NAME
Math::Big  routines (cos,sin,primes,hailstone,euler,fibbonaci etc) with big numbers
SYNOPSIS
use Math::Big qw/primes fibonacci hailstone factors wheel
cos sin tan euler bernoulli arctan arcsin pi/;
@primes = primes(100); # first 100 primes
$count = primes(100); # number of primes <= 100
@fib = fibonacci (100); # first 100 fibonacci numbers
$fib_1000 = fibonacci (1000); # 1000th fibonacci number
$hailstone = hailstone (1000); # length of sequence
@hailstone = hailstone (127); # the entire sequence
$factorial = factorial(1000); # factorial 1000!
$e = euler(1,64); # e to 64 digits
$b3 = bernoulli(3);
$cos = cos(0.5,128); # cosinus to 128 digits
$sin = sin(0.5,128); # sinus to 128 digits
$cosh = cosh(0.5,128); # cosinus hyperbolicus to 128 digits
$sinh = sinh(0.5,128); # sinus hyperbolicus to 128 digits
$tan = tan(0.5,128); # tangens to 128 digits
$arctan = arctan(0.5,64); # arcus tangens to 64 digits
$arcsin = arcsin(0.5,32); # arcus sinus to 32 digits
$arcsinh = arcsin(0.5,18); # arcus sinus hyperbolicus to 18 digits
$pi = pi(1024); # first 1024 digits
$log = log(64,2); # $log==6, because 2**6==64
$log = log(100,10); # $log==2, because 10**2==100
$log = log(100); # base defaults to 10: $log==2
REQUIRES
perl5.006002, Exporter, Math::BigInt, Math::BigFloat
EXPORTS
Exports nothing on default, but can export primes()
, fibonacci()
, hailstone()
, bernoulli
, euler
, sin
, cos
, tan
, cosh
, sinh
, arctan
, arcsin
, arcsinh
, pi
, log
and factorial
.
DESCRIPTION
This module contains some routines that may come in handy when you want to do some math with really, really big (or small) numbers. These are primarily examples.
FUNCTIONS
 primes()

@primes = primes($n); $primes = primes($n);
Calculates all the primes below N and returns them as array. In scalar context returns the prime count of N (the number of primes less than or equal to N).
This uses an optimized version of the Sieve of Eratosthenes, which takes half of the time and half of the space, but is still O(N).
 fibonacci()

@fib = fibonacci($n); $fib = fibonacci($n);
Calculates the first N fibonacci numbers and returns them as array. In scalar context returns the Nth number of the Fibonacci series.
The scalar context version uses an ultrafast conquerdivide style algorithm to calculate the result and is many times faster than the straightforward way of calculating the linear sum.
 hailstone()

@hail = hailstone($n); # sequence $hail = hailstone($n); # length of sequence
Calculates the Hailstone sequence for the number N. This sequence is defined as follows:
while (N != 0) { if (N is even) { N is N /2 } else { N = N * 3 +1 } }
It is not yet proven whether for every N the sequence reaches 1, but it apparently does so. The number of steps is somewhat chaotically.
 base()

($n,$a) = base($number,$base);
Reduces a number to
$base
to the$n
th power plus$a
. Example:use Math::BigInt :constant; use Math::Big qw/base/; print base ( 2 ** 150 + 42,2);
This will print 150 and 42.
 to_base()

$string = to_base($number,$base); $string = to_base($number,$base, $alphabet);
Returns a string of
$number
in base$base
. The alphabet is optional if$base
is less or equal than 36.$alphabet
is a string.Examples:
print to_base(15,2); # 1111 print to_base(15,16); # F print to_base(31,16); # 1F
 factorial()

$n = factorial($number);
Calculate
n!
forn
= 0>.Uses internally Math::BigInt's bfac() method.
 bernoulli()

$b = bernoulli($n); ($c,$d) = bernoulli($n); # $b = $c/$d
Calculate the Nth number in the Bernoulli series. Only the first 40 are defined for now.
 euler()

$e = euler($x,$d);
Calculate Euler's constant to the power of $x (usual 1), to $d digits. Defaults to 1 and 42 digits.
 sin()

$sin = sin($x,$d);
Calculate sinus of
$x
, to$d
digits.  cos()

$cos = cos($x,$d);
Calculate cosinus of
$x
, to$d
digits.  tan()

$tan = tan($x,$d);
Calculate tangens of
$x
, to$d
digits.  arctan()

$arctan = arctan($x,$d);
Calculate arcus tangens of
$x
, to$d
digits.  arctanh()

$arctanh = arctanh($x,$d);
Calculate arcus tangens hyperbolicus of
$x
, to$d
digits.  arcsin()

$arcsin = arcsin($x,$d);
Calculate arcus sinus of
$x
, to$d
digits.  arcsinh()

$arcsinh = arcsinh($x,$d);
Calculate arcus sinus hyperbolicus of
$x
, to$d
digits.  cosh()

$cosh = cosh($x,$d);
Calculate cosinus hyperbolicus of
$x
, to$d
digits.  sinh()

$sinh = sinh($x,$d);
Calculate sinus hyperbolicus of $<$x>, to
$d
digits.  pi()

$pi = pi($N);
The number PI to
$N
digits after the dot.  log()

$log = log($number,$base,$A);
Calculates the logarithmn of
$number
to base$base
, with$A
digits accuracy and returns a new number as the result (leaving$number
alone).BigInts are promoted to BigFloats, meaning you will never get a truncated integer result like when using
Math::BigInt
blog()>.
CAVEATS
Primes and the Fibonacci series use an array of size N and will not be able to calculate big sequences due to memory constraints.
The exception is fibonacci in scalar context, this is able to calculate arbitrarily big numbers in O(N) time:
use Math::Big; use Math::BigInt qw/:constant/; $fib = Math::Big::fibonacci( 2 ** 320 );
The Bernoulli numbers are not yet calculated, but looked up in a table, which has only 40 elements. So
bernoulli($x)
with $x > 42 will fail.If you know of an algorithmn to calculate them, please drop me a note.
BUGS
Please report any bugs or feature requests to bugmathbigrat at rt.cpan.org
, or through the web interface at https://rt.cpan.org/Ticket/Create.html?Queue=MathBig (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::Big
You can also look for information at:
GitHub
RT: CPAN's request tracker
MetaCPAN
CPAN Testers Matrix
CPAN Ratings
LICENSE
This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.
AUTHOR
Tels http://bloodgate.com 20012007.
Peter John Acklam <pjacklam@gmail.com> 2016.