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:

the digits are in [0, b-1] and e in [emin, emax], the number is said "normalized" if . The following queries may be used:

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 normalized float of F

prop = "denorm"

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

prop = "tiniest"

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

prop = "eps"

then pr is the epsilon machine ( generally ( ) 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

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).

Sometimes you can see the following definition for the epsilon machine : but in this function we use the traditional one (see prop = "eps" before) and so if normal rounding occurs, and otherwise.

Examples

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

See also

• nearfloat — get previous or next floating-point number
• log2 — Base-2 logarithm. Base-2 exponents and mantissae of some decimal numbers
• -0 — Processing of -0 versus 0