math::bigfloat.3

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\&\f(CW\*(C`/^[+\-]\ed+E[+\-]?\ed+$/\*(C'\fR
.IP "\(bu" 2
\&\f(CW\*(C`/^[+\-]\ed*\e.\ed+E[+\-]?\ed+$/\*(C'\fR
.PP
all with optional leading and trailing zeros and/or spaces. Additionally,
numbers are allowed to have an underscore between any two digits.
.PP
Empty strings as well as other illegal numbers results in 'NaN'.
.PP
\&\fIbnorm()\fR on a BigFloat object is now effectively a no-op, since the numbers 
are always stored in normalized form. On a string, it creates a BigFloat 
object.
.Sh "Output"
.IX Subsection "Output"
Output values are BigFloat objects (normalized), except for \fIbstr()\fR and \fIbsstr()\fR.
.PP
The string output will always have leading and trailing zeros stripped and drop
a plus sign. \f(CW\*(C`bstr()\*(C'\fR will give you always the form with a decimal point,
while \f(CW\*(C`bsstr()\*(C'\fR (s for scientific) gives you the scientific notation.
.PP
.Vb 6
\&        Input                   bstr()          bsstr()
\&        \*(Aq\-0\*(Aq                    \*(Aq0\*(Aq             \*(Aq0E1\*(Aq
\&        \*(Aq  \-123 123 123\*(Aq        \*(Aq\-123123123\*(Aq    \*(Aq\-123123123E0\*(Aq
\&        \*(Aq00.0123\*(Aq               \*(Aq0.0123\*(Aq        \*(Aq123E\-4\*(Aq
\&        \*(Aq123.45E\-2\*(Aq             \*(Aq1.2345\*(Aq        \*(Aq12345E\-4\*(Aq
\&        \*(Aq10E+3\*(Aq                 \*(Aq10000\*(Aq         \*(Aq1E4\*(Aq
.Ve
.PP
Some routines (\f(CW\*(C`is_odd()\*(C'\fR, \f(CW\*(C`is_even()\*(C'\fR, \f(CW\*(C`is_zero()\*(C'\fR, \f(CW\*(C`is_one()\*(C'\fR,
\&\f(CW\*(C`is_nan()\*(C'\fR) return true or false, while others (\f(CW\*(C`bcmp()\*(C'\fR, \f(CW\*(C`bacmp()\*(C'\fR)
return either undef, <0, 0 or >0 and are suited for sort.
.PP
Actual math is done by using the class defined with \f(CW\*(C`with =\*(C'\fR Class;> (which
defaults to BigInts) to represent the mantissa and exponent.
.PP
The sign \f(CW\*(C`/^[+\-]$/\*(C'\fR 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.
.ie n .Sh """mantissa()""\fP, \f(CW""exponent()""\fP and \f(CW""parts()"""
.el .Sh "\f(CWmantissa()\fP, \f(CWexponent()\fP and \f(CWparts()\fP"
.IX Subsection "mantissa(), exponent() and parts()"
\&\f(CW\*(C`mantissa()\*(C'\fR and \f(CW\*(C`exponent()\*(C'\fR return the said parts of the BigFloat 
as BigInts such that:
.PP
.Vb 4
\&        $m = $x\->mantissa();
\&        $e = $x\->exponent();
\&        $y = $m * ( 10 ** $e );
\&        print "ok\en" if $x == $y;
.Ve
.PP
\&\f(CW\*(C`($m,$e) = $x\->parts();\*(C'\fR is just a shortcut giving you both of them.
.PP
A zero is represented and returned as \f(CW0E1\fR, \fBnot\fR \f(CW0E0\fR (after Knuth).
.PP
Currently the mantissa is reduced as much as possible, favouring higher
exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0).
This might change in the future, so do not depend on it.
.Sh "Accuracy vs. Precision"
.IX Subsection "Accuracy vs. Precision"
See also: Rounding.
.PP
Math::BigFloat supports both precision (rounding to a certain place before or
after the dot) and accuracy (rounding to a certain number of digits). For a
full documentation, examples and tips on these topics please see the large
section about rounding in Math::BigInt.
.PP
Since things like \f(CWsqrt(2)\fR or \f(CW\*(C`1 / 3\*(C'\fR must presented with a limited
accuracy lest a operation consumes all resources, each operation produces
no more than the requested number of digits.
.PP
If there is no gloabl precision or accuracy set, \fBand\fR the operation in
question was not called with a requested precision or accuracy, \fBand\fR the
input \f(CW$x\fR has no accuracy or precision set, then a fallback parameter will
be used. For historical reasons, it is called \f(CW\*(C`div_scale\*(C'\fR and can be accessed
via:
.PP
.Vb 2
\&        $d = Math::BigFloat\->div_scale();               # query
\&        Math::BigFloat\->div_scale($n);                  # set to $n digits
.Ve
.PP
The default value for \f(CW\*(C`div_scale\*(C'\fR is 40.
.PP
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 the \fIscale\fR:
.PP
.Vb 7
\&        $x = Math::BigFloat\->new(2);
\&        Math::BigFloat\->accuracy(5);            # 5 digits max
\&        $y = $x\->copy()\->bdiv(3);               # will give 0.66667
\&        $y = $x\->copy()\->bdiv(3,6);             # will give 0.666667
\&        $y = $x\->copy()\->bdiv(3,6,undef,\*(Aqodd\*(Aq); # will give 0.666667
\&        Math::BigFloat\->round_mode(\*(Aqzero\*(Aq);
\&        $y = $x\->copy()\->bdiv(3,6);             # will also give 0.666667
.Ve
.PP
Note that \f(CW\*(C`Math::BigFloat\->accuracy()\*(C'\fR and \f(CW\*(C`Math::BigFloat\->precision()\*(C'\fR
set the global variables, and thus \fBany\fR newly created number will be subject
to the global rounding \fBimmediately\fR. This means that in the examples above, the
\&\f(CW3\fR as argument to \f(CW\*(C`bdiv()\*(C'\fR will also get an accuracy of \fB5\fR.
.PP
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:
.PP
.Vb 4
\&        use Math::BigFloat;     
\&        $x = Math::BigFloat\->new(2);
\&        $y = $x\->copy()\->bdiv(3);
\&        print $y\->bround(5),"\en";               # will give 0.66667
\&
\&        or
\&
\&        use Math::BigFloat;     
\&        $x = Math::BigFloat\->new(2);
\&        $y = $x\->copy()\->bdiv(3,5);             # will give 0.66667
\&        print "$y\en";
.Ve
.Sh "Rounding"
.IX Subsection "Rounding"
.IP "ffround ( +$scale )" 2
.IX Item "ffround ( +$scale )"
Rounds to the \f(CW$scale\fR'th place left from the '.', counting from the dot.
The first digit is numbered 1.
.IP "ffround ( \-$scale )" 2
.IX Item "ffround ( -$scale )"
Rounds to the \f(CW$scale\fR'th place right from the '.', counting from the dot.
.IP "ffround ( 0 )" 2
.IX Item "ffround ( 0 )"
Rounds to an integer.
.IP "fround  ( +$scale )" 2
.IX Item "fround  ( +$scale )"
Preserves accuracy to \f(CW$scale\fR digits from the left (aka significant digits)
and pads the rest with zeros. If the number is between 1 and \-1, the
significant digits count from the first non-zero after the '.'
.IP "fround  ( \-$scale ) and fround ( 0 )" 2
.IX Item "fround  ( -$scale ) and fround ( 0 )"
These are effectively no-ops.
.PP
All rounding functions take as a second parameter a rounding mode from one of
the following: 'even', 'odd', '+inf', '\-inf', 'zero', 'trunc' or 'common'.
.PP
The default rounding mode is 'even'. By using
\&\f(CW\*(C`Math::BigFloat\->round_mode($round_mode);\*(C'\fR you can get and set the default
mode for subsequent rounding. The usage of \f(CW\*(C`$Math::BigFloat::$round_mode\*(C'\fR is
no longer supported.
The second parameter to the round functions then overrides the default
temporarily.
.PP
The \f(CW\*(C`as_number()\*(C'\fR function returns a BigInt from a Math::BigFloat. It uses
\&'trunc' as rounding mode to make it equivalent to:
.PP
.Vb 2
\&        $x = 2.5;
\&        $y = int($x) + 2;
.Ve
.PP
You can override this by passing the desired rounding mode as parameter to
\&\f(CW\*(C`as_number()\*(C'\fR:
.PP
.Vb 2
\&        $x = Math::BigFloat\->new(2.5);
\&        $y = $x\->as_number(\*(Aqodd\*(Aq);      # $y = 3
.Ve
.SH "METHODS"
.IX Header "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:
.Sh "accuracy"
.IX Subsection "accuracy"
.Vb 3
\&        $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
\&        $A = CLASS\->accuracy();         # read out global accuracy
.Ve
.PP
Set or get the global or local accuracy, aka how many significant digits the
results have. If you set a global accuracy, then this also applies to \fInew()\fR!
.PP
Warning! The accuracy \fIsticks\fR, e.g. once you created a number under the
influence of \f(CW\*(C`CLASS\->accuracy($A)\*(C'\fR, all results from math operations with
that number will also be rounded.
.PP
In most cases, you should probably round the results explicitly using one of
\&\fIround()\fR, \fIbround()\fR or \fIbfround()\fR or by passing the desired accuracy
to the math operation as additional parameter:
.PP
.Vb 4
\&        my $x = Math::BigInt\->new(30000);
\&        my $y = Math::BigInt\->new(7);
\&        print scalar $x\->copy()\->bdiv($y, 2);           # print 4300
\&        print scalar $x\->copy()\->bdiv($y)\->bround(2);   # print 4300
.Ve
.Sh "\fIprecision()\fP"
.IX Subsection "precision()"
.Vb 2
\&        $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
.Ve
.PP
Note: You probably want to use \fIaccuracy()\fR instead. With accuracy you
set the number of digits each result should have, with precision you
set the place where to round!
.Sh "\fIbexp()\fP"
.IX Subsection "bexp()"
.Vb 1
\&        $x\->bexp($accuracy);            # calculate e ** X
.Ve
.PP
Calculates the expression \f(CW\*(C`e ** $x\*(C'\fR where \f(CW\*(C`e\*(C'\fR is Euler's number.
.PP
This method was added in v1.82 of Math::BigInt (April 2007).
.Sh "\fIbnok()\fP"
.IX Subsection "bnok()"
.Vb 1
\&        $x\->bnok($y);              # x over y (binomial coefficient n over k)
.Ve
.PP
Calculates the binomial coefficient n over k, also called the \*(L"choose\*(R"
function. The result is equivalent to:
.PP
.Vb 3
\&        ( n )      n!
\&        | \- |  = \-\-\-\-\-\-\-
\&        ( k )    k!(n\-k)!
.Ve
.PP
This method was added in v1.84 of Math::BigInt (April 2007).
.Sh "\fIbpi()\fP"
.IX Subsection "bpi()"
.Vb 1
\&        print Math::BigFloat\->bpi(100), "\en";
.Ve
.PP
Calculate \s-1PI\s0 to N digits (including the 3 before the dot). The result is
rounded according to the current rounding mode, which defaults to \*(L"even\*(R".
.PP
This method was added in v1.87 of Math::BigInt (June 2007).
.Sh "\fIbcos()\fP"
.IX Subsection "bcos()"
.Vb 2
\&        my $x = Math::BigFloat\->new(1);
\&        print $x\->bcos(100), "\en";
.Ve
.PP
Calculate the cosinus of \f(CW$x\fR, modifying \f(CW$x\fR in place.
.PP
This method was added in v1.87 of Math::BigInt (June 2007).
.Sh "\fIbsin()\fP"
.IX Subsection "bsin()"
.Vb 2
\&        my $x = Math::BigFloat\->new(1);
\&        print $x\->bsin(100), "\en";
.Ve
.PP
Calculate the sinus of \f(CW$x\fR, modifying \f(CW$x\fR in place.
.PP
This method was added in v1.87 of Math::BigInt (June 2007).
.Sh "\fIbatan2()\fP"
.IX Subsection "batan2()"
.Vb 3
\&        my $y = Math::BigFloat\->new(2);
\&        my $x = Math::BigFloat\->new(3);
\&        print $y\->batan2($x), "\en";
.Ve
.PP