Rational | SuperCollider 3.13.0 Help

Description

A rational number. Alternative syntax: x %/ y

NOTE:

Operations with Rational can be one order of magnitude slower compared to Float.
Rational internally represents numerator and denominator as 64-bit Floats. If you want to initialize it with a term outside the range -2147483648 to 2147483647 you will need to force the number to be a Float by adding a decimal zero, e.g. -2147483649.0 and 2147483648.0.

Rational also accepts Floats and Strings in its new instantiation method. This class will always reduce a rational expression to its lowest terms (e.g. 3 %/ 2 instead of 6 %/ 4).Rational(6,4) // -> 3 %/ 2 Rational("8/4") // -> 2 %/ 1 Rational(0.33333) // -> 1 %/ 3

Instance Methods

%/

Alternative syntax for Rational(x,y)5 %/ 7 == Rational(5,7) // -> true

+

AdditionRational(3,2) + Rational(3,2) // -> 3 %/ 1 (3 %/ 2) + (3 %/ 2) // -> 3 %/ 1

-

SubtractionRational(6,5) - Rational(1,3) // -> 13 %/ 15 (6 %/ 5) - (1 %/ 3) // -> 13 %/ 15

*

MultiplicationRational(3,7) * Rational(9,5) // -> 27 %/ 35 (3 %/ 7) * (9 %/ 5) // -> 27 %/ 35

/

DivisionRational(5,3) / Rational(7,5) // -> 25 %/ 21 (5 %/ 3) / (7 %/ 5) // -> 25 %/ 21

.abs

Absolute value.Rational(-5,4).abs // -> 5 %/ 4

.asFloat

As FloatRational(5,7).asFloat // -> 0.71428571428571

.pow

.reciprocal

ReciprocalRational(5,7).reciprocal // -> 7 %/ 5

.squared

Power of twoRational(5,7).squared // -> 25 %/ 49

Examples

Basic operations

Comparisons

Sorting

Continued fractions

Recursive function to calculate finite continued fractions:f = { | x | if (x == 0) { 1 %/ 1 } { 1 + Rational(1, f.(x-1)) } }; a = 20 collect: f.(_); a.plot;

Stern-Brocot numbers

In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.f = { | n | var a = [ 1, 1 ]; n do: { | i | a = a add: ( a[i] + a[i+1] ) add: a[i+1] }; (a.size - 1) collect: { | i | a[i] %/ a[i+1] } }; Post << f.(25);

Conversion between Rational and Float

Conversion between Float and Rational can have different degrees of precision:pi; // 3.1415926535898 a = pi.asRational(99999); // 208341 %/ 66317 b = pi.asRational(999); // 355 %/ 113 c = pi.asRational(99); // 22 %/ 7 a.asFloat; // 3.1415926534674 b.asFloat; // 3.141592920354 c.asFloat; // 3.1428571428571 pi.equalWithPrecision(a.asFloat, 0.000000001); // true pi.equalWithPrecision(b.asFloat, 0.00001); // true pi.equalWithPrecision(c.asFloat, 0.01); // true

Sound Example

(
var is, f, l, ds, p, ps, next_i;

s.waitForBoot {

SynthDef(\blip, { | out, freq = 440, amp = 0.05, nharms = 10, pan = 0, gate = 1 |
        var audio = Blip.ar(freq, nharms, amp);
        var env = Linen.kr(gate, doneAction: 2);
        OffsetOut.ar(out, Pan2.ar(audio, pan, env) );
    }).add;

is = [ 8%/15, 5%/9, 9%/16, 3%/5, 5%/8, 2%/3, 45%/64, 32%/45, 3%/4, 4%/5, 5%/6, 8%/9, 9%/10, 15%/16, 16%/15, 10%/9, 9%/8, 6%/5, 5%/4, 4%/3, 45%/32, 64%/45, 3%/2, 8%/5, 5%/3, 16%/9,9%/5, 15%/8 ];

ds = Array.fill2D(25, 25, { | r, c | (c+11) %/ (r+13) }).flat.pow(pi) / pi;

ps = Array.geom( 7, 4 %/ 1, 4 %/ 7 );

f = rrand( 20, 16000 );

l = {
        loop {
            next_i=is.choose;
            if ( f <= 200  ) { next_i = max(next_i,next_i.reciprocal) };
            if ( f >= 2600 ) { next_i = min(next_i,next_i.reciprocal) };

" -> ".post;
            f = f * next_i.post.asFloat;
            " -> ".post;

(
                instrument: \blip,
                freq:       f.post,
                nharms:     rrand(1,4),
                dur:        is.choose.asFloat,
                pan:        rrand(-0.75,0.75),
                amp:        rrand(0.01,0.1)
            ).play;

" Hz\n    dur: ".post;
            (ds.choose.postln * p).asFloat.wait;

}
    };

fork {
        loop {
            p = ps.choose;
            Post << format("\n\n========== Tempo % ==========\n\n", p);
            rrand(3,13.0).wait;
        }
    };

s.sync;

{ l.fork } ! 3
}
)

helpfile source: HelpSource/Rational.schelp
link::Rational/Rational::

Rational
Extension

Description

Class Methods

.new

Instance Methods

%/

+

-

*

/

.abs

.asFloat

.pow

.reciprocal

.squared

Examples

Basic operations

Comparisons

Sorting

Continued fractions

Stern-Brocot numbers

Conversion between Rational and Float

Sound Example

RationalExtension

.new

.abs

.asFloat

.pow

.reciprocal

.squared

Rational
Extension