# number_properties

determine floating-point parameters

## Calling Sequence

    pr = number_properties(prop)

## Arguments

prop

  string

pr

  real or boolean scalar

## Description

This function may be used to get the characteristic numbers/properties of the floating point set denoted here by `F(b,p,emin,emax)` (usually the 64 bits float numbers set prescribe by IEEE 754). Numbers of `F` are of the form:

    sign * m * b^e

`e` is the exponent and `m` the mantissa:

    m = d_1 b^(-1) + d_2 b^(-2) + .... + d_p b^(-p)

`d_i` the digits are in `[0, b-1]` and `e` in `[emin, emax]`, the number is said "normalised" if `d_1 ~= 0`. The following may be gotten:

prop = "radix"

  then `pr` is the radix `b` of the set `F`

prop = "digits"

  then `pr` is the number of digits `p`

prop = "huge"

  then `pr` is the max positive float of `F`

prop = "tiny"

  then `pr` is the min positive normalised float of `F`

prop = "denorm"

  then `pr` is a boolean (%t if denormalised numbers are used)

prop = "tiniest"

  then if denorm = %t, `pr` is the min positive denormalised number else `pr` = tiny

prop = "eps"

  then `pr` is the epsilon machine ( generally (`b^(1-p))/2` ) which is the relative max error between a real `x` (such than `|x|` in `[tiny, huge]`) and `fl(x)`, its floating point approximation in `F`

prop = "minexp"

  then `pr` is `emin`

prop = "maxexp"

  then `pr` is `emax`

## Remarks

This function uses the lapack routine dlamch to get the machine parameters (the names (radix, digit, huge, etc...) are those recommended by the LIA 1 standard and are different from the corresponding lapack's ones) ; CAUTION: sometimes you can see the following definition for the epsilon machine : `eps = b^(1-p)` but in this function we use the traditional one (see prop = "eps" before) and so `eps = (b^(1-p))/2` if normal rounding occurs and `eps = b^(1-p)` if not.

## Examples

    b = number_properties("radix")
    eps = number_properties("eps")

## See Also

- nearfloat
- frexp