number_properties

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")

See Also

• nearfloat — get previous or next floating-point number
• frexp — dissect floating-point numbers into base 2 exponent and mantissa

Authors

Bruno Pincon