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This I<Raku> module provides several routines to operate with the
integral and fractional parts of a decimal number.  The C<*frac*>
routines also operate on complex numbers.


code

=begin code :lang<raku>
use Math::FractionalPart :ALL;
say modf(3.2);            # OUTPUT: «3 0.2␤»
say modf(-3.2);           # OUTPUT: «-3 -0.2␤»
say fractional(-3.2);     # OUTPUT: «-0.2␤»
say fractional-abs(-3.2); # OUTPUT: «0.2␤»
=end code


=begin code :lang<raku>
sub modf($x is copy --> List) is export(:modf) {...}
=begin code

The c<modf> routine (currently not available in the I<Raku> core) is
similar to those in other languages including I<C>, I<C++>, I<Python>,
and I<Haskell>. It coerces its input into a base 10 number and returns
the integral and fractional parts in a list as shown below. (Note the
C<modf> routine has been submitted as a PR for the Raku core and may
be part of the language soon.)

=begin code :lang<raku>
say modf(3.24);  # OUTPUT: «3 0.24␤»
say modf(-2.7);  # OUTPUT: «-2 -0.7␤»
say modf(10);    # OUTPUT: «10 0␤»
say modf(0x10);  # OUTPUT: «16 0␤»
say modf(-0o10); # OUTPUT: «-8 0␤»
=end code


Note the sign of the input value is applied to both parts, unless the
part is zero.  As expected, the fractional part of an integer will be
zero.


If the user is only interested in the fractional part of a number,
there are three different algebraic routines that operate on numbers
and return their fractional parts. They all return the same result
when operating on non-negative numbers, but all three return different
results when operating on negative numbers. See the L<References|#References>
for more details.  Note that Ref. 2 shows I<frac> operating in the
I<complex plane> as C<frac(x + i y) = frac(x) + i frac(y)>.


The following table shows the routines (along with their aliase) that have been implemented in
this module.


table_head

---   | ---                         | ---               | ---


table_row

table

=begin table
Name  | Raku formula                | Example           | Notes
---   | ---                         | ---               | ---
fractional  | x - E<0x230a>xE<0x230b>                     | frac(-1.3): 0.7   | 1
fractional-abs | \|x\| - E<0x230a>\|x\|E<0x230b>             | afrac(-1.3): 0.3  | 2
fractional-wolfram | x - E<0x230a>\|x\|E<0x230b>E<0x22c5>sign(x) | ofrac(-1.3): -0.3 | 3
=end table


=begin code :lang<raku>
say convert2decimal(1.5e-3);    # OUTPUT: «0.0015␤»
say convert2decimal(1.5e-3, 5); # OUTPUT: «0.000015␤»
say convert2decimal(0xa);       # OUTPUT: «10␤»
=end code


A routine to aid processing numerical data, this routine converts
numbers into a decimal format. The user may choose the precision of
the output by adding the desired number of places as a second
argument.


Aliases: C<convert>, C<to-decimal>, and C<decimal>.


=begin code :lang<raku>
say decimal-places(3.24); # OUTPUT: «2␤»
=end code


Sometimes it is useful to know the number of digits in the fractional
part of a number. For example, in creating tests for operations on
numbers, one must often compare results of operations on real numbers
when being able to compare to the same numbers of decimal places is
required.


Such a function is C<decimal-places>, with alias names of C<ndp> and
C<frac-part-digits>.  The functions return the number of decimal
digits to the right of the decimal point for a real number.


1. See Ref. 1, *frac* version 1 (per Graham, Knuth, et alii, 1992).


2. See Ref. 2, *frac* version 2 (per Dainith, 2004); Ref. 3, p. 7. Consider mnemonic 'a' for 'absolute value' or 'astronomical'.


3. See Ref. 3, *frac* version 3 (an *odd function*); Ref. 2: Wolfram's *FractionPart* function. Consider mnemonic 'o' for 'odd function'.


1. Wikipedia article on L<Fractional Part|https://en.m.wikipedia.org/wiki/Fractional_part>.


2. Wolfram article on L<Fractional Part|https://mathworld.wolfram.com/FractionalPart.html>.


3. I<Celestial Calculations: A Gentle Introduction to Computational Astronomy>, J. L. Lawrence, 2018, MIT Press.


This library is free software; you can redistribute it or modify it under the Artistic License 2.0.


README

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Math::FractionalPart v0.0.6

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