## Names:

tripledouble, TD represents a number as the sum of three IEEE doubles.

## Description:

• tripledouble is both a function and a constant.
• As a function, it rounds its argument to the nearest number that can be written as the sum of three double precision numbers.
• The algorithm used to compute tripledouble(x) is the following: let xh = double(x), let xm = double(x - xh) and let xl = double(x - xh - xm). Return the number xh + xm + xl. Note that if the current precision is not sufficient to represent exactly xh + xm + xl, a rounding will occur and the result of tripledouble(x) will be useless.
• As a constant, it symbolizes the triple-double precision format. It is used in contexts when a precision format is necessary, e.g. in the commands roundcoefficients and implementpoly. See the corresponding help pages for examples.

## Example 1:

> verbosity=1!;
> a = 1+ 2^(-55)+2^(-115);
> TD(a);
1.00000000000000002775557561562891353466491600711096
> prec=110!;
> TD(a);
Warning: double rounding occurred on invoking the triple-double rounding operator.
Try to increase the working precision.
1.000000000000000027755575615628913
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