Source Edit

This module implements rational numbers, consisting of a numerator and a denominator. The denominator can not be 0.

Example:

  1. import std/rationals
  2. let
  3.   r1 = 1 // 2
  4.   r2 = -3 // 4
  6. doAssert r1 + r2 == -1 // 4
  7. doAssert r1 - r2 ==  5 // 4
  8. doAssert r1 * r2 == -3 // 8
  9. doAssert r1 / r2 == -2 // 3

Imports

math, hashes

Types

  1. Rational[T] = object
  2.   num*, den*: T

A rational number, consisting of a numerator num and a denominator den. Source Edit

Procs

  1. func `$`[T](x: Rational[T]): string

Turns a rational number into a string.

Example:

  1. doAssert $(1 // 2) == "1/2"

Source Edit 

  1. func `*`[T](x, y: Rational[T]): Rational[T]

Multiplies two rational numbers. Source Edit 

  1. func `*`[T](x: Rational[T]; y: T): Rational[T]

Multiplies the rational x with the int y. Source Edit 

  1. func `*`[T](x: T; y: Rational[T]): Rational[T]

Multiplies the int x with the rational y. Source Edit 

  1. func `*=`[T](x: var Rational[T]; y: Rational[T])

Multiplies the rational x by y in-place. Source Edit 

  1. func `*=`[T](x: var Rational[T]; y: T)

Multiplies the rational x by the int y in-place. Source Edit 

  1. func `+`[T](x, y: Rational[T]): Rational[T]

Adds two rational numbers. Source Edit 

  1. func `+`[T](x: Rational[T]; y: T): Rational[T]

Adds the rational x to the int y. Source Edit 

  1. func `+`[T](x: T; y: Rational[T]): Rational[T]

Adds the int x to the rational y. Source Edit 

  1. func `+=`[T](x: var Rational[T]; y: Rational[T])

Adds the rational y to the rational x in-place. Source Edit 

  1. func `+=`[T](x: var Rational[T]; y: T)

Adds the int y to the rational x in-place. Source Edit 

  1. func `-`[T](x, y: Rational[T]): Rational[T]

Subtracts two rational numbers. Source Edit 

  1. func `-`[T](x: Rational[T]): Rational[T]

Unary minus for rational numbers. Source Edit 

  1. func `-`[T](x: Rational[T]; y: T): Rational[T]

Subtracts the int y from the rational x. Source Edit 

  1. func `-`[T](x: T; y: Rational[T]): Rational[T]

Subtracts the rational y from the int x. Source Edit 

  1. func `-=`[T](x: var Rational[T]; y: Rational[T])

Subtracts the rational y from the rational x in-place. Source Edit 

  1. func `-=`[T](x: var Rational[T]; y: T)

Subtracts the int y from the rational x in-place. Source Edit 

  1. func `/`[T](x, y: Rational[T]): Rational[T]

Divides the rational x by the rational y. Source Edit 

  1. func `/`[T](x: Rational[T]; y: T): Rational[T]

Divides the rational x by the int y. Source Edit 

  1. func `/`[T](x: T; y: Rational[T]): Rational[T]

Divides the int x by the rational y. Source Edit 

  1. func `//`[T](num, den: T): Rational[T]

A friendlier version of initRational.

Example:

  1. let x = 1 // 3 + 1 // 5
  2. doAssert x == 8 // 15

Source Edit 

  1. func `/=`[T](x: var Rational[T]; y: Rational[T])

Divides the rational x by the rational y in-place. Source Edit 

  1. func `/=`[T](x: var Rational[T]; y: T)

Divides the rational x by the int y in-place. Source Edit 

  1. func `<`(x, y: Rational): bool

Returns true if x is less than y. Source Edit 

  1. func `<=`(x, y: Rational): bool

Returns tue if x is less than or equal to y. Source Edit 

  1. func `==`(x, y: Rational): bool

Compares two rationals for equality. Source Edit 

  1. func abs[T](x: Rational[T]): Rational[T]

Returns the absolute value of x.

Example:

  1. doAssert abs(1 // 2) == 1 // 2
  2. doAssert abs(-1 // 2) == 1 // 2

Source Edit 

  1. func cmp(x, y: Rational): int

Compares two rationals. Returns

  • a value less than zero, if x < y
  • a value greater than zero, if x > y
  • zero, if x == y

Source Edit 

  1. func `div`[T: SomeInteger](x, y: Rational[T]): T

Computes the rational truncated division. Source Edit 

  1. func floorDiv[T: SomeInteger](x, y: Rational[T]): T

Computes the rational floor division.

Floor division is conceptually defined as floor(x / y). This is different from the div operator, which is defined as trunc(x / y). That is, div rounds towards 0 and floorDiv rounds down.

Source Edit 

  1. func floorMod[T: SomeInteger](x, y: Rational[T]): Rational[T]

Computes the rational modulo by floor division (modulo).

This is same as x - floorDiv(x, y) * y. This func behaves the same as the % operator in Python.

Source Edit 

  1. func hash[T](x: Rational[T]): Hash

Computes the hash for the rational x. Source Edit 

  1. func initRational[T: SomeInteger](num, den: T): Rational[T]

Creates a new rational number with numerator num and denominator den. den must not be 0.

Note: den != 0 is not checked when assertions are turned off.

Source Edit 

  1. func `mod`[T: SomeInteger](x, y: Rational[T]): Rational[T]

Computes the rational modulo by truncated division (remainder). This is same as x - (x div y) * y. Source Edit 

  1. func reciprocal[T](x: Rational[T]): Rational[T]

Calculates the reciprocal of x (1/x). If x is 0, raises DivByZeroDefect. Source Edit 

  1. func reduce[T: SomeInteger](x: var Rational[T])

Reduces the rational number x, so that the numerator and denominator have no common divisors other than 1 (and -1). If x is 0, raises DivByZeroDefect.

Note: This is called automatically by the various operations on rationals.

Example:

  1. var r = Rational[int](num: 2, den: 4) # 1/2
  2. reduce(r)
  3. doAssert r.num == 1
  4. doAssert r.den == 2

Source Edit 

  1. func toFloat[T](x: Rational[T]): float

Converts a rational number x to a float. Source Edit 

  1. func toInt[T](x: Rational[T]): int

Converts a rational number x to an int. Conversion rounds towards 0 if x does not contain an integer value. Source Edit 

  1. func toRational(x: float; n: int = high(int) shr 32): Rational[int] {.
  2.     ...raises: [], tags: [], forbids: [].}

Calculates the best rational approximation of x, where the denominator is smaller than n (default is the largest possible int for maximal resolution).

The algorithm is based on the theory of continued fractions.

Example:

  1. let x = 1.2
  2. doAssert x.toRational.toFloat == x

Source Edit 

  1. func toRational[T: SomeInteger](x: T): Rational[T]

Converts some integer x to a rational number.

Example:

  1. doAssert toRational(42) == 42 // 1

Source Edit