path: root/upstream/debian-unstable/man3/Math::BigFloat.3perl

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.\"
.IX Title "Math::BigFloat 3perl"
.TH Math::BigFloat 3perl 2024-05-30 "perl v5.38.2" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH NAME
Math::BigFloat \- arbitrary size floating point math package
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 1
\&  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
\&                                  # \*(Aqeven\*(Aq, \*(Aqodd\*(Aq, \*(Aq+inf\*(Aq, \*(Aq\-inf\*(Aq, \*(Aqzero\*(Aq,
\&                                  # \*(Aqtrunc\*(Aq, or \*(Aqcommon\*(Aq
\&  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(\*(Aq0x123\*(Aq);            # from hexadecimal
\&  $x = Math::BigFloat\->new(\*(Aq0o377\*(Aq);            # from octal
\&  $x = Math::BigFloat\->new(\*(Aq0b101\*(Aq);            # from binary
\&  $x = Math::BigFloat\->from_hex(\*(Aq0xc.afep+3\*(Aq);  # from hex
\&  $x = Math::BigFloat\->from_hex(\*(Aqcafe\*(Aq);        # ditto
\&  $x = Math::BigFloat\->from_oct(\*(Aq1.3267p\-4\*(Aq);   # from octal
\&  $x = Math::BigFloat\->from_oct(\*(Aq01.3267p\-4\*(Aq);  # ditto
\&  $x = Math::BigFloat\->from_oct(\*(Aq0o1.3267p\-4\*(Aq); # ditto
\&  $x = Math::BigFloat\->from_oct(\*(Aq0377\*(Aq);        # ditto
\&  $x = Math::BigFloat\->from_bin(\*(Aq0b1.1001p\-4\*(Aq); # from binary
\&  $x = Math::BigFloat\->from_bin(\*(Aq0101\*(Aq);        # 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(\*(Aq\-\*(Aq);               # create a \-1
\&  $x = Math::BigFloat\->binf();                  # create a +inf
\&  $x = Math::BigFloat\->binf(\*(Aq\-\*(Aq);               # 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
\&  $y = $x\->as_float();    # return as a Math::BigFloat
\&  $y = $x\->as_rat();      # return as a Math::BigRat
\&
\&  # Boolean methods (these don\*(Aqt 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\*(Aqs number)
\&  $x\->blog($base);        # logarithm of $x to base $base (e.g., base 2)
\&  $x\->bexp();             # calculate e ** $x where e is Euler\*(Aqs 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\*(Aqth 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\*(Aqs 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
\&  $x\->fparts();            # numerator and denominator
\&  $x\->numerator();         # numerator
\&  $x\->denominator();       # denominator
\&
\&  # 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\->bfstr();        # string in fractional 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)
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
Math::BigFloat provides support for arbitrary precision floating point.
Overloading is also provided for Perl operators.
.PP
All operators (including basic math operations) are overloaded if you
declare your big floating point numbers as
.PP
.Vb 1
\&  $x = Math::BigFloat \-> new(\*(Aq12_3.456_789_123_456_789E\-2\*(Aq);
.Ve
.PP
Operations with overloaded operators preserve the arguments, which is
exactly what you expect.
.SS Input
.IX Subsection "Input"
Input values to these routines may be any scalar number or string that looks
like a number. Anything that is accepted by Perl as a literal numeric constant
should be accepted by this module.
.IP \(bu 4
Leading and trailing whitespace is ignored.
.IP \(bu 4
Leading zeros are ignored, except for floating point numbers with a binary
exponent, in which case the number is interpreted as an octal floating point
number. For example, "01.4p+0" gives 1.5, "00.4p+0" gives 0.5, but "0.4p+0"
gives a NaN. And while "0377" gives 255, "0377p0" gives 255.
.IP \(bu 4
If the string has a "0x" or "0X" prefix, it is interpreted as a hexadecimal
number.
.IP \(bu 4
If the string has a "0o" or "0O" prefix, it is interpreted as an octal number. A
floating point literal with a "0" prefix is also interpreted as an octal number.
.IP \(bu 4
If the string has a "0b" or "0B" prefix, it is interpreted as a binary number.
.IP \(bu 4
Underline characters are allowed in the same way as they are allowed in literal
numerical constants.
.IP \(bu 4
If the string can not be interpreted, NaN is returned.
.IP \(bu 4
For hexadecimal, octal, and binary floating point numbers, the exponent must be
separated from the significand (mantissa) by the letter "p" or "P", not "e" or
"E" as with decimal numbers.
.PP
Some examples of valid string input
.PP
.Vb 1
\&    Input string                Resulting value
\&
\&    123                         123
\&    1.23e2                      123
\&    12300e\-2                    123
\&
\&    67_538_754                  67538754
\&    \-4_5_6.7_8_9e+0_1_0         \-4567890000000
\&
\&    0x13a                       314
\&    0x13ap0                     314
\&    0x1.3ap+8                   314
\&    0x0.00013ap+24              314
\&    0x13a000p\-12                314
\&
\&    0o472                       314
\&    0o1.164p+8                  314
\&    0o0.0001164p+20             314
\&    0o1164000p\-10               314
\&
\&    0472                        472     Note!
\&    01.164p+8                   314
\&    00.0001164p+20              314
\&    01164000p\-10                314
\&
\&    0b100111010                 314
\&    0b1.0011101p+8              314
\&    0b0.00010011101p+12         314
\&    0b100111010000p\-3           314
\&
\&    0x1.921fb5p+1               3.14159262180328369140625e+0
\&    0o1.2677025p1               2.71828174591064453125
\&    01.2677025p1                2.71828174591064453125
\&    0b1.1001p\-4                 9.765625e\-2
.Ve
.SS Output
.IX Subsection "Output"
Output values are usually Math::BigFloat objects.
.PP
Boolean operators \f(CWis_zero()\fR, \f(CWis_one()\fR, \f(CWis_inf()\fR, etc. return true or
false.
.PP
Comparison operators \f(CWbcmp()\fR and \f(CWbacmp()\fR) return \-1, 0, 1, or
undef.
.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:
.SS "Configuration methods"
.IX Subsection "Configuration methods"
.IP \fBaccuracy()\fR 4
.IX Item "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
\&    $A = CLASS\->accuracy();    # read out global accuracy
.Ve
.Sp
Set or get the global or local accuracy, aka how many significant digits the
results have. If you set a global accuracy, then this also applies to \fBnew()\fR!
.Sp
Warning! The accuracy \fIsticks\fR, e.g. once you created a number under the
influence of \f(CW\*(C`CLASS\->accuracy($A)\*(C'\fR, all results from math operations with
that number will also be rounded.
.Sp
In most cases, you should probably round the results explicitly using one of
"\fBround()\fR" in Math::BigInt, "\fBbround()\fR" in Math::BigInt or "\fBbfround()\fR" in Math::BigInt
or by passing the desired accuracy to the math operation as additional
parameter:
.Sp
.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
.IP \fBprecision()\fR 4
.IX Item "precision()"
.Vb 4
\&    $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
.Sp
Note: You probably want to use "\fBaccuracy()\fR" instead. With "\fBaccuracy()\fR" you
set the number of digits each result should have, with "\fBprecision()\fR" you
set the place where to round!
.SS "Constructor methods"
.IX Subsection "Constructor methods"
.IP \fBfrom_hex()\fR 4
.IX Item "from_hex()"
.Vb 2
\&    $x \-> from_hex("0x1.921fb54442d18p+1");
\&    $x = Math::BigFloat \-> from_hex("0x1.921fb54442d18p+1");
.Ve
.Sp
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.
.Sp
If called as an instance method, the value is assigned to the invocand.
.IP \fBfrom_oct()\fR 4
.IX Item "from_oct()"
.Vb 2
\&    $x \-> from_oct("1.3267p\-4");
\&    $x = Math::BigFloat \-> from_oct("1.3267p\-4");
.Ve
.Sp
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.
.Sp
If called as an instance method, the value is assigned to the invocand.
.IP \fBfrom_bin()\fR 4
.IX Item "from_bin()"
.Vb 2
\&    $x \-> from_bin("0b1.1001p\-4");
\&    $x = Math::BigFloat \-> from_bin("0b1.1001p\-4");
.Ve
.Sp
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.
.Sp
If called as an instance method, the value is assigned to the invocand.
.IP \fBfrom_ieee754()\fR 4
.IX Item "from_ieee754()"
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-order.
.Sp
.Vb 4
\&        # both $dbl and $mbf are 3.141592...
\&        $bytes = "\ex40\ex09\ex21\exfb\ex54\ex44\ex2d\ex18";
\&        $dbl = unpack "d>", $bytes;
\&        $mbf = Math::BigFloat \-> from_ieee754($bytes, "binary64");
.Ve
.IP \fBbpi()\fR 4
.IX Item "bpi()"
.Vb 1
\&    print Math::BigFloat\->bpi(100), "\en";
.Ve
.Sp
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".
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.SS "Arithmetic methods"
.IX Subsection "Arithmetic methods"
.IP \fBbmuladd()\fR 4
.IX Item "bmuladd()"
.Vb 1
\&    $x\->bmuladd($y,$z);
.Ve
.Sp
Multiply \f(CW$x\fR by \f(CW$y\fR, and then add \f(CW$z\fR to the result.
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.IP \fBbdiv()\fR 4
.IX Item "bdiv()"
.Vb 2
\&    $q = $x\->bdiv($y);
\&    ($q, $r) = $x\->bdiv($y);
.Ve
.Sp
In scalar context, divides \f(CW$x\fR by \f(CW$y\fR and returns the result to the given or
default accuracy/precision. In list context, does floored division
(F\-division), returning an integer \f(CW$q\fR and a remainder \f(CW$r\fR so that \f(CW$x\fR = \f(CW$q\fR * \f(CW$y\fR +
\&\f(CW$r\fR. The remainer (modulo) is equal to what is returned by \f(CW\*(C`$x\->bmod($y)\*(C'\fR.
.IP \fBbmod()\fR 4
.IX Item "bmod()"
.Vb 1
\&    $x\->bmod($y);
.Ve
.Sp
Returns \f(CW$x\fR modulo \f(CW$y\fR. When \f(CW$x\fR is finite, and \f(CW$y\fR is finite and non-zero, the
result is identical to the remainder after floored division (F\-division). If,
in addition, both \f(CW$x\fR and \f(CW$y\fR are integers, the result is identical to the result
from Perl's % operator.
.IP \fBbexp()\fR 4
.IX Item "bexp()"
.Vb 1
\&    $x\->bexp($accuracy);            # calculate e ** X
.Ve
.Sp
Calculates the expression \f(CW\*(C`e ** $x\*(C'\fR where \f(CW\*(C`e\*(C'\fR is Euler's number.
.Sp
This method was added in v1.82 of Math::BigInt (April 2007).
.IP \fBbnok()\fR 4
.IX Item "bnok()"
.Vb 1
\&    $x\->bnok($y);   # x over y (binomial coefficient n over k)
.Ve
.Sp
Calculates the binomial coefficient n over k, also called the "choose"
function. The result is equivalent to:
.Sp
.Vb 3
\&    ( n )      n!
\&    | \- |  = \-\-\-\-\-\-\-
\&    ( k )    k!(n\-k)!
.Ve
.Sp
This method was added in v1.84 of Math::BigInt (April 2007).
.IP \fBbsin()\fR 4
.IX Item "bsin()"
.Vb 2
\&    my $x = Math::BigFloat\->new(1);
\&    print $x\->bsin(100), "\en";
.Ve
.Sp
Calculate the sinus of \f(CW$x\fR, modifying \f(CW$x\fR in place.
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.IP \fBbcos()\fR 4
.IX Item "bcos()"
.Vb 2
\&    my $x = Math::BigFloat\->new(1);
\&    print $x\->bcos(100), "\en";
.Ve
.Sp
Calculate the cosinus of \f(CW$x\fR, modifying \f(CW$x\fR in place.
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.IP \fBbatan()\fR 4
.IX Item "batan()"
.Vb 2
\&    my $x = Math::BigFloat\->new(1);
\&    print $x\->batan(100), "\en";
.Ve
.Sp
Calculate the arcus tanges of \f(CW$x\fR, modifying \f(CW$x\fR in place. See also "\fBbatan2()\fR".
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.IP \fBbatan2()\fR 4
.IX Item "batan2()"
.Vb 3
\&    my $y = Math::BigFloat\->new(2);
\&    my $x = Math::BigFloat\->new(3);
\&    print $y\->batan2($x), "\en";
.Ve
.Sp
Calculate the arcus tanges of \f(CW$y\fR divided by \f(CW$x\fR, modifying \f(CW$y\fR in place.
See also "\fBbatan()\fR".
.Sp
This method was added in v1.87 of Math::BigInt (June 2007).
.IP \fBas_float()\fR 4
.IX Item "as_float()"
This method is called when Math::BigFloat encounters an object it doesn't know
how to handle. For instance, assume \f(CW$x\fR is a Math::BigFloat, or subclass
thereof, and \f(CW$y\fR is defined, but not a Math::BigFloat, or subclass thereof. If
you do
.Sp
.Vb 1
\&    $x \-> badd($y);
.Ve
.Sp
\&\f(CW$y\fR needs to be converted into an object that \f(CW$x\fR can deal with. This is done by
first checking if \f(CW$y\fR is something that \f(CW$x\fR might be upgraded to. If that is the
case, no further attempts are made. The next is to see if \f(CW$y\fR supports the
method \f(CWas_float()\fR. The method \f(CWas_float()\fR is expected to return either an
object that has the same class as \f(CW$x\fR, a subclass thereof, or a string that
\&\f(CW\*(C`ref($x)\->new()\*(C'\fR can parse to create an object.
.Sp
In Math::BigFloat, \f(CWas_float()\fR has the same effect as \f(CWcopy()\fR.
.IP \fBto_ieee754()\fR 4
.IX Item "to_ieee754()"
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.
.Sp
.Vb 2
\&    # $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");
.Ve
.Sp
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".
.Sp
See also <https://en.wikipedia.org/wiki/IEEE_754>.
.SS "ACCURACY AND PRECISION"
.IX Subsection "ACCURACY AND 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 global 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);                 # gives 0.66667
\&    $y = $x\->copy()\->bdiv(3,6);               # gives 0.666667
\&    $y = $x\->copy()\->bdiv(3,6,undef,\*(Aqodd\*(Aq);   # gives 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(CWbdiv()\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";               # gives 0.66667
\&
\&    or
\&
\&    use Math::BigFloat;
\&    $x = Math::BigFloat\->new(2);
\&    $y = $x\->copy()\->bdiv(3,5);             # gives 0.66667
\&    print "$y\en";
.Ve
.SS Rounding
.IX Subsection "Rounding"
.IP "bfround ( +$scale )" 4
.IX Item "bfround ( +$scale )"
Rounds to the \f(CW$scale\fR'th place left from the '.', counting from the dot.
The first digit is numbered 1.
.IP "bfround ( \-$scale )" 4
.IX Item "bfround ( -$scale )"
Rounds to the \f(CW$scale\fR'th place right from the '.', counting from the dot.
.IP "bfround ( 0 )" 4
.IX Item "bfround ( 0 )"
Rounds to an integer.
.IP "bround  ( +$scale )" 4
.IX Item "bround ( +$scale )"
Preserves accuracy to \f(CW$scale\fR digits from the left (aka significant digits) and
pads the rest with zeros. If the number is between 1 and \-1, the significant
digits count from the first non-zero after the '.'
.IP "bround  ( \-$scale ) and bround ( 0 )" 4
.IX Item "bround ( -$scale ) and bround ( 0 )"
These are effectively no-ops.
.PP
All rounding functions take as a second parameter a rounding mode from one of
the following: 'even', 'odd', '+inf', '\-inf', 'zero', 'trunc' or 'common'.
.PP
The default rounding mode is 'even'. By using
\&\f(CW\*(C`Math::BigFloat\->round_mode($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(CWas_number()\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(CWas_number()\fR:
.PP
.Vb 2
\&    $x = Math::BigFloat\->new(2.5);
\&    $y = $x\->as_number(\*(Aqodd\*(Aq);      # $y = 3
.Ve
.SH "NUMERIC LITERALS"
.IX Header "NUMERIC LITERALS"
After \f(CW\*(C`use Math::BigFloat \*(Aq:constant\*(Aq\*(C'\fR all numeric literals in the given scope
are converted to \f(CW\*(C`Math::BigFloat\*(C'\fR objects. This conversion happens at compile
time.
.PP
For example,
.PP
.Vb 1
\&    perl \-MMath::BigFloat=:constant \-le \*(Aqprint 2e\-150\*(Aq
.Ve
.PP
prints the exact value of \f(CW2e\-150\fR. Note that without conversion of constants
the expression \f(CW2e\-150\fR is calculated using Perl scalars, which leads to an
inaccuracte result.
.PP
Note that strings are not affected, so that
.PP
.Vb 1
\&    use Math::BigFloat qw/:constant/;
\&
\&    $y = "1234567890123456789012345678901234567890"
\&            + "123456789123456789";
.Ve
.PP
does not give you what you expect. You need an explicit Math::BigFloat\->\fBnew()\fR
around at least one of the operands. You should also quote large constants to
prevent loss of precision:
.PP
.Vb 1
\&    use Math::BigFloat;
\&
\&    $x = Math::BigFloat\->new("1234567889123456789123456789123456789");
.Ve
.PP
Without the quotes Perl converts the large number to a floating point constant
at compile time, and then converts the result to a Math::BigFloat object at
runtime, which results in an inaccurate result.
.SS "Hexadecimal, octal, and binary floating point literals"
.IX Subsection "Hexadecimal, octal, and binary floating point literals"
Perl (and this module) accepts hexadecimal, octal, and binary floating point
literals, but use them with care with Perl versions before v5.32.0, because some
versions of Perl silently give the wrong result. Below are some examples of
different ways to write the number decimal 314.
.PP
Hexadecimal floating point literals:
.PP
.Vb 3
\&    0x1.3ap+8         0X1.3AP+8
\&    0x1.3ap8          0X1.3AP8
\&    0x13a0p\-4         0X13A0P\-4
.Ve
.PP
Octal floating point literals (with "0" prefix):
.PP
.Vb 3
\&    01.164p+8         01.164P+8
\&    01.164p8          01.164P8
\&    011640p\-4         011640P\-4
.Ve
.PP
Octal floating point literals (with "0o" prefix) (requires v5.34.0):
.PP
.Vb 3
\&    0o1.164p+8        0O1.164P+8
\&    0o1.164p8         0O1.164P8
\&    0o11640p\-4        0O11640P\-4
.Ve
.PP
Binary floating point literals:
.PP
.Vb 3
\&    0b1.0011101p+8    0B1.0011101P+8
\&    0b1.0011101p8     0B1.0011101P8
\&    0b10011101000p\-2  0B10011101000P\-2
.Ve
.SS "Math library"
.IX Subsection "Math library"
Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:
.PP
.Vb 1
\&    use Math::BigFloat lib => "Calc";
.Ve
.PP
You can change this by using:
.PP
.Vb 1
\&    use Math::BigFloat lib => "GMP";
.Ve
.PP
\&\fBNote\fR: General purpose packages should not be explicit about the library to
use; let the script author decide which is best.
.PP
Note: The keyword 'lib' will warn when the requested library could not be
loaded. To suppress the warning use 'try' instead:
.PP
.Vb 1
\&    use Math::BigFloat try => "GMP";
.Ve
.PP
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:
.PP
.Vb 1
\&    use Math::BigFloat only => "GMP,Pari";
.Ve
.PP
The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar,
and when this also fails, revert to Math::BigInt::Calc:
.PP
.Vb 1
\&    use Math::BigFloat lib => "Foo,Math::BigInt::Bar";
.Ve
.PP
See the respective low-level library documentation for further details.
.PP
See Math::BigInt for more details about using a different low-level library.
.SS "Using Math::BigInt::Lite"
.IX Subsection "Using Math::BigInt::Lite"
For backwards compatibility reasons it is still possible to
request a different storage class for use with Math::BigFloat:
.PP
.Vb 1
\&    use Math::BigFloat with => \*(AqMath::BigInt::Lite\*(Aq;
.Ve
.PP
However, this request is ignored, as the current code now uses the low-level
math library for directly storing the number parts.
.SH EXPORTS
.IX Header "EXPORTS"
\&\f(CW\*(C`Math::BigFloat\*(C'\fR exports nothing by default, but can export the \f(CWbpi()\fR
method:
.PP
.Vb 1
\&    use Math::BigFloat qw/bpi/;
\&
\&    print bpi(10), "\en";
.Ve
.SH CAVEATS
.IX Header "CAVEATS"
Do not try to be clever to insert some operations in between switching
libraries:
.PP
.Vb 4
\&    require Math::BigFloat;
\&    my $matter = Math::BigFloat\->bone() + 4;    # load BigInt and Calc
\&    Math::BigFloat\->import( lib => \*(AqPari\*(Aq );    # load Pari, too
\&    my $anti_matter = Math::BigFloat\->bone()+4; # now use Pari
.Ve
.PP
This will create objects with numbers stored in two different backend libraries,
and \fBVERY BAD THINGS\fR will happen when you use these together:
.PP
.Vb 1
\&    my $flash_and_bang = $matter + $anti_matter;    # Don\*(Aqt do this!
.Ve
.IP "stringify, \fBbstr()\fR" 4
.IX Item "stringify, bstr()"
Both stringify and \fBbstr()\fR 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.
.IP \fBbrsft()\fR 4
.IX Item "brsft()"
The following will probably not print what you expect:
.Sp
.Vb 2
\&    my $c = Math::BigFloat\->new(\*(Aq3.14159\*(Aq);
\&    print $c\->brsft(3,10),"\en";     # prints 0.00314153.1415
.Ve
.Sp
It prints both quotient and remainder, since print calls \f(CWbrsft()\fR in list
context. Also, \f(CW\*(C`$c\->brsft()\*(C'\fR will modify \f(CW$c\fR, so be careful.
You probably want to use
.Sp
.Vb 3
\&    print scalar $c\->copy()\->brsft(3,10),"\en";
\&    # or if you really want to modify $c
\&    print scalar $c\->brsft(3,10),"\en";
.Ve
.Sp
instead.
.IP "Modifying and =" 4
.IX Item "Modifying and ="
Beware of:
.Sp
.Vb 2
\&    $x = Math::BigFloat\->new(5);
\&    $y = $x;
.Ve
.Sp
It will not do what you think, e.g. making a copy of \f(CW$x\fR. Instead it just makes
a second reference to the \fBsame\fR object and stores it in \f(CW$y\fR. Thus anything
that modifies \f(CW$x\fR will modify \f(CW$y\fR (except overloaded math operators), and vice
versa. See Math::BigInt for details and how to avoid that.
.IP "\fBprecision()\fR vs. \fBaccuracy()\fR" 4
.IX Item "precision() vs. accuracy()"
A common pitfall is to use "\fBprecision()\fR" when you want to round a result to
a certain number of digits:
.Sp
.Vb 1
\&    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\en";                           # print "12000"
\&    my $y = Math::BigFloat\->new(3);         # rounds $y to "0"!
\&    print "$y\en";                           # print "0"
\&    $z = $x / $y;                           # 12000 / 0 => NaN!
\&    print "$z\en";
\&    print $z\->precision(),"\en";             # 4
.Ve
.Sp
Replacing "\fBprecision()\fR" with "\fBaccuracy()\fR" is probably not what you want,
either:
.Sp
.Vb 1
\&    use Math::BigFloat;
\&
\&    Math::BigFloat\->accuracy(4);          # enables global rounding:
\&    my $x = Math::BigFloat\->new(123456);  # rounded immediately
\&                                          #   to "12350"
\&    print "$x\en";                         # print "123500"
\&    my $y = Math::BigFloat\->new(3);       # rounded to "3
\&    print "$y\en";                         # print "3"
\&    print $z = $x\->copy()\->bdiv($y),"\en"; # 41170
\&    print $z\->accuracy(),"\en";            # 4
.Ve
.Sp
What you want to use instead is:
.Sp
.Vb 1
\&    use Math::BigFloat;
\&
\&    my $x = Math::BigFloat\->new(123456);    # no rounding
\&    print "$x\en";                           # print "123456"
\&    my $y = Math::BigFloat\->new(3);         # no rounding
\&    print "$y\en";                           # print "3"
\&    print $z = $x\->copy()\->bdiv($y,4),"\en"; # 41150
\&    print $z\->accuracy(),"\en";              # undef
.Ve
.Sp
In addition to computing what you expected, the last example also does \fBnot\fR
"taint" the result with an accuracy or precision setting, which would
influence any further operation.
.SH BUGS
.IX Header "BUGS"
Please report any bugs or feature requests to
\&\f(CW\*(C`bug\-math\-bigint at rt.cpan.org\*(C'\fR, 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.
.SH SUPPORT
.IX Header "SUPPORT"
You can find documentation for this module with the perldoc command.
.PP
.Vb 1
\&    perldoc Math::BigFloat
.Ve
.PP
You can also look for information at:
.IP \(bu 4
GitHub
.Sp
<https://github.com/pjacklam/p5\-Math\-BigInt>
.IP \(bu 4
RT: CPAN's request tracker
.Sp
<https://rt.cpan.org/Dist/Display.html?Name=Math\-BigInt>
.IP \(bu 4
MetaCPAN
.Sp
<https://metacpan.org/release/Math\-BigInt>
.IP \(bu 4
CPAN Testers Matrix
.Sp
<http://matrix.cpantesters.org/?dist=Math\-BigInt>
.IP \(bu 4
CPAN Ratings
.Sp
<https://cpanratings.perl.org/dist/Math\-BigInt>
.IP \(bu 4
The Bignum mailing list
.RS 4
.IP \(bu 4
Post to mailing list
.Sp
\&\f(CW\*(C`bignum at lists.scsys.co.uk\*(C'\fR
.IP \(bu 4
View mailing list
.Sp
<http://lists.scsys.co.uk/pipermail/bignum/>
.IP \(bu 4
Subscribe/Unsubscribe
.Sp
<http://lists.scsys.co.uk/cgi\-bin/mailman/listinfo/bignum>
.RE
.RS 4
.RE
.SH LICENSE
.IX Header "LICENSE"
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::BigInt and Math::BigInt as well as the backends
Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.
.PP
The pragmas bignum, bigint and bigrat.
.SH AUTHORS
.IX Header "AUTHORS"
.IP \(bu 4
Mark Biggar, overloaded interface by Ilya Zakharevich, 1996\-2001.
.IP \(bu 4
Completely rewritten by Tels <http://bloodgate.com> in 2001\-2008.
.IP \(bu 4
Florian Ragwitz <flora@cpan.org>, 2010.
.IP \(bu 4
Peter John Acklam <pjacklam@gmail.com>, 2011\-.