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I just read this topic (especially the last comments).
Then I was wondering, why we actually need this was of giving the remainder. But it seems, that not many people "on google" were interested in that before...
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IEEEremainder() is a static method that returns the answer by performing the remainder operation on two parameters as approved by the IEEE-754 Standard. In math, the value of the remainder can be calculated by subtracting the divisor (num2) from dividend (num1) and then multiplying the answer by n.
To reduce the loss of precision when an underflow occurs, IEEE 754 includes the ability to represent fractions smaller than are possible in the normalized representation, by making the implicit leading digit a 0. Such numbers are called denormal.
The standard specifies optional extended and extendable precision formats, which provide greater precision than the basic formats. An extended precision format extends a basic format by using more precision and more exponent range.
When you have to represent very small or very large numbers, a fixed point representation will not do. The accuracy will be lost. Therefore, you will have to look at floating-point representations, where the binary point is assumed to be floating.
If you're looking for reasons why you would want it, one is for what is known as "range reduction"
Let's say you want sind function for computing the sine of an argument in degrees. A naive way to do this would be
sind(x) = sin(x*pi/180)
However pi here is not the true irrational number pi, but instead the floating point number closest to pi. This leads to things like sind(180) == 1.2246467991473532e-16, and SO questions like this and this (and many, many more).
But sine is a periodic function, so if we compute
remainder(x,90.0)
we get a value on the interval [-45,45]. Note that 0, 90, 180, 270, etc. become exactly 0, and multiplying by pi/180 is still 0. Therefore taking the appropriately signed sin or cos, we can get the exact result at these values (and if you do some basic error analysis, you can demonstrate that it also reduces the error at other values).
Two follow up points:
sin or cos to use? Well, that's what remquo is for.sind(30.0) == 0.5 exactly, due to the vagaries of intermediate rounding. There are ways to fix this, e.g. see what the Julia library does.
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