Module: Toybox.Math

Overview

The Math Module provides various math methods available for use by Apps.

Example:

Prints the circumference of a circle.

using Toybox.System;
using Toybox.Math;
var r = 5;
var circumference = (2 * Math.PI * r);

System.println(circumference);

Example:

Prints the area of a square with Math.pow via direct call.

using Toybox.System;
using Toybox.Math;

System.println(Math.pow(10, 2));

Example:

Solves for c using the Pythagorean Theorem and multiple Math API methods.

using Toybox.System;
using Toybox.Math;
var a = 2;
var b = 3;
var c = Math.sqrt((Math.pow(a, 2) + Math.pow(b, 2)));

System.println(c);

Since:

API Level 1.0.0

Classes Under Namespace

Classes: Filter, FirFilter, IirFilter

Constant Summary

Constant Variables

Type	Name	Value	Since	Description
Type	E	2.7182818284590452354	API Level 1.0.0	32-bit floating point representation of E
Type	PI	3.14159265358979323846	API Level 1.0.0	32-bit floating point representation of PI

Instance Method Summary

• acos(x as Lang.Numeric) as Lang.Decimal

  Get the arc cosine of an angle.

• asin(x as Lang.Numeric) as Lang.Decimal

  Get the arc sine of an angle.

• atan(x as Lang.Numeric) as Lang.Decimal

  Get the arc tangent of an angle.

• atan2(y as Lang.Numeric, x as Lang.Numeric) as Lang.Decimal

  Get the arc tangent of y/x in radians.

• ceil(x as Lang.Numeric) as Lang.Numeric

  Compute the ceiling of a value.

• cos(x as Lang.Numeric) as Lang.Decimal

  Get the cosine of an angle.

• floor(x as Lang.Numeric) as Lang.Numeric

  Compute the floor of a value.

• ln(x as Lang.Numeric) as Lang.Decimal

  Get natural logarithm of a value.

• log(x as Lang.Numeric, base as Lang.Numeric) as Lang.Decimal

  Get logarithm of a value using the specified base.

• mean(data as Lang.Array<Lang.Numeric>) as Lang.Double

  Get the arithmetic mean (average) of an array of data.

• mode(data as Lang.Array<Lang.Object>) as Lang.Object

  Get the most common value found in an array of data.

• pow(x as Lang.Numeric, y as Lang.Numeric) as Lang.Decimal

  Calculate x to the power of y.

• rand() as Lang.Number

  Returns a pseudo-random Number.

• round(x as Lang.Numeric) as Lang.Numeric

  Round a value.

• sin(x as Lang.Numeric) as Lang.Decimal

  Get the sine of an angle.

• sqrt(x as Lang.Numeric) as Lang.Decimal

  Calculate the square root of a value.

• srand(seed as Lang.Number) as Void

  Seed the random number generator.

• stdev(data as Lang.Array<Lang.Numeric>, xbar as Lang.Double or Null) as Lang.Double

  Get the standard deviation of a sample of population data.

• tan(x as Lang.Numeric) as Lang.Decimal

  Get the tangent of an angle.

• toDegrees(x as Lang.Numeric) as Lang.Decimal

  Convert an angle from radians to degrees.

• toRadians(x as Lang.Numeric) as Lang.Decimal

  Convert an angle from degrees to radians.

• variance(data as Lang.Array<Lang.Numeric>, xbar as Lang.Numeric or Null) as Lang.Double

  Get the sample variance of an array of data.

Instance Method Details

acos(x as Lang.Numeric) as Lang.Decimal

Get the arc cosine of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The cosine value

Returns:

• Lang.Float, Lang.Double —

  The interval [0..PI] in radians, or NaN if invalid

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

asin(x as Lang.Numeric) as Lang.Decimal

Get the arc sine of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The sine value

Returns:

• Lang.Float, Lang.Double —

  The interval [-PI/2..PI/2] in radians, or NaN if invalid

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

atan(x as Lang.Numeric) as Lang.Decimal

Get the arc tangent of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The tangent value

Returns:

• Lang.Float, Lang.Double —

  The interval [-PI/2..PI/2] in radians, or NaN if invalid

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

atan2(y as Lang.Numeric, x as Lang.Numeric) as Lang.Decimal

Get the arc tangent of y/x in radians.

Parameters:

• y — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The proportion of the y coordinate

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The proportion of the x coordinate

Returns:

• Lang.Float, Lang.Double —

  The principal arc tangent of y/x, in the interval [-PI..PI] radians, or NaN if invalid

  • Float if both inputs are Number or Float

  • Double if either input is Long or Double

Since:

API Level 1.3.0

ceil(x as Lang.Numeric) as Lang.Numeric

Compute the ceiling of a value.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  A numeric value

Returns:

• Lang.Number, Lang.Float, Lang.Long, Lang.Double —

  The smallest integer greater than or equal to x Return type matches the input parameter type

Since:

API Level 1.3.0

cos(x as Lang.Numeric) as Lang.Decimal

Get the cosine of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The angle in radians

Returns:

• Lang.Float, Lang.Double —

  The cosine value of x in radians

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

floor(x as Lang.Numeric) as Lang.Numeric

Compute the floor of a value.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  A numeric value

Returns:

• Lang.Number, Lang.Float, Lang.Long, Lang.Double —

  The largest integer less than or equal to x Return type matches the input parameter type

Since:

API Level 1.3.0

ln(x as Lang.Numeric) as Lang.Decimal

Get natural logarithm of a value

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The value for which to get the logarithm

Returns:

• Lang.Float, Lang.Double —

  natural logarithm of x

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 2.3.0

log(x as Lang.Numeric, base as Lang.Numeric) as Lang.Decimal

Get logarithm of a value using the specified base

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The value for which to get the logarithm

• base — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The base value.

Returns:

• Lang.Float, Lang.Double —

  specified base logarithm of x

  • Float if both inputs are Number or Float

  • Double if either input is Long or Double

Since:

API Level 1.0.0

mean(data as Lang.Array<Lang.Numeric>) as Lang.Double

Get the arithmetic mean (average) of an array of data.

Parameters:

• data — (Lang.Array) —

  An array of Number, Float, Long, or Double values

Returns:

• Lang.Double —

  The arithmetic mean of the values in data

Since:

API Level 3.1.0

Throws:

• (Lang.InvalidValueException) —

  Thrown if the provided data array is empty.

mode(data as Lang.Array<Lang.Object>) as Lang.Object

Get the most common value found in an array of data.

Parameters:

• data — (Lang.Array) —

  An array of Objects

Returns:

• Lang.Object —

  The most frequently occurring value in data.

Since:

API Level 3.1.0

Throws:

• (Lang.InvalidValueException) —

  Thrown if there is no most frequently occurring value or the passed in value array is empty

pow(x as Lang.Numeric, y as Lang.Numeric) as Lang.Decimal

Calculate x to the power of y.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  Base

• y — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  Exponent

Returns:

• Lang.Float, Lang.Double —

  x to the power of y

  • Float if both inputs are Number or Float

  • Double if either input is Long or Double

Since:

API Level 1.0.0

rand() as Lang.Number

Returns a pseudo-random Number. Use the srand() function to seed the random number generator.

Returns:

• Lang.Number —

  Non-negative random number

Since:

API Level 1.0.0

round(x as Lang.Numeric) as Lang.Numeric

Round a value.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  A numeric value

Returns:

• Lang.Number, Lang.Float, Lang.Long, Lang.Double —

  The closest integer to x. Decimal values >= .5 will be rounded up Return type matches the input parameter type

Since:

API Level 1.3.0

sin(x as Lang.Numeric) as Lang.Decimal

Get the sine of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The angle in radians

Returns:

• Lang.Float, Lang.Double —

  The sine value of x in radians

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

sqrt(x as Lang.Numeric) as Lang.Decimal

Calculate the square root of a value.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The value for which to get the square root

Returns:

• Lang.Float, Lang.Double —

  The square root of x, or NaN if invalid

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.0.0

srand(seed as Lang.Number) as Void

Seed the random number generator.

Note:

srand() does not return any value.

Parameters:

• seed — (Lang.Number) —

  The value used for seeding rand()

Since:

API Level 1.0.0

stdev(data as Lang.Array<Lang.Numeric>, xbar as Lang.Double or Null) as Lang.Double

Get the standard deviation of a sample of population data.

Parameters:

• data — (Lang.Array) —

  An array of Number, Float, Long, or Double values with at least two elements.

• xbar — (Lang.Double) —

  The mean, if known. Otherwise, pass null and the mean of data will be calculated.

Returns:

• Lang.Double —

  The standard deviation of the samples

Since:

API Level 3.1.0

Throws:

• (Lang.InvalidValueException) —

  Thrown if the provided data array has fewer than two elements.

tan(x as Lang.Numeric) as Lang.Decimal

Get the tangent of an angle.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The angle in radians

Returns:

• Lang.Float, Lang.Double —

  The tangent value of x in radians Toybox::Lang::Float if input is Toybox::Lang::Number or Toybox::Lang::Float Toybox::Lang::Double if input is Toybox::Lang::Long or Toybox::Lang::Double

Since:

API Level 1.0.0

toDegrees(x as Lang.Numeric) as Lang.Decimal

Convert an angle from radians to degrees.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The angle in radians

Returns:

• Lang.Float, Lang.Double —

  The angle of x in degrees

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.3.0

toRadians(x as Lang.Numeric) as Lang.Decimal

Convert an angle from degrees to radians.

Parameters:

• x — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The angle in degrees

Returns:

• Lang.Float, Lang.Double —

  The angle of x in radians

  • Float if input is Number or Float

  • Double if input is Long or Double

Since:

API Level 1.3.0

variance(data as Lang.Array<Lang.Numeric>, xbar as Lang.Numeric or Null) as Lang.Double

Get the sample variance of an array of data.

Returns the sample variance with Bessel's correction.

Parameters:

• data — (Lang.Array) —

  An array of Number, Float, Long, or Double values with at least two elements.

• xbar — (Lang.Number, Lang.Float, Lang.Long, Lang.Double) —

  The mean, if known. Otherwise, pass null and the mean of data will be calculated.

Returns:

• Lang.Double —

  The variance of the samples

Since:

API Level 3.1.0

Throws:

• (Lang.InvalidValueException) —

  Thrown if the provided data array has fewer than two elements.