Manpages - Math_BigFloat.3perl

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); # $yth 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 (twos 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)

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

• Leading and trailing whitespace is ignored.
• Leading and trailing zeros are ignored.
• If the string has a 0x prefix, it is interpreted as a hexadecimal number.
• If the string has a 0b prefix, it is interpreted as a binary number.
• 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.
• One underline is allowed between any two digits, including hexadecimal and binary digits.
• 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.

accuracy()

$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

precision()

$x->precision(-2); # local for $x, round at the second

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!

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_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.

“\x40\x09\x21\xfb\x54\x44\x2d\x18”; $dbl = unpack “d>”, $bytes; $mbf = Math::BigFloat -> from_ieee754($bytes, “binary64”);

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).

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).

bdiv()

$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).

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.

bexp()

$x->bexp($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).

bnok()

$x->bnok($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).

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 $y divided by $x, modifying $y in place. See also batan(). This method was added in v1.87 of Math::BigInt (June 2007).

as_float()

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().

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 https://en.wikipedia.org/wiki/IEEE_754.

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);

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 Math::BigFloat->round_mode(zero); $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 or use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3,5);

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 using Math::BigFloat->round_mode($round_mode); you can get and set the default mode for subsequent rounding. The usage of $Math::BigFloat::$round_mode is no longer supported. The second parameter to the round functions then overrides the default temporarily.

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

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.

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.

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.