Approximate equality: Difference between revisions

=={{header|Nim}}==

To compare the floating point values, we use a relative tolerance.

In order to display the values “a” and “b” as provided, without any rounding, we transmit them as strings to a comparison procedure which compute the floating point values. If the first value “a” is provided as an operation, we use a comparison procedure which accepts the computed value of “a” as second parameter. Here, “b” is never provided as an operation and can always be transmitted as a string.

<lang Nim>from math import sqrt

import strformat

import strutils

const Tolerance = 1e-10

proc `~=`(a, b: float): bool =

## Check if "a" and "b" are closed.

## We use a relative tolerance to compare the values.

result = abs(a - b) < max(abs(a), abs(b)) * Tolerance

proc compare(a, b: string) =

## Compare "a" and "b" transmitted as strings.

## Values are computed using "parseFloat".

let r = a.parseFloat() ~= b.parseFloat()

echo fmt"{a} ~= {b} is {r}"

proc compare(a: string; avalue: float; b: string) =

## Compare "a" and "b" transmitted as strings.

## The value of "a" is transmitted and not computed.

let r = avalue ~= b.parseFloat()

echo fmt"{a} ~= {b} is {r}"

compare("100000000000000.01", "100000000000000.011")

compare("100.01", "100.011")

compare("10000000000000.001 / 10000.0", 10000000000000.001 / 10000.0, "1000000000.0000001000")

compare("0.001", "0.0010000001")

compare("0.000000000000000000000101", "0.0")

compare("sqrt(2) * sqrt(2)", sqrt(2.0) * sqrt(2.0), "2.0")

compare("-sqrt(2) * sqrt(2)", -sqrt(2.0) * sqrt(2.0), "-2.0")

compare("3.14159265358979323846", "3.14159265358979324")</lang>

{{out}}

<pre>100000000000000.01 ~= 100000000000000.011 is true

100.01 ~= 100.011 is false

10000000000000.001 / 10000.0 ~= 1000000000.0000001000 is true

0.001 ~= 0.0010000001 is false

0.000000000000000000000101 ~= 0.0 is false

sqrt(2) * sqrt(2) ~= 2.0 is true

-sqrt(2) * sqrt(2) ~= -2.0 is true

3.14159265358979323846 ~= 3.14159265358979324 is true</pre>