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

       Math::BigFloat -	Arbitrary size floating	point math package

	 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("lib");	 # name	of backend math	library

	 # 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
	 $x = Math::BigFloat->from_ieee754($b, "binary64");  # from IEEE-754 bytes
	 $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
	 $x->to_ieee754($format); # to bytes encoded according to IEEE 754-2008

	 # Other conversion methods

	 $x->numify();		 # return as scalar (might overflow or underflow)

       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.

       Input values to these routines may be any scalar	number or string that
       looks like a number and represents a floating point number.

       o   Leading and trailing	whitespace is ignored.

       o   Leading and trailing	zeros are ignored.

       o   If the string has a "0x" prefix, it is interpreted as a hexadecimal

       o   If the string has a "0b" prefix, it is interpreted as a binary

       o   For 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.

       o   One underline is allowed between any	two digits, including
	   hexadecimal and binary digits.

       o   If 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 constructor from_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-2

       Output 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.

       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:

   Configuration methods
	       $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	to new()!

	   Warning! The	accuracy sticks, 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->new(7);
	       print scalar $x->copy()->bdiv($y, 2);	       # print 4300
	       print scalar $x->copy()->bdiv($y)->bround(2);   # print 4300

	       $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!

   Constructor methods
	       $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

	       $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

	   If called as	an instance method, the	value is assigned to the

	       $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

	   Interpret the input as a value encoded as described in
	   IEEE754-2008.  The input can	be given as a byte string, hex string
	   or binary string. The input is assumed to be	in big-endian byte-

		   # both $dbl and $mbf	are 3.141592...
		   $bytes = "\x40\x09\x21\xfb\x54\x44\x2d\x18";
		   $dbl	= unpack "d>", $bytes;
		   $mbf	= Math::BigFloat -> from_ieee754($bytes, "binary64");

	       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).

   Arithmetic methods

	   Multiply $x by $y, and then add $z to the result.

	   This	method was added in v1.87 of Math::BigInt (June	2007).

	       $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)".


	   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 %

	       $x->bexp($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).

	       $x->bnok($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).

	       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).

	       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).

	       my $x = Math::BigFloat->new(1);
	       print $x->batan(100), "\n";

	   Calculate the arcus tanges of $x, modifying $x in place. See	also

	   This	method was added in v1.87 of Math::BigInt (June	2007).

	       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).

	   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()".

	   Encodes the invocand	as a byte string in the	given format as
	   specified in	IEEE 754-2008. Note that the encoded value is the
	   nearest possible representation of the value. This value might not
	   be exactly the same as the value in the invocand.

	       # $x = 3.1415926535897932385
	       $x = Math::BigFloat -> bpi(30);

	       $b = $x -> to_ieee754("binary64");  # encode as 8 bytes
	       $h = unpack "H*", $b;		   # "400921fb54442d18"

	       # 3.141592653589793115997963...
	       $y = Math::BigFloat -> from_ieee754($h, "binary64");

	   All binary formats in IEEE 754-2008 are accepted. For convenience,
	   som aliases are recognized: "half" for "binary16", "single" for
	   "binary32", "double"	for "binary64",	"quadruple" for	"binary128",
	   "octuple" for "binary256", and "sexdecuple" for "binary512".

	   See also <>.

       See 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 like sqrt(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,	and the	operation in
       question	was not	called with a requested	precision or accuracy, and the
       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 the scale:

	   $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
	   $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 thus	any
       newly created number will be subject to the global rounding
       immediately. This means that in the examples above, the 3 as argument
       to "bdiv()" will	also get an accuracy of	5.

       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


	   use Math::BigFloat;
	   $x =	Math::BigFloat->new(2);
	   $y =	$x->copy()->bdiv(3,5);		   # gives 0.66667
	   print "$y\n";

       bfround ( +$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

       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

       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

       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

       Please note that	':constant' does not affect integer constants, nor
       binary nor hexadecimal constants. Use bignum or Math::BigInt to get
       this to work.

   Math	library
       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 => '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

	   use Math::BigFloat lib => 'Foo,Math::BigInt::Bar';

       See the respective low-level library 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';

       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.

   Using Math::BigInt::Lite
       For 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.

       "Math::BigFloat"	exports	nothing	by default, but	can export the "bpi()"

	   use Math::BigFloat qw/bpi/;

	   print bpi(10), "\n";

       Do not try to be	clever to insert some operations in between switching

	   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, and VERY BAD THINGS will happen when you use these together:

	   my $flash_and_bang =	$matter	+ $anti_matter;	   # Don't do this!

       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 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";


       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 the	same object 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
	   does	not "taint" the	result with an accuracy	or precision setting,
	   which would influence any further operation.

       Please report any bugs or feature requests to "bug-math-bigint at", or	through	the web	interface at
       <> (requires
       login).	We will	be notified, and then you'll automatically be notified
       of progress on your bug as I make changes.

       You can find documentation for this module with the perldoc command.

	   perldoc Math::BigFloat

       You can also look for information at:

       o   RT: CPAN's request tracker


       o   AnnoCPAN: Annotated CPAN documentation


       o   CPAN	Ratings


       o   MetaCPAN


       o   CPAN	Testers	Matrix


       o   The Bignum mailing list

	   o   Post to mailing list

	       "bignum at"

	   o   View mailing list


	   o   Subscribe/Unsubscribe


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

       Math::BigFloat and Math::BigInt as well as the backends
       Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.

       The pragmas bignum, bigint and bigrat also might	be of interest because
       they solve the autoupgrading/downgrading	issue, at least	partly.

       o   Mark	Biggar,	overloaded interface by	Ilya Zakharevich, 1996-2001.

       o   Completely rewritten	by Tels	<> in 2001-2008.

       o   Florian Ragwitz <>, 2010.

       o   Peter John Acklam <>, 2011-.

perl v5.32.0			  2020-06-14		     Math::BigFloat(3)


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