- Autocreating constants
Math::BigFloat - Arbitrary size floating point math package
use Math::BigFloat; # Number creation $x = Math::BigFloat->new($str); # defaults to 0 $nan = Math::BigFloat->bnan(); # create a NotANumber $zero = Math::BigFloat->bzero(); # create a +0 $inf = Math::BigFloat->binf(); # create a +inf $inf = Math::BigFloat->binf('-'); # create a -inf $one = Math::BigFloat->bone(); # create a +1 $one = Math::BigFloat->bone('-'); # create a -1 # Testing $x->is_zero(); # true if arg is +0 $x->is_nan(); # true if arg is NaN $x->is_one(); # true if arg is +1 $x->is_one('-'); # true if arg is -1 $x->is_odd(); # true if odd, false for even $x->is_even(); # true if even, false for odd $x->is_positive(); # true if >= 0 $x->is_negative(); # true if < 0 $x->is_inf(sign); # true if +inf, or -inf (default is '+') $x->bcmp($y); # compare numbers (undef,<0,=0,>0) $x->bacmp($y); # compare absolutely (undef,<0,=0,>0) $x->sign(); # return the sign, either +,- or NaN $x->digit($n); # return the nth digit, counting from right $x->digit(-$n); # return the nth digit, counting from left # The following all modify their first argument: # set $x->bzero(); # set $i to 0 $x->bnan(); # set $i to NaN $x->bone(); # set $x to +1 $x->bone('-'); # set $x to -1 $x->binf(); # set $x to inf $x->binf('-'); # set $x to -inf $x->bneg(); # negation $x->babs(); # absolute value $x->bnorm(); # normalize (no-op) $x->bnot(); # two's complement (bit wise not) $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) $x->bdiv($y); # divide, set $i to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus $x->bpow($y); # power of arguments (a**b) $x->blsft($y); # left shift $x->brsft($y); # right shift # return (quo,rem) or quo if scalar $x->blog($base); # logarithm of $x, base defaults to e # (other bases than e not supported yet) $x->band($y); # bit-wise and $x->bior($y); # bit-wise inclusive or $x->bxor($y); # bit-wise exclusive or $x->bnot(); # bit-wise not (two's complement) $x->bsqrt(); # calculate square-root $x->bfac(); # factorial of $x (1*2*3*4*..$x) $x->bround($N); # accuracy: preserver $N digits $x->bfround($N); # precision: round to the $Nth digit # The following do not modify their arguments: bgcd(@values); # greatest common divisor blcm(@values); # lowest common multiplicator $x->bstr(); # return string $x->bsstr(); # return string in scientific notation $x->bfloor(); # return integer less or equal than $x $x->bceil(); # return integer greater or equal than $x $x->exponent(); # return exponent as BigInt $x->mantissa(); # return mantissa as BigInt $x->parts(); # return (mantissa,exponent) as BigInt $x->length(); # number of digits (w/o sign and '.') ($l,$f) = $x->length(); # number of digits, and length of fraction $x->precision(); # return P of $x (or global, if P of $x undef) $x->precision($n); # set P of $x to $n $x->accuracy(); # return A of $x (or global, if A of $x undef) $x->accuracy($n); # set A $x to $n Math::BigFloat->precision(); # get/set global P for all BigFloat objects Math::BigFloat->accuracy(); # get/set global A for all BigFloat objects
All operators (inlcuding basic math operations) are overloaded if you declare your big floating point numbers as
$i = new Math::BigFloat '12_3.456_789_123_456_789E-2';
Operations with overloaded operators preserve the arguments, which is exactly what you expect.
Input to these routines are either BigFloat objects, or strings of the following four forms:
all with optional leading and trailing zeros and/or spaces. Additonally, numbers are allowed to have an underscore between any two digits.
Empty strings as well as other illegal numbers results in 'NaN'.
bnorm() on a BigFloat object is now effectively a no-op, since the numbers are always stored in normalized form. On a string, it creates a BigFloat object.
Output values are BigFloat objects (normalized), except for bstr() and bsstr().
The string output will always have leading and trailing zeros stripped and drop a plus sign.
bstr() will give you always the form with a decimal point, while
bsstr() (for scientific) gives you the scientific notation.
Input bstr() bsstr() '-0' '0' '0E1' ' -123 123 123' '-123123123' '-123123123E0' '00.0123' '0.0123' '123E-4' '123.45E-2' '1.2345' '12345E-4' '10E+3' '10000' '1E4'
Some routines (
is_nan()) return true or false, while others (
bacmp()) return either undef, <0, 0 or >0 and are suited for sort.
Actual math is done by using BigInts to represent the mantissa and exponent. The sign
/^[+-]$/ is stored separately. The string 'NaN' is used to represent the result when input arguments are not numbers, as well as the result of dividing by zero.
exponent() return the said parts of the BigFloat as BigInts such that:
$m = $x->mantissa(); $e = $x->exponent(); $y = $m * ( 10 ** $e ); print "ok\n" if $x == $y;
($m,$e) = $x->parts(); is just a shortcut giving you both of them.
A zero is represented and returned as
0E0 (after Knuth).
Currently the mantissa is reduced as much as possible, favouring higher exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0). This might change in the future, so do not depend on it.
Accuracy vs. Precision
See also: Rounding.
Math::BigFloat supports both precision and accuracy. For a full documentation, examples and tips on these topics please see the large section in Math::BigInt.
Since things like sqrt(2) or 1/3 must presented with a limited precision lest a operation consumes all resources, each operation produces no more than
In case the result of one operation has more precision than specified, it is rounded. The rounding mode taken is either the default mode, or the one supplied to the operation after the scale:
$x = Math::BigFloat->new(2); Math::BigFloat::precision(5); # 5 digits max $y = $x->copy()->bdiv(3); # will give 0.66666 $y = $x->copy()->bdiv(3,6); # will give 0.666666 $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667 Math::BigFloat::round_mode('zero'); $y = $x->copy()->bdiv(3,6); # will give 0.666666
- ffround ( +$scale )
Rounds to the $scale'th place left from the '.', counting from the dot. The first digit is numbered 1.
- ffround ( -$scale )
Rounds to the $scale'th place right from the '.', counting from the dot.
- ffround ( 0 )
Rounds to an integer.
- fround ( +$scale )
Preserves accuracy to $scale digits from the left (aka significant digits) and pads the rest with zeros. If the number is between 1 and -1, the significant digits count from the first non-zero after the '.'
- fround ( -$scale ) and fround ( 0 )
These are effetively no-ops.
All rounding functions take as a second parameter a rounding mode from one of the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
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.
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
$x = Math::BigFloat->new(2.5); $y = $x->as_number('odd'); # $y = 3
# not ready yet
use Math::BigFloat ':constant' all the floating point constants in the given scope are converted to
Math::BigFloat. This conversion happens at compile time.
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.
Math 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 => 'BitVect';
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';
Calc.pm uses as internal format an array of elements of some decimal base (usually 1e7, but this might be differen for some systems) with the least significant digit first, while BitVect.pm uses a bit vector of base 2, most significant bit first. Other modules might use even different means of representing the numbers. See the respective module documentation for further details.
Please note that Math::BigFloat does not use 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';
Use the lib, Luke! And see "Using Math::BigInt::Lite" for more details.
It is possible to use Math::BigInt::Lite with Math::BigFloat:
# 1 use Math::BigFloat with => 'Math::BigInt::Lite';
There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you can combine these if you want. For instance, you may want to use Math::BigInt objects in your main script, too.
# 2 use Math::BigInt; use Math::BigFloat with => 'Math::BigInt::Lite';
Of course, you can combine this with the
# 3 use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
If you want to use Math::BigInt's, too, simple add a Math::BigInt before:
# 4 use Math::BigInt; use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
Notice that the module with the last
lib will "win" and thus it's lib will be used if the lib is available:
# 5 use Math::BigInt lib => 'Bar,Baz'; use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo';
That would try to load Foo, Bar, Baz and Calc (in that order). Or in other words, Math::BigFloat will try to retain previously loaded libs when you don't specify it one.
Actually, the lib loading order would be "Bar,Baz,Calc", and then "Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the same as trying the latter load alone, except for the fact that Bar or Baz might be loaded needlessly in an intermidiate step
The old way still works though:
# 6 use Math::BigInt lib => 'Bar,Baz'; use Math::BigFloat;
But examples #3 and #4 are recommended for usage.
The following does not work yet:
$m = $x->mantissa(); $e = $x->exponent(); $y = $m * ( 10 ** $e ); print "ok\n" if $x == $y;
There is no fmod() function yet.
- stringify, bstr()
Both stringify and bstr() 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.
The following will probably not do what you expect:
It prints both quotient and reminder since print works in list context. Also, bdiv() will modify $c, so be carefull. You probably want to use
print $c / 123.456,"\n"; print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c
- Modifying and =
$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 the same object and stores it in $y. Thus anything that modifies $x will modify $y, and vice versa.
$x->bmul(2); print "$x, $y\n"; # prints '10, 10'
If you want a true copy of $x, use:
$y = $x->copy();
See also the documentation in overload regarding
bpow()now modifies the first argument, unlike the old code which left it alone and only returned the result. This is to be consistent with
badd()etc. The first will modify $x, the second one won't:
print bpow($x,$i),"\n"; # modify $x print $x->bpow($i),"\n"; # ditto print $x ** $i,"\n"; # leave $x alone
This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.
Mark Biggar, overloaded interface by Ilya Zakharevich. Completely rewritten by Tels http://bloodgate.com in 2001.