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# Function `std.math.operations.isClose`

Computes whether two values are approximately equal, admitting a maximum relative difference, and a maximum absolute difference.

``` bool isClose(T, U, V) (   T lhs,   U rhs,   V maxRelDiff = CommonDefaultFor!(T, U),   V maxAbsDiff = 0.0 ); ```

## Parameters

NameDescription
lhs First item to compare.
rhs Second item to compare.
maxRelDiff Maximum allowable relative difference. Setting to 0.0 disables this check. Default depends on the type of `lhs` and `rhs`: It is approximately half the number of decimal digits of precision of the smaller type.
maxAbsDiff Maximum absolute difference. This is mainly usefull for comparing values to zero. Setting to 0.0 disables this check. Defaults to `0.0`.

## Returns

`true` if the two items are approximately equal under either criterium. It is sufficient, when `value ` satisfies one of the two criteria.

If one item is a range, and the other is a single value, then the result is the logical and-ing of calling `isClose` on each element of the ranged item against the single item. If both items are ranges, then `isClose` returns `true` if and only if the ranges have the same number of elements and if `isClose` evaluates to `true` for each pair of elements.

Use `feqrel` to get the number of equal bits in the mantissa.

## Example

``````assert(isClose(1.0,0.999_999_999));
assert(isClose(0.001, 0.000_999_999_999));
assert(isClose(1_000_000_000.0,999_999_999.0));

assert(isClose(17.123_456_789, 17.123_456_78));
assert(!isClose(17.123_456_789, 17.123_45));

// use explicit 3rd parameter for less (or more) accuracy
assert(isClose(17.123_456_789, 17.123_45, 1e-6));
assert(!isClose(17.123_456_789, 17.123_45, 1e-7));

// use 4th parameter when comparing close to zero
assert(!isClose(1e-100, 0.0));
assert(isClose(1e-100, 0.0, 0.0, 1e-90));
assert(!isClose(1e-10, -1e-10));
assert(isClose(1e-10, -1e-10, 0.0, 1e-9));
assert(!isClose(1e-300, 1e-298));
assert(isClose(1e-300, 1e-298, 0.0, 1e-200));

// different default limits for different floating point types
assert(isClose(1.0f, 0.999_99f));
assert(!isClose(1.0, 0.999_99));
static if (real.sizeof > double.sizeof)
assert(!isClose(1.0L, 0.999_999_999L));
``````

## Example

``````assert(isClose([1.0, 2.0, 3.0], [0.999_999_999, 2.000_000_001, 3.0]));
assert(!isClose([1.0, 2.0], [0.999_999_999, 2.000_000_001, 3.0]));
assert(!isClose([1.0, 2.0, 3.0], [0.999_999_999, 2.000_000_001]));

assert(isClose([2.0, 1.999_999_999, 2.000_000_001], 2.0));
assert(isClose(2.0, [2.0, 1.999_999_999, 2.000_000_001]));
``````

## Authors

Walter Bright, Don Clugston, Conversion of CEPHES math library to D by Iain Buclaw and David Nadlinger