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14 Sep
2017
14 Sep
'17

5:57 p.m.

On Wed, Sep 13, 2017 at 04:36:49PM +0200, Thibault Hilaire wrote:

Of course, for a lost of numbers, the decimal representation is simpler, and just as accurate as the radix-2 hexadecimal representation. But, due to the radix-10 and radix-2 used in the two representations, the radix-2 may be much easier to use.

Hex is radix 16, not radix 2 (binary).

In the "Handbook of Floating-Point Arithmetic" (JM Muller et al, Birkhauser editor, page 40),the authors claims that the largest exact decimal representation of a double-precision floating-point requires 767 digits !! So it is not always few characters to type to be just as accurate !! For example (this is the largest exact decimal representation of a single-precision 32-bit float):

1.17549421069244107548702944484928734882705242874589333385717453057158887047561890426550235133618116378784179687e-38 and 0x1.fffffc0000000p-127 are exactly the same number (one in decimal representation, the other in radix-2 hexadecimal)!

That may be so, but that doesn't mean you have to type all 100+ digits in order to reproduce the float exactly. Just 1.1754942106924411e-38 is sufficient:

py> 1.1754942106924411e-38 == float.fromhex('0x1.fffffc0000000p-127') True

You may be mistaking two different questions:

(1) How many decimal digits are needed to exactly convert the float to decimal? That can be over 100 for a C single, and over 700 for a double.

(2) How many decimal digits are needed to uniquely represent the float? Nine digits (plus an exponent) is enough to represent all possible C singles; 17 digits is enough to represent all doubles (Python floats).

I'm not actually opposed to hex float literals. I think they're cool. But we ought to have a reason more than just "they're cool" for supporting them, and I'm having trouble thinking of any apart from "C supports them, so should we". But maybe that's enough.

-- Steve