Cldr v1.5.1 Cldr.Math View Source

Math helper functions for number formatting

Link to this section Summary

Functions

Returns the adjusted modulus of x and y

Returns a tuple representing a number in a normalized form with the mantissa in the range 0 < m < 10 and a base 10 exponent

Returns a tuple representing a number in a normalized form with the mantissa in the range 0 < m < 10 and a base 10 exponent

Returns the default number of rounding digits

Returns the default rounding mode for rounding operations

Returns the remainder and dividend of two integers

Return the natural log of a number

Return the log10 of a number

Calculates the modulo of a number (integer, float or Decimal)

Raises a number to a integer power

Calculate the nth root of a number

Round a number to an arbitrary precision using one of several rounding algorithms

Rounds a number to a specified number of significant digits

Calculates the square root of a Decimal number using Newton’s method

Convert a Decimal to a float

Check if a number is within a range

Link to this section Types

Link to this type normalised_decimal() View Source
normalised_decimal() ::
  {%Decimal{coef: term(), exp: term(), sign: term()}, integer()}
Link to this type number_or_decimal() View Source
number_or_decimal() ::
  number() | %Decimal{coef: term(), exp: term(), sign: term()}
Link to this type rounding() View Source
rounding() ::
  :down | :half_up | :half_even | :ceiling | :floor | :half_down | :up

Link to this section Functions

Returns the adjusted modulus of x and y

Returns a tuple representing a number in a normalized form with the mantissa in the range 0 < m < 10 and a base 10 exponent.

  • number is an integer, float or Decimal

Examples

Cldr.Math.coef_exponent(Decimal.new(1.23004))
{#Decimal<1.23004>, 0}

Cldr.Math.coef_exponent(Decimal.new(465))
{#Decimal<4.65>, 2}

Cldr.Math.coef_exponent(Decimal.new(-46.543))
{#Decimal<-4.6543>, 1}
Link to this function coef_exponent_digits(number) View Source
coef_exponent_digits(number_or_decimal()) :: {Cldr.Digits.t(), integer()}

Returns a tuple representing a number in a normalized form with the mantissa in the range 0 < m < 10 and a base 10 exponent.

The mantissa is represented as tuple of the form Digits.t.

  • number is an integer, float or Decimal

Examples

Cldr.Math.coef_exponent_digits(Decimal.new(1.23004))
{{[1, 2, 3, 0], 1, 1}, 0}

Cldr.Math.coef_exponent_digits(Decimal.new(465))
{{[4, 6, 5], 1, 1}, -1}

Cldr.Math.coef_exponent_digits(Decimal.new(-46.543))
{{[4, 6, 5, 4], 1, -1}, 1}
Link to this function default_rounding() View Source
default_rounding() :: integer()

Returns the default number of rounding digits

Link to this function default_rounding_mode() View Source
default_rounding_mode() :: atom()

Returns the default rounding mode for rounding operations

Link to this function div_mod(int1, int2) View Source
div_mod(integer(), integer()) :: {integer(), integer()}

Returns the remainder and dividend of two integers.

Return the natural log of a number.

  • number is an integer, a float or a Decimal

  • For integer and float it calls the BIF :math.log10/1 function.

  • For Decimal the log is rolled by hand.

Examples

iex> Cldr.Math.log(123)
4.812184355372417

iex> Cldr.Math.log(Decimal.new(9000))
#Decimal<9.103886231350952380952380952>

Return the log10 of a number.

  • number is an integer, a float or a Decimal

    • For integer and float it calls the BIF :math.log10/1 function.

    • For Decimal, log10 is is rolled by hand using the identify log10(x) = ln(x) / ln(10)

Examples

iex> Cldr.Math.log10(100)
2.0

iex> Cldr.Math.log10(123)
2.089905111439398

iex> Cldr.Math.log10(Decimal.new(9000))
#Decimal<3.953767554157656512064441441>

Calculates the modulo of a number (integer, float or Decimal).

Note that this function uses floored division whereas the builtin rem function uses truncated division. See Decimal.rem/2 if you want a truncated division function for Decimals that will return the same value as the BIF rem/2 but in Decimal form.

See Wikipedia for an explanation of the difference.

Examples

iex> Cldr.Math.mod(1234.0, 5)
4.0

iex> Cldr.Math.mod(Decimal.new("1234.456"), 5)
#Decimal<4.456>

iex> Cldr.Math.mod(Decimal.new(123.456), Decimal.new(3.4))
#Decimal<1.056>

iex> Cldr.Math.mod Decimal.new(123.456), 3.4
#Decimal<1.056>

Raises a number to a integer power.

Raises a number to a power using the the binary method. There is one exception for Decimal numbers that raise 10 to some power. In this case the power is calculated by shifting the Decimal exponent which is quite efficient.

For further reading see this article

This function works only with integer exponents!

Examples

iex> Cldr.Math.power(10, 2)
100

iex> Cldr.Math.power(10, 3)
1000

iex> Cldr.Math.power(10, 4)
10000

iex> Cldr.Math.power(2, 10)
1024

Calculate the nth root of a number.

  • number is an integer or a Decimal

  • nth is a positive integer

Examples

iex> Cldr.Math.root Decimal.new(8), 3
#Decimal<2.0>

iex> Cldr.Math.root Decimal.new(16), 4
#Decimal<2.0>

iex> Cldr.Math.root Decimal.new(27), 3
#Decimal<3.0>
Link to this function round(number, places \\ 0, mode \\ :half_up) View Source

Round a number to an arbitrary precision using one of several rounding algorithms.

Rounding algorithms are based on the definitions given in IEEE 754, but also include 2 additional options (effectively the complementary versions):

Rounding algorithms

Directed roundings:

  • :down - Round towards 0 (truncate), eg 10.9 rounds to 10.0

  • :up - Round away from 0, eg 10.1 rounds to 11.0. (Non IEEE algorithm)

  • :ceiling - Round toward +∞ - Also known as rounding up or ceiling

  • :floor - Round toward -∞ - Also known as rounding down or floor

Round to nearest:

  • :half_even - Round to nearest value, but in a tiebreak, round towards the nearest value with an even (zero) least significant bit, which occurs 50% of the time. This is the default for IEEE binary floating-point and the recommended value for decimal.

  • :half_up - Round to nearest value, but in a tiebreak, round away from 0. This is the default algorithm for Erlang’s Kernel.round/2

  • :half_down - Round to nearest value, but in a tiebreak, round towards 0 (Non IEEE algorithm)

Link to this function round_digits(digits_t, options) View Source
Link to this function round_significant(number, n) View Source
round_significant(number_or_decimal(), integer()) :: number_or_decimal()

Rounds a number to a specified number of significant digits.

This is not the same as rounding fractional digits which is performed by Decimal.round/2 and Float.round

  • number is a float, integer or Decimal

  • n is the number of significant digits to which the number should be rounded

Examples

iex> Cldr.Math.round_significant(3.14159, 3)
3.14

iex> Cldr.Math.round_significant(10.3554, 1)
10.0

iex> Cldr.Math.round_significant(0.00035, 1)
0.0004

More on significant digits

  • 3.14159 has six significant digits (all the numbers give you useful information)

  • 1000 has one significant digit (only the 1 is interesting; you don’t know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders; they may have rounded something off to get this value)

  • 1000.0 has five significant digits (the “.0” tells us something interesting about the presumed accuracy of the measurement being made: that the measurement is accurate to the tenths place, but that there happen to be zero tenths)

  • 0.00035 has two significant digits (only the 3 and 5 tell us something; the other zeroes are placeholders, only providing information about relative size)

  • 0.000350 has three significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to have a value of zero)

  • 1006 has four significant digits (the 1 and 6 are interesting, and we have to count the zeroes, because they’re between the two interesting numbers)

  • 560 has two significant digits (the last zero is just a placeholder)

  • 560.0 has four significant digits (the zero in the tenths place means that the measurement was made accurate to the tenths place, and that there just happen to be zero tenths; the 5 and 6 give useful information, and the other zero is between significant digits, and must therefore also be counted)

Many thanks to Stackoverflow

Link to this function sqrt(number, precision \\ 0.0001) View Source

Calculates the square root of a Decimal number using Newton’s method.

  • number is an integer, float or Decimal. For integer and float, sqrt is delegated to the erlang :math module.

We convert the Decimal to a float and take its :math.sqrt only to get an initial estimate. The means typically we are only two iterations from a solution so the slight hack improves performance without sacrificing precision.

Examples

iex> Cldr.Math.sqrt(Decimal.new(9))
#Decimal<3.0>

iex> Cldr.Math.sqrt(Decimal.new(9.869))
#Decimal<3.141496458696078173887197038>
Link to this function to_float(decimal) View Source
to_float(%Decimal{coef: term(), exp: term(), sign: term()}) :: float()

Convert a Decimal to a float

  • decimal must be a Decimal

This is very likely to lose precision - lots of numbers won’t make the round trip conversion. Use with care. Actually, better not to use it at all.

Link to this function within(number, range) View Source
within(number(), integer() | Range.t()) :: boolean()

Check if a number is within a range.

  • number is either an integer or a float.

When an integer, the comparison is made using the standard Elixir in operator.

When number is a float the comparison is made using the >= and <= operators on the range endpoints. Note the comparison for a float is only for floats that have no fractional part. If a float has a fractional part then within returns false.

Since this function is only provided to support plural rules, the float comparison is only useful if the float has no fractional part.

Examples

iex> Cldr.Math.within(2.0, 1..3)
true

iex> Cldr.Math.within(2.1, 1..3)
false