# Ratio Math Functions

These functions let you apply a Ratio (a fraction) to an amount, multiplying or dividing an amount by a ratio of two natural numbers.

The Ratio Math functions have to be imported.

# assertIsRatio(ratio)

ratio: Ratio
Returns: None.

Throws an error if the argument is not a valid Ratio.

Throws messages for errors:

Ratio ${ratio} must be a record with 2 fields.
Parameter must be a Ratio record, but ${ratio} has ${q(name)

assertIsRatio(aRatio);

# makeRatio(numerator, numeratorBrand, denominator?, denominatorBrand?)

numerator: BigInt
numeratorBrand: Brand
denominator: BigInt - Optional, defaults to 100n.
denominatorBrand): Brand - Optional, defaults to the numeratorBrand value.
Returns: Ratio

Returns a Ratio based on the arguments passed into the function.

By default, the denominator is 100n (i.e., the Ratio is a percent).

// Use default values to create a ratio of 50 / 100 Quatloos
const ratio = makeRatio(50n, quatloosBrand);
// Specify all values to create a ratio of 75 Quatloos / 4 Moolas (the current exchange rate)
const ratio = makeRatio(75n, quatloosBrand, 4n, moolasBrand);

# makeRatioFromAmounts(numeratorAmount, denominatorAmount)

numeratorAmount: Amount
denominatorAmount: Amount
Returns: Ratio

Returns a Ratio, representing a fraction and consisting of an immutable pair of two Amounts. The numeratorAmount is the Ratio's numerator and the denominatorAmount is the Ratio's denominator.

const fiftyCents = AmountMath.make(centsBrand, 50n);
const dollar = AmountMath.make(centsBrand, 100n);
const halfADollar = makeRatioFromAmounts(fiftyCents, dollar);

# floorMultiplyBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's numerator's Brand. Note that the denominator Brand has to be the same as the amount Brand.

The resulting Amount is determined by:

Multiplying the amount value by the ratio's numerator's value.
Dividing the result from step 1 by the ratio's denominator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded down to the next integer.

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 3 = 141
141 / 5 = 28.2
Floor(28.2) = 28

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand: The amount and ratio's denominator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 28 Swiss francs
const exchange = floorMultiplyBy(dollars47, exchangeRatio);

# ceilMultiplyBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's numerator's Brand. Note that the denominator Brand has to be the same as the amount Brand.

The resulting Amount is determined by:

Multiplying the amount value by the ratio's numerator's value.
Dividing the result from step 1 by the ratio's denominator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded up to the next integer.

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 3 = 141
141 / 5 = 28.2
Ceiling(28.2) = 29

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand: The amount and ratio's denominator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 29 Swiss francs
const exchange = ceilMultiplyBy(dollars47, exchangeRatio);

# multiplyBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's numerator's Brand. Note that the denominator Brand has to be the same as the amount Brand.

The resulting Amount is determined by:

Multiplying the amount value by the ratio's numerator's value.
Dividing the result from step 1 by the ratio's denominator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded to the nearest integer according to banker's rounding rules (opens new window).

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 3 = 141
141 / 5 = 28.2
BankersRounding(28.2) = 28

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's denominator ${q( ratio.denominator.brand: The amount and ratio's denominator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 28 Swiss francs
const exchange = multiplyBy(dollars47, exchangeRatio);

# floorDivideBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's denominator's Brand.

The resulting value is determined by:

Multiplying the amount value by the ratio's denominator's value.
Dividing the result from step 1 by the ratio's numerator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded down to the next integer.

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 5 = 235
235 / 3 = 78.33333...
Floor(78.3333...) = 78

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand: The amount and ratio's numerator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 78 dollars
const exchange = floorDivideBy(dollars47, exchangeRatio);

# ceilDivideBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's denominator's Brand.

The resulting value is determined by:

Multiplying the amount value by the ratio's denominator's value.
Dividing the result from step 1 by the ratio's numerator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded up to the next integer.

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 5 = 235
235 / 3 = 78.33333...
Ceiling(78.3333...) = 79

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand: The amount and ratio's numerator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 79 dollars
const exchange = ceilDivideBy(dollars47, exchangeRatio);

# divideBy(amount, ratio)

amount: Amount
ratio: Ratio
Returns: Amount

Returns an immutable Amount. Its Brand is the ratio's denominator's Brand.

The resulting value is determined by:

Multiplying the amount value by the ratio's denominator's value.
Dividing the result from step 1 by the ratio's numerator's value.
If that results in an integer, that value is returned. Otherwise, the value is rounded to the nearest integer according to banker's rounding rules (opens new window).

For example, if the amount value is 47 and the ratio is 3 / 5, the calculation would go

47 * 5 = 235
235 / 3 = 78.33333...
BankersRounding(78.3333...) = 78

Throws errors with messages:

Expected an amount: ${amount}): First argument isn't an Amount.
amount's brand ${q(amount.brand)} must match ratio's numerator ${q(ratio.numerator.brand: The amount and ratio's numerator must have the same brand.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, dollarBrand);
const dollars47 = AmountMath.make(dollarBrand, 47n);
// Returns an amount of 78 dollars
const exchange = divideBy(dollars47, exchangeRatio);

# invertRatio(ratio)

ratio: Ratio
Returns: Ratio

Returns a Ratio such that the ratio argument's numerator is the returned value's denominator and the ratio argument's denominator is the returned value's numerator.

const exchangeRatio = makeRatio(3n, swissFrancBrand, 5n, usDollarBrand);
// Returns a ratio of 5 US dollars / 3 swiss Francs
const invertedRatio = invertRatio(exchangeRatio);

# addRatios(left, right)

left: Ratio
right: Ratio
Returns: Ratio

Returns a Ratio that's the sum of the left and right parameters.

The Brands of the numerators of left and right must be identical. similarly, the Brands of the denominators of left and right must also be identical. If either of these conditions aren't met, then no Ratio is returned and an error is thrown instead.

If the denominator values aren't identical, then both Ratios are multiplied by the lowest common denominator, and then the Ratios are added.

For example:

Let's assume left = { numerator: 44n kilometers, denominator: 3n hours } and right = { numerator: 25n kilometers, denominator: 2n hours }.
left would be multiplied by 2/2, and right would be multiplied by 3/3, resulting in left = { numerator: 88n kilometers, denominator: 6n hours } and right = { numerator: 75n kilometers, denominator: 6n hours }
left and right would then be added together, resulting in { numerator: 163n kilometers, denominator: 6n hours }. This Ratio would then be returned.

# subtractRatios(left, right)

left: Ratio
right: Ratio
Returns: Ratio

Returns a Ratio that's the result when the right parameter is subtracted from the left one.

If the denominator values aren't identical, then both Ratios are multiplied by the lowest common denominator, and then right is subtracted from left.

For example:

Let's assume left = { numerator: 44n kilometers, denominator: 3n hours } and right = { numerator: 25n kilometers, denominator: 2n hours }.
left would be multiplied by 2/2, and right would be multiplied by 3/3, resulting in left = { numerator: 88n kilometers, denominator: 6n hours } and right = { numerator: 75n kilometers, denominator: 6n hours }
right would then be subtracted from left would then be added together, resulting in { numerator: 13n kilometers, denominator: 6n hours }. This Ratio would then be returned.

# multiplyRatios(left, right)

left: Ratio
right: Ratio
Returns: Ratio

Returns a Ratio that's the product of the left and right parameters.

# oneMinus(ratio)

ratio: Ratio
Returns: Ratio

Subtracts the ratio argument from 1 and returns the resultant Ratio.

This function requires the ratio argument to be between 0 and 1. It also requires the numerator and denominator Brands to be the same. If either of these conditions aren't met, an error is thrown and no Ratio is returned.

# ratioGTE(left, right)

left: Ratio
right: Ratio
Returns: Boolean

Returns true if left is larger than or equal to right, false otherwise.

An error is returned if the Brands of left and right aren't identical.

# ratiosSame(left, right)

left: Ratio
right: Ratio
Returns: Boolean

Returns true if the left and right Ratios are the same, false otherwise. Note that for the two Ratios to be considered the same, the AmountValue and Brand of both the numerator and denominator of one Ratio must be identical to the AmountValue and Brand of the numerator and denominator of the other Ratio.

# quantize(ratio, newDen)

ratio: Ratio
newDen: BigInt
Returns: Ratio

Creates and returns a new Ratio that's equivalent to the ratio argument, but with a new denominator specified by the newDen argument.

# parseRatio(numeric, numeratorBrand, denominatorBrand?)

numeric: ParsableNumber
numeratorBrand: Brand
denominatorBrand: Brand - Optional, defaults to numeratorBrand.
Returns: Ratio

Creates a Ratio from the numeric argument, and returns that Ratio.

# assertParsableNumber(specimen)

specimen: Object
Returns: None.

Throws an error if the argument is not a ParsableNumber.

← ZoeHelper Functions Zoe Data Types →