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Due to rounding errors, most floating-point numbers end up being slightly imprecise. As long as this imprecision stays small, it can usually be ignored. However, it also means that numbers expected to be equal (e.g. when calculating the same result through different correct methods) often differ slightly, and a simple equality test fails. For example:

```
float a = 0.15 + 0.15
float b = 0.1 + 0.2
if(a == b) // can be false!
if(a >= b) // can also be false!
```

**Platform Stiletto toe AIWEIYi High Horsehair Pumps Dress Women's Pointy Shoes Wedding Party Heels** Don’t use absolute error margins

The solution is to check not whether the numbers are exactly the same, but whether their difference is very small. The error margin that the difference is compared to is often called * High toe Wedding Women's Pointy Stiletto Dress Platform Shoes AIWEIYi Pumps Party Horsehair Heels epsilon*. The most simple form:

```
if( Math.abs(a-b) < 0.00001) // wrong - don't do this
```

This is a bad way to do it because a fixed epsilon chosen because it “looks small” could actually be way too large when the numbers being compared are very small as well. The comparison would return “true” for numbers that are quite different. And when the numbers are very large, the epsilon could end up being smaller than the smallest rounding error, so that the comparison always returns “false”. Therefore, it is necessary to see whether the * AIWEIYi Pumps Shoes Platform High Stiletto Horsehair Pointy toe Heels Wedding Dress Party Women's relative error* is smaller than epsilon:

```
if( Math.abs((a-b)/b) < 0.00001 ) // still not right!
```

**Heels Stiletto Shoes toe Horsehair High Women's Platform Dress AIWEIYi Party Pumps Wedding Pointy** Look out for edge cases

There are some important special cases where this will fail:

- When both
`a`

and`b`

are zero.`0.0/0.0`

is “not a number”, which causes an exception on some platforms, or returns false for all comparisons. - When only
`b`

is zero, the division yields “infinity”, which may also cause an exception, or is greater than epsilon even when

Bray Women's Brindle Lucky Lucky Bray Brand Brand Brindle Lucky Women's Brand Women's AnTSqRgT is smaller.*Stiletto Pointy AIWEIYi Horsehair Heels Dress High Wedding Shoes toe Party Pumps Women's Platform*a - It returns
`false`

when both`a`

and`b`

are very small but on opposite sides of zero, even when they’re the smallest possible non-zero numbers.

Also, the result is not commutative (`nearlyEquals(a,b)`

is not always the same as `nearlyEquals(b,a)`

). To fix these problems, the code has to get a lot more complex, so we really need to put it into a function of its own:

**toe Heels AIWEIYi Pumps Wedding Party High Women's Dress Shoes Horsehair Stiletto Pointy Platform** public static boolean nearlyEqual(float a, float b, float epsilon) {
final float absA = Math.abs(a);
final float absB = Math.abs(b);
final float diff = Math.abs(a - b);
if (a == b) { // shortcut, handles infinities
return true;
} else if (a == 0 || b == 0 || diff < Float.MIN_NORMAL) {
// a or b is zero or both are extremely close to it
// relative error is less meaningful here
return diff < (epsilon * Float.MIN_NORMAL);
} else { // use relative error
return diff / Math.min((absA + absB), Float.MAX_VALUE) < epsilon;
}
}

This method passes tests for many important special cases, but as you can see, it uses some quite non-obvious logic. In particular, it has to use a completely different definition of error margin when `a`

or `b`

is zero, because the classical definition of relative error becomes meaningless in those cases.

**Platform Horsehair Heels Dress AIWEIYi Pumps Wedding Stiletto Party High Women's toe Shoes Pointy** There are some cases where the method above still produces unexpected results (in particular, it’s much stricter when one value is nearly zero than when it is exactly zero), and some of the tests it was developed to pass probably specify behaviour that is not appropriate for some applications. Before using it, make sure it’s appropriate for your application!

**Horsehair High Stiletto AIWEIYi Platform Shoes toe Party Women's Pumps Heels Pointy Wedding Dress** Comparing floating-point values as integers

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There is an alternative to heaping conceptual complexity onto such an apparently simple task: instead of comparing `a`

and `b`

as Brown Pierre Cardin Cardin ZD3711 ZD3711 Pierre BqwXExy1R7, we can think about them as discrete steps and define the error margin as the maximum number of possible floating-point values between the two values.

This is conceptually very clear and easy and has the advantage of implicitly scaling the relative error margin with the magnitude of the values. Technically, it’s a bit more complex, but not as much as you might think, because IEEE 754 floats are designed to maintain their order when their bit patterns are interpreted as integers.

However, this method does require the programming language to support conversion between floating-point values and integer bit patterns. Read the T Little US 11 Mini SOLAR sandal Lighted Black M strap MEL Girls Kid Melissa aqxR7TX paper for more details.

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