Math::BigFloat(3pm) Perl Programmers Reference Guide Math::BigFloat(3pm)

## NAME

Math::BigFloat - Arbitrary size floating point math package

## SYNOPSIS

use Math::BigFloat; # Configuration methods (may be used as class methods and instance methods) Math::BigFloat->accuracy(); # get class accuracy Math::BigFloat->accuracy($n); # set class accuracy Math::BigFloat->precision(); # get class precision Math::BigFloat->precision($n); # set class precision Math::BigFloat->round_mode(); # get class rounding mode Math::BigFloat->round_mode($m); # set global round mode, must be one of # 'even', 'odd', '+inf', '-inf', 'zero', # 'trunc', or 'common' Math::BigFloat->config(); # return hash with configuration # Constructor methods (when the class methods below are used as instance # methods, the value is assigned the invocand) $x = Math::BigFloat->new($str); # defaults to 0 $x = Math::BigFloat->new('0x123'); # from hexadecimal $x = Math::BigFloat->new('0b101'); # from binary $x = Math::BigFloat->from_hex('0xc.afep+3'); # from hex $x = Math::BigFloat->from_hex('cafe'); # ditto $x = Math::BigFloat->from_oct('1.3267p-4'); # from octal $x = Math::BigFloat->from_oct('0377'); # ditto $x = Math::BigFloat->from_bin('0b1.1001p-4'); # from binary $x = Math::BigFloat->from_bin('0101'); # ditto $x = Math::BigFloat->bzero(); # create a +0 $x = Math::BigFloat->bone(); # create a +1 $x = Math::BigFloat->bone('-'); # create a -1 $x = Math::BigFloat->binf(); # create a +inf $x = Math::BigFloat->binf('-'); # create a -inf $x = Math::BigFloat->bnan(); # create a Not-A-Number $x = Math::BigFloat->bpi(); # returns pi $y = $x->copy(); # make a copy (unlike $y = $x) $y = $x->as_int(); # return as BigInt # Boolean methods (these don't modify the invocand) $x->is_zero(); # if $x is 0 $x->is_one(); # if $x is +1 $x->is_one("+"); # ditto $x->is_one("-"); # if $x is -1 $x->is_inf(); # if $x is +inf or -inf $x->is_inf("+"); # if $x is +inf $x->is_inf("-"); # if $x is -inf $x->is_nan(); # if $x is NaN $x->is_positive(); # if $x > 0 $x->is_pos(); # ditto $x->is_negative(); # if $x < 0 $x->is_neg(); # ditto $x->is_odd(); # if $x is odd $x->is_even(); # if $x is even $x->is_int(); # if $x is an integer # Comparison methods $x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0) $x->bacmp($y); # compare absolutely (undef, < 0, == 0, > 0) $x->beq($y); # true if and only if $x == $y $x->bne($y); # true if and only if $x != $y $x->blt($y); # true if and only if $x < $y $x->ble($y); # true if and only if $x <= $y $x->bgt($y); # true if and only if $x > $y $x->bge($y); # true if and only if $x >= $y # Arithmetic methods $x->bneg(); # negation $x->babs(); # absolute value $x->bsgn(); # sign function (-1, 0, 1, or NaN) $x->bnorm(); # normalize (no-op) $x->binc(); # increment $x by 1 $x->bdec(); # decrement $x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bmuladd($y,$z); # $x = $x * $y + $z $x->bdiv($y); # division (floored), set $x to quotient # return (quo,rem) or quo if scalar $x->btdiv($y); # division (truncated), set $x to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus (x % y) $x->btmod($y); # modulus (truncated) $x->bmodinv($mod); # modular multiplicative inverse $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod) $x->bpow($y); # power of arguments (x ** y) $x->blog(); # logarithm of $x to base e (Euler's number) $x->blog($base); # logarithm of $x to base $base (e.g., base 2) $x->bexp(); # calculate e ** $x where e is Euler's number $x->bnok($y); # x over y (binomial coefficient n over k) $x->bsin(); # sine $x->bcos(); # cosine $x->batan(); # inverse tangent $x->batan2($y); # two-argument inverse tangent $x->bsqrt(); # calculate square-root $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) $x->bfac(); # factorial of $x (1*2*3*4*..$x) $x->blsft($n); # left shift $n places in base 2 $x->blsft($n,$b); # left shift $n places in base $b # returns (quo,rem) or quo (scalar context) $x->brsft($n); # right shift $n places in base 2 $x->brsft($n,$b); # right shift $n places in base $b # returns (quo,rem) or quo (scalar context) # Bitwise methods $x->band($y); # bitwise and $x->bior($y); # bitwise inclusive or $x->bxor($y); # bitwise exclusive or $x->bnot(); # bitwise not (two's complement) # Rounding methods $x->round($A,$P,$mode); # round to accuracy or precision using # rounding mode $mode $x->bround($n); # accuracy: preserve $n digits $x->bfround($n); # $n > 0: round to $nth digit left of dec. point # $n < 0: round to $nth digit right of dec. point $x->bfloor(); # round towards minus infinity $x->bceil(); # round towards plus infinity $x->bint(); # round towards zero # Other mathematical methods $x->bgcd($y); # greatest common divisor $x->blcm($y); # least common multiple # Object property methods (do not modify the invocand) $x->sign(); # the sign, either +, - or NaN $x->digit($n); # the nth digit, counting from the right $x->digit(-$n); # the nth digit, counting from the left $x->length(); # return number of digits in number ($xl,$f) = $x->length(); # length of number and length of fraction # part, latter is always 0 digits long # for Math::BigInt objects $x->mantissa(); # return (signed) mantissa as BigInt $x->exponent(); # return exponent as BigInt $x->parts(); # return (mantissa,exponent) as BigInt $x->sparts(); # mantissa and exponent (as integers) $x->nparts(); # mantissa and exponent (normalised) $x->eparts(); # mantissa and exponent (engineering notation) $x->dparts(); # integer and fraction part # Conversion methods (do not modify the invocand) $x->bstr(); # decimal notation, possibly zero padded $x->bsstr(); # string in scientific notation with integers $x->bnstr(); # string in normalized notation $x->bestr(); # string in engineering notation $x->bdstr(); # string in decimal notation $x->as_hex(); # as signed hexadecimal string with prefixed 0x $x->as_bin(); # as signed binary string with prefixed 0b $x->as_oct(); # as signed octal string with prefixed 0 # Other conversion methods $x->numify(); # return as scalar (might overflow or underflow)

## DESCRIPTION

Math::BigFloat provides support for arbitrary precision floating point. Overloading is also provided for Perl operators. All operators (including basic math operations) are overloaded if you declare your big floating point numbers as $x = Math::BigFloat -> new('12_3.456_789_123_456_789E-2'); Operations with overloaded operators preserve the arguments, which is exactly what you expect.InputInput values to these routines may be any scalar number or string that looks like a number and represents a floating point number.oLeading and trailing whitespace is ignored.oLeading and trailing zeros are ignored.oIf the string has a "0x" prefix, it is interpreted as a hexadecimal number.oIf the string has a "0b" prefix, it is interpreted as a binary number.oFor hexadecimal and binary numbers, the exponent must be separated from the significand (mantissa) by the letter "p" or "P", not "e" or "E" as with decimal numbers.oOne underline is allowed between any two digits, including hexadecimal and binary digits.oIf the string can not be interpreted, NaN is returned. Octal numbers are typically prefixed by "0", but since leading zeros are stripped, these methods can not automatically recognize octal numbers, so use the constructorfrom_oct()to interpret octal strings. Some examples of valid string input Input string Resulting value 123 123 1.23e2 123 12300e-2 123 0xcafe 51966 0b1101 13 67_538_754 67538754 -4_5_6.7_8_9e+0_1_0 -4567890000000 0x1.921fb5p+1 3.14159262180328369140625e+0 0b1.1001p-4 9.765625e-2OutputOutput values are usually Math::BigFloat objects. Boolean operators "is_zero()", "is_one()", "is_inf()", etc. return true or false. Comparison operators "bcmp()" and "bacmp()") return -1, 0, 1, or undef.

## METHODS

Math::BigFloat supports all methods that Math::BigInt supports, except it calculates non-integer results when possible. Please see Math::BigInt for a full description of each method. Below are just the most important differences:Configurationmethodsaccuracy()$x->accuracy(5); # local for $x CLASS->accuracy(5); # global for all members of CLASS # Note: This also applies to new()! $A = $x->accuracy(); # read out accuracy that affects $x $A = CLASS->accuracy(); # read out global accuracy Set or get the global or local accuracy, aka how many significant digits the results have. If you set a global accuracy, then this also applies tonew()! Warning! The accuracysticks, e.g. once you created a number under the influence of "CLASS->accuracy($A)", all results from math operations with that number will also be rounded. In most cases, you should probably round the results explicitly using one of "round()" in Math::BigInt, "bround()" in Math::BigInt or "bfround()" in Math::BigInt or by passing the desired accuracy to the math operation as additional parameter: my $x = Math::BigInt->new(30000); my $y = Math::BigInt-> ; print scalar $x->copy()->bdiv($y, 2); # print 4300 print scalar $x->copy()->bdiv($y)->bround(2); # print 4300precision()$x->precision(-2); # local for $x, round at the second # digit right of the dot $x->precision(2); # ditto, round at the second digit # left of the dot CLASS->precision(5); # Global for all members of CLASS # This also applies to new()! CLASS->precision(-5); # ditto $P = CLASS->precision(); # read out global precision $P = $x->precision(); # read out precision that affects $x Note: You probably want to use "accuracy()" instead. With "accuracy()" you set the number of digits each result should have, with "precision()" you set the place where to round!Constructormethodsfrom_hex()$x -> from_hex("0x1.921fb54442d18p+1"); $x = Math::BigFloat -> from_hex("0x1.921fb54442d18p+1"); Interpret input as a hexadecimal string.A prefix ("0x", "x", ignoring case) is optional. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand.from_oct()$x -> from_oct("1.3267p-4"); $x = Math::BigFloat -> from_oct("1.3267p-4"); Interpret input as an octal string. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand.from_bin()$x -> from_bin("0b1.1001p-4"); $x = Math::BigFloat -> from_bin("0b1.1001p-4"); Interpret input as a hexadecimal string. A prefix ("0b" or "b", ignoring case) is optional. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand.bpi()print Math::BigFloat->bpi(100), "\n"; Calculate PI to N digits (including the 3 before the dot). The result is rounded according to the current rounding mode, which defaults to "even". This method was added in v1.87 of Math::BigInt (June 2007).Arithmeticmethodsbmuladd()$x->bmuladd($y,$z); Multiply $x by $y, and then add $z to the result. This method was added in v1.87 of Math::BigInt (June 2007).bdiv()$q = $x->bdiv($y); ($q, $r) = $x->bdiv($y); In scalar context, divides $x by $y and returns the result to the given or default accuracy/precision. In list context, does floored division (F-division), returning an integer $q and a remainder $r so that $x = $q * $y + $r. The remainer (modulo) is equal to what is returned by "$x-"bmod($y)>.bmod()$x->bmod($y); Returns $x modulo $y. When $x is finite, and $y is finite and non- zero, the result is identical to the remainder after floored division (F-division). If, in addition, both $x and $y are integers, the result is identical to the result from Perl's % operator.bexp()$x->bexp($accuracy); # calculate e ** X Calculates the expression "e ** $x" where "e" is Euler's number. This method was added in v1.82 of Math::BigInt (April 2007).bnok()$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 v1.84 of Math::BigInt (April 2007).bsin()my $x = Math::BigFloat->new(1); print $x->bsin(100), "\n"; Calculate the sinus of $x, modifying $x in place. This method was added in v1.87 of Math::BigInt (June 2007).bcos()my $x = Math::BigFloat->new(1); print $x->bcos(100), "\n"; Calculate the cosinus of $x, modifying $x in place. This method was added in v1.87 of Math::BigInt (June 2007).batan()my $x = Math::BigFloat->new(1); print $x->batan(100), "\n"; Calculate the arcus tanges of $x, modifying $x in place. See also "batan2()". This method was added in v1.87 of Math::BigInt (June 2007).batan2()my $y = Math::BigFloat->new(2); my $x = Math::BigFloat->new(3); print $y->batan2($x), "\n"; Calculate the arcus tanges of $y divided by $x, modifying $y in place. See also "batan()". This method was added in v1.87 of Math::BigInt (June 2007).as_float()This method is called when Math::BigFloat encounters an object it doesn't know how to handle. For instance, assume $x is a Math::BigFloat, or subclass thereof, and $y is defined, but not a Math::BigFloat, or subclass thereof. If you do $x -> badd($y); $y needs to be converted into an object that $x can deal with. This is done by first checking if $y is something that $x might be upgraded to. If that is the case, no further attempts are made. The next is to see if $y supports the method "as_float()". The method "as_float()" is expected to return either an object that has the same class as $x, a subclass thereof, or a string that "ref($x)->new()" can parse to create an object. In Math::BigFloat, "as_float()" has the same effect as "copy()".ACCURACYANDPRECISIONSee also: Rounding. Math::BigFloat supports both precision (rounding to a certain place before or after the dot) and accuracy (rounding to a certain number of digits). For a full documentation, examples and tips on these topics please see the large section about rounding in Math::BigInt. Since things likesqrt(2)or "1 / 3" must presented with a limited accuracy lest a operation consumes all resources, each operation produces no more than the requested number of digits. If there is no global precision or accuracy set,andthe operation in question was not called with a requested precision or accuracy,andthe input $x has no accuracy or precision set, then a fallback parameter will be used. For historical reasons, it is called "div_scale" and can be accessed via: $d = Math::BigFloat->div_scale(); # query Math::BigFloat->div_scale($n); # set to $n digits The default value for "div_scale" is 40. In case the result of one operation has more digits than specified, it is rounded. The rounding mode taken is either the default mode, or the one supplied to the operation after thescale: $x = Math::BigFloat->new(2); Math::BigFloat->accuracy(5); # 5 digits max $y = $x->copy()->bdiv(3); # gives 0.66667 $y = $x->copy()->bdiv(3,6); # gives 0.666667 $y = $x->copy()->bdiv(3,6,undef,'odd'); # gives 0.666667 Math::BigFloat->round_mode('zero'); $y = $x->copy()->bdiv(3,6); # will also give 0.666667 Note that "Math::BigFloat->accuracy()" and "Math::BigFloat->precision()" set the global variables, and thusanynewly created number will be subject to the global roundingimmediately. This means that in the examples above, the 3 as argument to "bdiv()" will also get an accuracy of5. It is less confusing to either calculate the result fully, and afterwards round it explicitly, or use the additional parameters to the math functions like so: use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3); print $y->bround(5),"\n"; # gives 0.66667 or use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3,5); # gives 0.66667 print "$y\n";Roundingbfround ( +$scale ) Rounds to the $scale'th place left from the '.', counting from the dot. The first digit is numbered 1. bfround ( -$scale ) Rounds to the $scale'th place right from the '.', counting from the dot. bfround ( 0 ) Rounds to an integer. bround ( +$scale ) Preserves accuracy to $scale digits from the left (aka significant digits) and pads the rest with zeros. If the number is between 1 and -1, the significant digits count from the first non-zero after the '.' bround ( -$scale ) and bround ( 0 ) These are effectively no-ops. All rounding functions take as a second parameter a rounding mode from one of the following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'. The default rounding mode is 'even'. By using "Math::BigFloat->round_mode($round_mode);" you can get and set the default mode for subsequent rounding. The usage of "$Math::BigFloat::$round_mode" is no longer supported. The second parameter to the round functions then overrides the default temporarily. The "as_number()" function returns a BigInt from a Math::BigFloat. It uses 'trunc' as rounding mode to make it equivalent to: $x = 2.5; $y = int($x) + 2; You can override this by passing the desired rounding mode as parameter to "as_number()": $x = Math::BigFloat->new(2.5); $y = $x->as_number('odd'); # $y = 3

## Autocreating constants

After "use Math::BigFloat ':constant'" all the floating point constants in the given scope are converted to "Math::BigFloat". This conversion happens at compile time. In particular perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' prints the value of "2E-100". Note that without conversion of constants the expression 2E-100 will be calculated as normal floating point number. Please note that ':constant' does not affect integer constants, nor binary nor hexadecimal constants. Use bignum or Math::BigInt to get this to work.MathlibraryMath with the numbers is done (by default) by a module called Math::BigInt::Calc. This is equivalent to saying: use Math::BigFloat lib => 'Calc'; You can change this by using: use Math::BigFloat lib => 'GMP';Note: General purpose packages should not be explicit about the library to use; let the script author decide which is best. Note: The keyword 'lib' will warn when the requested library could not be loaded. To suppress the warning use 'try' instead: use Math::BigFloat try => 'GMP'; If your script works with huge numbers and Calc is too slow for them, you can also for the loading of one of these libraries and if none of them can be used, the code will die: use Math::BigFloat only => 'GMP,Pari'; The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; See the respective low-level library documentation for further details. Please note that Math::BigFloat doesnotuse the denoted library itself, but it merely passes the lib argument to Math::BigInt. So, instead of the need to do: use Math::BigInt lib => 'GMP'; use Math::BigFloat; you can roll it all into one line: use Math::BigFloat lib => 'GMP'; It is also possible to just require Math::BigFloat: require Math::BigFloat; This will load the necessary things (like BigInt) when they are needed, and automatically. See Math::BigInt for more details than you ever wanted to know about using a different low-level library.UsingMath::BigInt::LiteFor backwards compatibility reasons it is still possible to request a different storage class for use with Math::BigFloat: use Math::BigFloat with => 'Math::BigInt::Lite'; However, this request is ignored, as the current code now uses the low- level math library for directly storing the number parts.

## EXPORTS

"Math::BigFloat" exports nothing by default, but can export the "bpi()" method: use Math::BigFloat qw/bpi/; print bpi(10), "\n";

## CAVEATS

Do not try to be clever to insert some operations in between switching libraries: require Math::BigFloat; my $matter = Math::BigFloat->bone() + 4; # load BigInt and Calc Math::BigFloat->import( lib => 'Pari' ); # load Pari, too my $anti_matter = Math::BigFloat->bone()+4; # now use Pari This will create objects with numbers stored in two different backend libraries, andVERYBADTHINGSwill happen when you use these together: my $flash_and_bang = $matter + $anti_matter; # Don't do this! stringify,bstr()Both stringify andbstr()now drop the leading '+'. The old code would return '+1.23', the new returns '1.23'. See the documentation in Math::BigInt for reasoning and details.brsft()The following will probably not print what you expect: my $c = Math::BigFloat->new('3.14159'); print $c->brsft(3,10),"\n"; # prints 0.00314153.1415 It prints both quotient and remainder, since print calls "brsft()" in list context. Also, "$c->brsft()" will modify $c, so be careful. You probably want to use print scalar $c->copy()->brsft(3,10),"\n"; # or if you really want to modify $c print scalar $c->brsft(3,10),"\n"; instead. Modifying and = Beware of: $x = Math::BigFloat->new(5); $y = $x; It will not do what you think, e.g. making a copy of $x. Instead it just makes a second reference to thesameobject and stores it in $y. Thus anything that modifies $x will modify $y (except overloaded math operators), and vice versa. See Math::BigInt for details and how to avoid that.precision()vs.accuracy()A common pitfall is to use "precision()" when you want to round a result to a certain number of digits: use Math::BigFloat; Math::BigFloat->precision(4); # does not do what you # think it does my $x = Math::BigFloat->new(12345); # rounds $x to "12000"! print "$x\n"; # print "12000" my $y = Math::BigFloat->new(3); # rounds $y to "0"! print "$y\n"; # print "0" $z = $x / $y; # 12000 / 0 => NaN! print "$z\n"; print $z->precision(),"\n"; # 4 Replacing "precision()" with "accuracy()" is probably not what you want, either: use Math::BigFloat; Math::BigFloat->accuracy(4); # enables global rounding: my $x = Math::BigFloat->new(123456); # rounded immediately # to "12350" print "$x\n"; # print "123500" my $y = Math::BigFloat->new(3); # rounded to "3 print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y),"\n"; # 41170 print $z->accuracy(),"\n"; # 4 What you want to use instead is: use Math::BigFloat; my $x = Math::BigFloat->new(123456); # no rounding print "$x\n"; # print "123456" my $y = Math::BigFloat->new(3); # no rounding print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y,4),"\n"; # 41150 print $z->accuracy(),"\n"; # undef In addition to computing what you expected, the last example also doesnot"taint" the result with an accuracy or precision setting, which would influence any further operation.

## BUGS

Please report any bugs or feature requests to "bug-math-bigint at rt.cpan.org", or through the web interface at <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

## SUPPORT

You can find documentation for this module with the perldoc command. perldoc Math::BigFloat You can also look for information at:oRT: CPAN's request tracker <https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt>oAnnoCPAN: Annotated CPAN documentation <http://annocpan.org/dist/Math-BigInt>oCPAN Ratings <http://cpanratings.perl.org/dist/Math-BigInt>oSearch CPAN <http://search.cpan.org/dist/Math-BigInt/>oCPAN Testers Matrix <http://matrix.cpantesters.org/?dist=Math-BigInt>oThe Bignum mailing listoPost to mailing list "bignum at lists.scsys.co.uk"oView mailing list <http://lists.scsys.co.uk/pipermail/bignum/>oSubscribe/Unsubscribe <http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>

## LICENSE

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.

## SEE ALSO

Math::BigFloat andMath::BigInt(3)as well as the backendsMath::BigInt::FastCalc(3),Math::BigInt::GMP(3), andMath::BigInt::Pari(3). The pragmasbignum(3),bigint(3)andbigrat(3)also might be of interest because they solve the autoupgrading/downgrading issue, at least partly.

## AUTHORS

oMark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.oCompletely rewritten by Tels <http://bloodgate.com> in 2001-2008.oFlorian Ragwitz <flora@cpan.org>, 2010.oPeter John Acklam <pjacklam@online.no>, 2011-. perl v5.26.1 2017-07-18 Math::BigFloat(3pm)

perl 5.26.1 - Generated Sun Nov 5 18:24:55 CST 2017