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Function std.math.approxEqual

Computes whether a values is approximately equal to a reference value, admitting a maximum relative difference, and a maximum absolute difference.

bool approxEqual(T, U, V) (
  T value,
  U reference,
  V maxRelDiff = 0.01,
  V maxAbsDiff = 1e-05
);

Parameters

NameDescription
value Value to compare.
reference Reference value.
maxRelDiff Maximum allowable difference relative to reference. Setting to 0.0 disables this check. Defaults to 1e-2.
maxAbsDiff Maximum absolute difference. This is mainly usefull for comparing values to zero. Setting to 0.0 disables this check. Defaults to 1e-5.

Returns

true if value is approximately equal to reference 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 approxEqual on each element of the ranged item against the single item. If both items are ranges, then approxEqual returns true if and only if the ranges have the same number of elements and if approxEqual evaluates to true for each pair of elements.

See Also

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

Example

assert(approxEqual(1.0, 1.0099));
assert(!approxEqual(1.0, 1.011));
assert(approxEqual(0.00001, 0.0));
assert(!approxEqual(0.00002, 0.0));

assert(approxEqual(3.0, [3, 3.01, 2.99])); // several reference values is strange
assert(approxEqual([3, 3.01, 2.99], 3.0)); // better

float[] arr1 = [ 1.0, 2.0, 3.0 ];
double[] arr2 = [ 1.001, 1.999, 3 ];
assert(approxEqual(arr1, arr2));

Example

// relative comparison depends on reference, make sure proper
// side is used when comparing range to single value. Based on
// https://issues.dlang.org/show_bug.cgi?id=15763
auto a = [2e-3 - 1e-5];
auto b = 2e-3 + 1e-5;
assert(a[0].approxEqual(b));
assert(!b.approxEqual(a[0]));
assert(a.approxEqual(b));
assert(!b.approxEqual(a));

Example

assert(!approxEqual(0.0,1e-15,1e-9,0.0));
assert(approxEqual(0.0,1e-15,1e-9,1e-9));
assert(!approxEqual(1.0,3.0,0.0,1.0));

assert(approxEqual(1.00000000099,1.0,1e-9,0.0));
assert(!approxEqual(1.0000000011,1.0,1e-9,0.0));

Example

// maybe unintuitive behavior
assert(approxEqual(1000.0,1010.0));
assert(approxEqual(9_090_000_000.0,9_000_000_000.0));
assert(approxEqual(0.0,1e30,1.0));
assert(approxEqual(0.00001,1e-30));
assert(!approxEqual(-1e-30,1e-30,1e-2,0.0));

Authors

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

License

Boost License 1.0.