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($n); # set accuracyMath::BigFloat->accuracy(); # get accuracyMath::BigFloat->precision($n); # set precisionMath::BigFloat->precision(); # get precisionMath::BigFloat->round_mode($m); # set rounding mode, must be # 'even', 'odd', '+inf', '-inf', # 'zero', 'trunc', or 'common'Math::BigFloat->round_mode(); # get class rounding modeMath::BigFloat->div_scale($n); # set fallback accuracyMath::BigFloat->div_scale(); # get fallback accuracyMath::BigFloat->trap_inf($b); # trap infinities or notMath::BigFloat->trap_inf(); # get trap infinities statusMath::BigFloat->trap_nan($b); # trap NaNs or notMath::BigFloat->trap_nan(); # get trap NaNs statusMath::BigFloat->config($par, $val); # set configuration parameterMath::BigFloat->config($par); # get configuration parameterMath::BigFloat->config(); # get hash with configurationMath::BigFloat->config("lib"); # get name of backend library# Generic constructor method (always returns a new object)$x = Math::BigFloat->new($str); # defaults to 0$x = Math::BigFloat->new('256'); # from decimal$x = Math::BigFloat->new('0256'); # from decimal$x = Math::BigFloat->new('0xcafe'); # from hexadecimal$x = Math::BigFloat->new('0x1.cafep+7'); # from hexadecimal$x = Math::BigFloat->new('0o377'); # from octal$x = Math::BigFloat->new('0o1.3571p+6'); # from octal$x = Math::BigFloat->new('0b101'); # from binary$x = Math::BigFloat->new('0b1.101p+3'); # from binary# Specific constructor methods (no prefix needed; when used as# instance method, the value is assigned to the invocand)$x = Math::BigFloat->from_dec('234'); # from decimal$x = Math::BigFloat->from_hex('c.afep+3'); # from hexadecimal$x = Math::BigFloat->from_hex('cafe'); # from hexadecimal$x = Math::BigFloat->from_oct('1.3267p-4'); # from octal$x = Math::BigFloat->from_oct('377'); # from octal$x = Math::BigFloat->from_bin('0b1.1001p-4'); # from binary$x = Math::BigFloat->from_bin('0101'); # from binary$x = Math::BigFloat->from_bytes($bytes); # from byte string$x = Math::BigFloat->from_base('why', 36); # from any base$x = Math::BigFloat->from_ieee754($b, $fmt); # from IEEE-754 bytes$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 = $x->as_int(); # return as BigInt$y = $x->as_float(); # return as a Math::BigFloat$y = $x->as_rat(); # return as a Math::BigRat# Boolean methods (these don't modify the invocand)$x->is_zero(); # true if $x is 0$x->is_one(); # true if $x is +1$x->is_one("+"); # true if $x is +1$x->is_one("-"); # true if $x is -1$x->is_inf(); # true if $x is +inf or -inf$x->is_inf("+"); # true if $x is +inf$x->is_inf("-"); # true if $x is -inf$x->is_nan(); # true if $x is NaN$x->is_finite(); # true if -inf < $x < inf$x->is_positive(); # true if $x > 0$x->is_pos(); # true if $x > 0$x->is_negative(); # true if $x < 0$x->is_neg(); # true if $x < 0$x->is_non_positive() # true if $x <= 0$x->is_non_negative() # true if $x >= 0$x->is_odd(); # true if $x is odd$x->is_even(); # true if $x is even$x->is_int(); # true if $x is an integer# Comparison methods (these don't modify the invocand)$x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0)$x->bacmp($y); # compare abs values (undef, < 0, == 0, > 0)$x->beq($y); # true if $x == $y$x->bne($y); # true if $x != $y$x->blt($y); # true if $x < $y$x->ble($y); # true if $x <= $y$x->bgt($y); # true if $x > $y$x->bge($y); # true if $x >= $y# Arithmetic methods (these modify the invocand)$x->bneg(); # negation$x->babs(); # absolute value$x->bsgn(); # sign function (-1, 0, 1, or NaN)$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 $x to quotient$x->bmod($y); # modulus (x % y)$x->bmodinv($mod); # modular multiplicative inverse$x->bmodpow($y, $mod); # modular exponentiation (($x ** $y) % $mod)$x->btdiv($y); # division (truncated), set $x to quotient$x->btmod($y); # modulus (truncated)$x->binv() # inverse (1/$x)$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->bilog2(); # log2($x) rounded down to nearest int$x->bilog10(); # log10($x) rounded down to nearest int$x->bclog2(); # log2($x) rounded up to nearest int$x->bclog10(); # log10($x) rounded up to nearest int$x->bnok($y); # combinations (binomial coefficient n over k)$x->bperm($y); # permutations$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->bdfac(); # double factorial of $x ($x*($x-2)*($x-4)*...)$x->btfac(); # triple factorial of $x ($x*($x-3)*($x-6)*...)$x->bmfac($k); # $k'th multi-factorial of $x ($x*($x-$k)*...)$x->bfib($k); # $k'th Fibonacci number$x->blucas($k); # $k'th Lucas number$x->blsft($n); # left shift $n places in base 2$x->blsft($n, $b); # left shift $n places in base $b$x->brsft($n); # right shift $n places in base 2$x->brsft($n, $b); # right shift $n places in base $b# Bitwise methods (these modify the invocand)$x->bblsft($y); # bitwise left shift$x->bbrsft($y); # bitwise right shift$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 (these modify the invocand)$x->round($A, $P, $R); # round to accuracy or precision using # rounding mode $R$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 (these don't modify the invocand)$x->bgcd($y); # greatest common divisor$x->blcm($y); # least common multiple# Object property methods (these don't 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$x->mantissa(); # return (signed) mantissa as BigInt$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 (these don't 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$x->bdstr(); # string in decimal notation (no padding)$x->bfstr(); # string in fractional notation$x->to_hex(); # as signed hexadecimal string$x->to_bin(); # as signed binary string$x->to_oct(); # as signed octal string$x->to_bytes(); # as byte string$x->to_ieee754($fmt); # to bytes encoded according to IEEE 754-2008$x->as_hex(); # as signed hexadecimal string with "0x" prefix$x->as_bin(); # as signed binary string with "0b" prefix$x->as_oct(); # as signed octal string with "0" prefix# Other conversion methods (these don't modify the invocand)$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.
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.
Leading and trailing whitespace is ignored.
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.
If the string has a "0x" or "0X" prefix, it is interpreted as a hexadecimal number.
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.
If the string has a "0b" or "0B" prefix, it is interpreted as a binary number.
Underline characters are allowed in the same way as they are allowed in literal numerical constants.
If the string can not be interpreted, NaN is returned.
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.
Some examples of valid string input
Input string Resulting value123 1231.23e2 12312300e-2 12367_538_754 67538754-4_5_6.7_8_9e+0_1_0 -45678900000000x13a 3140x13ap0 3140x1.3ap+8 3140x0.00013ap+24 3140x13a000p-12 3140o472 3140o1.164p+8 3140o0.0001164p+20 3140o1164000p-10 3140472 472 Note!01.164p+8 31400.0001164p+20 31401164000p-10 3140b100111010 3140b1.0011101p+8 3140b0.00010011101p+12 3140b100111010000p-3 3140x1.921fb5p+1 3.14159262180328369140625e+00o1.2677025p1 2.7182817459106445312501.2677025p1 2.718281745910644531250b1.1001p-4 9.765625e-2Output
Output values are usually Math::BigFloat objects.
Boolean operatorsis_zero(),is_one(),is_inf(), etc. return true or false.
Comparison operatorsbcmp() andbacmp()) 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 seeMath::BigInt for a full description of each method. Below are just the most important differences:
Configuration methods
- accuracy()
$x->accuracy(5); # local for $xCLASS->accuracy(5); # global for all members of CLASS # Note: This also applies to new()!$A = $x->accuracy(); # read out accuracy that affects $x$A = CLASS->accuracy(); # read out global accuracySet 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 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->new(7);print scalar $x->copy()->bdiv($y, 2); # print 4300print scalar $x->copy()->bdiv($y)->bround(2); # print 4300- precision()
$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 dotCLASS->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 $xNote: 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
- from_dec()
$x -> from_hex("314159");$x = Math::BigInt -> from_hex("314159");Interpret input as a decimal. It is equivalent to new(), but does not accept anything but strings representing finite, decimal numbers.
- from_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.
- from_bytes()
$x = Math::BigFloat->from_bytes("\xf3\x6b"); # $x = 62315Interpret the input as a byte string, assuming big endian byte order. The output is always a non-negative, finite integer.
- 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.
# Both $dbl, $xr, $xh, and $xb below are 3.141592...$dbl = unpack "d>", "\x40\x09\x21\xfb\x54\x44\x2d\x18";$raw = "\x40\x09\x21\xfb\x54\x44\x2d\x18"; # raw bytes$xr = Math::BigFloat -> from_ieee754($raw, "binary64");$hex = "400921fb54442d18";$xh = Math::BigFloat -> from_ieee754($hex, "binary64");$bin = "0100000000001001001000011111101101010100010001000010110100011000";$xb = Math::BigFloat -> from_ieee754($bin, "binary64");Supported formats are all IEEE 754 binary formats: "binary16", "binary32", "binary64", "binary128", "binary160", "binary192", "binary224", "binary256", etc. where the number of bits is a multiple of 32 for all formats larger than "binary128". Aliases are "half" ("binary16"), "single" ("binary32"), "double" ("binary64"), "quadruple" ("binary128"), "octuple" ("binary256"), and "sexdecuple" ("binary512").
See also"to_ieee754()".
- from_base()
- 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).
- as_int()
$y = $x -> as_int(); # $y is a Math::BigIntReturns $x as a Math::BigInt object regardless of upgrading and downgrading. If $x is finite, but not an integer, $x is truncated.
- as_rat()
$y = $x -> as_rat(); # $y is a Math::BigRatReturns $x a Math::BigRat object regardless of upgrading and downgrading. The invocand is not modified.
- as_float()
$y = $x -> as_float(); # $y is a Math::BigFloatReturns $x a Math::BigFloat object regardless of upgrading and downgrading. The invocand is not modified.
Arithmetic methods
- bdiv()
$x->bdiv($y); # set $x to quotient($q, $r) = $x->bdiv($y); # also remainderThis is an alias for"bfdiv()".
- 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.
- bfdiv()
$q = $x->bfdiv($y);($q, $r) = $x->bfdiv($y);In scalar context, divides $x by $y and returns the result to the given accuracy or precision or the default accuracy. In list context, does floored division (F-division), returning an integer $q and a remainder $r
$q = floor($x / $y)$r = $x - $q * $yso that the following relationship always holds
$x = $q * $y + $rThe remainer (modulo) is equal to what is returned by
$x->bmod($y).- binv()
$x->binv();Invert the value of $x, i.e., compute 1/$x.
- bmuladd()
$x->bmuladd($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).
- bexp()
$x->bexp($accuracy); # calculate e ** XCalculates the expression
e ** $xwhereeis Euler's number.This method was added in v1.82 of Math::BigInt (April 2007).
- bnok()
- bperm()
- 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
$ydivided by$x, modifying $y in place. See also"batan()".This method was added in v1.87 of Math::BigInt (June 2007).
- bgcd()
$x -> bgcd($y); # GCD of $x and $y$x -> bgcd($y, $z, ...); # GCD of $x, $y, $z, ...Returns the greatest common divisor (GCD), which is the number with the largest absolute value such that $x/$gcd, $y/$gcd, ... is an integer. For example, when the operands are 0.8 and 1.2, the GCD is 0.4. This is a generalisation of the ordinary GCD for integers. See"gcd()" in Math::BigInt.
String conversion methods
- bstr()
my $x = Math::BigRat->new('8/4');print $x->bstr(), "\n"; # prints 1/2Returns a string representing the number.
- bsstr()
- bnstr()
- bestr()
- bdstr()
- to_bytes()
- 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.
# $x = 3.1415926535897932385$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"from_ieee754()",https://en.wikipedia.org/wiki/IEEE_754.
ACCURACY AND PRECISION
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 inMath::BigInt.
Since things likesqrt(2) or1 / 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 calleddiv_scale and can be accessed via:
$d = Math::BigFloat->div_scale(); # queryMath::BigFloat->div_scale($n); # set to $n digitsThe default value fordiv_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 = $x->copy()->bdiv(3,6,undef,'odd'); # gives 0.666667Math::BigFloat->round_mode('zero');$y = $x->copy()->bdiv(3,6); # will also give 0.666667Note thatMath::BigFloat->accuracy() andMath::BigFloat->precision() set the global variables, and thusany newly created number will be subject to the global roundingimmediately. This means that in the examples above, the3 as argument to"bdiv()" will also get an accuracy of5.
It is less confusing to either calculate the result fully, and afterwards round it explicitly, or use the additional parameters to the math functions like so:
use Math::BigFloat;$x = Math::BigFloat->new(2);$y = $x->copy()->bdiv(3);print $y->bround(5),"\n"; # gives 0.66667oruse Math::BigFloat;$x = Math::BigFloat->new(2);$y = $x->copy()->bdiv(3,5); # gives 0.66667print "$y\n";Rounding
- 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 $scale'th place right from the '.', counting from the dot.
- bfround ( 0 )
Rounds to an integer.
- bround ( +$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 usingMath::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_int()" method 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_int()":
$x = Math::BigFloat->new(2.5);$y = $x->as_number('odd'); # $y = 3NUMERIC LITERALS
Afteruse Math::BigFloat ':constant' all numeric literals in the given scope are converted toMath::BigFloat objects. This conversion happens at compile time.
For example,
perl -MMath::BigFloat=:constant -le 'print 2e-150'prints the exact value of2e-150. Note that without conversion of constants the expression2e-150 is calculated using Perl scalars, which leads to an inaccuracte result.
Note that strings are not affected, so that
use Math::BigFloat qw/:constant/;$y = "1234567890123456789012345678901234567890" + "123456789123456789";does not give you what you expect. You need an explicit Math::BigFloat->new() around at least one of the operands. You should also quote large constants to prevent loss of precision:
use Math::BigFloat;$x = Math::BigFloat->new("1234567889123456789123456789123456789");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.
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.
Hexadecimal floating point literals:
0x1.3ap+8 0X1.3AP+80x1.3ap8 0X1.3AP80x13a0p-4 0X13A0P-4Octal floating point literals (with "0" prefix):
01.164p+8 01.164P+801.164p8 01.164P8011640p-4 011640P-4Octal floating point literals (with "0o" prefix) (requires v5.34.0):
0o1.164p+8 0O1.164P+80o1.164p8 0O1.164P80o11640p-4 0O11640P-4Binary floating point literals:
0b1.0011101p+8 0B1.0011101P+80b1.0011101p8 0B1.0011101P80b10011101000p-2 0B10011101000P-2Math 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 Math::BigInt::Calc:
use Math::BigFloat lib => "Foo,Math::BigInt::Bar";See the respective low-level library documentation for further details.
SeeMath::BigInt for more details about using a different low-level library.
EXPORTS
Math::BigFloat exports nothing by default, but can export the"bpi()" method:
use Math::BigFloat qw/bpi/;print bpi(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 thesame object and stores it in $y. Thus anything that modifies $x will modify $y (except overloaded math operators), and vice versa. SeeMath::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 doesmy $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"; # 4Replacing"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 $y = Math::BigFloat->new(3); # rounded to "3print "$y\n"; # print "3"print $z = $x->copy()->bdiv($y),"\n"; # 41170print $z->accuracy(),"\n"; # 4What you want to use instead is:
use Math::BigFloat;my $x = Math::BigFloat->new(123456); # no roundingprint "$x\n"; # print "123456"my $y = Math::BigFloat->new(3); # no roundingprint "$y\n"; # print "3"print $z = $x->copy()->bdiv($y,4),"\n"; # 41150print $z->accuracy(),"\n"; # undefIn 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 tobug-math-bigint at rt.cpan.org, or through the web interface athttps://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::BigFloatYou can also look for information at:
GitHub
RT: CPAN's request tracker
MetaCPAN
CPAN Testers Matrix
LICENSE
This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.
SEE ALSO
Math::BigInt andMath::BigRat as well as the backend librariesMath::BigInt::FastCalc,Math::BigInt::GMP, andMath::BigInt::Pari,Math::BigInt::GMPz, andMath::BigInt::BitVect.
The pragmasbigint,bigfloat, andbigrat might also be of interest. In addition there is thebignum pragma which does upgrading and downgrading.
AUTHORS
Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.
Completely rewritten by Telshttp://bloodgate.com in 2001-2008.
Florian Ragwitz <flora@cpan.org>, 2010.
Peter John Acklam <pjacklam@gmail.com>, 2011-.
Module Install Instructions
To install Math::BigInt, copy and paste the appropriate command in to your terminal.
cpanm Math::BigIntperl -MCPAN -e shellinstall Math::BigIntFor more information on module installation, please visitthe detailed CPAN module installation guide.