7853981633974 -inf:+inf:14:-0.7853981633974 1:5:13:0.1973955598499 1:5:14:0.19739555984988 0:0:10:0 0:1:14:0 0:2:14:0 1:0:14:1.5707963267949 5:0:14:1.5707963267949 -1:0:11:-1.5707963268 -2:0:77:-1.5707963267948966192313216916397514420985846996875529104874722961539082031431 2:0:77:1.5707963267948966192313216916397514420985846996875529104874722961539082031431 -1:5:14:-0.19739555984988 1:5:14:0.19739555984988 -1:8:14:-0.12435499454676 1:8:14:0.12435499454676 -1:1:14:-0.78539816339744 # test an argument X > 1 and one X < 1 1:2:24:0.463647609000806116214256 2:1:14:1.1071487177941 -2:1:14:-1.1071487177941 &bpi 150:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940813 77:3.1415926535897932384626433832795028841971693993751058209749445923078164062862 +0:3.141592653589793238462643383279502884197 11:3.1415926536 &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 7:6:7 100:90:17310309456440 100:95:75287520 2:0:1 7:0:1 2:1:2 &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 -inf:-inf inf:inf NaN:NaN 71243225429896467497217836789578596379:71243225429896467497217836789578596379 # 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 &bmuladd abc:abc:0:NaN abc:+0:0:NaN +0:abc:0:NaN +0:0:abc:NaN NaNmul:+inf:0:NaN NaNmul:-inf:0:NaN -inf:NaNmul:0:NaN +inf:NaNmul:0:NaN +inf:+inf:0:inf +inf:-inf:0:-inf -inf:+inf:0:-inf -inf:-inf:0:inf +0:+0:0:0 +0:+1:0:0 +1:+0:0:0 +0:-1:0:0 -1:+0:0:0 123456789123456789:0:0:0 0:123456789123456789:0:0 -1:-1:0:1 -1:-1:0:1 -1:+1:0:-1 +1:-1:0:-1 +1:+1:0:1 +2:+3:0:6 -2:+3:0:-6 +2:-3:0:-6 -2:-3:0:6 111:111:0:12321 10101:10101:0:102030201 1001001:1001001:0:1002003002001 100010001:100010001:0:10002000300020001 10000100001:10000100001:0:100002000030000200001 11111111111:9:0:99999999999 22222222222:9:0:199999999998 33333333333:9:0:299999999997 44444444444:9:0:399999999996 55555555555:9:0:499999999995 66666666666:9:0:599999999994 77777777777:9:0:699999999993 88888888888:9:0:799999999992 99999999999:9:0:899999999991 11111111111:9:1:100000000000 22222222222:9:1:199999999999 33333333333:9:1:299999999998 44444444444:9:1:399999999997 55555555555:9:1:499999999996 66666666666:9:1:599999999995 77777777777:9:1:699999999994 88888888888:9:1:799999999993 99999999999:9:1:899999999992 -3:-4:-5:7 3:-4:-5:-17 -3:4:-5:-17 3:4:-5:7 -3:4:5:-7 3:-4:5:-7 9999999999999999999:10000000000000000000:1234567890:99999999999999999990000000001234567890 3.2:5.7:8.9:27.14 -3.2:5.197:6.05:-10.5804 &bmodpow 3:4:8:1 3:4:7:4 3:4:7:4 77777:777:123456789:99995084 3.2:6.2:5.2:2.970579856718063040273642739529400818 &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