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# 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 traditionnal 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")

### Authors

Bruno Pincon

## Comments

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