## Name:

accurateinfnorm computes a faithful rounding of the infinity norm of a function

## Usage:

accurateinfnorm(function,range,constant) : (function, range, constant) -> constant accurateinfnorm(function,range,constant,exclusion range 1,...,exclusion range n) : (function, range, constant, range, ..., range) -> constant

## Parameters:

• function represents the function whose infinity norm is to be computed
• range represents the infinity norm is to be considered on
• constant represents the number of bits in the significant of the result
• exclusion range 1 through exclusion range n represent ranges to be excluded

## Description:

• The command accurateinfnorm computes an upper bound to the infinity norm of function function in range. This upper bound is the least floating-point number greater than the value of the infinity norm that lies in the set of dyadic floating point numbers having constant significant mantissa bits. This means the value accurateinfnorm evaluates to is at the time an upper bound and a faithful rounding to constant bits of the infinity norm of function function on range range.

If given, the fourth and further arguments of the command accurateinfnorm, exclusion range 1 through exclusion range n the infinity norm of the function function is not to be considered on.
• Users should be aware about the fact that the algorithm behind accurateinfnorm is highly inefficient and that other, better suited algorithms, such as supnorm, are available inside Sollya. As a matter of fact, while accurateinfnorm is maintained for compatibility reasons with legacy Sollya codes, users are advised to avoid using accurateinfnorm in new Sollya scripts and to replace it, where possible, by the supnorm command.

## Example 1:

> p = remez(exp(x), 5, [-1;1]);
> accurateinfnorm(p - exp(x), [-1;1], 20);
4.52055246569216251373291015625e-5
> accurateinfnorm(p - exp(x), [-1;1], 30);
4.520552107578623690642416477203369140625e-5
> accurateinfnorm(p - exp(x), [-1;1], 40);
4.5205521043867324948450914234854280948638916015625e-5

## Example 2:

> p = remez(exp(x), 5, [-1;1]);
> midpointmode = on!;
> infnorm(p - exp(x), [-1;1]);
0.45205~5/7~e-4
> accurateinfnorm(p - exp(x), [-1;1], 40);
4.5205521043867324948450914234854280948638916015625e-5