Function approxEqRel [src]

Performs an approximate comparison of two floating point values x and y. Returns true if the absolute difference between them is less or equal than max(|x|, |y|) * tolerance, where tolerance is a positive number greater than zero. The tolerance parameter is the relative tolerance used when determining if the two numbers are close enough; a good value for this parameter is usually sqrt(floatEps(T)), meaning that the two numbers are considered equal if at least half of the digits are equal. Note that for comparisons of small numbers around zero this function won't give meaningful results, use approxEqAbs instead. NaN values are never considered equal to any value.

Prototype

pub fn approxEqRel(comptime T: type, x: T, y: T, tolerance: T) bool

Parameters

T: typex: Ty: Ttolerance: T

Example

 test approxEqRel {
    inline for ([_]type{ f16, f32, f64, f128 }) |T| {
        const eps_value = comptime floatEps(T);
        const sqrt_eps_value = comptime sqrt(eps_value);
        const nan_value = comptime nan(T);
        const inf_value = comptime inf(T);
        const min_value = comptime floatMin(T);

        try testing.expect(approxEqRel(T, 1.0, 1.0, sqrt_eps_value));
        try testing.expect(!approxEqRel(T, 1.0, 0.0, sqrt_eps_value));
        try testing.expect(!approxEqRel(T, 1.0, nan_value, sqrt_eps_value));
        try testing.expect(!approxEqRel(T, nan_value, nan_value, sqrt_eps_value));
        try testing.expect(approxEqRel(T, inf_value, inf_value, sqrt_eps_value));
        try testing.expect(approxEqRel(T, min_value, min_value, sqrt_eps_value));
        try testing.expect(approxEqRel(T, -min_value, -min_value, sqrt_eps_value));
    }

    comptime {
        // `comptime_float` is guaranteed to have the same precision and operations of
        // the largest other floating point type, which is f128 but it doesn't have a
        // defined layout so we can't rely on `@bitCast` to construct the smallest
        // possible epsilon value like we do in the tests above. In the same vein, we
        // also can't represent a max/min, `NaN` or `Inf` values.
        const eps_value = 1e-4;
        const sqrt_eps_value = sqrt(eps_value);

        try testing.expect(approxEqRel(comptime_float, 1.0, 1.0, sqrt_eps_value));
        try testing.expect(!approxEqRel(comptime_float, 1.0, 0.0, sqrt_eps_value));
    }
}

Source

  pub fn approxEqRel(comptime T: type, x: T, y: T, tolerance: T) bool {
    assert(@typeInfo(T) == .float or @typeInfo(T) == .comptime_float);
    assert(tolerance > 0);

    // Fast path for equal values (and signed zeros and infinites).
    if (x == y)
        return true;

    if (isNan(x) or isNan(y))
        return false;

    return @abs(x - y) <= @max(@abs(x), @abs(y)) * tolerance;
}  