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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 :
| prop = "radix" | -> pr is the radix b of the set F |
| prop = "digits" | -> pr is the number of digits p |
| prop = "huge" | -> pr is the max positive float of F |
| prop = "tiny" | -> pr is the min positive normalised float of F |
| prop = "denorm" | -> pr is a boolean : %t if denormalised numbers are used |
| prop = "tiniest" | -> if denorm = %t, pr is the min positive denormalised number else pr = tiny |
| prop = "eps" | -> 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" | -> pr is emin |
| prop = "maxexp" | -> 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.
b = number_properties("radix")
eps = number_properties("eps")
Bruno Pincon
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