The numbers sqrt, log and exp can give, and when they give null (Feel.Analysis.Images.Number, D-161).
The three are increasing where they are defined and correctly rounded to 34 digits (Feel.Runtime.Number.Power, D-62),
so the numbers the run gives for the numbers of an interval are between the run's own results for its ends, and the ends
are computed by the run: the rounding is its own, and rounding keeps the order (as in Feel.Analysis.Intervals). The ends
of a result are included, which makes a set larger and never smaller. An open end is the number nearest to it only at
zero, where the domain ends: sqrt of (0..4) is from 1E-3088, the root of the smallest number, and not from 0.
| Function | Defined for | null for |
|---|---|---|
sqrt(x) | x >= 0 | a negative x |
log(x) | x > 0 | x <= 0 |
exp(x) | every x | an x whose result is past the range, or is too small to write |
The exponential. exp(x) is a number for every x up to exp_range/0's high, the largest x for which the run
gives one (found with the run, at the precision of a number of that size: 34 digits). For a larger x the result is past
the largest number. At the other end the result is written with its 34 digits from the first, which reach down to -6176
from a result of 1E-6143 up, so every x from low up gives a number (D-161). Below it a result needs a digit below
-6176 unless its last digits happen to be zeros, which they do for about one x in 10 just below low and for fewer
further down, so the numbers between low and cut may or may not be written, and an interval of them gives Null and
every number from the smallest there is to the result at low. Below cut the result is below the smallest number
(1E-6176) and none is written.
Summary
Functions
The numbers exp(x) can be for the numbers of the set, and whether it can be null.
The numbers of the exponential exp_range/0 speaks of: {low, high, cut}.
The numbers log(x) can be for the numbers of the set, and whether it can be null.
The run's result of sqrt, log or exp for a number: {:ok, number}, or an error where the run gives null.
The numbers sqrt(x) can be for the numbers of the set, and whether it can be null.
Types
@type result() :: {Feel.Type.NumberSet.t(), boolean()} | :error
The numbers of the result, and whether a number of the argument gives null.
Functions
@spec exp(Feel.Type.NumberSet.t()) :: result()
The numbers exp(x) can be for the numbers of the set, and whether it can be null.
iex> alias Feel.Type.NumberSet
iex> set = NumberSet.interval(Decimal.new(0), Decimal.new(1))
iex> {values, null?} = Feel.Analysis.Images.Number.Real.exp(set)
iex> {NumberSet.format(values), null?}
{"[1..2.718281828459045235360287471352662]", false}The numbers of the exponential exp_range/0 speaks of: {low, high, cut}.
iex> {low, high, cut} = Feel.Analysis.Images.Number.Real.exp_range()
iex> {Decimal.to_string(low, :normal), Decimal.to_string(high, :normal), Decimal.to_string(cut, :normal)}
{"-14144.78022626242263692252150612604", "14149.38539644841072829055748903541", "-14221"}@spec log(Feel.Type.NumberSet.t()) :: result()
The numbers log(x) can be for the numbers of the set, and whether it can be null.
iex> alias Feel.Type.NumberSet
iex> set = NumberSet.interval(Decimal.new(1), Decimal.new(1))
iex> {logs, null?} = Feel.Analysis.Images.Number.Real.log(set)
iex> {NumberSet.format(logs), null?}
{"0", false}@spec run(String.t(), Decimal.t()) :: Feel.Runtime.Number.result()
The run's result of sqrt, log or exp for a number: {:ok, number}, or an error where the run gives null.
iex> {:ok, root} = Feel.Analysis.Images.Number.Real.run("sqrt", Decimal.new(4))
iex> Decimal.to_string(root, :normal)
"2"
iex> Feel.Analysis.Images.Number.Real.run("log", Decimal.new(0))
{:error, :out_of_domain}@spec sqrt(Feel.Type.NumberSet.t()) :: result()
The numbers sqrt(x) can be for the numbers of the set, and whether it can be null.
iex> alias Feel.Type.NumberSet
iex> set = NumberSet.interval(Decimal.new(0), Decimal.new(100))
iex> {roots, null?} = Feel.Analysis.Images.Number.Real.sqrt(set)
iex> {NumberSet.format(roots), null?}
{"[0..10]", false}