number_properties — determine floating-point parameters
pr = number_properties(prop)
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:
then pr is the radix b
of the set F
then pr is the number of digits
p
then pr is the max positive float of
F
then pr is the min positive normalised
float of F
then pr is a boolean (%t if denormalised
numbers are used)
then if denorm = %t, pr is the min positive
denormalised number else pr = tiny
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
then pr is emin
then pr is emax
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.