NAME

BigRoot - Class for supporting roots with arbitrary precision.

SYNOPSIS

use BigRoot;

# Can change precision level (Default precision is 30)
BigRoot.precision = 50;

my $root2 = BigRoot.newton's-sqrt: 2;
# 1.41421356237309504880168872420969807856967187537695

say $root2.WHAT;
# (FatRat)

# Can use other root numbers
say BigRoot.newton's-root: root => 3, number => 30;
# 3.10723250595385886687766242752238636285490682906742

# Numbers can be Int, Rational and Num:
say BigRoot.newton's-sqrt: 2.123;
# 1.45705181788431944566113502812562734420538186940001

# Can use other rational roots
say BigRoot.newton's-root: root => FatRat.new(2, 3), number => 30;
# 164.31676725154983403709093484024064018582340849939498

# Results are rounded:

BigRoot.precision = 8;
say BigRoot.newton's-sqrt: 2;
# 1.41421356

BigRoot.precision = 7;
say BigRoot.newton's-sqrt: 2;
# 1.4142136

# By default, results are cached for given precision.
BigRoot.precision = 150_000;
BigRoot.newton's-sqrt: 2;
my $start = now;
BigRoot.newton's-sqrt: 2;
say (now - $start) < 0.1;
# (True)

# Cache can be disabled with:
BigRoot.use-cache = False;

DESCRIPTION

This module provides a way of having arbitrary precision for roots. In order to do that it calculates the roots using Newton's method and uses raku's FatRat primitives.

The module supports rooting Int, Num, and Rational numbers and allows using a Rational number as the root. Also, the level of precision can be changed.

METHODS

method precision

method precision is rw

Allows for getting/setting the level of precision. Defaults to 30.

To put precision into scale:

• NASA uses 15 decimals for Pi

• 1/10^30: a millimeter compared to the diameter of the universe

• 1/10^35: diameter of a human hair compared to the diameter of the universe

• 1/10^42: size of a proton compared to the diameter of the universe

• 1/10^62: Planck length compared to the diameter of the universe

• 1/10^86: one atom out of all atoms of the universe

method newton's-root

method newton's-root(RootNumber:D :$root, PositiveNumber:D :$number) returns FatRat

Calculates the nth-root for the given number

method newton's-sqrt

method newton's-sqrt(PositiveNumber:D $number)

Calculates square root for the given number.

Same as newton's-root(root => 2, :$number)

method use-cache

method use-cache is rw

Allows enabling/disabling result cache (cache is enabled by default)